A Study of the Gamma Radiation Produced in the Alpha-Particle Bombardment of 0¹⁶ Citation Pearson, John Davie (1963) A Study of the Gamma Radiation Produced in the Alpha-Particle Bombardment of 0¹⁶. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/EYG1-JW84. https://resolver.caltech.edu/CaltechTHESIS:10032012-105301296 Abstract This thesis describes an investigation of gamma rays from the reaction O^(16)(α,γ)Ne^(20). The excitation function for gamma radiation has been studied for laboratory alpha-particle energies E_α from 4.8 to 9.9 Mev. Resonances were observed at E_α = 5.374, 5.94, 6.61, 6.930, 7.94, 8.17, 8.54, and 9.40 Mev, corresponding to Ne^(20) states at excitation energies of 9.029, 9.48, 10.02, 10.270, 11.08, 11.27, 11.56, and 12.25 Mev. Gamma-ray angular distribution measurements establish spins and parities of 4^+, 2^+, and 4^+ for the 9.029.-, 10270-, and 11.08-Mev states respectively. The 2^+ assignment for the 10.270-Mev state is supported by the results of triple angular-correlation studies made on the gamma-ray cascade from this state. Decay schemes have been investigated and estimates made of radiative widths and total widths. It is concluded that the 10.270-Mev state is the first T = 1 state of Ne^(20) on the basis of measurements of its excitation energy, spin and parity, total width, and M1 radiative width. The excitation function for 6.13-Mev gamma rays from the reaction O^(16)(α, α'γ)O^(16) has been studied for E_α from 8.9 to 9.9 Mev. The data indicates a resonance at E_α = 9.57 Mev corresponding to a state in Ne^(20) at 12.39 Mev. There is some evidence for a weaker resonance at E_α = 9.25 Mev corresponding to a state at 12.13 Mev. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Lauritsen, Thomas (advisor) Fowler, William A. (advisor) Barnes, Charles A. (advisor) Kavanagh, Ralph William (advisor) Thesis Committee: Unknown, Unknown Defense Date: 1 January 1963 Record Number: CaltechTHESIS:10032012-105301296 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:10032012-105301296 DOI: 10.7907/EYG1-JW84 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 7220 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 03 Oct 2012 20:15 Last Modified: 09 Jan 2024 00:04 Thesis Files Preview PDF - Final Version See Usage Policy. 35MB Repository Staff Only: item control page

A STUDY OF THE GAMMA RADlA TION PRODUCED IN THE ALPHA PARTICLE BOMBARDMENT OF o16 Thesis by John Davie Pearson In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1963 ACKNOWLEDGEMENTS It is a pleasure for the author to acknowledge the discussions and encouragement offered by Professors T. Lauritsen, W. A. Fowler, Co A. Barnes, and Ro W o Kavanagh during the course of this experiment. He is particularly indebted to Dr. Ro H. Spear of the University of Melbourne, Australia, whose collaboration made this experiment possible, and to J. Do Larson for assistance with the experimental apparatus., The author also wishes to express his appreciation to Professors A. Bohr, B. Mottelson, and R. F. Christy for their advice on the theoretical cons ide rations. The research was assisted by the joint program of the Office of Naval Research and the U. s. Atomic Energy Commission. ABSTRACT This thesis describes an investigation of gamma rays from the reaction d 6 (a., y)Ne 20 • The excitation function for gamma radiation has been studied for laboratory alpha-particle energies t~ 9. 9 Mev. Resonances were observed at E a. Ea. from 4. 8 = 5.. 374, 5. 94, 6. 61, 6. 930, 7. 94, 8.17, 8. 54, and 9. 40 Mev, corresponding to Ne 20 states at excitation energies of 9. 029, 9. 48, 10. 02, 10. 270, . 11. 08, 11. 27, 11. 56, and 12. 25 Mev. Gamma-ray angular distribution measurements establish spins and parities of 4 +, 2 +, and 4 + for the 9. 029.~, 10. 270-, and 11. 08-Mev states respectively. The 2 + assignment for the 10. 270- Mev state is supported by the results of triple angular-correlation . studies made on the gamma-ray cascade from this state. Decay . schemes have been investigated and estimates made of radiative It is concluded that the 10. 270-Mev state widths and total widths. is the first T = 1 state of Ne 20 on the basi~ of measurements of its excitation energy, spin and parity, total width, and Ml radiative width. The excitation function for 6.13-Mev gamma rays from the reaction Mev. 1 o16 (a., a. y)d 6 has been studied for . E a. from 8. 9 to 9. 9 The data indicates a resonance at Ea. to a state in Ne 20 at 12. 39 Mev. weaker resonance at E Mev. a. = 9. 57 Mev corresponding There is some evidence for a = 9. 25 Mev corresponding to a state at 12.13 TABLE OF CONTENTS PAGE PART I ·INTRODUCTION • • II METHODS AND APPARATUS III • • • • • • • • • • 4 Alpha Particle Beams • • • • •. • • • • • • • Target Chambers • • • • • • • • • • • • • • Targets • • • • • • • • • • • • • • • • • • • • Current Integration • • • • • . • • • • • • • • • Nai(T1) Detectors and Associated Electronics • • Angular Distribution Equipment • • • • • • • • • Nai(Tl} Detector Efficiencies ani Standard Spectra • 4 4 RESULTS. • • 0 .. . . . . . . . . .. . . • • • Excitation Function • • • • • • • 5. 37 -Mev Resonance • • • • • • • 6. 93-Mev Resonance • • • • • • • 7.94-Mev Resonance • • • • • • • ~her Resonances • • • • • • • • IV SUMMARY APPENDIX A. APPENDIX B. TABLES • 7 9 10 12 !6 • 23 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 23 28 • • • • • • • • • • • • • • • • • • Angular Distribution Considerations 36 53 66 79 • • • • 83 20 A Comparison of the F . Ground State (3Decay and Ml y -Decay of the 10. Z 7 -Mev Level in N e 0 • • • • , • .. • • • • • • • • 94 t?i • • • • ... . • • • • • • • • • • • • • • • ••••• FIGURES 1 • • • • • • 0 0 ••••••• ~ . • • • • • •. • . • • • • • • • • • •• • • • • • • • • •• •• • • • 122 125 130 -1- I. IN TR ODUC TION At the time work was commenced on this experiment, informa-. tion about the energy levels of Ne 20 in the energy range 9. 5 to 11 Mev was practically non-existent. With the developm'e nt of the 10-Mev tan2·0 dem Van de Graaff, this region of excitation energy in Ne. became . acc~.s..~ sible to the. close scrutiny that is possible with this type of accelerator. Interest in this energy region stems in part from the fact that the first T ' 20 20 20 =1 level 1n Ne , the analog of the F and Na ground states, is expected in this region (1). Litherland~ al. of Ne 20 Shortly after the experiment was started, (2) showed it was possible to group the low-lying states into rotational bands. The possibility that higher excited states would be members of these rotational bands gave. additional impetus to the experimental work. The general properties of excited states of Ne 20 are also of astrophysical significance due to the possible role played by this nucleus in the formation of heavier elements in stellar evolution (3). The technique used in this experiment involves the measurement of gamma-~ay transitions in Ne . m 016 • 20 following the alpha-capture reaction A rather special gr'?UP of levels is selected in this fashion. The reaction, which involves a spin zero projectile and a spin zero target nucleus, populates only levels -belonging to the natural parity .+ . - ·+ sequence: 0 . , 1 , 2 , etc. An II after the fact II analysis. of ·the _experi- mental method shows that of the levels above, only those levels that emit gamma rays with energies above 6 Mev were detectable above the background of other reactions. In spite of these limitations, the ......, -2- technique has been fruitful. Eight resonances have been found in the yield of the capture radiation, and at least one resonance has been found in the inelastic scattering of alpha particles that leave its 6. 13 -Mev, 3 o16 in second excited state. ' Furthe rmo:re the high energy gamma-ray transitions that are easily observed in this experiment terminate on low-lying excited states of Ne 20 with known spins and parities. With the zero channel spin in the entrance channel and a known final state, measurements of a gamma-ray angular distribution can in principle lead to the spin and parity assignment of the initial state, and give the type of gamma-ray multipolarity. Furthermore in the light self-conjugate nuclei (nuclei for which Z = N), such as Ne 20 , a special set of isotopic spin selection rules influences the strength of dipole transitions. dipole El, and magnetic dipole For both electric Ml radiation, these rules imply that the stronger transitions c.an occur only between levels which differ by one unit in the . isotopic spin, or simply ~T = 1. Hence measurement of the radiative width, or strength of a dipole transition can lead to an isotopic spin assignment. The identification and strength measure- ments of e lectric quadrupole radiation .(E2) can also supply usefUl information about the structure of a nucleus. that the first three levels of Ne 20 Litherland et al. used the fact were connected by very strong E2. transitions as confirming evidence that these levels form a rotational band. While it has not been possible to reach such conclusions from . information gained about E2 transitions in this experiment, many of these transitions exhibit radiative widths in excess of what would be -3- calculated on the basis of a simple, single-particle model. The properties of the gamma rays from one of the eight resonances allowed the identification of a previously unreported level at 10. 270 -Mev excitation energy as the fir:s t T = 1 level in Ne 20 • Precise determination of the resonance ene rgyfor the capture reaction as 6. 930, Mev located the resonance within 50 kev of the estimated position of the first T = llevel., Angular distribution measurements show the level has spin and parity 2 +, and the decay is predominantly Ml. Measure- ments of the radiative width for the dipole transition showed that an isotopic spin change is involved. Attempts to measure the alpha-capture reaction by o16 are . faced with the experimental difficulty of small cross sections. For this reason, only the three stronger of the eight capture resonances have been investigated in detail, and even for the.se strong resonances· occasionally it has bee~ found necessa·ry to compromise good experimental technique for counting rate. Furthermore the slightest impurity of an element with reactions of the type: alpha particle in, · light particle out, followed by a gamma ray, can be a serious source of background in these measurement's. This thesis contains two main parts: the first part describes the experimental apparatus, the second part is a presentation and discussion of the results. In the second section, the three resonances which have received more attention are described in detail. For easy reference, figure 1 displays a copy of the energy level diagram for Ne 20 from Lauritsen and Ajzenberg-Selove (4). -4II. METHODS AND APPARATUS ALPHA-PARTICLE BEAMS The high energy ion beams used as a source of projectiles in this exj;>eriment have been obtained from the Office of Naval Research tandem Van de Graaff accelerator. This machine was obtained from the High Voltage Engineering Co. and is described thoroughly in the literatur·e {5-10). In particular the alpha-particle beams used in this experiment · were obtained by stripping a the accelerator. He 0 beam at the high voltage terminal of The formation and injection of this He 0 beam is- described by Rose et al. {8), ani involves neutralizing the He+ . beam from a small Van de Graaff accelerator. The high energy helium ion beams available at the target after magnetic analysis were He+ with currents up to . 3. 2JJ.a and energies up to 5.4 Mev, and He++ wi~h cur- rents up to 1. 3 JJ.a and energies up to l_Q Mev. TARGET CHAMBERS Three target chambers were used during the course of the experiment. The original target chamber arrangement is shown in figure 2. An adjustable bellows preceding the slit system made it possible to place the . target chamber on the beam axiso The slits were then adjusted to give a beam spot of approximately 3/16 11 x 3/16 11 as viewed on the quartz in the target chamber. Additional pumping of roughly 90 1. /sec was pro- vided by the charcoal trap cooled to liquid nitrogen temperatures. pressures thus obtained were 2 ..: 4 X 10- The 6 Torr. at the Pe~ning gauge. Difficulty was experienced in maintaining a constant beam spot -5size on·.the target. This stemmed in part from the poor angular reso- lution afforded by the short distance between pairs of slits, and in part from placing the target chamber only 8 ft from the target quadrupole · magnetic lens which results in a rapidly diverging beam. Even though the problem with the beam size could be overcome, the most serious difficulty with this target chamber was carbon buildup on the target during bombardment. The alpha-particle reactions on carbon are listed below (4): Reaction Excitation energy . 20 in Ne at threshold Threshold 0 Mev 4. 73 Mev 5.11 8. 82 6.15 9.64 6.40 9.84 5. 91 9.46 TJ'le last column gives the excitation energy in Ne barding 20 obtained by bom-· o16 with alpha particles of the threshold energy. in this tabl~, gamma rays from the C 13 As seen ·. +a. reactions have energies cl:ose to those of gamma ray transitions in Ne and first excited state, and therefore source of backgz:ound. 20 to the ground state c 13 on the target is a serious Direct interference with the measurements made in this experiment occurs at .higher. energies when the 6.13-Mev . · f rom ra d 1.at1on c 13 ( a., ny >o16 1.s · the same as prod uce d 1.n · the 1.ne · 1ashe · scattering from d 6• The target chamber designed to reduce the problems experienced -6with the first target chamber is shown in figure ·3. in the "clean system 11 the target. Several features significantly reduced the. carbon build-up on The influx of oil vapors from the low yacuum side is re- duced by the 12" in-line cold trap. The 3/8 11 diameter beam tube of . this trap offers sufficient resistance so that the 9 i /sec titanium- getter ion pump is abl~ to reduce the pressure in the target chamber.· Demountable vacuum seals are made with 11 viton 11 compound rings without lubrication. Pressures as low as 2 x 10 -8 11 0 11 Torr. have been obtained at the pump after an outgassing procedure during which the target chamber and pump assembly were heated to 100°C for 30 minutes, Typical pressures obtained with the beam on the target were 1 x 10- 7 Torr. A comparison of the carbon deposit on targets during bombardment in this system with that in the original system indicates that the quantity of carbon deposited is proportional to the pressure in the target chamber times the total charge deposited by the beam. Since a loss or gain of ele.c trons by the target interferes with accurate beam-current measurements, thes.e phenomena are avoided by maintaining the target at + 300 volts with a nearby Faraday ring around the beam path at - 300 volts. This arrangement was used in the target chamber illustrated in figure 3. Tests of the charge colo. lection efficiency showed that it was necessary to put the target at ground potential and run the Faraday ring at + 300 volts before the counts per fixed charge dropped to half the value obtained by the usual potential arrangement. By placing the target chamber 26. 5 ft from .the target quadrupole -7lens, and by using a larger slit system, the beam size definition was improved. Micrometers on this new slit system allowed reproducible slit settings. The most serious fa_ult with this system has been the difficulties. experienced with the un-lubricated viton "O" rings. For example, the target rod and quartz rod can be moved only after the lid screws have been loose11ed. Sliding these rods over the un.:.lubricated eventually destroys the 11 0 11 loosened, these seals leak. ring. 11 0 11 rings Furthermore, with the lid screw The strong magnet on the ion pump required the magnetic shielding shown in figure 3. Tests on the effe·ctiveness of this shielding are described in "Angular Distribution Equipment" in . this section. In order to check the alpha-capture cross sections obtained from metallic oxide targets, the yield of gamma rays from one resonance was studied by bombarding ice targets in the special target chamber shown in figure 4. Thin ice targets were manufactured by closing the valve to the vacuum system and either warming up the water vial or by allowing both the target rod and water vial to come to room temperature and then cooling both simultaneously. TARGETS The targets used in this investigation were primarily me~alli_c oxide targets of tantalum and tungsten. _one resonance was studied usiD:g ice targets, and the method of manufacture of these ice targets is given in the previous section. -8The tungsten oxide targets w e re obtained from Mr. J. DQmingo of this laboratory who produced them by radio-frequency heating of a: tungsten blank in an atmosphere of oxygen depleted in reduction by a · factor of 2. 5 in the 0 18 o18 • While the content was beneficial in re- ducing the number of low energy gamma rays and the neutron continuum observed in the Nai(T.l) detector, these targets had a considerable amount of carbon contamination. Carbon contamination is judged as "serious" in this experiment when the yield of the 6.13 -Mev radiation from the c 13 {a., ny) o16 reaction equals the yield of the 8. 64-Mev gamma . . 16 . 20 ray from the 6. 93-Mev resonance 1n 0 (a., y)Ne • From the known 16 cross sections (ll), "serious" contamination amounts to 4. 5 x 10 2 . . carbon atoms per em , or roughly a layer 33 atoms thick. By · elastic scattering of protons, Domingo finds wo 2 • 6 is the composition ·o f the front surface of the targets with an uncertainty of lOo/o on the oxygen content. This composition is roughly that of the blue oxide of tungsten, W 0 (12). 4 11 However in view of the method of manufacture, the measured atomic ratio, 0/W = 2. 6, is probably more reliable, and this number is used in the calculations of the radiative widths. The tantalum oxide targets were made by anodizing tantalum in a 30/o dibasic ammonium citrate solution. The apparatus used for this process is illustrated schematically in figure 5 . The 250 volt power supply and the 10 kO resistor act as a constant current supply which steadily increases the voltage across the growing oxide layer. The smooth increase in voltage i s vital since it allows the metal at the edge o£ the fluid meniscus time to anodize before the meniscus is drawn -9over this point by the increasing voltage. Step increases in the voltage . across the oxide layer often lead to spark break, downs in this vicinity making the sample useless for further anodizing. The voltage drop across the high resistance of the oxide layer can be related to the thickness of the layer, and for a variety of electrolytes the thickness is 15 to 16 A/volt at 0.1 ma/cm 2 current density {13). Thicknesses from the interference colors are given by Charlesby ~ al. (14). The compo- sition of the oxide layer is given by Vermilyea (13) as anhydrous, amorphous Ta o • 2 5 The cleanest anodized targets were made from 0. 00025 11 tantalum suture foils obtained from the Ethicon Suture Laboratories. A newly anodized foil put through the 11 out-gassing 11 procedure in the clean vacuum system would show no signs of .the 6.13,:_ Mev radiation from c 13 (a, ny)o16• CURRENT INTEGRATION The current collected from the target was integrated with an Eldorado model CI-llO current integrator. A bombardment continued until a predetermined charge had been collected from the target. The value of the. charge used in the calculation of the radiative widths was taken as the number indicated by this instrument. Some 29 separate calibrations of the integrator over a period of a year indicate the rootmean-square deviation from the charge indicated and the actual charge is 0. 53o/o. The largest deviation noted was 1. 3%. To allow for possible uncertainties in the calibrationprocedure as well as the possible error in the total charge, a 1% uncertainty has been assigned to the charge -10- measurement used in the calculation of radiative widths. Nai(T.l) DETECTORS AND ASSOCIATED ELECTRONICS The majority of the experimental work has been done with a 4 11 x 4" {15). Nai(T.l) scintillation spectrometer discussed by Kavanagh Minor changes have been made; a 5 11 CBS 7819 photomultiplier has been used instead of the equivalent DuMont 6364, and a semipermanent optical connection betwee·n the crystal and photomultiplier has been obtained by the use of a clear silicone gel (Dow Corning QC-2-0057) instead of the high viscosity silicone fluid described by Kavanagh. ' were a Occasionally other Nai(Tl) crystals were used. These 3 11 x 3 11 Nai mounted on a DuMont 6363 photomultiplier, and a 2 11 x 2" Nai mounted on a RCA 6342-A photomultiplier. Both of these scintillation spectrometers are from the Harshaw "Integral Line 11 series. The electronics following the Nai(T.l) detector consisted of an integrating type preamplifier, a Hamner model N328 pulse amplifier with double delay-line clipping,· and a Radiation Instrument Development Laboratory model 34-12 400 channel pulse-height analyzer. The linearity of the system was judged to be 0. 5% or better, and the gain ·at a fixed counting rate has been found to be constant to one part in 900 over a period of 40 minutes {see the discussion of "Angular Distribution Equipment" in this section). The 5 11 CBS 78t9 exhibits characteristic gain changes with large changes in the counting rates (16), however such gain changes are of no significance for the low counting rates experienced in this experiment. -11Coincidence studies were performed with a fast-slow coincidenc.e system shown in fi&ure 6. Signals accurately defined in time were de- rived from the zero crossing of the pulse from the Hamner amplifier by the pick-off circuit shown in figure 7. Fast coincidences were de- tected by a three tunnel diode coincidence mixer designed in this laboratory by R. W. Kavanagh. Outputs from the integral discriminators of the Hamner amplifiers and the output of the fast coincidence mixer were fed to a slow coincidence mixer, which generates an output pulse for a triple coincidence between the inputs, and a pulse for a double coincidence between the fast coincidence mixer input and either of the other two inputs. Due to the low counting rate, it was desirable to save both the singles spectrum and the coincidence spectrum from one of the counters during a run, by storing the singles spectrum iri the first half of the 400 channel analyzer memory and "shifting" to the second half for coincidence pulses. The shifting was performed by reseting the address converters of the analyzer to 200 instead of 0 "and gate" shown in figure 6. with a pulse from the two transistor This pulse was generated by the last part of the reset pulse for the address converters and a pulse from the triple coincidence mixer. Usually the shifting of the coincidence pulses from one detector was done with the requirement that there had been a double coincidence between the fast coincidence mixer and the integral discriminator of the amplifier for the other detector. -12- ANGULAR DISTRIBUTION EQUIPMENT The angular distribution table used in conjunction with the clean target chamber is a circular steel table, 4 ft in diameter and standing 55" high, equipped with two carts for carrying Nai(Ti} their associated lead shielding about its center. detectors and The 4 11 x 4 11 Nai(Ti) scintillation spectrometer shielding is equipped with wheels and travels along the top of one of the carts between two rails, thus allowing for a djt-.s t ment of the target-detecto r distance. The target chamber, in-line cold · trap, and angular distribution table were aligned with resp e ct to the beam axis by a telescope and two reference points that had b e en established pre·viously. Alignment of the heavy steel table is best approached through successive approximations where the table is first leveled, placed under the beam axis, releveled, and so forth. Unfortunat ely the glass target chambers are usually skewed, and the final alignment of the target chamber was made by compromising the alignment of the in-line cold trap. The beam was c e ntere d in the target chamber with the aid of the quartz shown in figur e 3. The r e quir e ment that the beam should not hit the 3/8" beam tube of the in-line cold trap was met by shadowing the beam tube on t he quartz and adjusting the slits preceding the cold trap so tha t the b e am was confine d w ithi n thi s circle. It was found that this minimum r e quirement w a s ins uffici e nt to keep the beam spot size from changing as the target quadrupole magnet was varied. Consequently during angular distribution runs, the slits were decreased 100 mils from · the s e ttings used for maximum beam. was approximately 3/32" x 3/32". The beam spot size thus obtained -13To enhance the angular resolution of the 4 11 x 4 11 Nai(T.l) crystal, a 1-5/8" thick lead collimator with a 1-1/2" diameter hole was placed immediately in front of the Nai crystal. The principal effect of this collimator was to keep the gamma rays out of the edges of the crystal. For a typical geometry where the collimator face was 0. 85 11 from the target, Rose 1 s {17) smoothing factors for the collimator and crystal arrangement were - 86% for P 2 (cos 8) and - 66% for P for gamma-ray energies in the 4 to 8 Mev range. within a few per cent of the averages of P the hole of the collimator. 2 4 (cos S) These numbers are (cos 8} and P 4 (cos S) over A further discussion of smoothing factors is given in Appendix A. Several tests were necessary to prove the angular distribution apparatus. Gain changes induced in the photomultiplier by a magnetic field would pose a serious problem in an angular· distribution study. Although the 9 lb Alnico magnet of the ion pump was shielded by a series of three mild steel, cans shown in figure 3 it was still possible to demonstrate the presence of a magnetic field with a compass. It was hoped that the magnetic shield provided in the photomultiplier mount would be sufficient for the final reduction of this field. The effectiveness of the magnetic shielding was determined by measuring the gain change of the system as a function of detector angle. The gain change was measured by monitoring the counts from a differential discriminator set on the falling, high energy edge of a gamma-ray full-energy peak. For these measurements, the 2. 615-Mev gamma rays from a ThB source were used. The source was attached to the Nal -14- mount approximately eight hours before use, allowing sufficient time for the photomultiplier gain to reach equilibrium {16), and proper aging of the source. The gain change may be computed from =where N = average number of counts per run ~N = deviation from average counts S = gain change = window width n = counting rate at the low energy side of the window 1 W n 2 = counting rate at the high energy side of the window. In such a measurement it is convenient to use a multichannel analyzer, in which case S = gain change in channels W = window width in channels. The quantity in parentheses can be derived from a spectrum, and is independent ~f running time. With a width of 4 channels, centered around channel 100, the sensitivityof a typical run was limited by statistics to changes larger than 3 x 10- 2 channels per 100. However random gain changes in the electronics over a period of 40 minutes needed to complete a run amounted to ll . x 10 -2 providing the basic limitation of the technique. channels per 100, thus The results of these investigations, corrected for the 10-1/2 hr half-life of the source are presented in figure 8. The gain change, if any, is smaller than 0.1 -15- channels per 100 for a - 90° to around the beam direction. + 90° rotation of the Nai detector In view of other uncertainties in the angular distribution data, this gain change is negligible. Tests for possible beam misalignment, and other built-in anisotropies in the angular distribution apparatus were made bymeasuring the angular distribution of the isotropic 3. 56-Mev gamma ray produced in the Be 9 (p, a-y}Li 6 reaction at 2. 56 Mev bombarding energy (18) • . This reaction proceeds from the 2 +, T at 8. 89 Mev by alpha decay to the Li 6 = 1 level in B 10 0 +, T = 1, second excited state of at 3. 56 Mev (19). A target of 0. 05 mil Be foil mounted over a 3/8" hole p~nched in a 10. 2 mil piece of tantalum and backed up by another piece of 10. 2 mil tantalum in the form of a sandwich was mounted in the clean target chamber and bombarded by protons. The excitation function for gamma rays in the energy range 2. 90 to 3. 62 Mev is shown in figure 8-B. It is- very interesting to note that the value for the resonance energy, E r = 2, 566 kev,- obtained from the data of this figure by assuming a resonance width of value of E r r = 40 kev is surprisingly close to the accepted = 2, 562 ± 4 kev (19) in view of the fact that no effort was made to obtain precise energy definition of the beam. A representative angular distribution for the 3. 56-Mev gamma ray is shown in figure 8-C. (- + 2%} and background The data, corrected for target absorption (- - 5%}, -has been normalized to unity at 0°. The straight line is the expected behavior for a point ·source- 'displaced towards the north (the 90° point) from the center of the angular -16distribution table by 44 mils. The final test of the angular distribution apparatus was the experimental determination of a known angular distribution. The results are described in the section on the 5. 37-Mev resonance in "Results. 11 Nai{Tl ) DETECTOR EFFICIENCIES AND STANDARD SPECTRA Nai efficieneiee have been calculated after the method of Lazar et al. (20) using the tabulated cross sections (21) for gamma-ray :ah:. sorption, Compton scattering, and pair production. similar to those for the Calculatio.ns Nai efficiency yield the smoothing factors of Rose (17), which are necessary for correcting gamma-ray yields and ang':llar distributions for the finite size of the Nai(T£) detector. A further discussion of the smoothing factors is given in this section under "Angular Distribution Equipment" and in Appendix A. lations have been programmed for the Burroughs The calcu- computer by Mr. J. D. Larson. The cross sections used in the efficiency calculations are those that give the initial probability of a gamma-ray interaction in the crystal. The shape of the observed gamma-ray spectra depends on subsequent interactions which are not directly calculable. · the serve d 1n o16 (a.v)Ne 20 1 Since gamma rays ob- . . 11yob scure dby ot h er reactlon are partla gamma-rays, it is necessary to relate the counts observed in a fraction of the spec;:trum to the total number detected by the Nai. This has been done with the .aid of gamma- ray spectra obtained from reactions that . produce single, or very nearly single, gamma-ray lines. These 11 standard spectra" were obtained for gamma-ray energies -17of 4. 43 Mev, 6.13 Mev, 7. 48 Mev and 9.17 Mev, for the variety of . distances and collimator conf igurahons use d in t h e experiment. N 15 (p,·ay)C 597 kev, 12 1 Reactions used to produce these lines were resonances in at 898 kev proton bombarding energy, F 10 9 Be {p, y)B respectively. o16 (a, v)Ne 20 at 991 kev, and 19 16 (p, ay)0 at c 13 {p, y)N14 at 1747 kev The last two reactions have weak cascade radiations. The 7. 48 Mev gamma-ray spectra have been correct~d for a 3.1% contribution for cascades in B 10 to the 2.17 Mev level (22). The 9.17 Mev spectra have been corrected for 10.1 o/o c~scade through the. 6. 44 Mev level in ~ 4 (19) • . A typical standard spectrum for a 6.13 Mev gamma ray is shown in figure 9. The shape of the low energy tail of the standard spectra has been obtained by two methods of extrapolation. The first method is a · horizontal extrapolation based on the calculated shape of the Compton electron energy spectra {23). The second method is based on the techniques of Zerby and Moran (24), who have made Monte Carlo calculations on gamma-ray shapes. They argue that the counts in the first channel of the spectrum, or the 11 zerQ energy intercept, nare due to Compton scattering events resulting in a forward going gamma-ray that has no further interactions in the crystal. For a cylindrically shaped crystal whose axis of symmetry passes through the target, the number of counts in the first channel is giveri by · the integral = ~ ~Es crystal where 2 2 21rR m c .D - J.(e) . 0 0 i. (e)e fJ. sin e de E2 -18- 0 = counts in the first channel N = source strength N .b.E = energy width of the first channel = gamma-ray energy Ro = classical electron radius E moe 2 = electron rest mass = electron density in Nai .t(e) = path length at ;;tngle e in the crystal D JJ. = linear attenuation coefficient for the ga~ma ray in Nai, and where the angle a is the angle between the gamma ray direction and the axis of s'ymmetry. The integrations have been performed with the aid of the Burroughs 220 • . The calculated spectral shapes obtained by Zerby and Moran fit the experimental spectra for gamma-ray energies of 1 Mev or less. For the higher gamma-ray energies of interest in this experiment, the fits in the low energy part of the spectra are not as good. This discrepancy they explain as due to a background from gamma-ray back scattering, pair productionin the lead shielding for the background, and so forth. Nai crystal, true room While such phenomena are indeed taking place, experience seems to indicate (25) that the zero intercel?t value is too low. Similar arguments can be advanced against the validity of the horizontal extrapolation of the low energy tail. For the hig:P, energy gamma-rays, there is a definite, downward slope in the spectra. This slope can be seen in the spectrum of the 6.13-Mev gamma-ray shown -19- . in figure 9. Due to these uncertainties, both methods of extrapolation have been carried through, t~e number of counts in the spectrum has been taken as the average of the two estimates, and an uncertainty has been assigned that encompasses both possibilities. Both methods of extrapolation are illustrated in figure 9, and the difference in the total number of counts is 5 o/o• CALIBRATIONS The 90° beam-analyzing magnet is a 34 11 radius, uniform field device with focussing, corrected to the second order, in the horizontal median plane. The magnetic field is determined from the nuclear mag- netic resonance frequency of a proton sample placed close to the beam path in the magnet. The beam position in the magnet is defined by two slits placed 34. 5 11 from the entrance and exit pole faces, at conjugate focal points of the magnet. This arrangement of slits -hCi.s the property that the momentum resolution is independent of the entranc-:: angle. of no lateral extent, the momentum resolution is g i ve n by: where P =average momentum .C.P = momentum deviation tr:~,.x l.-: _ .i""l} sl = entrance slit width s 2 R = exit slit width = magnet ' radi\£81:= -34 11 For a beam -20- To restrict the possible orbits in the 90° analyzing magnet, a third slit was installed 36" from the exit slit and immediately preceding the switching magnet. The maximum deviation within the magnet from the central ray is given by the smaller of 1 [ 2 . 2 d ::::: ± Z {S 2 + s 3 ) + (2S 2 + s 3 ) . d J 1/2 · w =± 2 where d =maximum deviation from central ray s 3 = switching magnet slit width W = vacuum box width = 1-1/4" In the first equation, the distance between the exit and switching magnet slits has been approximated by 34 " . This extra slit also provides a possible improve.m ent in the momentum resolution of the system, and the resolution is now given by the smaller of the values .6-P P" = ± .6-P --p-- ± sl + sz 4R 2(S - s ) + sl 2 3 6R In the latter.equation, the 36" distance between the exit slit and the switching magnet slit has been approximated by 34 11 • With slit settings of 0.100 ", (). 050" and 0.100" for the entrance slit, exit slit, · and switching magnet slit respectively, the first equation gives ·.6-P /P = ± 1. 09 x· 10 -3 , and· the second . I -3 gives .6-P P = ± 0. 97 x 10 • -21- While this improvement in the resolution is not really significant, the maximum deviation from the central ray has been reduced to l/8 11 • The calibration points chosen were the at 3492 ± 3 kev, and the The Na 23 (a., n)AJ. 26 Marion (26}, and the A£ 27 (p, n}Si 27 Na 23 {A, n}A£ 26 resonance threshold at 5798 ± 4 kev. · f rom the comp1"1 a t"10n o f resonance energy va l ue 1s Al-7 (p, n)Si 27 threshold value is the weighted mean of the values giv~n by Bromley~ al. (10}. Thick targets of high purity NaC1 evaporated on a tungsten blank and spectroscopic· grade aluminum were bombarded with alpha particles and protons respectively. Neutrons were detected by a NE- 402, B 10 loaded, ZnS scintillator, mounted o n a DuMont 6392 photomultiplier, placed 1. 7 8n from the target. Counts due to thermal neutrons in the target room were reduced by l/8 11 thick cadmium shield. Runs were made with and without a 1 11 thick paraffin moderator. Typical results are given in figure 10. In general it was found that the reproducibility of the measurements for a given arrangement of the controls on the tandem was far better than the estimates of the reproducibility obtai ned from the slit settings. runs #2 and #4 on the AI. 27 .27 (p, n)S1 This is illustrated by threshold made Jariuary 12. How- ever the r eproducibility of the measurements after the beam controls had b e en changed was not quite as good. This fact is illustrated by the comparison of run #1 made on January 16 with the runs made earlier on the 27 7 Ai (p, n)Si the Na 23 (a., n}AJ. 26 threshold. Similar results have be e n observed with resonance. A summary of the values for the magnet constant d e fined according to the equation -22- . E ) E \1 + 2E 0 where K = magnet calibration constant E = beam e n e rgy in Mev E 0 = rest m a ss energy of the particle in Mev f =· proton resonance frequency in Me/sec e = electron charges per particle 16 M = mas s of particle in amu (o ) is . plotted at the bottom of figure 10. The uncertainties. assigned to each point of the plot ar·e primarily due to the uncertainty of the threshold e nergy or resonance energy. ments is 1996. 8 ± 3 x 10 -S • The weighted mean value of these measureThe uncertainty assigned is roughly twice the standard deviation of the measurements, and is somewhat less than the value (± 4) estimated from the slit settings for a beam of no lateral e xtent. Prior to the final AJ. were made on the 0 16 27 (a, }')Ne (p, n)Si 20 27 threshold measurements, runs r e sonance at 6. 93 Mev. of the thick target yield is al s o give n in figure 10. is 6. 930 ± 0. 010' Mev. The front edg e The resonant energy The 1/4 to 3/4 rise of the front edge indicates a total width of 2. or 3 kev. E s timating the beam stability to be 1-2 kev from the reproducibility of the AJ. 27 (p, n)Si and from the ~xperimental width of the Na 27 23 thr~shold . measurements, (a, n)AJ. 26 resonance whose natural width is less than 1 kev, gives a width for the 6. 93 Mev resonance in N e 20 of2 .kevorless. -23- III. RESULTS EXCITATION FUNCTION The excitation function for gamma- ray transitions in Ne 20 to the ground state and first excited state produced in the alpha-capture · reaction by 0 16 for alpha-particle energies o£4. 8 to 10 Mev is shown in figures 11 and 12. The abscissas of these plots are the alpha-particle 20 E , and the calculated excitation energy in Ne , a. · db y us1ng · the Q va1ue; o16 ·+ a.- Ne 20 --4.730 M. e .v (24). E , o bta1ne bombarding energy, X The ordinate is the number of counts, N, falling in channels of the spectra obtained from the 400 channel analyzer that correspond to the energy range; 0. 86 (E - 1. 63) Mev to 1.10 E of the beam current. X X Mev, for a fixed integration - This variable energy window includes the full energy peak and the two escape peaks of ground state gamma-ray ~ransi tiona, as well as the full energy peak, the first escape peak, and roughly half of the second escape peak of gamma-ray transitions to · the first excited state. ·An illustration of the window used at 5.40-Mev bombarding energy is given in figure 13. The gamma ray observed at that energy is the 7. 40 -Mev transition from a level at 9. 0 29 Me:v to the first excited st.ate. The only correction made to the number of counts d e termined in this fashion was a subtraction of the time dependent room background of approximately 6 counts/min in the window. In the lower half of the excitation fwiction shown in figure , ll. · .the ~ r egion has been covered in 20 kev steps or less of the bombarding energy. A target of anodized tantalum foil with an oxide layer 51 kev thick to 7 -Me v alpha particles was placed perpendicular to the beam in the: clean . . -24- vacuum system. Nai(Tl} The gamma rays were detected by the 4 11 x 4n scintillator placed 1. 0 6n from the target at 0° with respect to the beam axis. The counts in the · variable energy window have been normalized to a charge of 300 JJ.C of He++. Resonances in the gamma- ray yield are seen at 5. 37-, 5. 94-, 6. 61-, and 6. 93-Mev alpha-particle bombarding energy. A preliminary investigation indicated a weak resonance in the vicinity of 4. 95-Mev, but this investigation has not been followed up. ·Resonances found in this region of excitation energy in Ne by elastic scattering of alpha particles on on the top of the page. 20 o16 are shown by arrows The set of solid arrows is from the work of McDermott et al. (28), the dotted arrows are from the preliminary work of Davis et al. {29). Except for a discrepancy in energy, which will be discussed later, the resonances at 5. 37 and S. 95 · Mev correspond to those found by McDermott et al. They have also postulated a broad 4 +level just beyond their range of 6. 5 Mev, which probably is the resonance seen at 6. 61' Mev. Corroborating evidence for the existence of the 5. 95- and 6. 61-Mev resonances is supplied by Davis~ al. The resonance at 6. 93 Mev with the relatively large radiative width seen in this experiment will be ascribed to the and Na 20 ground states. 2 +, T = 1, analog of the F 20 Davis et al. have found a level in this region but it is apparently unrelated to the resonance seen in this experiment. Six levels seen in this region by elastic scattering of alpha particles on o16 are not seen in this work. One of these six, the 5 at 8. 84-Mev excitation energy, has such a high spin that gamma radiation -25- to the ground state or the first excited state is unlikely. The 0 + and . 2 + resonances in the vicinity of 5-Mev bombarding energy ma.rked with B 1 s in figure 11 have widthlof 800 kev, and gamma rays from these levels would be difficult to observe with targets of thicknesses used in this experiment. The remaining three levels are all odd parity and would have to decay by El or M2 or radiation to the ground state 2 + first excited state to be detected. {30) indicate M2 Since theoretical estimates transitions will have sma.ll radiative widths ( -7 xlO - 3 ev for a 9 Mev M2 transition), it is supposed that the isotopic spin selection rule {31) forbidding El transitions between . the T = 0 levels in question is primarily responsible for the absence of these three resonances. Othe r experiments indicate that El transitions between the low-lying T =· 0 levels in Ne 20 are very slow when compared to the W eis skopf single particle estimate {30). 3. 34-Mev transition (32) between the The radiative width for the 2-, 4-97 -Mev level and the 1. 63-Mev level has a ratio to this estimate of jMj 2 5 = 1. 6 x 10- • Toppel et al. {33), who performed the only previous experiment with the o16 (a., y)Ne 20 reaction, s e arched for, but did not find, the 5. 54- Mev tra nsition from the 3 , 7 .17-Mev level to the The ·that limit they set on this transition is a ratio of j M 12 ;5 5 x 10- 5 IM 1 2 + 2 , 1. 63-Mev level. $ 4. 3 x 10- 5 • By as swning applies to the thre ,e missing El transitions in question, the estimated radiative widths obtained for these transitions of the experiment. {r ..., 0. 02 ev) are much smaller than the sensitivity 'Y -26There are indications of two additional levels in this region of excitation from the (d, n) reaction on ~9 • Neutrons corresponding to a level at 9. 22-Mev excitation energy in Ne 20 . have been seen in a cloud chamber experiment (34)p and by a proton- recoil neutron spec. 19 20 trometer (35) • . Gamma rays w1th 9. 22-Mev energy from the F (d, ny)Ne reaction (36) have been attributed to this level. The angular distribution of the neutrons (35) indicate the proton is captured with 1 = 1, giving a sequence of possible spin values of 0-, 1-, 2 for this level. Its ab- sence from this work and the alpha-scattering data would indicate 0 or 2 as possible spins. energy in · N~ 20 The other level in this region of excitation indicated by work on the the. vicinity of 10 Mev. F 19 (d, n)Ne 20 .reaction is in Unfortunately the evidence for the position of this resonance is somewhat contradictory. The upper half o'f the excitation function is shown in figure 12. The data in this figure was obtained from a tungsten oxide target 55 kev thick to 7-Mev alpha-particles, and has been normalized to an integrated beam current of 150 !J.C of He ++• The to the beam and 1. 06" from the target. 40 kev steps or less. Nai(Tl) detector was at 45 0 The region has ·been covered in Resonances in the gamma-ray yield are clearly indicated at 7. 94-, 8.17-, 8. 54-, 9. 40-, ·and 9. 57-Mev bombarding energy. Gamma rays from the first resonance at 7. 93 Mev cascade mainly through the 4 + second excited state of Ne 20 9 Its presence in the excitation function for radiation to the ground state and the first excited state of Ne 20 . is primarily due to summing of the cascade gamma rays -27- in the Nai crystal. The resonance at 9. 57 -Mev is primarily due to pulse pile-up from the very strong 6.13-Mev radiation from an inelastic . scatter1ng resonance on 016 at t h.1s energy. The solid arrows at the top of the diagra1n indicate levels found . t h 1S . reg1on . . . . N e 20 1n o f exc1tat1on energy 1n action. b y th e F·19 (d, ny }Ne 20 re- The first row of arrows is from the work of Butler (37}, who used a gamma-ray threshold technique. The second row of arrows represents levels reported by Rabson et al. {36} from gamma rays detected in a pair spectrometer. this experiment and the There .i s general agreement between F 19 (d, ny}Ne 20 experiments on level position and decay schemes of the levels at 11.27- and 12. 2 5-Mev excitation energy. Butler also sees a level near 11. 08-Mev, but claims it is due . . . d state o f to a gamma-ray trans1t1on to t h e f.1rst exc1te N e 20 • The dotted arrows are the continuation of the preliminary resUlts of Davis et al. In general it seems that these two .techniques are com- plementary, for the resonances reported in this work do not f!how up clearly in the elastic scattering results, the broad resonances (125 to 600 kev} easily found by the elastic scattering of alpha-particles, apparently have smal~ radiative widths for gamma-ray transitions to the ground state and first excited state of Ne 20 • In both halves of the excitation function, the resonances are seen to be superimposed on a background of counts. In the region between resonances, · the pulse-height spectra usually have some indication of the photo-peaks. of the 6.13-Mev radiation from C 13 (a, ny)o16 followed by a smooth decrease in the number of counts towards higher energies with -28· no s1gns o f gamma rays f rom N e 20 • Figure 16 shows spectra from an on-off resonance sequence. The sensitivity of the experiment is roughly the height of the background. At 6. 0-Mev bombarding energy, this implies that a narrow wry - 1. 3 ev to be detected, and at 8. 5Mev bombarding energy a product of wr - O. 5 ev would be sufficient. If . y resonance would need a product these hypothetical resonances had total widths of 1 kev, the numbers above would imply cross sections of O. 5 !J.barns and 0.12 !J.barns respectively. _ The next three sections will describe in detail the resonances at 5. 37-, 6. 93-, and 7. 94-Mev bombarding energy. · A less detailed description of the remaining resonances will be given at the end of "Results. 11 5. 37 -MEV RESONANCE The detailed studies made on the gamma rays from the 5. 37 -Mev re sonanee include a precis.e determination of the resonance energy, measurements of the gamma- ray angular distributions, and determinations of the radiative width. The original purpose of the angular distri- bution measu~ements made on this re sonarice was to test the ability of the apparatus to resolve a P 4 (cos 6) term in an angular distribution. The choice of this transition for the test was rather fortunate since pre ·cise energy determinations of the resonance energy gave a value 58 kev lower than that obtained by McDermott et al. and without the information from the angular distribution direct comparison of the two experimental results would be difficult. The capture gamma rays from this resonance ·result from the 7. 40-Mev transition from the corresponding level at 9. 029 Mev to the 2 +, first excited state of Ne 20 at 1. 63 Mev. A spectrum for th~s gamma -29ray along with the cascade scheme is shown in figure 13. The small bump at channel 125 corresponding to the energy of direct transitions to the ground state can be accounted for by summing of the two cascade members in the Nai detector. The dotted curve in figure 13 is from a similar run 100 kev lower in energy. The slightly lower background in the second spectrum is partially due to radiation from the a decrease of the 6.13-Mev c13 (a., n'{)016 reaction that occurs in going from 5. 40 Mev to 5. 30 Mev alpha bombarding energy {11). Precise determinations of the resonant energy were made with slit settings on the analyzing magnet and switching magnet idential to those used during the calibration of the analyzing magnet (see page 20). The excitation functions for the 7. 40-Mev gamma ray obtained with the He+ and He++ beams available from the tandem accelerator at this · energy are shown in figure 14. Plotted in this figure are the number of counts in the energy window of 6. 56 Mev to 8. 58 Mev for an integrated beam current of 90 f.LC as a function of the bombardfng energy. The value for the resonant energy as determined from these two excitation functfons is 5. 37 2 Mev and 5. 37 8 Mev. Considering other measurements made during the course of the experiment, the best value for the ·resonant energy is 5374 ± ' 10 kev, where the uncertainty is primarily . due to uncertainties in the value of the magnet calibration constant., Using the 16 20 Q-value for 0 +a. - ·Ne of 4. 7JO Mev (27), the excitation ener.gy . . 20 of the corresponding level in Ne is 9. 029 ± O. 008 Me.v. This value is 58 kev lower than the value obtained by McDermott et al.{28) at Columbia. A possible explanation of this discrepancy is · a saturation -30problem in the analyzing magnet used at Columbia at that time (38). Evidence that magnet saturation effects are of no consequence in this experiment is given by the two excitation functions in figure 14 which required the maximum and minimum magnet currents used in the study of the 0 16 -alpha-capture reaction. Angular distribution results are given in figure 15. The target- collimator-Nai detector geometry was similar to that shown in figure 28. The exact distances were 0.86" to the collimator, and 2.84 11 to the Nai. The main objective of this study was to show the ability of the apparatus to resolve a effect of the P 4 P 4 {cos e) term in an angular distribution. The (cos ~}term can be seen directly in the d~crease of the · low angle points in the uncorrected angular distribution .shown at the top of figure 15 for gamma rays in the energy window, 6. 56 Mev to 8. 58 Mev. The smooth curve through the points is. the result of a least squares analysis for the coefficients iri the formula which gave {normalized to A 0 = 1}, W{e) = 1 + {0. 306 ± 0. 017)P~ (cos e) - {0.186 ± 0.020)P {cos e) 4 The uncertainty on each point is the standard deviation in the number of counts, and this uncertainty is indicated on one· of the points. Estimates of the background contribution to the counts taken on resonance were ·made by running an angular distribution below resonance. The relationship of the on resonance and the below resonance -31runs is shown on the ex<;:itation function in figure 14 by two arrows. Subtracting the background determined in this fashion from the uncorrected data of figure 15 with additional corrections for target absorption (+ 2. 2o/o), beam displacement (+ 1.1%), and Doppler shift(- 4. 3%) gave the lower : set of points in the same figure. The smooth curve through these corrected data points is the result of a least squares analysis which gave W(e) = 1 + {0. 439 ± O. 052)P 2 (cos e) - (0. 243 ± O. 057)P (cos e) 4 The uncertainty on each point is primarily due to the statistical error of the counts after background subtraction. Rose's smoothing factors {ref. 39, also see Appendix A) appropriate for the detector geometry are J /J = 0. 884 ± 0~ 009, and 2 0 J4/Jo = o. 653 ± o. 020 where the uncertainty corresponds to a possible error of 0.1 11 in the distance from the target to the Nai crystal. The corrected angular distribution is W(e) = 1 + (0. 497 ± O. 059)P (cos e) - (0. 37 2 ± O. 087)P (cos e) 2 4 This angular distribution agrees favorably with the expeCted angular distribution for an E2 transition from a in table 3. 4 + level t~ a 2 +level given The uncertainty in the final form of this angular distribution are mainly due to the uncertainty of the measured angular distribution. The radiative widthfor the 7.40-Mev gamma-ray transition has been determined from the formula for the heigh,t of a thick target step for an· isolated resonance {40) -32rro- r r SY(S) = Y(S) = step height in counts at angle e with respect 2€ where to the beam direction <T r = reaction cross section at resonance for producing the 7. 40-Mev gamma ray r =total width e: = stopping power per molecule of target material ze = charge of the bombarding particle Q = integrated beam current per run n = number of oxygen atoms per molecule _of target material S = spectrum fraction where SY(e) is the total number of counts detected by the Nal at angle e £,(e) = efficiency for detecting gamma rays in the detector at angle where &<e) = 21 Jo I Nai e with respect to the beam. J '• A. J i P.(cos e) 1 0 1. i In the formula for 8<e>. 21 Jo is the detection efficiency of the Nai crystal for gamma rays that have an isotropic angular distribution. J /J 1 0 are Rose's smoothing factors. and the Ai are defined so that the angular distribution for the gamma radiation with respect to the beam axis is given by ·w(a) = l A . P.{cos e) l 1 . with A 0 =1 i A de'rivation of this formula for the detector efficiency is given in -33- Appendix A. The reaction cross section at resonance for gamma-ray · f rom pro d uchon- o16 (a., v)Ne 20 1n · t h e energy range und er cons1"d er1 ation is given by (41): ·a = r where r =· alpha particle width (1 r '( . = radia tive width for the gamma ray r = total width = r '( + r a. 21TX = De Broglie wavelength for the bombarding particle w = statistical factors = (2J + 1) where . o f t h e compoun d 1 eve 1 1n . · N e ZO f orme d b y J = sp1n 016 +a. It will be assumed that the alpha particle width is much larger than the, gamma-ray width, in which case ~ubstituting for the value of v .r in the first equation and solving for wr'( gives fo·r H~+ beams: . wr = 0.1989 X 10 - 3 . s Y(O) E E '( · · (ev) Q t(O)n where E = beam e_ne rgy in the laboratory in Mev Q = ·ch~rge in micro-Coulombs of He ·+ + E = stopping cross section in units of 10 - lS ev-cm 2 -34- The radiative width for the 7. 40-Mev gamma-ray transition from th.e 9. 027 -Mev level to the 2 + first excited state of Ne been determined with the aid of this formula. 20 has As an illustration of these calculations, the numbers used for determining the radiative width from the gamma- ray spectra that gave the function in figure 14 are typical. He+ excitation By summing these spectra over the energy range 5. 92 Mev to 7. 91 Mev, a thick target step of 7 50 counts was obtained. The quantities put in the formula for the radiative width in terms of tl?-is height are: S = spectrurn fraction for 0. 80 E "( a 7. 40 -Mev gamma ray = 1. 81 € to 1. 07 E '( for = stopping power of Ta 0 for alpha particles 2 5 2 with 5. 37 Mev= 238 x 10-15 ev-cm · (43) n = 5 (target material was Ta 2 65 ) C(e) = efficiency at 0° = 0.104 Q = integrated beam current 90 f.LC of He +• . The yield at 0° was taken as 7 50 counts with + 5% correction for target absorption and absorption in the glass walled target chamber. . The value obtained for the product wr'( was wr'( = 3.1 ± o. 4 ev The uncertainties assigned to th e above quantities were: -35- s- 6% € c<e) - z. 6 statistics - 7 absorptions 2 Q- 1 total ll% where the uncertainty in the spectrum fraction includes both methods of ext:rapolating the low energy tails of the standard gamma-ray spectra used to determine the value of S. Other measurements used for the calculation of the radiative width of this transition include data from other tantalum oxide targets as well as tungsten oxide targets, for Nai detector geometries with . . and without the collimator, and for a variety of distances between the target and the Nai detector .ranging from 0. 6" to z.. 8". The best values for the parameters describing the .7. 40-Mev gamma-ray transition are: wry = 3. 4 ::1: o. 4 ev -ry = o. 38 ::1: o. 05 ev IMI z. = 7.0 where a spin of 4 has been used in the calculation of . w. The quantity IM I2 is the ratio of the measured width to the width prediCted by the W eisskopf single particle estimate for an E2 transition with this energy calculated with the specific formula given by Wilkinson (43). The final answer is assigned a 10% uncertainty due to the fact that there are -36- possible systematic errors in the measurements, especially in the value for the spectrwn fraction, S. It seems quite certain that the 9. 03-Mev level seen in this work is the same level reported by McDermott et al. (28). The argwnents in favor of this identification are the approximate agreement of the resonant energies, and. the spin value. The width reported by McDermott et al. for this level is 4 kev (lab} and this agrees with the value of 3 to 4 kev indicated by the front edge rise of the excitation functions in figure 14. Due to the lack of experimental information at the present time, the only theoretical significance that can be attached to the radiative width of the 7. 40-Mev transition is that its strength of 7. 0 Weisskopf units shows an enhancement typical of E2 · transitions in the light nuclei (44}. is the 4 + Litherland et al. (2) have proposed that the 9. 03-Mev level . member of a K = 0 + band based on either the 0 , 6. 75-Mev level or the . 0 +, 7. 22-Mev level in Ne 20 • While the result from this experiment sheds no additional light on this suggestion, the strength of the transition to the ground state band would indicate ,the band containing the 7. 40 -Mev level has a particle configuration similar to the co.n..;. figuration for the ground state band• . 6. 93-MEV RESONANCE Detailed studies made on the ga,mma rays from the 6.93-Mev resonance include a precise determination of the resonant energy, gamma-ray angular distributions, determination of radiative widths, · investigation of the cascade scheme_. and triple angular correlation -37- measurements. Interest in the corresponding level at 10. 27-Mev exci- tation energy in Ne Ne 20 20 is due to the fact that the first , corresponding to the ground state of F 20 =1 level in T and Na 20 , is expected in this region of excitation {l)o The principal gamma ray seen in this experiment is the result of the 8. 64-Mev transition from the 10. 27 -Mev level to the excited state of Ne 16. 20 at 1. 63 Mev. 2 + first Typical spect·ra are shown in figure Again, as was the case for the 5. 37 -Mev res ·o nance, the small bump corresponding to transitions direct to the ground state can be partially accounted for by summing of the cascade members in the detector. Nai(T£) The dotted curve in figure 16 is a spectrum obtained below resonance at 6. 89 Mev. in this region. The background behavior is rather complicate d The 6.13-Mev radiation from the C 13 . 16 (a., ny)O . reachon is rapidly decreasing with energy from a strong resonance at 6. 878 Mev, while the 6. 92- and 7 .12-Mev gamma-rays from the same reaction are increasing with energy (11). The low energy portion of the spectrum, presuma bly neutron b ac k groun d an d gamma rays f rom t h e __ 1 )Ne21 0 18{a', Ihi reaction, increases with energy through this region. Precise determination of. the resonance' energy was made at the same time the analyzing magnet was calib rated. The excitation function ~ obtained at that time for gamma rays in the energy range 7.10 Mev to 9. 80 Mev is shown in figure 10 along with the data used for determining the magnet calibration constant. energy is E r The best value for the ~eson.ance = o930 ± 10 kev , where the uncertainty is primarily due to uncertainty in the calibration constant. · The rise of the front edge of this excitation function is consistent with a total width of 1 to 2 kev -38- or less as is explained in the section on energy calibrations. Angular distribution measurements on the 8. 64-Mev gamma ray have been made several times. these runs is shown in figure 17. Data typical of that obtained during The target-collimator-Na I detector geometry is similar to that shown in figure 28. The exact distances were 0. 89 11 to the collimator from the target, and 2. 81 11 to the Nai from the target. The number of counts in the gamma-ray spectra from 6. 90 to 9. 07 Mev with corrections for background, target absorption (+ 2. 3%). beam displacement (+ 0. 8%}, and doppler shift (- 1. 6%} are plotted as a function of cosine of the angle in figure 17. The errors on the data: points are primarily statistical errors, and a typical value is shown on one of the data points. The background correction was ob- tained from angular distributions run above and below resonance. The interpolated values are the curve plotted at the bottom of figure 17. The energy relationship of above, on, and below res~nance angular distribution runs is shown on the excitation function inserted in figure 17. The curve. through the angular distribution data points is the result of a least squares analysis which gave: W(8} = 1 + (0. 475 ± o. 025)P (cos 8) ,+ (o. 004 ± 0. 03l)P (cos 6} 2 4 Rose 1 s smoothing factors appropriate for the geometry are 0. 885 ± 0. 008, J /J = 2 0 J /J = 0. 658 ± 0. 020, whe ~e the uncertainties a're 4 0 due to a possible error of 0.1 11 in the distance to the detector. Appli- cation of these sm::>othing factors to the data in figure 17 gives: W{8} = 1 + (0. 537 ± 0. 03l)P (cos 8) + (0. 006 ± o. 047)P (cos 6) 2 4 ·- 3 9Errors in the final answer are primarily the statistical errors of the data. From this measu·rement and similar measurements, the best value for the gamma- ray angular distribution is: =1 + (0. 529 ± 0. 017)P 2 {cos 6) + {0. 021 ± 0. 026)P4 (cos 6) W {6) These numbers are close to the expected angular distribution for an 2+ 1eve l to a . . f rom a Ml trans1hon the coeffici.e nt of P 2 (cos 6) term is approximately two standard devi- ations from: the value for a pure · M l the P of the 4 2 + level given in table 3, however transition. The total absence . of (cos 6) term in the angular distribution initiated the investigation E2 transition discussed in the previous section on the 5. 37-Mev resonance. The angular distribution for that transition showed the apparatus is able to resolve a P 4 (cos 6) term in an angular distribution. The spin of 2 + for the 10. 27 -Mev level in Ne transition~ as well as Ml transitions to the 20 wouid allow E2 2 + first excited state. Theoretical angular distributions for such transitions are a m i xture of the two possible angular distributions with an additional interference term (45). For the transition in question 11 the angular distribution would have the form: W(6) ~ W{6;Ml) + 2pW(6;Ml +E2) + where and W{6;Ml) and W{6;E2) o2 W{6;E2) are the angular distributions ·for pure E2 transitions respectively, and where W(6;Ml +E2) the interference term. to unity, ~he With the coefficient of P 0 Ml represents (cos 6) normalized numerical formula for this angular distribution is: -40- ..!. + o(15 /7 v~ o2 (15 19 8 > = l + ..:;;2;..__ _ _---:;-----W(8} 2 l +o o is the mixing parameter, and is defined as the ratio of The quantity the reduced matrix elements for the E2 and Ml o2 is the 'r atio of the two intensities. The reduced matrix elements may be made real {46) in which case the sign of or minus. operators, and hence o can be either plus An additional discussion is given in Appendix A. Plots of the Legendre polynomial coef.t;icients as a function of the mixing parameter together with the experimental values are given in figure 18. The value for the mixing parameter obtained from this plot is: 0 = {2. 0 ± .1. 2) X 10 -2 or that the intensity of the electric quadrupole radiation is 4 x 10 intensity of the magnetic dipole radiation. can only be determined from the ficient for P 4 of P Ml 2 2 o (cos 8} coefficient, while the coefThe mechanism transition visible is the interference with radiation which gives a term proportional to (cos 8). the Iri this case the value for (cos <?)provides the nec essa ry uniqueness. that makes this very weak E2 the P -4 o in the coefficient It is worth noting that only a small change in the uncer- tainty assigned to up to - 3. 2 x 10 o would allow the probable values to range ·from zero -2 • The radiative width for the 8. 64-Mev gamma-ray transition from the 10. 27 -Mev level to the 2 + fir~t excited state of Ne computed with the formula given on page 33. 20 has been Typical of the numbers -41- used in these calculations are those u sed to calculate the radiative width from the angular distribution da ta in figure 17. The height of the thick targe t step was taken as the number of counts in the upper curve of figure 17 with an add itional (+ lo/o) correction for the gamma':"ray absorption in the 1/ 16" glass-walled target chamber. Other numbers used in the formula for the radiative width were: S = spe ctrum fraction of 0. 8 E gamma ray= 1. 74 E 6. 93-Mev == 20 6 x 10 n = 5 }::. {targe t material was G(e) = 2.49 X 10 -2 Ta Ta 0 ) 2 5 (1 + 0.47 5 P2{cos e) + o. 004 p 4 {cos e) ) . Q = 240 f.LC of He An average value of w r 28 ± 3 ev. " for a 8. 64-Mev o for alpha particles with 2 5 2 ev- em {43) == stopping cross sect ion of -15 " to 1. 07 E ++ " for the seven data points in figure 13 is The uncertainties on the above numbers, statistics of the data points, and corrections to the data are: s 9% E - 3 £·(e) - 6 statis t ics - 2 corrections to data - 2 Q- 1 total - 11 o/o The principal uncertainty is the spectrum fraction. The nine per cent uncerta inty attached t o this number covers both possible methods of extrapolating the low energy tails of the standard spectra. -42- Other sources used for the calculation of the radiative width of the 8. 64 - Mev gamma-ray transition includes data from tungsten oxide, tantalum oxide, as well as ice targets taken with the Nai(T£) detectors with and without the collimator, for a variety of distances between detector and target. The best values for the parameters des- cribing the 8. 64-Mev gamma-ray transition are: w r y = 2 7. 8 ± 3 ev r y = 5. 6 ± o. 6 ev jMj where jM J 2 2 = o. 41 is the ratio of the measured radiative width to the Weiskopf single particle estimate for (43}. Ml transitions with this energy The value of w has been computed using a spin of 2 for the 10.27- Mev level. Since there are possible systematic errors in the calcula- tion of the radiative width, the final answer is assigned an ll% uncertainty. The ice targets were used as an independent means of checking the yieldl? from the metallic oxide targets. Gamma-ray yields from the bombardment of ice targets made in situ with the speci"aUy_- designed target chamber shown in figure 4 were detected in a 3 11 x 3 11 Nai crystal placed 1. 93" from the target at 0° with respect to the beam. At this single angle, it is possible to treat the gamma-ray absorption in the metal pieces ofthe target chamber · with - Rose 1 s ing factors . smooth:.. These measurements give for the radiative width: -43- wr'{ = 29. 8 ± 6 ev The larger 1ll1Certainty is due to a poorer spectrum obtained from the ice tar gets. By using the radiative widths above and the value of o2 ' obtained from t he angular distribution measurements, the following parameters are obtained for the 8. 64-Mev E2 to the 2 + first excited state in N e transition from the 10. 27 -Mev level 20 : + 4 • 1 x 10- 3 r '{ = 2 • 2 -l. 9 ev . -2 = l. 7 X 10 Investigations of cascade gamma rays from the 10. 27 -Mev level were made with the .fast-slow coincidence system d esc ribed previously. · As is to be expected, the 8 . 64-l. 63-Mev cascade pair dominate the co- . incidence spectra. A typical coincidence spectrum for the 8. ·64-Mev gamma rays detected in a 3" x 3" Nal crystal placed 0. 88" from the target at 90 0 . . to the beam is shown in figure 19C • . These high energy gamma rays we re in coincidence with low energy gamma r ay s in the energy w indow 1. 275 to 1. 85 0-Me v d etect e d i n the 4" x 4 11 Nal placed l. 25 11 froni the target, and oppos ec:l t o the 3 11 x 3" N al crystal. This en- ergy w ind ow is shown in the sin gles spectrum obtained from the 4 11 x 4 11 Nal crystal in figure 19B. The rapidly rising tail in the high energy gamma ,ray spectra starting in channel 55 was present in coincidence runs made off the resonances, and is due to real coincidences presumably from 0 18 (a., ny}N~ 21 or other (n, y) proces ses. In particular -44- the energy window set around the photo peak of the 1. 63-Mev gamma ray would also include the l. 40 - Mev gamma ray .transition from the second excited state to the fi~st excited state of Ne 21 (4). Possible identifications of these gamma rays are given ip. the low energy gammaray spectra of figure 19B. By interchanging the role of the two crystals in the operation of the coincidence circuit, a spectrum for the 1. 63-Mev gamma rays was obtained. This spectrum, shown in figure l9D, was 's hifted out of the singles spectra shown in figure l9B, on the condition that there was a fast co_incidence, and that the high energy gamma ray was above 3. 85 · Mev (shown by the arrow in figure 19A)~ It is interesting · to note that other possible gamma-ray transitions in Ne 20 . that cascade through the 1. 63-Mev level do not show up strongly in the spectrum in figure l9C. Of particular interest are a possible 6. 0 2-Mev E .2 ·t ransition to the 4 + second excited state of Ne 20 at 4. 25 Mev which then decays by emission of a 2. 62-Mev gamma ray to the l. 63 -Mev first excited state and a possible 5. 30 -Mev El transition to the 4 . 97- Mev, -2- third exc-i ted state which then decays to the first excited · state by emitting a 3. 34-Mev gamma ray (47). The strengths of these possible transitions can be roughly estimated at lOo/o or less of the 8. 64Mev transition strength from the data in figure 19C. A more direct measure of these strengths was made by coincidence measurements- with an integral bias set above the l. 63 -Mev gamma ray in the low energy channel at 2. 26 Mev. In this fashion, the 8. 64-Mev transition will not b e -45- observed. The resulting high ene rgy gamma-ray spectra showed the 1. 63-Mev gamma ray, but little else that was recognizable as a gammaray spectrum. By attribU:ting all the counts in these spectra from 3. 67 Mev to 5. 40 Mev to the pos sible El transition to the third excited state, and all the counts from 5. 40 to 6. 60 Mev as due to the possible E2 transition to the second excited state the following upper limits for the radiative widths of these transitions were obtained: Transition E Type ry IMI2 6. 02 Mev 10. 27 - 4. 25 E2 ;$ o. 48 ev ;$ 22.8 So 30 10~ 27 - 4. 97 El ;$ 0 0 44 ev 3 , ;$ 6 X 10- where the upper limit obtained for the possible a restriction. E2 transition is hardly These radiative width limit determin;;ttions, which are admittedly crude, were · made by assuming an isotropic angular distribution for the two coincident gamma rays, and then calculating the detection efficiency of the coincidence circuit from the _product of the individual Nal detector efficiencies and the appropriate spectrum fractions.. Calculating the radiative width for the 8. 64-1. 63 -Mev gamma ray pair in this fashion gave a number 20% lower than the previously determined width, and the efficiencies calculated above have been de creased by this 20%. A~ estimated background of roughly 40% of the total. counts has not been subtracted from the data. It is felt that these radiative widths are good upper limit estimates by roughly this factor of two. -46- The calculation of the radiative width for the transition direct to the ground state is hindered by the difficulty of estimating the summing contribution from the 8. 64-l. 63 -Mev gamma-ray pairs. Such summing calculations are similar in nature to the calculations made for the coincidence circuit, but have the additional difficulty that they involve inte g rals over the spectrum shapes of the two gamma rays. Since these integrals can only be done analytically in cases where vast simplifications are made about the gamma-ray spectrum shapes, it is desirable to choose spectra obtained with a detector geometry that has low detection efficiency, and hence a small summing contribution. Spectra obtained during angular distribution measurements with the collimator have this desired property, and the spectrum in figure 16 which is the sum of spectra obtained during an angular distribution measurement was used for the calculations described below. In this spectrum there were 1532 counts in the 8 0 .64-Mev gammaray photo peaks in the region 7. 29 Mev to 9. 08 Mev that when combined · with a pulse from a l. 63 -Mev gamma ray above 0. 44 Mev could add up to a count in the energy region 9. 08 to ll. 30 Mev. If it is assumed that the spectrum for the 1. 63-Mev gamma ray is a delta function at 1. 63 Mev, then the probability, P, for this occurrence per pulse in the 8. 64-M•:lV photo peaks is: p :: where c c._, X 1 S = 2. 28 X 10 -2 1s the detection efficiency for the 1. 63-Mev gamma rays, and S is the spectrum fraction for pulses above 0. 44 Mev for this gamma ray. In this fashion 35 of the counts in the energy range 9. 08 to ll. 30 Mev -47- can be attribute d to summing . If it is assumed that both gamma-ray spe ct r a are rectangular in shape, one half of this number would be obta ine d. Using the mean of these two estimates and subtracting a background of 85 counts, leave s 68 counts to be attributed to 10. 27- Mev gamma rays. Substituting the appropriate numbers in the formula for the yield for a thick target gives for this wr = r "= " 0~ 95 E2 transition: ± o. 24 ev 0.19 ± o. 05 ev jMj2 = o. 6 The e rrors on these numbers are mainly due to the summing estimate (± 9 counts), and the large ba c kground subtraction. Triple angular correlation measurements were made on the 8. 641. 63-M ev gamma rays from the 10. 27 -Mev level as preparation for simi- lar measurements on gamma rays from the 7. 93-Mev resonance. The coincidence counts between pulses detected above 3. 90 Mev in the 4 11 x 4 11 Nai crystal and pulses detected above 0. 95 Mev in a 2 11 x 2" Nai c rystal ar.e plotte d as a fun ction of the cosine of the angle between the 4 11 x 4 11 crystal and the b eam direc_tion in figure 20. The data points have b e en corre cted for backg round, as determined from runs made below and above resonance, target absorption, and beam displacement effects with respect to the angle of the 4" x 4" crystal. The Nal crysta ls without collimators w ere placed i n a plane with distances to t h e targe t of 1. 05" and O. 98 11 f or the 4n x 4" and 2" x 2 11 crystals respec tiv ~ly. A sketch of this g e ometry is given in figure 20. This -4 8 g eometry has very poor angular resolution,. Lt was felt that the loss o f coinc ide nce counting rate would not justify the proper geometry for h igh angular resolution. The oretical curve s for v a rious spin sequences and gamma-ray m ult ipola rit i e s are al s o plot ted in figure 20. The co{dficients for the 19 possibl e ang ular functions involved in specifying the triple angular corr e lation function for point counters have been modified by smoothing fa ctors to obtain the the oretical curves for the detector geometry of this e x periment. The the ore tical curves obtained in this fashion were then a djusted in amplitude to g i v e the best fit to the experimental points of fig ur e 20. The "goodnes s of fit" to the experimental points was judged by the chi-squared t e st (48 ), and a summary of the probabilities for t h e various patterns is give n in the caption for figure 20. is to the spin-gamma-ra y multipole sequence: The best fit 2+(Ml)2+(E2)0+. This s upplies confirming evide nce for the spin assignment of 2 + for the 10 . 27 -Mev level obtained b y the doubl e angular correlation measurements. There is apo s sibilitythat the more complexgamma.. :I:ay cascades starting from the 10. 27 -Me v leve l and going through the ·1. 63 - Mev first excited s tate may have contribut ed coincidence counts to the data in figu re 20. However the pre v iously d e scribed search for such cascades by coincidenc e techniques indicates th e se more complex cascades are w eak. P a rtic ular d e tails a bout the calculation of the theore tical triple a n gular c orre lation fun c tions ar e give n in Appendix A. The e xperimental information about ·the new level at 10. 27 -Mev 20 excit ati on ene r gy in N e i n dicate s that this l e vel is the first T 1 . 20 .. 20 20 level 1n Ne corres ponding t o the g round state of F and Na • = -49The T = 1 assignment is supported by the excitation energy~ spin and parity, radiative width, and alpha-particle width. The calculation of the expected position of the first in Ne 20 T = 1 level . . 20 20 is hindered by the 1naccurate value for the Ne - Na mass difference. Without this mass difference it is impossible to determine the Coulomb radius f~r the mass 20 isotopic spin triplet. Calculating the Coulomb radius of nearby isotopic spin doublets and triplets and comparing these radii with the formula R gives r 0 the value: r 0 = roA1/3 = {1. 45 + 0. 05) x 10 -13 em where the uncertain- ty includes most of the examples from mass 17 to mass 22. Using the radius from the formula for calculating the Coulomb energy difference in F 20 and Ne 20 difference gives level in Ne 20 and making corrections for the neutron-proton mass 10. 23 + o. 14 Mev for the position of the first T = 1 • . Wilkinson {49) obtains a value of H). 22 Mev for the position of the first ·· T difference in F 19 -Ne = 1 level in Ne 20 · by usi~g the Coulomb energy 19 1 1 13 doublet corrected by {1 - A) • In principle, this latter method is probably more accurate sin:: e the only assumption· is that the charge distribution in Ne 19 is similar to that in Ne 20 • Typi- cal discrepancies of values calculated in this fashion with known positions of T = 1 levels in the self conjugate light nuclei is of the order of 50 kev. The excitation energy of the new level at 10. 27 Mev is then in the correct energy range for the level to be the first T = 1 lev el in Ne 20 • Besides showing that the 10. 27-Mev level is at the correct excitation energy, it is p.lso necessary to demonstrate that this leve l ·has properties similar to the Na 20 .. F 20 ground states. . 20 Unfortunately Na -50- i s diffi cult to make and so far this nucleus has escaped close scrutiny. ':!:'he most direct information pertaining to the ground state spin of F i s from a measurement of the c'ircular polarization of the Ne Mev gamma ray that follows the beta decay of the F 20 20 20 • 1. 63- ground state {50). The results of this experiment are consistent only with a spin of z. Measurement of a small a _n isotropy in the beta-gamma angular distribution of this decay by Boehm!:!_ al. · {51) supplies confirming evidence. The positive parity assignment given to the ground state of F 20 based on the allowed beta-ray transition to the of N·~ 20 {52}. is z+ first excited state The spin of the new level seen in this experiment at 10. 27 Mev is 2 on the basis of gamma-ray angular distribution measurements; theparity"is positive from the nature of the alpha captu;e reaction on ·o 16 • The strong 8. 64-Mev transition to the first excited state can be used as further evidence for the T = 1 nature of the new level. Argu- ments about the strengths of Ml transitions in self c ·o njugate nuclei are based on the theoretical estimates of Morpurgo (53}. who was able to show the isotopic spin scalar part of the Ml matrix element is approxi- mately 1 /10~ the intensity of the vect~n part. result to mean: T 11 Morpurgo interprets this Ml transition strengths between levels with the same in self-conjugate nuclei are expected to be on the average weaker by a factor of a 100 than the average normal Ml transition strengths. 11 Warburton {54) changes this estimate to a factor of 30 by arguing that the average nucleaxlevel will h a ve an isotopic spin impurity of 3% in intensity~ From his compilation of Ml transition rates in s .elf-conjugatenuclei for A :S 20, Warburton concludes the average normal Ml transition -51- for these nuclei are 0.15 Weisskopf units (i.e. the ratio of the experimental width to the width calculated from the W eis skopf single particle limit is 0.15), and the seven known Ml transitions with L':I.T = 0 are roughly 1/10 of this number. The difficulty with such arguments for a particular case is that one can never be sure that it is not an exception. For example, the largest isotopic spin impurity is lOo/o, the strongest Mi transition is 4 Weisskopf units (44}, and combining these numbers it is possible to argue that the fastest "inhibited 11 Ml transition would be 0. 4 Weisskopf units. However .Warburton concludes from his compilation that transi- tions stronger than 0.1 Weisskopf units are most probablyisotopic spin changing transitions in the light self-conjugate nuclei. By applying such argwnents to the 8 . 64~Mev gamma ray with its tran.sition strength of · 0. 41 Weisskopf units, further evidence is supplied for the T = 1 assign- ment. Electric dipole transitions in self-conjugate nuclei have isotopic spin selection rules similar to those for magnetic dipol e transitions (31). Wilkinson (43 ) finds that the average of the El strengths in the light nuclei is 0 . 05 5 Weiskopf units, anq for transitions weaker than 1. 5 x 10 - 3 Weisskopf units the chances are 10 to 1 the isotopic spin has not changed. The upper limit for the strength of the 5. 30-Mev El transition from the 10. 27 - Mev level to the 4. 97 -Mev level is four times this number, and probably it is not wise to draw any further conclusions. Somewhat similar arguments can be based on the alpha-particle width. Since both 0 16 and He 4 are T = 0 particles, a T = 1 assign- ment for the 10. 27-Mev levei would imply the formation of this level -52- by o16 + a. takes place through a impurity" is T = 0 impurity (55). An "average -3% in intensity {44), and hence one might expect a small alpha-particle width for such a T = 1 level. The front edge rise of the excitation function for the 6. 93 -Mev resonance is consistent with a total width of 1 to 2 kev or less. Attributing all of the possible 2 kev width to the alpha-particle width, and calculating 2 .· the dimensionless reduced width, a , from the formula where r a. = alpha-particle width {center of mass) k = wave number = O.l542(2ME) 1/2 x 10 -13 · em M = reduced mass = 3. 2 amu E = center of mass energy = 0. BE a. 1 3 13 R =channel radius= (1.414xl6 / + 2.190) x 10em P a value of 2 1 =penetration factor (56) . a $ 0. 8 x 10 -3 of the Wigner limit 2 (a = 1) is obtained. Even though numbers of this orde r of magnitude are not uncommon for the dimensionless reduced widths of the T = 0 levels in Ne 20 (28). this number is the upper limit for the 10. 27 -Mev level and the dimensionless reduc e d width may w e ll be considerably smaller. It should be noted once again that the radiative widths have been calculated under the assumption that r'V << ra.. None of the results from this experiment can be used to justify this assumption. If this should fail to be the cas e. all the numbers quoted for the radiative widths would be increased, thus strengthing the arguments for the T = 1 -53assignment. In the preliminary results of Davis et al. (29) on elastic scattering of alpha-particles on o16, no signs of this 2 + resonance are seen at 6. 93 Mev, but a narrow resonance of this sort might have easily been missed. ment of 5 The proad (- 150"kev) resonance with a tentative spin assignthat they do find at 6. 97 Mev has not been seen in this experi- ment. 7. 94-MEV RESONANCE Measurements made on the gamma rays from the 7. 94-Mev 20 resonance, corresponding to a level in· Ne at 11. 08-Mev excitation energy,· include a determination of the resonant energy, gatnma-ray angular distributions, determination of the radiative width, investigation of the cascade scheme, and triple angular correlations. The principal gamma ray seen at this resonance is the 6. 83- · Mev transition to the 4 + second excited state of .Ne 20 at 4. 25 Mev. This level in turn cascades through the 2 +first. excited state giving 2. 62- and 1. 63 -Mev gamma rays. The simultaneous detection of the high energy gamma ray together with other members of the cascade is responsible for the presence of this resonance in the excitation function for radiation to the first excited state and the ground s-tate shown in figure 12. Spectra obtained during these early measurements showed no strong transitions to the first excited state, and this was taken for evidence that the spin of this level was relatively high; possibly 4 +. 5-, 6 +, or However estimates of the radiative width from preliminary -54- coincidence measurements gave wr'( = 43 ev which .is only a reason. able number for an uninhibited Ml transition from a more, when the ground state of F in Ne 20 20 4 + level. Further- is equated to the 10. 27 -Mev level , this level corresponds in energy almost exactly to .the se·c ond e xcited state of F 20 . - The possibility that this level was another T = 1 level lead to the additional work described below. Gamma-ray spectra shown in figure 21 were obtained at bombarding energies below, on, and above the 7. ,94--Mev resonance. The energies · at which these .spectra were taken are shown on the excitation function for the 6~ 83-Mev radiation in figure 22A. The on resonance spectrum in figure 21B shows the 6. 83-Mev radiation and the very strong 4 . 43-Me v radiation from c 12 (a, a 1y)C12 • As observed with the other cascade gamma rays there is a summing contribution ab::>ve the 6. 83 -Mev gamma ray that hides possible transitions to the ground state and first excited state. Off resonance spectra in the same figure also shows the 4. 43-Mev carbon gamma ray together with the weaker 6 •. 13-Mev and some suggestion of the 7 -Mev radiations from c 13 (a, ny)o16• Fortunately the yield of gamma rays from c 13 (a, ny)o16, which is the most serious background in the study of the 6. 83-Mev radiation, is smoothly decreasing with increasing alpha-particle bombarding energy in the region of interest from a series of strong resonances at 7. 927, 7. 88 and 7. 736 Mev to a minimum at 8. 05 Mev (11).· The fact that the yield of these gamma rays appears weak in comparison to the 12 4 . 43-Mev radiation from c is due to the low, 1.11%, abundance of l3 . C in natural carbon. The rise and fall of the 4. 43-Mev radiation seen -55in these three spectra is due to the first strong resonance in the c 12 (a. a 1y)c 12 reaction at 7. 96 Mev (57}. Fortunately the counting rates are very low (7. 3 counts per channel per second aV-erage in channels 49 to 61) and pulse pile-up leading to additional counts under the 6. 83 -Mev gamma- ray photo peaks is negligible. It is felt that in spite of the serious background problem reasonable measurements would be possible on the 6. 83 - Mev gamma ray. Prior to the measurements of the resonant energy for this gamma ray, the slits on the 90° analyzing magnet were re.moved for the installation of new equipment. For this reason no effort has been made to establish the resonant energy with the precision attempted for the 6. 93and 5. 37 -Mev resonances. With slit widths of 0. 200n at the entrance and exit of the 90°analyzing magnet. the average of three determinations is 9744 ± 20 kev. resonance in Ne The magne t calibration is based on the 6. 93-Mev 20 , and the uncertainty quoted is roughly half the value indicated by the slit settings, and twice the spread of the measurements. The fact that the measurements are more reproducible than the estimate obtained from the slit geometry of the. 90° analyzing magnet for a b e am of no lateral e xte nt is not su_!prising in view of the finite size of the beam, and the automatic centering of the beam in the e x it slit of the 90° magnet by the 'energy r .egulation circuit of the accelerator. typical excitation functions are shown in figure 22. Two Even though the one shown in figure 22A lacks a point at the bottom of the front edge rise, the resulting uncertaiinty in the resonant energy is only ± 3 kev. -56The total width as dete_rmined from the 1/4 to 3/4 rise of the front edge of the excitation function in figure 22B indicates a width of 3. 2 kev. The beam stability is in the order of 1 to 2 kev indicating the total width of the resonance is less than this number. Angular distribution measurements were made with a .targetcollimator-Nai{T.l) detector geometry similar to that shown in figure 27. The exact distances. were 0. 86 11 from the collimator to the target, and 2. 84 11 from the Nai crystal to the target. Angular distributions were made on, below, and above resonance, at energies shown by arrows on the excitation function for the 6. 83 -Mev gamma ray in figure 22A. The gamma-ray spectra in figure 21 were obtained during these measurements, and ar-e the sum of spectra at various angles. To minimize 'possible errors in the estimate of theI background contribution to the · . counts on resonance, the measurements .were made in two different sequences. During the first sequence, complete angular distributions .·. were made, first on resonance, then below, and finally above resonance. Fo~ the second sequence, these three runs were made at each angle before the angle was changed. The argument in· favor of the first sequence of runs is that a minimum of adjustment of the accelerator was required during the three angular distribution measurements. How- ever the fact that these measurements required 6. 75 hr. favored the second approach. An estimate of the constancy of the background was obtained from the angular distribution of the ray. c 12 11 4. 43 -Mev gamma The angular distributions for this gamma ray obtained during the first sequence of runs showed pronounced quadrupole patterns which -57bec.ame "washed out" as the energy increased past the 7. 96-Mev resonance. The patterns obtained during the second sequence of runs show a 10°/o discontinuity, probably from a change in the beam spot size. ever, th~s How- discontinuity is reflected in the background estimates of t;he second sequence of runs, and it is felt that the discontinuity has been properly handled • . A plot of the angular distribution for the 6. 83-Mev gamma ray is shown in figure 23. This plot was obtained by summing the spectra over the energy r~ge, 5. 72 to 7. 40 Mev, for the data combined after subtraction of the background and corrections tor beam spot displacement (-1. 9°/o}, target absorption (1. 8°/o), and Doppler shift (-3. 5°/o}. The smooth curve througp. the data points is the result of a least squares analysis which gave: W(9} = I + (0. 252 + 0. 019)P (cos 9) ~ (0. ·033 + 0. 024)P (cos 9). 2 4 Angular distributions for gamma rays in the energy ranges 5. 37 to 7 .• 40 Mev _a nd 6. II to 7. 40 Mev were also measured and the angular distribution functions are within half a standard deviation of the numbers given above. The average backgrou:nd removed from the data in figure 23 is shown by the lower curve. Uncertainties indicated on the data points are primarily due to the uncertainty in the background subtraction. Rose 1 s smoothing factors appropriate for the geometry are : J /J 2 0 = 0. 883 + 0. 008 and J 4 / J 0 =. 0. 652 ~ 0. 02I, where the uncertain- ties allow for a possible error of 0. 1" in the target-detector distance. Using these numbers to correct the measured angular distribution, one obtains: W(9) = 1 + (0. 285 .±. 0. 022}P 2 (cos 9)- (0. 051 ~ 0. 037)P4 (cos 9) -58Comparing these coefficients with the theoretical angular distributions for transitions to a 4+ level given in table 3 shows the angular distri- bution is intermediate between the expected angular distributions of a 4 +(M1)4 + transition and a . An assignment of 4 2 +(E2)4 + transition. + to the 11. 08-Mev level would allow a mixture of Ml . and E2 decays to the 4 + second excited state. In this case the angular distribution is given by: w{a) = 1 + ~ + o{45 /17 >1/ 2 - o 2 (3 25/107 8) p 2(cos a) 2 1 +o where the mixing coefficient, o, elements for the transitio~s E2 and Ml is the ratio of the reduced matrix respectively. As explained previously, the sign of o can be either plus or minus, allowing two possible values for the coefficient of the second Legendre polynomial. Plots of the Legendre polynomial coefficients. as a funct.i on of the mixing · coefficient together with the •. e xperimental values are given in figure 24. The value of the mixing coe fficient as determined from the second L~gendre polynomial coeffiCient is: 0 = -0. 238 ± o. 023 ' 2 or the intensity of the E~ of the Ml radiation. This value for the. mixing parameter is consistent radiation is 5. 66 x 10- with the value obtained from times the intensity p 4(cos a). In spite of the fact that the c oeffi<:ient for P 2 (cos a) is four -59standard deviations from the value expected for a 2 +(E2)4 +transition, it does not seem wise tc;:> rule out the possibility that the 11. 08-Mev . level has a spin of 2 + on the angular distribution data alone since there is a serious background problem. Triple angular correlation me_asurements made on the 6. 832. 62-Mev gamma rays using the techniques described in the discussion of similar measurements for the gamma rays from the 6. 93-Mev resonance on page 47 failed to give additional information because of poor statistics. Shown in figure 25 are the coincidence counts between pulses detected above 5. 10 Mev in the 4 11 x 4 11 Nal crystal and pulses detected above .1. 7 3 Mev in a 2 11 x 2 11 Nal crystal plotted against the cosine of the angle between the 4 11 x 4 11 rection. Nal crystal and the beam di- The chi-squared values for the fits given in the figure captio~ for figure 25 ·indicate that at best the triple· angular correlation data could be used to rule out possible 3 and 5 assignments for the 11.08- Mev level. Estimates of the radiative width for the 6. 83-Mev gamma ray have been made from data obtained from s·everal tantalum oxide targets and a variety of Nai(TJ) detector geometries. the product The average value for wry is: . wry = 46 ± 5 ev As an example of these calculations, the average value for the radiative width obtained from the seven angular distribution data plots in figure 23 was wry = 47. 5 ± 5 ev. The numbers used in the calculations of the radiative width from the height of the thick target step given in the discussion of the 5. 37-Mev resonance were: -60- S = spectrum fraction for 0. 84E to 1. 09E y y for a 6. 83 -Mev gamma ray = l. 92 € Ta o for alpha particles with 2 5 2 7. 94 Mev =191 x 10-lS ev-cm = stopping cross section for n = 5 (target material was c Ta 2 o 5) c,(9) =detector efficiency= 2. 52 x 10 -2 (1 + 0. 252P (cos 9) 2 - o. 033 p 4(cos e) ) Q = 500 J.LC of He ++ where the height of the thick target step was taken as the number of counts in figure 23 with an additional ( + 1o/o) correction for the absorption in the glass -walled target chamber. · The uncertainties on the above constants, statistics of the data points.~ and corrections are: s - 6o/o 8<e> - 6 € ~ 2 corrections to data - 2 stati~.tics 3 Q- 1 total 10% A 10% error .is as signed to the average value for the product quoted above since there are possible systematic errors in the calculations. The size of the term, wry , can be used as further evidence· . . that the spin of the 11. 08-Mev level .is 4+. of ~ = - 0. 238 A spin of 4+ and the value determined from the ang':Jlar distribution give the follow- ing numbers for the radiative widths of the 6. 83.-Mev Ml and E2 transitions: -61- r y {Ml) = 4. 8 ± 0. 5 ev 2 I M 1 = 0. 7 2 - - for Ml r y {E2) = O. 29 ± O. 07 ev 2 I M 1 = 7. 3 - - for E2 2+, the gamma ray is Assuming the 11. 08-Mev level is E2, and the radiative width is: r y {E2) = 9. 2 ± 1. 0 ev IM1 2 = 236-- for EZ Considering that the strengths of the E2 transitions in the ground state band of Ne 20 are only 38 and 28 Weisskopf units for the transitions, first excited state to ground state, and second excited state to first excited state (32), a value of 6 -: 9 times these numbers for a transition from a level which is not in the ground state band is unreasonable. How- ever, Wilkinson {44) has estimated a valqe of 300 Weisskopf units for a supposed E2 transition in ~ al. {58). B Even though thi.s 10 B from the data of Meyer-Schutzmeister 10 transition is exceptionally strong when compared to other E2 transitions in the light nuclei it may be the 6. 83 -Mev transition is another such exception. Fu~ther evidence for the 4 + assignment can be obtained from the small radiative widths for transitions to the first exdted state and ground state. By making estimates of the summing contributions from the main cascade to counts attributable to the .9. 45- and 11. 08-Mev transitions, the limits wry $ O. 7 ev and wry $ 6. 8 x 10- 3 ev are obtairied for the two . transitions. By then assuming the 11. 08-Mev level -62is 2. + or 4 +. the following assignments would be made: a) 2.+ assignment for the 11. 08-Mev level 1) 9. 45 -Mev transition r y-< 0.14 ev jMj2 :$7.9 x 10jMj 2 3 :$ 0. 7 for pure Ml for pure E2 2) 11. 08-Mev transition r y-< 1.4xl0- 3 JMI2 :$ 3. 5 x 10 - 3 for E2 b) 4 +assignment for 11. 08-Mev level 1) 9. 45 ~Mev transition r y :$ o. 08 ev j M j 2 :$ 0. 4 for E 2 2) 11. 08-Mev transition r y :$ 8 X 10- 4 ev for E4 In view of all the evidence. the possibility that the 11. 08-Mev 2+ 1s . very sma 11 • . 1eve 1 1s . The . 2 + . assignment would require expla- nations for the four standard deviations in the angular distribution fits, an enormous E2 width to the second excited state with weak E2 transi- tions to· the two lower states. and a weak Ml transition to the second . d state. exc1te If a 4+ ass1gnment . . ma d e. reasona bl e va1 ues are 1s obtained. + Investigation o f other .cascades from the 4 • 11. 08-Mev level by coincidence techniques was hindered by the three gamma-ray cascade initiated by the 6. 83 -Mev radiation. Neither a possiple 3. 43 -Mev. -63E2 g a mma-ray transition to a level of 7. 65 Mev that is thought to be 6 + {59), nor a possible 4. 0 6-Mev, El transition to a level at 7. 02 Mev that is thought to be 4 - (59) were seen. The upper limit for these transi- tion strengths can be placed no lower than 1/5 of the main transition strength, and while this limit is hardly a restriction on the possible E2 transition, this limit on the 2 IM 1 $ 4. 3 X 10 -2 • r y (El) ;S 1. 4 ev or El transitions gives In: this estimate an allowance has been made for the fact that - 30o/o of the decays from the 7. 02-Mev level give low energy gamma rays followed by alpha particies. The experimental data can be used to infer a for the ll. 08-Mev level. T =1 assignment The evidence for this assignment is the Ml width, the excitation ene rgy of the level, and the alpha-particle width. The excitation energy of ll. 084-Mev places this level 810 ± 18 kev above the 10. 27 Mev level. kev (19). to the F The second excited state of F Thu~ within the errors, the 20 occurs at 828 ± 8 11. _08-Mev level would correspond second excited state if it had a T = 1 assignment. T = 1 assignment can be made on the basis of the tion strength. 20 The 6. 83 -Mev Ml transi- A comparison of the 0. 7 2 Weisskopf units for the strength for this transition to the Ml strengths in other self conjugate light nuclei in Warburton's compilation (54) places this transition in the category of most likely an isotopic spin changing transition. A T = 1 assignment would also imply a small alpha-particle width for break - up into a. + o 16 • Attributing all of the measured width of 3. 2 kev to the aipha-particle width, an upper limit of 2.1 x 10single p~rticle limit. 3 is obtained for the ratio to the Wigner While such a number does no:t confirm ·the T =1 -64assignment, it is important for the arguments that it is small (55). The one missing piece of information is the spin of the second . d state o f exc1te F 20 • Th e proton group to t h"1s state f rom the r_l9(d, p)F 20 stripping reaction reported by El Bedewi {60) exhibits a characteristic l. = 2 Butler pattern. On this basis, spin values of 1 +, 2 +, or El Bedewi has assigned possible 3 + to this level. However his data shows this proton group is only 1/16 as strong as the l and 7th excited states. = 2 groups to the first A possible explanation fo·r the weakness of this group is that with the neutron being captured into the s-d shell, it would be necessary to resort to spin flip stripping to make a . 4 + level. The H. 08-Mev level has possibly been seen in two other experiments. · Butler {37) using a gamma-ray threshold technique on the F 19 (d, ny)F . N e 20 • 1n 20 reaction reports a level at 11. 08-Mev excitation energy This level decays by emitting a 9. 6-Mev ga~ma ray in a transition to the first excited state. While the excitation energy of this level agrees with the energy found in this experiment, .there is no agreement on ~he cascade scheme. Possibly the 9. 6-Mev gamma ray that Butler reports is the result of detection of the 6. 83-:Mev gamma ray and one of the other cascade members in his two crystal gamma-ray · spectrometer. Davis et al. (29) have reported a poorly resolved level at 11.10 Mev in Ne 20 in their preliminary results from alpha-particle . . 016 • scatter1ng 1n From the experimental data and discussion given above, the 11. 08-Mev level in Ne of the F 20 20 is 4 +, and mo~t- likely the . second excited state. Ne 20 T = 1 analog -65OTHER RESONANCES The resonances described in this section have not received the attention given to the resonances at 5. 37, 6. 93, and 7. 94 Mev. Most of the results quoted below have been derived from . the excitation function presented in figure 11 and figure 12. Resonant energies have not been determined with the highest attainable precision, and the values quoted below are based on the 5. 374-Mev and the 6. 930-Mev resonances in 0 16 . (a., y)Ne 20 • Where applicable, radiative width estimates have been made from the formula for the height of a thick target step given in the discuss1on of the 5. 37-Mev resonance. The modifications made to this formula for those resonahces that show measureable widths follow the form of Fowler~ al. {40}. In particular the maximum yield is related to the radiative width by: = o.l989 x 10 where -3 S€EY(6) 0 Y(6)max is the .maximum yield at angle thickness in energy units. max 'IT t;(e) J,1. 2 tan -1 t i' e, and t is the target The other factors are . defined on page 32. Similarly; the area under the yield curve is related to the radiative width by: O.l989xl0 where -3 S€E Q c;(e) n f Y{6) dE • t f Y(6) dE is the area in counts- e nergy uz:tits. In the estimates of the radiative widths for the resonances dis- cussed below, it has be e n a s sumed that the angular distribution is -66is ot·r opic. The error introduced in this fashion is arbitrarily' taken to be 25o/o. For one of the resonances, sufficient information is availabie about the spin of the level and probable multipolarity of the radiation to allow a reasonable estimate of the correction factor for the angular distribution. This estimate is given in the discussion of the 6. 61-Mev resonance. 5. 94-MEV RESONANCE This resonance is shown on the excitation function for radiation to the ground state and first excited state of Ne 20 given iri figure 11. Even though the region has only been covered in 20-kev steps, the yield curve for the 5. 9-4-Mev resonance shows a definite thin target shape. The yield in figure 11 reaches a maximum at 5. 955 ± 0. 010 Mev. The calculated ~arget thickness at this energy is 52 ± 5 kev, and this value and the value of the maximum yield give 5. 93 ± 0. 03 Mev as the 20 resonance energy, corresponding to a level in Ne · at 9. 48 ± 0. 03 Mev. The uncertainty assigned to the resonant energy allows for uncertainties in the beam energy as well as an additional uncertainty in the location of the maximum yield. The width of the yield curve is 63 ± 10 kev, indicating a resonant width of 29 ± 15 kev in the center of mass. Gamma-ray spectra obtained at this bombarding energy show the 7. 85-Mev transition to the first excited state of Ne transition to the ground state. 20 , with a weaker . Estimates of the radiative width for the transition to the first excited state by the height formula and the area formula give wr'{ = 1. 56 and 1• .25. ev respectively. Probably the area under the yield curve is the b ette r estimate in these circumstances, and -67- the best estimate is considered to be wry = 1. 3 ± O. 5 ev. The uncer- tainty in this number allows for a substantial background sub,traction that was estimated by drawing a straight line under the yield curve, as well as the possible error incurred by neglecting angular distri- . bution effects. Similar estimates for the radiative width of the 9. 48- Mev transition direct to the ground state gave wry;$ O. 3 ev,. This width is only a rough upper limit due to poor statistics, ·a large background, and the difficulty of estimating the summing contribution from the 7. 85-1.·63 -Mev cascade gamma rays to the counts in the photo-peak region of the 9. 48-Mev gamma ray. The gamma-ray decay scheme indicates possible spin values . + . . 20 of 1- or 2 for the 9. 48-Mev level in Ne • McDermott et al. (28) have found a 2 + resonance with a width of 24 kev in the center of mass at 6. 03-Mev bombarding energy corresponding to a level at 9. 55 Mev in Ne 20 • Most likely the two resonances are the same even though the energy discrepency is 70 kev instead of the 58 kev noted in the discussion of the 5. 37-Mev resonance. Corroborating evidence for the identity of this resonance. is obtained from the preliminary data of Davis et al. (2.9) who report a resonance at 5. 95 Mev bombarding energy with . . . . t tentahve sp1n-par1ty ass1gnmen , 2.+o A 2. + spin value for this reso- nance would then allow E2 and Ml transitions to the first excited state, as well as E2 transitions to the ground state. The parameters in these cases are: a} 7. 85-Mev transition to the first excited state ry = o. 26± 0.1 ev -68- IM 1 ]M j 2 = 3. 2 - - for pure E2 2 = 0.025-- for pure Ml b) 9. 48 -Mev transition to the ground state ry ~ 0.06 ev ]M ] 2 ~ 0. 3 - - for E2 The spin assignment of 2+ also allows calculation of the reduced width for the alpha particle. These numbers are: r a = 29 ± 15 kev a2 = 1. 49o/o where the total width has been taken as the alpha particle width. 6. 61-MEV RESONANCE This resonance is shown on the excitation function for radiation to the ground state and first excited st~te of Ne 20 given in figure 11. Parameters describing this resonance hav·e been calculated in the same fashion as the parameters used· to d~scribe the 5. 94-Mev resonance. The width of the yield curve in figure 11 at half maximum is 199 ± 30 kev. The target thickness at this energy is 51 ± 5 kev indicating a resonance width of 155 ± 30 kev in the center of mass. The maximum yield is at 6. 63 Mev, locating the -resonance at 6. 61 ± O. 03 Mey, corresponding to a level in Ne 20 at 10. 02 ± 0. 03 Mev. Gamma-ray .spectra obtained in this energy region show the 8. 39-Mev gamma ray from the transition to the first excited state with little if any direct transitions to the ground state. Coincidence measurements made at this energy showed an 8. 4- Mev gamma ray in coincidence with a 1. 63-Mev gamma ray. but poor -69statistics prevent any statements about possible transitions to higher . . d states 1n . N e 20 • exc1te The radiative width has been estimated from the data used to obtain the excitation function shown in figure 11. A value of w r y =8 ± 3 e v was obtained for the gamma-ray transition to the first excited state. The large uncertainty again is pri marily due to the background and possible errors incurred by n e glecting the angular distribution. An . estimate of the gamma-ray transition width to the ground state ·can only be given in the form of an upp e r limit since it is possible to attribute all of the counts seen in the r e gion to the 10. 0-Mev gamma-ray photopeaks to summing of the cascade radiation from the 8. 39-1. 63-Mev transitions. At most for the transition to the ground state, wry ~ O. 6 ev. The gamma-ray decay scheme indicates possible spin values of 3 - or 4 + for the 10._02-Me v leve l in Ne 20 • . Of the other experi- ments that yield information about levels in Ne 20 in this excitation energy range, the results of McDe rmott et al. and Davis et al. from the -elas tic scattering of alpha particles in o16 are the most helpful. Although McDe rmott e t al. _stopp e d a t 6.5-Mev bombarding energy, they found it n e cessary to postulate a bro ad 4 + resonance just b e yond their range in orde r to obta in g ood t h e ore ti cal fits to their data above 5. 6 Mev. Davis ~ al. report in their pre liminary data a broad resonance at 6. 58 M e v . having a width of approximately 120 kev, and_tentative spinp a rity of 4 +. If it is assume d this resonance is 4 +, then the parameters fo r the gamma radiation to the first excited state and ground state are: -70- a) 8. 39-Mev transition to the first excited state r y = o. 9 ± o. 4 ev jMj 2 = 6.9-- for E2 b) 10. 02-Mev transition to the ground state r y ::; o. 01 where it has been asswned the gamma-ray angular distribution is isotropic. It is worthwhile to illustrate the steps that should be taken to correct the data for angular distribution effects. for the 10. 02-Mev level in Ne first excited state was pure 20 E2. A 4 + assignment would imply the transition to the The angular distribution of the radi- ation with respect to the beam axis is given in table 3. figure ll was obtained with the 4 11 x 4 11 The data in Nai crystal placed 1. 06 11 from the target at 0° with respect to the beam. appropriate for this geometry are 2+ Rose 1 s smoothing factors J 2 /J 0 = O. 514 and J 4 /J 0 = 0. 028. Applying these nwnbers to the theoretical angular distribution gives a correction factor of 1. 25 at 0° that should be divided into the widths given above. Asswning a spin of 4 + for the 10. 02-Mev level in Ne allows the determination of the alpha particle parameters. 20 also If all the measured width of this resonance is attributed to the alpha-particle width, the following numbers a:J;"e obtained: r a = 155 ± 30 kev a 2 = 25. 4o/o -71- 8.17-MEV RESONANCE This resonance is shown on the excitation function for radiation to the ground state and first excited state of Ne as a single high point. 20 given in figure 12, A separate excitation function run over the region of this resonance in 10 kev steps shows a:. typical thick target excitation function that rises on the low energy side in less thanlO kev. From this excitation function it is possible to place the resonant energy at 8.17 ± 0. 03 Mev~ corresponding to a level in Ne 20 at 11. 27 ± 0. 03 Mev, and with a resonant width of 4 kev or less in the center of mass. Gamma-ray spectra obtained at this alpha-particle bombarding energy show the 11. 27 -Mev transition to the ground state with no clear indication of the pss sible 9. 64-Mev transitions to the first excited state. However even in the best spectrum obtained at this energy, poor statistics prevent the upper limit estimate of the strength of the transition to the first excited state from being set lower than 1/3 of the transition strength to the ground state. Estimates of the radiative width for the wry = O. 9 ± O. 4 ev, indieating the 9. 64-Mev transition to the first excited state has wr ;:5 o. 3 '( 11. 27 -Mev transition to the ground state gave ev. Additional evidence for the validity of the upper limit set on the transition to the first excited state was obtained from coincidence measurements at this energy. A 1000 tJ.C run gave 25 coincidence counts which leads to an upper limit e stimate of wr'( - 0. 4 ev if all the counts are attributed to the possible 9. 64-1. 63-Mev gamma-ray cascade. It is. interesting to speculate on the possible spin values for this resonance. of Ne 20 The fact that the transit ion is primarily to the ground state limits the possible spin value s to 1 or + 2 • A 1 assignment -72- would probably mean the transition to the ground state is 2 + assignment would mean E2. El, while a In either case these transitions are weak, and the parameters would be: a) 1- assignment for the 11. 27 -Mev level r '( = 0. 3 ev ]MI b) 2 = 4. 2 X 10 :...2 for El 2 + assignment for the 11. 27-Mev level r '( = 0.18 ev ]Mj 2 =0.37--for E2 As mentioned previously, both Butler {37) and Rabson ~ al. (36) have reported a level in the vicinity of this excitation energy in Ne 20 from the F 19 {d,n'()Ne 20 reaction. The gamma ray they report is due to a direct transition to the ground state. Davis et al. have also reported a resonance at 8. 20-Mev bombarding energy, but assign a resonance width of approximately 125 kev. It seems unlikely that the resonance they report i .s the resonance reported here. 8. 54-MEV RESONANCE This resonance is seen as a single high point on the excitation function for radiation to the ground state and first excited state of Ne given in figure 12. The data used to derive this excitation function is the only source of information on this resonance. The resonant energy is 8 . 54 ± 0. 04 Mev, corresponding to a level in Ne excitation energy. 20 20 at 11. 56 ± 0. 04 Mev The uncertainty assigned to the resonance energy corresponds to the 40 kev steps used to cover this energy region. The gamma-ray spectrum obtained at 8. 54-Mev bombarding energy shows -73the distinct features of a weak 9. 94-Mev gamma ray from the transition to the first excited state of Ne 20 • This gamma ray is clearly absent in the spect~a obtained at 8. 50- and 8. 58-Mev bombarding energy. Estimates of the radiative width were made by assuming the s i ngle high point is the height of a thick target step. Such an assumption wr = o. 5 ± o. 3 ev. In view of the fact 'Y that the excitation function was run in 40 kev steps, and the fact that the gives for the radiative width: tungsten oxide target was 50 ke v thick to alpha particles with this energy, a resonance with as much as 15 kev total width might appear as a single high point. This uncertainty, poor statistics, .and possible angular dis- tribution effects are the primary sources of the large uncertainty quoted on the number above. There is no e vidence for a transition to the ground state. however a width of wr 'Y < o. 2 ev probably would go undetected. 9.40-Mev Resonance This resonance is shown on the excitation function for radiation to the ground state and first excited state of Ne 20 given in figure 12. On the basis of the experimental widths of the yield curves for the 6. 93and 7. 94:..Mev resonances, the t h ickness of the target used for the measurement of the excitation f unction shown in figure 12 was 47 ± 5 kev for alpha particles of this energ y. The width of the yield curve for the 9. 39-Me v resonance is 68 ± 15 k e v at half maximum, indicating a resonance width of 40 ± 16 kevin the center of mass. The maximum yield is at 9. 42 Mev, and hence the resonance is located at 9. 40 :I: 0. 04 Mev corresponding to a level in Ne 20 at 12. 25 ± 0. 04 Mev. Gamma-ray .spectra obtained at this bombarding energy show the -7410. 62-Mev transition to the first excited state with no clear indication of a transition to the ground state. Estimates of the radiative width for the transition to the first excited state gave wry =7 ± 3 ev. Transi- tions to the ground state can not be ruled out due to the summing problem, however a lower limit of wr'Y < 1 ev can be set on this transition. Coinci- dence measurements made at this energy showed the 10. 67 -Mev and 1. 63Mev gamma rays, but due to poor statistics, no statement can be made about transitions to low-lying states above the first excited state of Ne 20 . Both Butler and Rabson et al. have reported a level in the vicinity of this excitation energy in Ne 20 from the _19 F" {d, ny)Ne 20 reaction. The levels they report decay by the same gamma-ray cascade scheme as noted in this work. Davis et al. have also reported a resonance at 9. 42-Mev bombarding energy, but they do not assign a width. 9.57-Mev Resonance The presence of this resonance on the excitation function for radiation to the ground state and first excited state of Ne 20 . shown in figure 12 is primarily due to pulse pile up of the very intense 6.13-Mev radiation from a resonance in the barding energy. o 16 16 {a, a 1y)o reaction at this bom- Even though the threshold for this reaction is at 7. 68 Mev, this is the first strong resonance that has been observed. The fact that the first strong resonance occurs 2 Mev above the threshold is not surprising if one considers the fact that the outgoing, inelastically scattered alpha particle will have only 1. 22 Mev ·in the center of mass, a nd must penetrate a Coulomb barrier of 4. 0 Mev for particles from 0 16 • s-wave alpha • -75A separate excitation function for the 6. 13-Mev radiation is shown in figure 26. The data was obtained from the same data used for the ex- citation function given in figure 121 and the experimental conditions are given on,page 32. from the C 13 The contribution to the yield of 6. 13-Mev radiation (a.~ n-y )0 16 reaction has been estimated by smoothly matching the excitation function obtained by Spear et al. (11) for this reaction to the data at 9. 05 Mev. cedure. The eros ses in figure 26 are the result of the pro- As seen in this figure 1 the width at half maximum for the 9. 57- Mev resonance is 74 + 15 kev. The target thickness at this bombarding energy i s 4 7 + 5 kev, thus indicating a resonance width of 46 + 16 kevin the center of mass. The maximum in the yield occurs at 9. 57 Mev, placing the resonance at 9. 57 + 0. 04 Mev, and corresponding to a level in Ne 20 at 12. 39 + 0. 04 Mev• .The product (UJI'a.ra. 1 )/r has been computed from the height and the area of the yield curve for the 9. 57-Mev resonance. tained WaS (UJr r I)/ r a. a. = 3 -+ 1 kev 1 The value .ob- where the uncertainty is primarily due to the uncertainty in the width of the resonance. It is possible to restrict the spin values that can be assigned to this level on the basis that the required width for particle limit. r a. 1 By equating· r a. should not exceed the Wigner single I to r , one obta:ins the following table: -76JiT w ra.l liT ra 1w 92 3 2+ 7 430 ev 0+ 768 ev 56 o/o 5 600 1 400 150 4+ 9 333 400 83 1 3 1000 1 2+ 116 860 3 7 430 116 370 . 5 o+ 11 272 2+ · + 2 116 230 1 3000 3 18.8 15900 2+ 5 600 3 18.8 3200 4+ 9 333 3 18.8 1800 6+ 13 231 3 18.8 1230 In this table, J;r is a possible spin and parity value for the 12. 39-Mev level in N e 20 ' and' 1. is the r elative angular momentum (in units of -n:) with parity ;r removed by the outgoing inelastically scattered alpha particle. · The requirements on J;r and 1 iT is summarized by the vector equation: The quantity r a. 1 is the channel width for the inelastically scattered. alpha particle, r a.w , is the Wigner single particle limit . for alpha pai-ticles with this energy {lo 22 Mev} and relative angular momentum, 1., and e 2 is the ratio of r .a. I to r a.w I • As seen in this table, 3 ana 4 + are distinct possibilities for the spin of .the 12. 39-Mev level, however 2 + and 5 - . can not be entirely ruled out in view of the large un- certainty in the quantity (wra. ,ra.)jr. The preliminary .d ata of Davis et al • .on the elastic scattering of alpha particles on o16 shows evidence for a resonance at this bombarding which is seen to vanish at 90° and -77140. 8° in the center of mass indicating the spin is 3-. Radiative transitions from the 12. 39 -Mev level in Ne 20 .to the first excited state and ground state are difficult .to estimate due to the pulse pile-up from the intense 6.13-Mev radiation. Crude estimates give: wr 'I = 3. 5 ± 2 ev - wr'I :s 1 ev first excited state ground state The ground state radiative width is given in the form of an upper limit since it is possible to attribute all the counts seen in the gamma-ray spectra in the energy region of the 12. 39-Mev photo peaks to pulse pileup. Similar problems were encountered in making the estimate for the radiative width to the first excited state, but a comparison of two runs made at 9. 59-Mev bombarding energy with beam currents that differed by a factor of two showed that not all of the counts were due to pulse pile-up. A coincidence measurement made at this energy did not yield sufficient counts to give a recognizable spectrum, but if all the coincidence counts obtained are attributed to the 10. 7 6- and 1. 63 -Mev cascade gamma rays, a value of wr'I = 3. 6 is obtained for this transition. In the excitation function for 6. 13 -Mev radiatj.on for o 16 (a, a 'y)o16 . shown in figure 26, a small bump is seen at 9. 25-Mev bombarding energy. This bump is reproducible, and probably is due to a reso- nance in o16 (a, a'y)o16 reaction, and would correspond to a level in N 20 at 12.13 :1: 0. 04 Mev. for the quantity The area under this bump indicates a value {wra r a ,)jr = 100 ± 50 ev. Arguments based on the size of the Wigner single particle limit are of no assistance in limiting the -78possible spin values for this resonance due to the small size of the quantity {wra r a ,)jr • . -79- IV. SUMMARY The .results from this experiment are summarized in table 1 and table 2. The final state parameters listed in table 1 have been taken from Lauritsen and Ajzenberg-Selove {4) and the spin and parity assignments for the 9. 48- and 10. 02-Mev levels are based on the experiments of McDermott et al. {28) and Davis et al. (29}. this table is from this expe riment. Otherwise the data in The isotopic spin assignments that have been made are based on the assumption that the 10. 270-Mev level is the first T = 1 level in Ne 20 • Table 2 lists the alpha-particle parameters for those resonances in table 1 for which the spin of the corresponding level in Ne 20 is known. In figure 27, the energy level diagram of F 20 has been adapted from Lauritsen and Ajzenberg-Selove and so arranged that the ground state corresponds in energy to the analog state it). Ne 20 at 10.270 Mev. This arrangement shows that with the single exception of the 12. 39-Mev level found in the inelastic scattering of alpha particles on Ne 20 o 16 , each l evel found in this experiment agrees in energy with a level in F 20 • Such agreement makes it tempting to assume that these levels are analogs; however more experimental information is necessary before such conclusions · can be drawn. Some systematic behavior can be seen in the data of table 1. The two strong~r resonances in the capture reaction are for magnetic dipole transitions between states that differ by one unit in their isotopic spin quantum number. Several of the E2 transitions are approximately seven times stronger than the single particle limit. Even though the single -80particle limit is proportional to the fourth power of the radius. it is necessary to increase the radius of Ne from 3. 25 ~ermis used for 20 the calculations to roughly 5. 3 Fermis before the single particle estimate would produce the factor of seven. Since such a radius seems unreasonably large, these enhanced radiative widths for the E2 transi;.. tions indicate that collective e ffects a re important evex: at these relatively high excitation energies. Ele ctric quadrupole radiative widths in excess of the single particle limit have been noted in a number of other transitions in the light nuclei (43), and typical strengths are roughly 1 to 30. The principal result of this experiment is the location and identification of the first T = 1 level in Ne 20 at 10. 27 Mev. The T =1 assignment was made on the basis of the excitation energy, the fact that the 2 + spin of this level is the same as the ground sta te of F 20 , and the large radiative width for the Ml transition to the f i rst excited state of Ne 20 • Since such an assignment implies this level is quite similar in structure to the F 20 ground state, it then becomes intere s ting to make a comparison of the Ml d e cay of the 10. 27 - Mev l evel in Ne 20 20 ground state. with the allow e d Gamow- Teller b e ta d e cay of the F The only difficulty is obtaining a s uita ble m o del. At present, no complete inter- m e dia te-coupling shell mode l c al c ula tio ns h a ve b ee n made for the mass 20 system. The difficulty with such calculations is the evaluation of a large number of radial inte gral s des c ribing possible residual interactions in the (2s,ld) shell. low-lying levels of . Ne Efforts to bypass these integrals by describing the 20 by simple configurati ons in this shell led -81Elliott and Lane {61) to the conclusion that it is important to include all configurations. The unified model of Bohr and Mottelson offers at least an approximate method of treating the residual interactions by the introduction of a permanently deformed well. This model has had sue- . cess in describing nuclei in this mass region, ar{d in view of recent success of Litherland et al. (2) with the appli·c ation of this model to the low-lying, T = 0, levels of Ne 20 , it seems rather natural to assume the model will offer a good de scription of the . . 20 the low-lymg levels of F and Na 20 T = 1 levels in Ne lO or • A calculation comparing the allowed Gamow - Teller beta decay of the F 20 . 20 ground state to the Ml decay of the 10. 27 -Mev level of Ne is given in Appendix B. At best, the calculation is premature. . 20 of information about the character of the excited states of F T = 1 levels in Ne 20 A paucity and the above the 10. 27 -Mev l e vel makes it impossible to argue, even qualitatively, that the unified model is applicable. is no indication that these levels have even the rotor. I(I +1) There spacing of a rigid However, by making some "hopefully- reasonable 11 guesses for unknown parameters, an intere sting, qualitative picture is obtained from the unified model. The very slow (log f t = 4. 99) but allowed Gamow- Teller beta decay of the of the K F 20 ground state (52) is a natural consequence selection rule of this mode l. However the strong Ml decay of the 10. 27 -Mev level is not so easily explained, and the estimate of this strength based on the factor of three. log ft value of the beta decay is low by a Probably this is not poor agreement in view of the un- certainties. · Finally it is tempting to put the 4 +, T = 1, level of Ne 20 -82at ll. 08 Mev into a rotational band based on the + 2 , 10. 27 -Mev level. However, the calculations in Appendix B indicate these levels are much too close in energy to be related in this fashion. The question this raises, of course, is just how many bands will be necessary to describe the T = 1 levels in Ne 20 or the low-lying levels of F 20 20 or Na . • While unobserved transitions usually deserve no additional commEmt, . the possible El gamma-ray transition from the 10. 27 -Mev level to the 4. 97 -Mev level in Ne 20 (see figure 1} should be mentioned once again because of the possible astrophysical importance of the 4. 97 -Mev level. This level lies just above the 0 16 +a . 20 threshold 1n Ne , and in the past it has been suggested (62) that it may play an important role in the formation of Ne 20 in the interior of helium burning stars. How- ever recent measurements {63) have shown the spin and parity of the 4. 97 -Mev level is o16 +a. 2 hence forbidding the formation of this level by The· fact that the expected El transition from the 10. 27 -Mev level to the 4. 97 -Mev level is much weaker than the Weisskopf single particle estimate (with a ratio of IM 1 2 < 6 x 10 - 3 } is surprising, how- ever this limit is not small enough to throw doubt on the for the .4. 97 -Mev level. 2 assignment -83APPENDIX A Angular Distribution Considerations In this appendix the theoretical angular distribution and angular correlation formulas that have been used in this experiment will be presented, and a discussion will be given of the modifications introduced in these formulas by the finite size of the A.l. Nai{T 1) detectors. Theoretical Formulas The theory of angular correlations of nuclear radiations is an important facet of nuclear spectroscopy, and the subject has been treated in some detail in a nwnber of excellent reviews {64, 65). Tables have been prepared for the explicit purpose of expediting the calculation of angular correlation functions, and several authors (66, 67) present articles with detailed instructions for the use of these tables. One of the clearer demonstrations of the modern techniques of using density matrices and statistical tensors for the derivation of correlation functions is given by Wiedenmuller (68), who derives a rrmaster formularr that gives the statistical tensor for the residual nucleus in terms of the statistical tensors for the initial state and the outgoing radiation. Similar formulas may be obtained from the review article of Devons and Goldfarb (65). It is probably worth noting that Wie denmuller's definition of a statistical tensor differs from the definition given by Devons ·,and Goldfarb, and one should take care not to go from one formulation to the other indiacrimately. The formulas listed below have been derived with a master -84formula similar to that of Wiedenm;ller' s but for statistical tensors defined in the same fashion as given by Devons and Goldfarb. problem as simple as the alpha-capture by 0 For a 16 , the master formula can be used directly to give the angular distribution of outgoing gamma radiation with respect to the beam axis. W(S} t::t. I This formula is: 1 2 (-1){(2L +1)(2L' +1)} / (Jl0, JlO I K 0) KLL' where Jl = spin of the initial state formed by the alpha capture reaction L~ L' - angular momentum removed by the outgoing gamma ray J2 = final state spin a = angle between the gamma-ray direction and the beam direction < J 1 Jl TL Jj.J 2 > = reduced matrix element for the multipole operator TL (J ~, J 2 M 2 J J 3 M )= Clebsch-Gordon coefficient that adds . J · to J 3 1 2 1 togiveJ 3 W(J J L L'; K J ) 2 1 1 = Racah coefficient. Some computation convenience is achieved by introducing the . z ficient of Sharp :et al. (69), in this case one obtains: 1 coef- -85- w(e) ~ L KLL 2 (-:l)K/ (J o, J o 1 1 I K o) z 1 (LJ1L' J 1 : J 2 K) 1 x PK(co.s 8) <Jll! TL I[ J2 > < Jl II TL' Jl J2 > * Numerical formulas for the angular distribution of gamma radiation with respect to the alpha-particle beam direction for pu:re multipole transitions to the ground state and first two excited state,s of Ne ZO are ·g iven in table 3. In this table, the angular distri!?ution functions have been normalized to the form: in which case the number of gamma rays at angle dO is given in terms of the source strength N e, N(S), in solid angle by: The numerical values in table 3 have been checked in all cases with values obtained from the formulas and tables of Sharp e t al. (69), and most cases have been compared with formulas obtained from the tables of Biedenharn and Rose ( 64) . The specific formulas for transitions involving mixed gamma ray multipoles are too extensive to warrant treatment ·here. The numeri- cal formulas, given in the text as needed, have been de:t:ived from the general formulas above. In these cases it is not possible to factor out the constant reduced matrix elements , and as a result an additional parameter, the mixing coefficient o or the ratio of the two reduced matrix elements, is introduced in the formulas . · :For the two examples -86in the text: 0 = <Jlj)E2jjJ2> <Jlil Ml {lJ2> where < J 1 Jl E2 Jl Jz > and < J 1 !! Ml Jl J 2 > are the reduced matrix elements for the electric quadrupole and magnetic dipole transitions respectively,. The transition rates or radiative widths ' are proportional . to the reduced matrix elements squared, hence to 2 o • By sui table phasing of the nuclear wave functions, the reduced matrix elements may be made real (47}, in which case o is either positive or negative. Physical significance can be attached to the sign of o only in regards to a specific nuclear model, and in such cases positive o corresponds to the phasing of the matrix elements of Blatt and Weisskopf (70), and the usual definition of the reduced matrix elements: where T LM is one of the multipole operators. Formulas for triple angular correlations involving the incident alpha particle and two outgoing cascade gamma rays are derived by a continuation of the process us~d to obtain a single cascade formula. For a· cascade of the form ·- ---,.,.--...----- 1'1 L2 ' ~2 ----~~------c L3 t3 ____.._____ d Ne20 -87- where 1 ; c, 1 and d are the initial state, intermediate state and final I state respectively, and where L ,L 2 2 I and L ,L 3 3 represent the multi- polarity of the first and second cascade gamma rays. The general formula has the same form as the single cascade formula being a sum over angular dep(O!ndent terms each of which is multiplied by a coefficient. The formula used was: where the coefficient is: = [ {21 1 + l) 4 {2K3 + l)(2K 2 +.1){2L 2 + l)(2L~ + 1)(2L 3 + 1)(2L; + 1) 1 + L2 + d + K 1 x {2c +1)~] 1I 2 {-1) 1 . x W(c c L L;; K d) 3 3 . . X where the term, { 3 - c {.t o,£ 0 1 1 ~ ~~ ~~ 1 .< : ~Kl K3 KzJ 11 I K 10) II Ll I c > < 11 II L~ II c >*< c II L 2 II d > < c [ l L ~ II d >* } is .a for the general case are: 9-J syrnbol. The angular dependent functions -88- AK K K 1 2 3 t9 2¢2, 8 3¢3) . 1 . 4Tr x .( 2K tl 3 where the M Y K (9¢} are spherical harmonics. The. angles 9 , cp 2 2 referring to the first gamma ray, are the Euler anglesdescribing the r otation ¢ 2 about the beam axis or the original about the new detector. Y -axis such that the new 83' ¢ Angles same fashion. Z-axis, followed by a rotation 3 9 2 Z- axis is in the direction of the for the second gamma ray are defined in the For the experimental arrangement of two coplanar de- tectors on opposite sides of the beam direction, the angular functions reduce to; O ( (K 3 - M) I <2 - 5 M> (K + M) ! 3 M>O \' .1 where ·the angles 9 L 2 and 8 3 ·are measured with respect to the beam axis. _ ·If the correlation function is normalized so the coefficient of the first term A 000 , is unity, then the pairs of coincidence gamma rays with the first gamma ray going into solid angle d0 2 at 8 2 ,¢.2. and with the second gamma ray going into solid angle dS1 2 . at 9 ¢ are given 3 3 -89in terms of the source strength N by: Even restricting the discussion to dipole and quadrupole transitions • as many as nineteen coefficients and angular functions may appear in a correlation function. For this reason the correlation functions have been computed with the aid of a high speed computer. Values ob- 't ained in this way have been compared with hand calculated values, and compared with correlation functions computed from the tables of Ferguson and Rutledge (71) wherever possible. A. 2. Smoothing Factors and the Collimator Geometry The discussion of angular distributions and correlation functions given above would be sufficient for gamma-ray detectors of no physical extent. For a detector geometry employing large cylindrically shaped Nal detectors whose axes of symmetry pass through the target spot, . . ' the experimental angular distribJition or triple angular correlation functions may be obtained from the functions for point detectors using a technique described by Rose (39). The essence of the technique is the expression of the angular parts of the correlation by a new set of angular functions based on a coordinate system coinciding with the axis of symmetry of t.he Nal d e tector. While it might appear off-hand as if little could be gained by this change , integrals over the volume of the gammaray d e t ector in this new coordinate system are performed more easily and the final correlation functions obt~ined are the same as the point counter functions with only minor changes. -90By way of illustration, consider the form of the angular distributiOn function that giVeS the number Of gamma rays in d.Q at 8 I with respect to the beam axis from a source of strength N: N{e ') = with ao =1 Expressing this distribution in terms of a coordinate system based on the s ymmetry axis of the crystal gives: where the M . Y l. {8, ¢) are spherical harmonics. The angles . e , ¢ and 1 1 ez. cPz are the coordinate_s of the beam direction and the ·gamma ray direction respectively in the new coordinate system and they form a spherical triangle with: The number of gamma rays that will be detected in the Nai crystal is given by the integral: S N(8 ') x (probability of detection) dO Crystal where the probability of detection depends only on the polar angle the new coordinate systerr1. Performing this integral gives: N counts at angle e '= 4 1T zrr ~ L with ao =1 e 2 in -91The quantities J 1 are defined by the integral: Ji. = J P..e(cos Crystal where p.. = linear attenuation coeffic'ient for the gamma ray in Nai 1. (a 2.) = path len g t h a t angle The term e in the Nai crys t al. 1 2 J 1s the efficiency integral and: 0 counts at angle eI = N X (effi ciency) X L a i. 1. where e' and el are the same angle. Quite similar arguments g i ve the following form for the triple angular correlation formulas: (co i ncidence counts ) at angle s ( e 2. • e 3 ) = N x { efficiency of) x ( efficie ncy of ) counter #1 J K {# 1) 2. with aooo . counter #2. JK ( # 2.) X 3 =l where the first g amma ray at angle e2. is detect e d in counter # 1 having inte gral factors J K {# 2.), and where the .second gam~a ray at angle . 2. . . is dete cted in counter # 2. having integral factors J K ( # 3). . 3 . The ratios J /J appe aring in the correlation formulas for 1 0 detectors with a finite siz e ar e known as Ros e 's smoothing factors. e 3 -92Since they are always smaller than one the angular distribution patterns measured with large counters are attenuated or nsmoothed outn when compared to measurements made wi,t h smaller counters. The attenuation problem can be serious, and for exampL! the ·4n x 4 17 Nal cryBtal used in this experiment is practiCally incapable of detecting P in angular distributions from gamma -ray sources 1 11 face of the crystal. 4 {co~ 8} terms or clo· ser to the The angular resolution of such a crystal may be enhanced by placing it some distance from the target, or by installing a collimator. The second method was chosen for this experiment, and a typical target-collimator-NaT{ Ti} 28. detector geometry is shown in figure For this geometry, Rose's smoothing factors are given by: Crystal where I-Ll = linear attenuation coefficient for the gamma ray in lead 11 {8) = path length in the lead collimator at angle 1-1 2 e =linear attenuation coefficient for .the gamma ray in Nal 1. {8) ~ path length in the 2 wher~ the angle Nal crystal at angle 8 8 · is measured with respect to the axis of symmetry of the Nal crystal. The collimator geometry was c;hosen instead of an open crystal some distance from the target since it is known that such geometries -93increase the photo-fractions of the gamma ray spectra {15}. seems to have been fortunate. Recent measurements and calculations by Twin and Willmott (72) indicate that the ratios 5 11 x 4 1; peak alone in a bare This choice Ji. jJ 0 for the full energy Nai are closer to unity than indicated by the calculated smoothing factors for the complete gamma-ray spectrum. For gamma-rays in the 4 to 8-Mev range, they quote ,- 5o/o for P 2 {cos 8} and - 20o/o for P 4 (cos 8) increase over the calculated values at 8 em between source and detector. The cause of this phe- nomena is an increase in the loss of secondary gamma rays and electrons through the sides of the crystal for primary events occurring near one of the surfaces of the Nai crystal. Hence the probability for producing full energy events in the crystal decreases more rapidly with the angle 8 than the probability for detecting the gamma ray. Several factors make such effects less important to. the measurements in this experiment. Gamma rays were k e pt away from the wings of the Nai by the collimator, and larger spectrum fractions {approximately 50o/o of the total) were ·used for angular distribution measurements. In any event the conclusions drawn on information obtained from angular distribution I measurements in this experiment were based primar-ily on P 2 {cos 8} terD;lS where the error incurred would be small even for an uncollimated crystal. -94Appendix B In this appendix, a comparison of the decay with the F 20 ground state beta Ml gamma-ray decay of the 10. 27-Mev level in Ne 20 will be made with the unified model of Bohr arid Mottelson (73, 74) using Nilsson (75) wave functions for the intrinsic states of this model. There are difficulties with this comparison due to the 'fact that there are too many parameters for the amount of experimental data that is presently available. However it is possible to assign reasonable values to some of these parameters, and then present the results as a graph plotted against the remaining parameters. Bl. Experimental Data The ' experimental data for the decay of the 10. 27 -Mev level in Ne 20 , and the F 20 beta decay is summarized in the following energy level diagram: 2t- T =I 10.27 ' 8.64 Mev 2+, T =0 _;.1.:..;; ·6;....::3- - - - " - - _ . c ; _ - o+ T=O 0 ' Ne20 The theoretical radiative width for a gamma-ray tra:nsition - of multipole order A. and energy E r _ . is given by: 87T(A. + 1) -A.[(2A.+l)ll] 2 (! ,) 2A. +1 B(A.) -95B(A.) is defined in terms of the matrix element between initial and final states for the multipole operator: B(A.) = L I i >'] 2 [<fjMA.p.(X) p.Mf where p. and Mf are the magnetic quantum numbers of A. and the final For magnetic dipoles, the operator Mlp. (X) state spin. is: = · 3 ) 1 / 2 · en ) ~ M l!-l ( 41T ( 2Mc L i=l where .eil-l and sil-l are the orbital angular momentum and spin opera- tors £or t h e 1· th · l e respechve . l y. partlc Th e gyromagnetic f actors, g, are : protons: :::: 5. 587 neutrons: :: - 3. 826 For electric quadrupole· radiation, the opera tor is: z Q2jJ- :::: e L (ri)2Y~ (ei) i=l where the sum in this case is only ove r proton states. oper~tors The multipole given above are those of Blatt a nd Weisskopf (70). For allowed Gamow-T e ller beta decay, the by (74): ft = 2740 0. 61 X 4 X BGT = 1122 BGT ft ' value is given -96- where BGT 1s defined by: 'i+' changes a neutron state to a proton state. The operator , For comparison with the theoretical estimates of the transition rates, it is convenient to remove the dimensioned fact~rs and constant numerical values from the matrix elements. The radiative widths for an 8 . 6 4-Mev gamma ray in terms of this dimensionless reduced transiB 1 are :_ tion probability r(Ml) = l. 778 B I (Ml) (ev) r(E2) = 0. 0389 B'(E2) (ev) The operators for B' are : A J M liJ- = I i i i (gi i liJ- + gsSliJ-) i=l z I Q 2IJ- = I (ri)2 Yi (~) i =l A ( GT)liJ- = l 1 1 1IJ- 7' + S . i=l Hence the experimental values indicated in the energy. level diagram give the following values for the B' : 1 2 ± (B '(Ml) ) / = l. 773 ± 0. 095 1 2 ± (B'(E2) ) / = ( 8 . 84 ~ ~: ;~ ) x 10- 2 or zero -97- 1 2 ± (B' (GT) ) / The large range on the = 0.107 E2 ' value is due to the fact that this value was derived from the angular distribution pattern of the 8. 64-Mev gamma ray. The same angular distribution pattern also requires the phase of 1 2 (B 1 (Ml) ) / B. 2. and 1 2 (B 1 (E2) ) / be the same Wave Functions The unified model finds application in the description of nuclei which have acquired non:-spherical shapes. {X', Y 1 , Z 1 ) fixed in the nucleus, the usual assumptions about the nuclear shape are axial symmetry about the through the In a coordinate system Z' = 0 plane. Z 1 axis, and reflection symmetry ·One of the prominent features of the model is the introduction of an additional quantum number jection of the total angular momentum functions are given by specifying space fixed axis, Z 11 ), structure of the nucleus. I, I M on the Z 1 axis. K, . and the wave function Wave XK on the of the intrinsic These wave functions have the form: jrMK > = t 2I+l )1/2 (x (x' )Dr K =0 that is the pro- (the projection of I K=I=O \ lb1T2 · K .K MK < 9.) .~ - 98 The 8. 1 I _,.. DMK(8i) are t he wave functions of the symmetric top where the are the Euler angles that specify the orientation of the nucleus with respec t to the space fixed axis, . (Xu, Y 11 , the wave functions for K =J:. 0 Z 11 ) . The second term in is a symmetrizing term included to give this wave function a d efinite parity, in this case, the parity of XK· ·The operator Ry 1 (1T) Holding K XK by 1T about the rotates and X K Y' axis. fixed , one finds these wave functions apply to a se ries o f levels, or a band, that has the spin sequence: K=f.O I = K, K + 1, K + 2, etc. K = 0 I = 0 +, 2 +, 4 +, etc. or I = 1-, 3 , 5-, etc. The energies of these levels are: E(I) = E. t ln r. where olxr il 2 + 2" ( I(I+l) - K L.,txr spacing that indicates beassumedthatthe 3 +, etc. ) is the moment of inertia of the nucleus around the The first three levels of Ne level in Ne 2 20 2 II i'l. /2 ol'xr 20 0 +, 2 +. an d are = 0. 27 Mev. 2+ groundstateof are the begi~ning. of a F 20 K = 2 X' axis. 4 + w1t . h a In this calculation it will , and 2+,. T=l, 10.27-.M ev band with members , The 1~e is a complication in the calculation. The K 2+, quantum numbers for the i n itial and final states connect,ed.by a tensor operator of rank A. must satisfy: -99- For the magnetic dipole and allowed Gamow-Teller beta decay, X. = 1, and hence the simple wave functions suggested above would hav.e nei.t her of these vector operators connecting them . The standard method of circumventing this to mix bands with different K initial and final states. K selection rule is into the wave functions describing the Fortunately the model readily provides the mechanism for the mixing in a Coriolis type of interaction between the particle motion and the slow rotation of the nucleus. Usually this inter- action is referred to as R. P. C. · (rotation-particle coupling), and it serves to mix bands that differ by one in the K quantum nurtlber. The program for this calculatfon is first to find suitable bands for mixing in the ground state bands of Ne 20 . and F 20 , and then to calculate the matrix elements for the various possible transitions • The intrinsic wave functions, X K' for . 20 Ne and F 20 will be. constructed from Nilsson single particle wave functions, Xn• for the 16 . ·core. These single particle wave four particles _outside the 0 functions are eigenfunctions for a harmonic oscillator potential with the spin orbit and I. 2 terms of the shell model, and an additional quad- rupole term .in the p .o tential. The parameters ·for .the p.6tentia1 .have been chosen so the predicted energy levels correspond to those of the shell model when the quadrupole term is zero. The size of the quadrupole term is given by the deformation parameter T}, measure of the variation of the nuclear radius. Nilsson (75): which is primarily a In the notation o£ -100- where: o= ~ LR = 0.281 LR :::: R 2 " - . Rxn R = average radius = l. 45 A l/ C x 10 -l3 em: = size of the spin-orbit potential = - 2 Mev 0 i'l. w 3 0 =15. 4 .Mev The s iz e of the spin orbit potentia l has b een deduced from the d ; - d / splitting in 0 3 2 5 2 17 (61) . 0 For the t erm -'l'l:w Nilsson suggests: 0 41 -n.w0 0 = Al/3 = 15. 1 Mev which agrees well with the value of 0 . < r 2 > in the s -d shell which g i ves: 115 -nwo= A2/3= 15. 7 Mev The term o has been d erive d from the r a diative width of the tion from the 2 + first excited state to the E2 .transi- 0 + ground state of N e 20 (3 2) with the a id of the fo rmula given by Mottel son and Nilsson (76) for the static quadrupole moment . . In this calculation, it will be assumed the value of 1'J also applie s to the g round stat e band of F mirror l eve l s of this band .i n Ne 20 20 and to the o The actual single particl e wave function s , Xn• are g iven by Nilsson in t e rms of expansion coefficie nts of the f. - S representation: -101- Xn = l a£ A IN P. As~> n =A + ~ where P.A The quantum number N is the total number of oscillator quanta, the orbital angul a r momentum with projection A, quantum number with proj e ction ~o and S + 1/2 is is the spin Nilsson abbreviates the quantum numb e rs by omitting S, which is always 1/2, and writing a 1 for a - 1/2 projectiono + to sig nify projection of S and - The particular terms for Nilsson orbits #6 and #7 which will be used in the following calculat ions will be written as : Orbit #6 Xn = ( ~ +) = a 1 !2 2 0 + j> + b 1 !2 0 0 + > + c 1 [ 2 2 1 - > Orbit # 7 For iJ > 0, the numerical values for the expansion coefficients are: 'll al bl cl a2 b2 6 0 . 805 0 .533 0 . 262 0 . 978 0.207 4 0 . 786 o. 520 0.336 0.967 0 . 257 2 0 . 787 0 . 396 0 . 472 0.943 o. 331 The unit of length for these wave functions i s given in terms of 1/2 -13 . ( i'i/Mw ) = L 64 x 10 em. 0 Wave functions for particles having a nega tive projection are ob tained by applying the rotation operator Ry 1( 1T) . to the positive projection -10 2- wave function. The values are: The phases are determined by the equation (75}: Ry;(rr}jN .R. AS~>= (-1) 1 +A+S +~ jN .R. Nilsson orbit #6 lies below tions 0 16 #7 -AS-~> in energy for prolate deforma- ('11 > 0}, and putting the two neutrons and two protons outside the N e 20 · t h.1s orb.1t g1ves . th e core 1n groun d state . Since the exclu - sion principle requires like particles to have opposite projections, the sum of these projections, Henc e one obtains the K = 0 K, is zero for the Ne 20 ground state. band for the first three levels of N e These four particles fill this orbit; n. 20 • additional particles would go into Nilsson orbit # 7. For the three neutrons and one proton of the one of the neutrons h~s to be put in orbit #7. projections, . 0, give the following K K = 2 F 20 ground state, The sum of the possible values: = neutrons ( + 23 +. 2l -. 2l ). +proton ( + 2l } K :: l = neutrons ( + ~ + i -i } + proton ( - i} As ·far as the Nilsson model is concerned, these two bands would be d e gene rate in energy; however in practice the former, or the maximum K -103- value , is the ground state (77). The indicated K = 1 band is the band that will b e mixed into the two ground bands to provide the observed Ml and allowed Gamow-Teller decays. Slater determinants f or the s e bands will be constructed from the four s i ngle particle wave functions. P( { +) The f ollowing notation w ill be used: = particle 1, a proton, in Nilsson orbit ft6 with a positive 1 projection, N( ;?_ -) 2 3 =pa rticle 3, a neutron, in Nilsson orbit # 7 with a negative projection, l. Ne 20 K = 0, T = 0, T g round state band, z =0 #7 Configuration: 1 t 1·I XK = 1 (4 !}l/2 #b N( ~ +)l N( ~ +) 2 l N(- +) 2 3 l N ( 2 +) 4 . l N(- -) 2 l 1 N( 7 -) 2 1 N(-z-)3 l . N( 2 -) 4 P( { +)1 1 P ( 2 +)2 l P( Z +)3 l P( 2 +)4 l P( - -) 2 l l P( 7 .... )2 1 P(- -) 2 3 l P( 2 -) 4 The small diag ram is a helpful way to picture the stat~ represented by the determinant . T and T z are the isotopic spin quantum numbers . ' K = l, T. = l, T z = - l 3. The intrinsic wave function for the band with K = 2, T in Ne 20 can be generated from the function for gives : F 20 K = l and T z = 0 = 2, T = l, T z = - l wave by changing a neutron state to a proton state. This - 105 - 4. Ne 20 , K =2 , T = 1, T z =0 t # 7 1I # Conf i gu ration: f N( +) 3 . 1 N( 2 +)4 N(..:.. -) 1 2 1 N(2 -) 2 1 N(- - ) 2 3 1 N( - -) 2 4 i +\ 3 P( 2 +)2 P{ 1 P( 2 +)1 1 P ( 2 +) 2 P( ~ +)3 1 P( 7 +)4 N{ i_ +) 2 1 3 N( 2 +)2 N( 2 +)3 N(2 +)4 N( ~ +)1 1 N( 2 +)2 N( _!_ +) 2 3 N( 2 +)4 l P( 2 +\ 1 P( 2 +)2 l P( 2 +)3 l P( 2 +)4 1 P{ 2 -\ l P( 2 l P( -2 -) . 3 1 P( 2 1 XK = (2 x4 n1/ 2 P( 1 1 2 {2 X 4 :! ) 7 A similar procedure gives the Ne 20 • i N( _!_ +) 2 2 1 N ( 2 +)1 1 6 K = 1, T = 1, i T +)3 -) 2 z P( i +)4 3 3 l -) 4 = 0 wave func tion for -10 6 - 5. Ne 20 , K = l~ T = l, T z = 0 ,, 1f 7 Configuration: I t l t 1 N ( 2 +\ XK = 1 N(- - ) l (2 X 4 !) 172 2 l # 6 +)2 N( .!_ +) 4-} 2 N(- -) 2 P( N( { N( 2 3 1 2 N({ +)4 1 3 i +)3 N(- - ) 2 4 i +)4 P( ~ +)l - \2 l P{- - ) 2 l l P(- -) 2 2 P(- -) 2 3 l P(- -) 2 4 N{ l . 2 +) l 3 N( 2 +)2 N(% +)3 N( ~ +)4 l N{ - - ) l N( 2 -) 2 . l N( - -) l N(- - ) P( l_ +) . 2 l l P( 2 +)2 1 P( 2 +)3 l P{ 2 +}4 l P{- - ) 2 l l P( 2 l P( 2 -)3 l P( 2 -) 4 l (2 X 4 !) 172 p ' 3 +) 2 l 1 -) 2 P( 2 3 2 .The orthogonal wave function to this last wave function gives the final wave function. 4 6. Ne 20 • K = l, T = 0, T z =0 t 11 rr 7 Configuration: lrI Jl rr 6 ,.I, ' XK = l (2 X 2 4 ! ) 17 l N ( - +) 2 l N{ l N(- - ) 2 l N.( .!._ +) 2 4 N ( .:.. - ) 2 2 1 l N { - -) 2 3 N( .!._ -) 2 4 ( 3 2 +}l ' P ( ~ +)2 3 P( 2 +}3 P{ ~ +}4 l P(- -) 2 l l P{ 2 - )2 1 P( i -)3 l P(- -} 2 4 3 N{ 2 +)l 3 N( 2 +)2 3 N( 2 +)3 3 N( 2 +)4 l N( 2 N( .!._ - ) 2 3 l N( 2 -)4 +) 2 1 l 2 (2 X 4 !}1 7 N(.:.. -) 2 l P( P( B. 3. i +)3 p + 4 i 4- N( -) 2 4 +)1 l P( 2 + ) 2 P( )1 1 P( 2 1 P( 2 -)3 -) 2 +)3 i +}4 1 P( 2 -) 4 P( E valuation of .Matr ix Elements To evaluate the matrix elements for Ml, E2., and the a llowed Gamow- Teller beta t ransitions, it is necessary to rotate the operators from the l abo ratory syste m, to the coordinate system fixed in the rotating nu c l e us. Repr es enting the operators by a general tensor operator , MA.q 1 ( X'), the rotation i s accomplishe d by: - 108- . M A.q (Xfl) The Euler a ngles, - 8. , are the s a me as t h ose of the D functions appear- 1 ing in t he wave functions. In this fashion, one o btains for the r educed tra n s ition probability B 1 : =I I' < IfMfK'I I ~ L - A. ->- M~1\.q 1 (X 1 ) D qq 1 (8.) I I.M.K. >[ 1 1 1 1 2 q~ M q f By doing the integrals over the collective coordinates ~ and performing the sum over Mf and q, this expression will r educe to: *' 0 and Kf =f. 0 Tra nsitions: Ki __...... Kf' where Ki Transitions: Ki - Kf, where Ki =f. 0 B' =[ and Kf = 0 L .n(riKi, A.q'[r£Kf) < xn£1MA.q'(5(•) lxni > Jz q' The Cleb sc h-Gordop. co effic ient, integral over the three rule : D (IiKi' A.q' [IfK£)' which arises from the functio ns, is the source of the K selection -109 - A simple p icture is a convenient method of r ep res enting the t r ans i tions to be calculated wave function for the 2 + level in eit her Ne20 or · - l _i20 wave function for the 2 + T = 0, first excited state of Ne 20 K=l Numerical values for the transition 1natrix elements will be lis t ed in the order of the numbering system in the d iagram ab ove. The Ml and beta decay transitions will b e listed first, and then followed by the E2 transitionso In the Ml transitions, the n e utron and proton contributions combine to form the isotopic spin vector part of the operator: M~p. {Vector) = A I i=l This operator will be used instead of listing the neutro n and proton con tributions separately. Transition 1: Ml : Ki = l - Kf = 0 B'(Ml) = [ 2(21, l -1j 2 0)< ({ +} j M~ _ (V ){( ~ +) > ] . , 1 Gamow - Teller allowed beta decay {GT) : B r ( G T) = [ { 2 ( 2 l ' l -lj 2 . 0 ) <: ( where : 4 I sl, -1' ( i > ] +) +) 2 2 - llO Cf g - + "'P 2 n. s } and 1 1, - 1 = _!__ .rz (1 X - i1 y ) = _!__ 1 .rz s 1 '. -l = _!__ .rz S = - 1 .rz (S - iSy ) X Values of the matrix elements over the intrinsic structure a r e : Numberical values as a functi on of the d efo rmation parameter T] 1 s Ml ' 2. 224 0.181 1.082 o. 1£n o. 230 2.547 o. 230 2. 239 0.31 4 3.163 0.314 2. 036 0.2 56 l. 572 4 2. 033 0.325 2 2. 130 0.445 Tra nsition 2 : Ki = l - Kf = l Ml : [(21, 10j2l){<( i+)l(M~ 0 (V)j(i+)> - < ( ..!_ +) j M r 2 · GT: B 1 (GT)= [(2 1,10!21) are: 51, -1 (Bf(Ml) )l/2 (B r( GT) )l /2 -1 (V) 6 B ' (Ml)= T] 1 0 ( V) ( ..!_ 2 +) > } ] 2. ~ {< ( i+)j S~ 0 I < i+> ~ 1 I 1 . 2 - < < 2 +> l 5 1 o I< 2 +> > } J - 111 - w he re: and where 51 o = 5 z Values for the m a trix elements over th e intrinsic s t ructure are : 2 < ( 2. +) !1 r ( 2. +) > = 1 + b z. 2 2 2 < ( {- +) j i z j ( ~ +) > = c{ < < ~ +) I sz I < ~ +) > = {- - b~ < c ~ +' I s zI c ~ > ~ c; +) The numerical values for the ( = - 3 3 l 1 ( 2 +)-+- ( 2 +) • 2 +) __.. ( 2 +), and the will be listed sepa r ately, and then combined. . ( i2 +) - (i 2 +) +) ( __I_ 2 - ( __I_ 2 +) transition 2 1l 1 z sz P. z sz 1 z sz 6 1.043 0.457 0.069 0.431 0.974 0.026 4 l. 066 0.434 0.387 o.. 953 0 ,. 047 2 1 0 ll 0 o. 390 o. 113 o. 223 o. 277 0.887 o. 113 The ope rators and the reduced transiti on probabilities have the values: - 112 - T] M l O(V) 5 1 o (B I (Ml) )1/2 1 2 (B 1 (GT ) ) / 6 o. 608 0.0 2 6 o. 248 0 .0 07 4 0.799 0.0 47 0.326 0.014 2 0.977 0~ 113 0.399 0.033 I I K. = 2 _,_ K_ = 0 Transition 3: l I This transition i s K forbidden~ a nd there is no contribution to the vector operators. K. = 2 - T ran sition 4 : K, = 1 l I Ml : B 1(Ml) = [ ( 2 2~ 1 - 1j21} < GT : B'(GT) =[ l <{ -)j M~, _1 (V)j{ 4+) >] 2 (2 2,1 -l j2 1} < <_{ -) js~, _1 j( { +} >] 2 where I ( M 1, -1 V ) 1 ( .!. i_ = ..fz 2 - + gp - gh S 2 ) and where 1 5 1, -1 1, -1 = _.!_i. .rz = _1_ s .rz Values for the matrix elements over the intrinsic structure a,re: < <.!. -> 11. - I<.!.+>>= 2 2 - z<6> 112 a 1c 1 2 < <.!. 2 ->Is - I< . .!. 2 +> > = - [ 1 - c 1 J - 113- Numerical values as a func tion of s i. '1 l] are : M{, _ (V) 1 8 1 _, 1 2 (B 1 (Ml) ) / 1 2 (B'(GT ) ) / ' - 0 / - l. 03 1 - 0. 9 31 -3.460 -0.659 -2. 00 2 -0 . 268 4 - 1. 2 90 - 0.887 -3.335 -0. 6 2 6 -1. 92 7 -0. 256 2 - 1 . 816 - 0. 778 - 3. 23 2 - 0 .546 - 1. 866 -0 . 224 F or the E2 t r ans itions, it is somewhat simpler to do t he indi- cated s um ove r the proton coo r dinates and not introduce the isotopic spin operator. 1 2 The valu e s of (B '(E 2) ) / listed b e low h a ve been multiplied by the scal e fac tor for T ransition 1: E 2: Ki = l - 2 r • 2. 96 . Kf = 0 I 2 Y ~ 1 ( e ' ) / ( 1+) > ] 2 B ' ( E 2) = [ (2 l, 2 -lj 2 o) < ( { +) r Values fo r the matrix element over the intrinsic structure are : Numerical values a s a function of ' 11 are: 2 -1 y2 (B ' (E2) )l/Z YJ r 6 - 0.755 -0.543 4 -0. 755 -0.543 2 -0. 687 -0.493 -114- Transition 2: E2: Ki = 0 - Kf = 1 B'(E2) = [ { {2 1, 2 o j2 1) { < ( i +) I r 2 Y~ I ( i +) > Values for the matrix elements over the intrinsic structure are: < ( i +}:j ~2Y~(e i ')( = [ 1Tr] 1/2 [ { - i b~ ] +) > The numerical values for the ( i +) - { ~ +) and { ~ +) - ( ~ +) will be listed separately, and then combined , 3 3 {- +) - {- +) 2 2 2 yO r 2 1 1 ( - +) - ( - +) 2 2 2 yO r 2 6 0.274 4 2 T ransition 3: E2: Transition 2 2 yO 2 {Br(E2) )1/2 1.194 -0. 920 0.331 0.253 I. 154 -0.902 0.324 o. 211 1. 0 i 6 -0. 805 0.289 K.l ' = 2 - r Kf = 0 B 1 (E2) = [- {2 2, 2 - 2j 2 0)< <{ -)jr 2 y~ (e')j(i +) >] 2 2 The value for the matrix e l ement ove r the intrinsic structure is: <(j -)jr2Y~2(8')j(i+)> = [ :Tr ]1/2 [ albl- ..fz blb2 ~ [ ~ ]1/2 cla2 ] -115- Numerical values as a function of 11 are: -2 y2 r 6 o. 205 o. 259 o. 391 4 2 Trans ition 4: 2 11 Ki = 2 - {B 1 {E2) }1 / 2 -0. 295 -0.372 -0.562 Kf = 1 The value for the matrix element over the intrinsic structure is zero. The vanishing of this matrix element is acCidental. B. 4. Band Mixing Matrix elements for the R. P. C. term that serves to mix bands differing by one in the K quantum number are discussed by Kerman {78). The relevant matrix elements are: HK{I) = ;n;x { A 1 2 ((I + K + l}(I- K) > / (-1) < x Kl L lx Ji K+l > } i=l K = 0 ·Where Ji = J. i + si • Wave functions are obtained by diagonalizing -116the 2 x 2 Hamiltonian matrix: whe re: 2 EK(I) = E. t + ( I{I+l) - K ) 1;-z. 1n r. J~ The m a trix is easily diagonalized, and the following table gives the unnormalized eigenfunction with their energy eigenvalues. Wave Function Eigenvalue W_ = E_{I M K >+[I M K+l > E w = [I M K > + E I I M K+l > E Hi g her energy solution: Lower energy solution Highe r energy solution: Lower energy solution: where the algebraic symbols are: E ± €± = E av. ± 12 [{.D. E) 2 + 4(HK(I) ) 2 ] 1 . /2 = =F~ ± K 1 -117- E av = R. P. C. 2 band with T = 1 in Ne K = 1 and For the 20 and F 20 , the term is given by; H]_{I) = -rj 2 1 2 {((I+2){I-l) ) / {-1) < X <i -)!J_[<i; +) >} The matrix element over the intrinsic structure as a function of TJ is: J For T} 6 -1. 962 4 -2.177 2 -2.594 = 6, the values of HK(I) as a function of I are: For the state band, K =0 HK(I) I HK(I) 2 3.294 4 6. 204 6 8.325 and 1 bands with T = 0 - 112 (units of~ of the Ne 20 ground is given by; The matrix element over the intrinsic structure as a function of T} is: -ll8- B. 5. , J 6 2. 292 4 2. 358 2 2. 575 Num·erical Re suits The procedure at this point should be · an application of the for- mulas in B. 4 to match the levels in F 20 and Ne 20 • Such a procedure has been demonstrated by Paul (79) for the l/2 and 3/2 bands in F 19 • Once the energy levels are matched, the indicated wave functions should be used in the calculation ofthe rates. of F 20 Ml, beta decay, and E2 transition Unfortunately the lack of information about the spin assignments levels or the possible. T = 1 levels in Ne 20 . makes this procedure im- Hence to obtain a qualitative picture from the calculation, the transition rates were calculated for a range of mixtures in the and T = 0 bands. By using sin e and cos e T = 1 <l:S the amplitudes of the two mixed bands, one obtains a convenient method of varying the mixture. The form of the wave functions used for the calculations were: initial state (T = 1 bands) 'll(I,M) =-sin eiji M K = 1 >+cos eiji M K = 2 > final state (T = 0 bands) Several assumptions functions. have prejudiced the form of these wave The final state wave function corresponds to the one in B. 4 -119that places the K = 0 band lower than the K = l band. describes this as a necessary condition since the Mottelson (80) K == l, T = 0 band being mixed in the ground state band is a spurious band, or a band that has been introduced by the additional collective coordinates {see ref. 77, for example), and indeed, he points out that such a band is introduced by the cranking model {81), to account for the moment c;>f inertia. c/X for the four particles this model, the first term in the expansion for outside the 0 16 . From . core 1s: In so far as .6.E is large, the amplitude for € 1i2 :::::: ~ 2 . [ I(I+l)] l/ 2 in B.4 is given by; € < (i l +) J X 4 > I( +) .6.E Combining these last two equations, and substituting the value for the matrix element for TJ = 4 state of Ne 20 given in B. 4 . is '""' 79 o/o K = 0 gives 9. ,_ 27° l or the ground band in intensity. The initial state wave function is associated with a definite level . 20 order 1n Ne or F 20 order for · TJ = 6 and 11. function of 9. l and • 2 The results of a calculation of this level jZc}X = Oo 27 Mev is given in figure 29d .6.E of B. 4. as a The energy scale has been adjusted in height so the lower of the two I= 2 levels corresponds to the 10.27Mev level in Ne I = l, T = l 20 • For those solution with EK=lU)< EK= (I), an 2 level {shown as a dotted line in figure 29d) is seen to lie b e low the 10. 27 -Mev level, and would imply the first T = l leve l in Ne 20 -12.0- or the I =l F 2.0 ground state should be spin one. level lies above the lower I = 2. level for most 8 0, l and the wave function used for numerical calculations corresponds to this solution. Approximate limits can be put on 8.. l The first excited state of F is at 0. 65 Mev (4), indicating 8i < 30°. 20 For small 8i, the separation of the two bands becomes very large, and hence 8i wip probably be larger than 10°. The results of the calculation for figure 2.9a, b, c T) = 6, 4, 2. are given in as a function of 8i and 8£" The lines marked Ml are, top to bottom, the upper limit, best value, and lower limit for the experimental Ml width. marked. Similar lines for the The line marked E2 transition are 13 is . the experimental value for the F 20 ground state beta decay. For all three transitions, the plotted solutions are those obtained from 1 2 - (B 1 ) / • for the beta decay and Ml decay. There are no solutions for The + (B 1 (E2) ) 1 / 2 limit of the experimental values will appear in the T) =4 T) (fig. 29b) plots in the upper left corner above + (B~')1 / 2 equal to the lower =6 (fig. 29a) 1 2 (B 1 (E2) ) / and = 0. In such plots, one hopes to find one point in common to all three experimental values. Here it is not the case. The Ml and E2 values for the 8. 64-Mev gamma ray do show some of the desired properties in the T) T) = 4 diagram, which corresponds most closely to the value of = 4. 26 for the Ne value for the 20 ground state band. Ml decay gives fall in the 11 reasonable 11 range. 8i = 24°. Picking 8f = 27°, the best These values of 8i and 8f A value for the radiative width of the E2 transition a little lower than the best experimental value (E2-on in -121- figure 29b) will overlap this point. for the Ml and Furthermore, the matrix el e ment s E2 .transitions have the same phase as is required by the expe rime ntal data shown in figure 18. The situation for the beta decay is not as satisfactory. three plots, a reasonable value for a£ makes a.1 too low or vice ver sa. Unexplained is the gap b e twe en the b e ta line and the cates the beta decay is either too weak or the In all Ml line s that indi- Ml decay too strong. For example, it is possible to make the two solutions overlap if the radiative width for the 8. 64-Mev transition is reduced from 5. 6 ev to 1. 9 e v. Hence for the assumptions that have been made. it seems the unified model is only able to give a qualitative p i cture of the expe rim e n~al The slow beta decay of the the selection rule; the fast Ml decay can be arranged by a reasona ble K F 20 data. ground state can be attributed t o mixture of bands in the initial and final states. Of course the assumptions of this calculation are open to question. The most questionable assumption is that a mixture is a good description of the F 20 K = 1 and K = 2 band ground state . Figure 29d indicates that this assumption can account for only 5 of the 12 levels in the first 3 Mev excitation energy in F 20 • If the remaining levels are members of bands that have intrinsic wave functions similar to the K =1 = 2 bands used in the calculation. the structure of the ground state 20 20 of F , or the first T = 1 level in Ne would be considerably more and K complex than assumed. 11.27t0,03 11. s6 * o. o4 (o +,1-. i +, 3-. 4 +l 8170*30 854o * 4o 9570 ,t 40 9400*40 (1 -orZ+) 4+;1 12.39 * o. 04 (3- or 4 +) 12.25 *0.04 (0+,1 -,2+,3- ,4+) (9250 * 40) (1 2. 13 * o. 04) 11 . 08 ,t0,02 7940,t20 * 16 46 ,t 1 6 40 :S4 S3 S2 155 ,t 30 10, 270 ,t o. 009 2+;1 (ref. 30) (4.);0 (ref. 28) 6930 ,t 10 29 ,t 15 2+10 10.02 ,to. 03 S3 4+;0 6610 ,t 30 rC. M. (ke v) Jw;T 9.48 ,to. 03 EX (Mevi 5940 ,t 30 (kev) 9. 0 29 ,t o. 008 0 Initial State 5374 ,t 9 E Energy-Lab Resonance E1 M1 2-;o 4+;0 4. 97 :so. 2 0.5 * 0.3 2+;0 ·O 1. 63 * :s 1. 4 2+;o I. 63 3. 5 *2 :s 1 7 * 3 s 1 * Decays by alpha emission to the 6.13-Mev l evel in d w ro.ro., . -y-r- " 3 1 ke v 0 +;0 2+;0 o +,o 0 1. 63 0 6 6 :s 0. 08 with with X :so. 043 ~ 0,4 7. 3 0.72 6 10- 3 0.6 * o. 15 S 3 ~ * o. 5 o . 29 * o. 07 4.8 0.41 6. 9 (for E2) 3. 2 (E2) or 0.025 (Ml) :s 0,3 7.0 IM 12 (ref. 43) t: ~)xl0- 0.017 * o. 6 :s o. « o . 19 ( 2. 2 5. 6 s 0.07 Decaya by alpha emiuion to the 6.13-Mev l e vel in ~ ..ro.ro., -,.r- = 100 50 ev :s ·o. 3 2+;0 1. 63 0+;0 o. 9 * 0.4 E1 0+;0 :S 12 :s 0.7 46 * 5 :s 2. z 0.95%0,24 27.8 *3 . :s o. 6 8 *3 * o. 1 :s o. 06 o. 26 o. 9 * o. 4 * o. 5 o. 38 ,t 0. 05 ·:s 0.3 1.3 3. 4 * 0.4 Radiation 0 EZ 2+;0 (4-);0 1 . 63 EZ 7,02 4. zs E2 0 +;0 0 E2 Ml 1. 63 (E4) o +,o 2+;0 0 E2 o. 1 . 63 (E2) (EZ or Ml) 2+;0 1. 63 2+;o E2 z+;o 1. 63 0+;0 Multi pole Jw;T Ex(Mev) wr ° FROM d 6 (o.,y)Ne 20 Final State (4) 2 TABLE 1 STATES IN NE I I N 1\) -123- TABLE 2 ALPHA PARTICLE PARAMETERS Ex (Mev) JlT;T r a {kev) e 2 {per cent) 5.374 9. 029 4 +;0 :::3 ::: 1. 3 5.940 9.48 2+;0 29 ± 15 1.5 6. 610 10.02 (4+);0 155 ± 30 25.0 6. 930 10. 27 2+;1 :::2 ::: o. 08 7.940 11.08 4 +;1 :::3 :::0.21 9. 570 12.39 {3 -) ; 46 ± 16 1. 23 3 :1: 1 56.0 E r {Mev) r a' to 6.13-Mev level in o16 = -124TABLE 3 GAMMA RAY ANGULAR DISTRIBUTION FUNCTIONS 20 FOR o16 (a., y)Ne In the followin g table, the coe fficients a 2 , a , and a will be given for 4 6 angular distributions of the f o rm where 9 i s measured with respect to the beam axis. J1T Initial State Gamma-Ray Multip ola rity a2 a4 a6 0 0 TRANSITIONS TO 0 +GROUND STATE 1 El -1. 000 2+ E2 +0. 714 -1.714 3 E3 +1. 000 +0. 273 0 -2. 27 3 TRANSITIONS TO 2+ FIRST EXCITED STATE 0+ E2 1 E1 2+ 0 0 0 -0.100 0 0 M1 +O. 500 0 0 2+ E2 -0. 153 3 4+ E1 -0.400 E2 +0. 510 -0.490 0 0 0 -0. 367 0 -0.014 0 TRANSITIONS TO 4+ SECOND EXCITED STATE 2+ E2 +0. 204 3 4+ E1 -0. 167 0 0 M1 +0. 500 0 0 4+ E2 -0.301 5 6+ E1 -0.333 E2 +0. 455 -0.601 0 -0. 242 0 0 0 -125- REFERENCES 1. T. Lauritsen, Ann. Rev. Nuclear Sci. l, 67 {1952); and also, T. Lauritsen and F. Ajzenberg-Selove, "The Light Isobars, 11 Joint Report of Haverford College and California Institute of Technology, August, 1960. 2. A. E. Litherland, J. A. Kuehner, H. E. Gove, M. A. Clark, and · E. Almqvist, Phys. Rev. Letters]_, 98 {1961). 3. E. M. Burbidge , G. R. · Burbidge , W. A. Fowler, and F. Hoyle, Revs. Mod. Phys. 29, 547 {1957). 4. T . Lauritsen and F. Ajzenberg -Se love, "Nuclear Data Sheets, 11 sets 5 and 6, National Academy of Sciences {1962). 5. R. J. Van de Graaff, Nuc. Instr. and Meth. ~. 195 {1960). 6. g. 63 {1961). P. H. Rose, Nuc. Instr. and Meth. g. 49 {1961). 7. H. E. Gove, Nuc. Instr. and Meth. 8. P. H. Rose, A. B. Wittkower, R. B. Bas tide, and A. J. Gale, Rev. Sci. Instr. 568 {1961). 9. H. E. Gove, J. A. Kuehner, A. E. Litherland, E. Almqvist, D. A. Bromley, A. J. Ferguson, P. H. Rose, R. P. Bastide, N. Brooks, and R. J. Connor, Phys. Rev. Letters..!_, 251 {1958). g. 10. D. A. Bromley, A. J. Ferguson, H. E. Gove, J. H. Kuehner, A. E. Litherland, E. Almqvist, and R. Batchelor, Can. J. Phys. ~. 1514 (1959). 11. R. H. Spear, J. D. Larson, and J. D. Pearson, Nuc. Phys. (to be published). 12. A. H. F. Muggleton and F. A. Howe, Nuc. Instr. and Meth. g, 192 (1961}. 13. D. A. Vermilyea, Acta Metallurgica .!_, 282 {1953). 14. A. Charles by and J ~ J. Polling, Pro. Phys. Soc. (London) 227, 438 {1954-5). 15. R. W. Kavanagh, Ph. D. Thesis, California Institute of Technology {1953 ). 16. H. Lung, Ph. Panus si, and J. Janke, Nuc. Instr • . and Meth. · :!_, 121 {1960 ). -126- 17. M. E. Rose, Phys. Rev. 2...!_, 610 (1953}. 18. J. Stolzfus, J. Friichtenicht, and E. Nelson, Bull. Am. Phys. Soc • .!._, 329 (1956). 19. F. Ajzenberg-Selove and T. Lauritsen, Nt?-c• Phys • ..!_!., 1 (1959). 20. N. H. Lazar, R. C. Davis, and P. R. Bell, Nucleonics 14 (# 4), 52 (1956) 21. G. W. Grodstein, "X-Ray Attenuation Coefficients from 10 kev to 100 Mev," NBS Circular 583 {1957). 22. W. F. Hornyak and T. Coor, Phys. Rev. 92, 67 5 (1953 ). 23. A. T. Nelms, "Graphs of the Compton Energy-Angle Relationship and the Klein-Nishina Formula from 10 kev to 500 Mev, 11 NBS Circular 542 (1953}. 24. C. D. Zerby and H. S. Moran, Nuc. Instr. and Metho. 14, 115 (1961); and also, C. D. Zerby and H. S. Moran, Oak RidgeNationa1 Laboratory Report, ONRL 3169 (1961). 25. R. L. Heath, IRE Transactions on Nuclear Science NS-9, 294 (1962). 26. J. B. Marion, Revs. Mod. Phys. ~~ 139 (1961). 27. F. Everling, L. A. Konig, J. H. E. Mattauch, and A. H. Wapstra, 11 1960 Nuclear Data Tables, Part l, 11 Report of the Nuclear Data Project, U.S. Government Printing Office, Washington 25 D. C. (19 61). . 28. L. C. McDermott, K. W. Jones, H. Smotrich, and R. E. Benenso:p., Phys. Rev. 118, 175 (1960). 29. R. H. Davis, M. K. Mehta, and W. Hunt, "Annual Progress Report for the Year 1961, 11 Department of Physics, Florida State University Tandem Accelerator Program, page 11; and also, W. F. Hunt, M. K. Mehta, and R. H. Davis, Bull. Am. Phys. Soc. ]_, 7 1 (19 6 2). 30. J. M. Blatt and V. F. Weisskopf, 11 Theoretical Nuclear Physics, 11 Wiley and Sons, New York (1952); p. 627. 31. L. Radicati, Phys. Rev. 87, 521 (1952); and also, M. Gell-Mann and V. Telegdi, Phys. Rev. 91, . 169 (1953). 32. M. A. Clark, H. E. Gove, and A. E. Litherland, Can. J. Phys. 39, 1241 (1961). -127- s. D. Bloom, and D. H. Wilkinson, Phil. Mag. ~' 33. B. J. Toppel, 61. (1957). 34. T. W. Bonner, Pro. Roy. Soc. (London), Al74, 339 {1940). 35. J. M. Calvert, A. A. Jaffee, and E. E. Maslin, Proc. Phys. Soc. {London) 68A, 1017 {19 5,5). 36. T. A. Rabson, W. D. Barfield, D. L. Bernard, T. W. Boriner, and W. W. Givens, Nuc. Phys. 21, 43 (1960) • . - 37 • . J. W. Butler, Phys. Rev. 118, 222(1960). 38. L. C. McDermott, private communication to R. H. Spear. 39. M. E. Rose, Phys. Rev. 91, . 610 (1953). 40. W. A. Fowler, C. C. Lauritsen, and T. Lauritsen, Revs. Mod. Phys. 20, 236 (1948). 41. H. E. Gove, 11 Nuclear Reactions, 11 Vol. 1 ed. by P. M. Endt and M. Demure, North Holand Pub. Co., Amsterdam (1960). 42. W. Whaling, Handbuch der Physik 34, 193 (1958); and also, D. Demirlioglu and W. Whaling, tobe published. 43. D. H. Wilkinson, 11 Nuclear Spectroscopy, 11 V. I,, ed. by F. Ajzenberg-Selove, Academic Press, New York (1960). 44. D. H. Wilkinson, "Proceedings of the Rehovoth Conference, 11 ed. by H. J. Lipkin, North Holland Publishing Co. • Amsterdam (1958 ). . . . . · 45. D. H. Wilkinson, Phil. Mag • .!_, 127 (1956). 46. S. P. Lloyd, Phys. Rev. 81, 161 (1951). 47. H. E. Gove, A. E. Litherland. and M. A. Clark, Can. J. Phys. ~· 1243 (1961) •. 48. J. Orear, University of California Radiation Laboratory Report, UCRL-8417 (1958). 49. D. H. Wilkinson, Phil. Mag• .!_, 1031 (1956). SO. E. Freiberg and V. Soergel, Zeit.· f~r Phys. 162, 114 (1961). 51. F. Boehm. V. Soerge1. and B. Stech, Phys. Rev. Letters .!..• 77 (1958). -12852. C. Wong, Phys. Rev. 95, 7 61 (1954}; and also, C. Wong, Ph. D. Thesis, CaliforniaInstitute of Technology (1953). 53. G. Morpurgo, Phys. Rev. llO, 721 (1958). 54. E. K. Warburton, Phys. Rev. 113, 595 (1959). 55. W. E. Burcham, Pro g. In Nuclear Phys. i_, 171, (1955). 56. W. T. Sharp, H. E. Gave, and E. B. Paul, "Graphs of Coulomb Wave Functions, 11 2nd edition, TP 1-70, A. E. C. L. report No. 268 (1955). 57 . J. D. Larson and R. H. Spear, Bull. Am. Phys. Soc • 58. L. Meyer-Schiitzmeister and S. $. Hanna, Phys. Rev. 108, 1506 (1957). 59. A. E. Litherland, M. A. Clark, and H. E. · Gave, Can. J. Phys. ~. 1249 (1961). 6Q. F! A. El Bedewi, Pro. Phys, Soc. (London) 69A, 221 (1956). 61. J. P. Elliott and A. M. Lane, Handbuch der Physik, 39, 241 (1957). In particular see page 347. · 62. H. Reeves and E. E. Saltpeter, Phys. Rev. 116, 1505 (1959). 63. H. E. Gave, A. E. Litherland, and M. A. Clark, Nature 1'91, 1381 (1961). 64. L. C. Biedeharn and M. E. Rose, Revs. Mod. Phys. 25, 729 (1953). 65. S. Devons and L. J. B. Goldfarb, Handbuck der Physik, 42, 362 (1957). .£, 505 (1961). · · 66. D. H. Wilkinson, "Illustration of Angular Correlation Computations Using the Racah Coefficient Methods, 11 Cavendish Laboratory, 1954. 67. L. C. Biedenharn, "Nuclear Spectroscopy, 11 ed. by F. AjzenbergSelove, Academic Press, New York (1960); page 732. 68. · H. A. Wiedemilller, Lecture Notes by F. B. Morinigo andY. R. Cusson, California Institute o f Technology (1962). 69. W. T. Sharp, J. M. Kennedy, B. J. Sears, and M. G. Hoyle, "Tables of Coefficients for Angular Distribution Analysis, n CRT-556, Atomic Energy of Canada, Limited (1959). -129- 70. Reference 30, page 599. 71. A. J. Ferguson and A. R. Rutledge, "Coefficients for Triple Angular Corre lation Analysis in Nuclear Bombardment Experiments, 11 CRP-Gl5, Atomic Energy of Canada Limited (1957). 72. P. J. TwinnandJ. C. Willmott, tobepublished. 73. A. Bohr, Klg. Danske Videnskab. Selskab., Mat. -fys. M e dd. 26, No. 14 (1952). 74. A. Bohr and B. R. Mottle son, Klg. Danske Videns.k ab. Selskab., Mat. -fys. Medd. 27, No. 16 (1953). 75. S. G. Nilsson, Kug. Danske Videnskab. Selskab., Mat. - fys. M e dd. 29, No. 16 (1955). 76. B. R. Mottleson and S. G. Nilsson, Kug. Danske Videnskab. Mat.fys. Skr • ..!_, No. 8 (1959). 77. A. K. Kerman, 11 Nuclear Reactions," Vol., 1, ed. by P. M. Endt and M. Demur, North Hol~and Pub. Co., Amsterdam (1958). 78. A. K. Kerman, Klg. Danske Videnskab. Selskab., Mat. -fys. Medd. 30, No. 15 (1956). 79. · E. B.· Paul, Phil. Mag. ~~ 311 (1957). 80. B. R. Mottelson, private communication. 81. D. Inglis, Phys. Rev• .!.21.• 1786 (1956); and also reference 77. -l30a- Figure l is the energy level diagram for Lauritsen and Ajzenberg-Selove (19). from 0 Ne 20 from The gamma-ray yield curve o16 (a, y)Ne 20 is on the left side above the threshold for 16 +a. . Many resonances found 1n the . been also reported 1n the 0 16 0 16 {a,y}Ne 20 reaction have 16 19 20 . . {a, a}O and F (d, ny)Ne · reachons. -1 30- 16 875 Ne"+n 1'19 10 15.3 2~ ' 4.730 ,. 0 +a ~· i ] 2379 No" + p - a 0 0" Ne2o F ig. 1 J•O+ Ne ' ' x --x' "T' ' The labe lled parts are: 1} beam See page 4 for furthe r d etails. beam viewers, 10) batteries supplying potentials to suppress secondary electrons. 5) Penning gauge, 6) glass walled target chamber, 7) target rod, 8) targe t, 9) quartz filled with charcoal (Dewar filled with liquid nitrogen to cool trap not shown), direction, 2} slit system (lucite walls) with orthogonal pairs of slits (3), 4) cold trap Figure 2 shows the original target chambero I PJ I ...... VJ ...... ~ 3 ~··~ ~ II, !;/~ ]i rod, 15) targe to See page 6 for furthe r detailso ~! 12} glass to kovar seal, 13) quartz viewer, 14) electron suppressor ring and supporting 9} mild steel cans, 10} glass target chamber, 11) viton 11 0" rings without vacuum grease, 5) liquid nitrogen res~rvoir, 6) 11 high vacuum" side, 7) 9 1/sec ion pump, 8) alnico magnet, side, 2) J:>eam axis, 3} stainless steel in-line cold trap, 4) 3/8" diameter b e am tube, Figure 3 shows the 11 clean vacuum" systemo . The labelled parts are: 1) 11 low vacuum" I I Ill N (JJ 1-' - 13 2- ! 9 N I. I. I· ,. r' •' 1¥= ·' .; ·:' i ,· "' :,_!. -·- . r0 UJ ...J "' "' (.) ({) . -- - - .. --- ~ Ol LL Ill Further details are given on page 7. 13) brass window 0. 0 625 11 thick. I I-' I w w target rod supporting a 0.125 11 copper disc (11) faced with a 0.020 11 tanta lum disc {12), filled with liquid nitrogen to cool 8 and 9 not shown), 10) 0. 375 11 diameter copper 8) water level vial of stainless steel, 9) target rod vial of stainless steel (Dewa r 6) electron suppressor ring and supporting rod, 7) brass walled target chamber, axis, 3) vacuum valves shown schematically, 4} auxiliary pump-out, 5) lucite insulator, The labelled parts are: 1) beam tube and vacuum system of accelerator, 2) beam Figure 4 shows the targe t chamber used for making and bombarding ice targe ts. -133- C\1 I The across the high resistance of the oxide layer, as measured by the vacuum See page 8 for further details. water after anodizing to remove the e l ectrolyte. Targets were boiled in distilled giving targets 55 kev thick A thick. 2 to 7 Mev alpha particles, or an oxide layer 2240 experiment were anodized to 150 volts at ...., 0.10 ma/cm tube voltmeter, may be related to the oxide layer thickness. The targe ts used in this ~oltage drop . Figure 5 shows the anodi~ing apparatus used to make tantalum oxide targets. Ill *""I I ...... w Fig. 5 CARBON ROD n SHEET + 2 50 VOLTS 3 °/o Dl- BASIC AMMONIUM CITRATE GLASS BEAKER TANTALUM CURRENT VACUUM TUBE VOLT METER 10 k I I .t:> UJ -l35a- Figure 6 is the block diagram for the fast-slow coincidence circuit used to investigate gamma-ray cascades and to measure Signals~ triple angular correlationso accurately defined in time, were derived from the z~ro crossing of the pulses from the Hamner amplifiers by the pick-of£ circuit shown in figure 7 o The measured fast coincidence resolving time was about 70 ns; the calculated resolving time from the clipping cable lengths is 50 ns. indicating a time jitter of ± 10 ns in the zero crossing of the pulses from the Hamner amplifiers. Typical counting rates gave calculated real to random ratios of 960 to 1 for the 8. 64-1. 63 - Mev gamma-ray cascade from the 6. 93-Mev resonance; measured real to random ratios were in excess of 500 to 1. a resolving time of 1. 4 !J.So The slow .coincidence mixer has As explained on page 11 in the text, economy in running time was achieved by storing both singles and coincidence pulses from one of the detectors in the 400 channel analyzer.. - I '.') · 0 TAH G[ T Ll r ····· ~INOOW L I '. + _J I ! '( " ~~ I - Pi ~ K- O FF L .. -~ - . ..J _l:- : - - ___ 1 ----~ L --- rI __ 1 RG -r· G2· U CI RCUi TS I t-1EWL ET T P/\CKt.'> RD /IMPU FI ERS _j C L] 20 AMPL! F tE: RS PU L SE OUT I --~1 T HAMNER I v w X I DC L AY UN F CLI PPIN '-.: -------~ 'v t\ RIM-'L E DELf•Y'-: r- -- - - - -- - , L- < > - ---l i__ -,-__j I ~-{_-=~-]SCI\ L.ER --l r-+---_l ___ --- ~ , 3 i 2 I 68 1 18cuBLC 1 I ? '--- 1 , __I I L- COINCIDEr-I CES OR SLOW CO INCIDENC E M IYE R II L___l ---- ---· -----·- --T. __ j c s-u RG . ., i J~ J . -- - ---, _j SCAL Ef, s t- --- -L . ! : r---- ----- l L. ___ _j . . TRi P LE r OINCIOENCE S 2 3 ·L --- J SC/\ L.E ~ 'Y I :· RES E T P 1 !LSI~ [ I A N ~' GATE -~~---- ----<---{ I I 1 --- H . - - --: ~ ~I F· . : L SE. i 1~ 1 L I · C ~ ,'. I I N [L I ! I j----<. I N P i J ; A '\!ALY SF.:R L... - -. --- - --- ·--- -------~ E' T HER X OR J -136a- Figure 7 is the schematic of the "pick-off" circuit used to detect the zero crossing of the Hamner amplifier pulse~ operation of this circuit is as follows. The The positive-going part of the signal from the Hamner cuts the current off in the second part of the tube, turning the tunnel diode off along path 1 of the . operating loop marked on the tunnel diode characteristic curve. As the signal starts to drop towards zero, the current in the tunnel diode rises up the front edge of its characteristic until it reaches 4. 7 ma, at which time it flips over to its quiescent point along path 2. As the signal continues negative, the diode between cathodes unhooks the two sections, thus limiting the output pulse to 0. ~5 volts into RO-ll4. With delay-line clipping, the wave forms indicated at the bottom of the figure are obtained. The 25 kO potentiometer allows adjustment of the quiescent point on the tunnel diode characteristic, and hence a small adjustment in the pick-off voltage. details. See page 11 for further -136 - TUNNEL DIODE UP TO IOOv I N o----j1--41~-....:...._....l\ \~--=-\~ 0 I .;-O_ 1m 5 . 6K OPERATING LOO P FOR T UN t--I EL 0 1ODE QUIESCENT POl NT 4.7ma 0.5 volts WAVE FORMS v INPUT FROM HAMNER AMPLIFIER OUTPUT PULSE {INTO RG-11 4 ) v SIGI\JAL AF TER LINE CLIPPING Fiq. 7 D ELAY .-137a- Fig ure 8 shows the results of tests made on the angular distribution apparatus. Figure 8A shows the gain change in channels per 100 induced in the photomultiplier by stray magnetic fields as a function of the detector a ngle. m e nts. An error bar shows the ac c uracy of the measure - Additional details are given on p a g e 13. Figure 8B shows the excitation function for the 3. 56-Mev ' gamma rays from . 9 6 Be {p. a.y)Li • The resonance energy. Er• m a rked on the abscissa has been calculated from the data in this figure by assuming a value of r:; 40 kev for the total width of the resonance. · Figure 8C shows a representative angular distribution for the i -s otropic 3._ 56-Me~ gamma rays from has been normalized to unity at 0°. Be 9 (p, a:y)Li 6• The data The line through the experi- mental points is the expected behavior of a point source· displ<;~.ced by 0. 044" towards the north (the 90° point) from the center of ~otation ofthe 4" x 4" Nai crystal. Additional information relating to figures BA and 8B is given on page 15 of the text. -1 3 ? - 0 zO w a::+ 0 . 1 ANGLE (NORTH Sl DE) <.,9W zO.... <((f) I.-J 60° Uw z ~- 0 . 1 90° ANGLE (SOUTH SIDE ) <(<( <..9I u Fig. BA (f) I- z 40 >a:: <( a:: 30 :J I- 70 54 KEV CD a:: <( 10 0 _J w >- 2 .6 Fig. 88 2. 7 PROTON ENERGY (MeV) (f) 1.04 60° Fig.8C 30° ANGLE - NORTH Sl DE 0° 19 16 (p, ny)o • · page 16. Additional deta il s are given on The lines marked (a) and (b) are, r es pe c tiye ly, the horizontal a nd zero intercept extrapolations of the low energy tail. 1" from the target. This .spectrum was obtained with the 4 11 x 4 11 Nai(T.f) d etecto r, without collimator, placed Figure 9 show's the 6.1~-Mev r adiation from the 597 kev resonance in F I Ill VJ 00 I ...... -138- _j w z z <! I u ..0 ~------~------~------~------~~--~o l{) 0 C\J en e- lL (~0 IX) T3NN'VHJ ~3d SJ..NnOJ -l39a- Figure 10 shows representative data obtained during the calibration runs. Data for the AJ. are plotted at the topo runs 27 (pp n)Si 27 threshold at 5i98 ± 4 kev Three runs are represented in ~ this plot; #4 of 1/12/62 and #1 of 1/16/62 were made with a 1 11 thick · moderator in front of the neutron detectorp run #2 of 1/12/62 was made without the moderatoro from tJ~ e Na 23 (ap n}Al 26 A typical excitation curve for neutrons resonance at 3492 ± 5 kev run with the He + beam is shown in the center right of the figureo A summary of the values obtained from these reactions for the magnet constant defined on page 22 is given at the bottom of the figureo The best value. 1996o 8 ± 3 x 10 -5 , is shown by an arrow on the abscissa. . 1 t h"1ck target exc1.tat1on . . A typ1ca curve f or t h e o16 (a, v)Ne 20 1 resonance at 6. 93 Mev obtained during the same sequence of runs is shown at the center left. From this run and similar runs~ the resonant energy is 6. 930 ± o. 010 Mev. There is a further discussion of the results and procedures used in obtaining this data in the text on page 19. - 139 6000 en 1-- 0 z #2 1/12/62 X #4 1/12/62 ::::> o :11: I ~ 4000 <{ a:: 1/16/62 ICD a:: <{ ~ 2000 1-- z ::::> 0 u 17. 11 ~ z 2000 17.16 0 (a, y) N/ 16 0 ::::> >a:: <{ a:: ICD I 000 a:: <{ I en 1-- z ::::> 0 u 18.60 18.68 26.40 26.50 FREQUENCY, (me/sec) SUMMARY of RESULTS (a) (b) ~----~~----~ (c) r-----~~----~ I 1992 FIG. 10 1994 ( d ) t-------o-------1 I I t 1996 1998 MAGNET CONSTANT X 10+ 5 2000 2002 X X in Ne 20 • The r ange covered further ·details. See page 23 for The detector was a 4 11 x 4 11 Nai crystal placed 1. 06rr from the tar ge t at 0° w ith respect to the beam dir ec tion . layer 51 kev thick to 7 Mev a lpha p articles. The targe t used for this excitation function was anodized t antalum vi.ith an oxide by the variable energy window is shown on the gamma -ray spectrum in figure 13. Ex , M ev, for 300 fJ,C of He++ is plotted against the The number of counts in the variable energy o16 (a, y )Ne 20 reaction for alpha-particle E a , and the excitation energy, . 0. 86(E - lo 63)Mev to 1.10 E bomba rding energy, window, bombarding energies . 4. 8 to 7. 2 Mev. · Figure 11 is the excitation function for the I I Ill 0 ~ t--' 0 Fig. II 4.5 1000 ( 300 fLC He++) N 2000 I 8.5 (J 1- 5.0 co CJ5 9 .0 q:A~P0° 5- 1- 1 I I 2+8 co c4bo8,.., 0 0 00 • ! cR:P 0 1s(a a) o's LEVELS FROM 0+8 -¢ 0 5.5 'if r ¢ p 9.5 6.0 (2+) 2+ J OCQ:o:PQjX>qjtiP <>cro 3- 11 4+ I 1 6.5 I 10.0 (4+) 1 'V' , -1 7.0 , Ea(MeV) I 0 I --+:>. 10.5 Ex(MeV) -.---J °o cfO [00 0 fX5 r (5-) 1 'II The number of pulses in the energy window o16 (a, y)Ne 20 reaction for alpha-particle a E, andtheexcitationenergy, x E, in Ne 20 • The detector was a 4 11 x 4 11 The target was oxidi zed tungsten details are given on page 26. This excitation function is a continuation of the excitation function in figure 11. Additional Nal crystal placed 1. 06 11 from the target at 45° with respect to the beam dir ection. with an oxide layer 55 kev thick to 7 Mev alpha particles. energy, O. 86(Ex- 1. 63) Mev to 1~ 10 Ex Mev for 150 fJ.C of He++ is plotted against the bombarding bombarding energies 7. 2 to 9. 9 Mev. · ·Figure 12 is the excitation function for the I I Ill I-' ~ I-' N 16 I + I + RABSON ET ~~0 RESONANCE (X 1/5) HEIGHT OF 6.93 MeV F (d, ny) Ne 20 LEV ELS FROM{BUTLER 19 16 0 AL. "' I 0 t,'l t + I ? ? t ~ "' I ~ I ? ~ ? + + I ~ ~ I "' "' ? I t t ~ I + I 'f t I (6+) 'f Fig. 12 7.0 10.5 7.5 11.0 8 .0 11 . 5 8 .5 9 .0 12.0 9.5 12.5 10.0 0 ~-,--,--,--,--,--,--,---,--.--,--,--,--,--,,--,--,--,--,--,--,---,--,--,--,--,--,--~--.--.~ (150 fLC He++) I "' .. I ? ? LEVELS FROM 0 (a a) 10 Ex (MeV ) Ea (MeV) I -.t> The targe t was an oxidized E X = 9o 0 5 Mev, i n Ne 20 • This Hence, this window includes the photo-peaks· of the gamma-ray spectrum excited state of Ne 20 • Additional d e tails are give n on page 23. half of the se cond escape peak of the gamma-ray spectrum from transitio ns to the first from transitions to the ground state and the full energy peak , first escape peak, and roug hly spectrum. window covers the energy range 0. 86(Ex- 1. 63) Mev to 1.10 Ex Me v in the gamma ray Ea::: 5. 40 Mev, corresponding to an excitation energy, and 12 is illustrate d by the bar above the abscissa for the alpha -particle bombarding energy, The variable ene rgy window u sed to de rive the excitation function shown in figures 11 Further details are given on page 28. tungsten blank with an oxide laye r 115 kev thick to alpha particles of this energy. pla ced 0 0 75 11 from the t a rg e t at 45° to the beam direction. The gamma rays were de t e cte d in a 4" x 4 11 Nal cry stal o16{a, y)Ne 20 • The filled curve was obta ined at 5. 40 Mev and the dotted curve at 5. 30 Mev bombarding energy. in Figure 13 shows the 7. 40-Mev gamma-ray s pectrum from che 5. 37 -Mev resonance ~ I II' N I r-' Q) • 3 I 20 X ....... \ 2 10 •• ~ •• • •• • •• • ··.. 6.13 ' t I 80 • x /\ 1 • • •• \ JXx J ~I X ~\ '\ t • t <'( \ f 7.40 'tl t t 9.03 CHANNEL I I 100 I · · M( rw:..~~a:nwmu I 140 160 t o+~o Ne •• . . ............. ~ I 120 7.40 9.03 2+__.1_1 .63 WIN DO~ ·.· ·. : .... . . . . x~ • .· ... · .... · • . . . ··.. I . t . . . ') •• ~~x__:&.xr ,0 ~J~ > \. \ r RESONANCE- Ea = 5.40 MeV · · · · BELOW RESONANCE- Ea = 5.30 MeV x - - ON VARIABLE ENERGY ATE 0 =5.40MeV I 60 .• \ \r XX 10 ·. \ ... • . \ ·• •' .,.,.,._ . ~ '.. \ \ X ~ .. \ •\ I 40 • \ ·.. \ \ \ t.. , \ ··.··:·.~ ~~\l\ Fig. l3 0I 20 .. "' ·~ u :::::> 1- (/) 0 1\ ~XI0 60 80 100 z 40 CL w 0:: u I <t: z z w .....J I{) do u I + 120 ~- \ ~ 140~--~------~------~--------~------~------~--------~------~ I I 1\) .t> and below resonance. Further details are given on pages 29 and 31 in the text. BELOW and ON indicate the energy relationship of angular distribution runs made on Arrows marked Values for the resonant energy deter- the He+ beam, and the lower curve with He++. mined from these excitation functions are indicated on the abscissa. The upper curve was obtained with The ordinate is the ~umber of counts in the energy window 6. 56 Mev to 8. 58 Mev for 90 IJ.C of integrated beam current. resonance. Figure 14 is the excitation function for 7 o 40 -Mev gamma r ::ys from the 5. 37 -Mev ~ I p! w I ...... u 0 :::> z I- (f) I (J) 0 ::1.. u He+ 5.50 7.40- MeV GAMMA-RAY EXCITAT ION FUNCTION 5.37-Mev RESONANCE BOMBARDING ENERGY- MeV o He++ F ig. l4 5.378 ~ 5.40 f 5.30 200 400 600~ 800 1000 5.60 I I ()J -~I -144a- Figure 15 shows the results of angular distribution measurements on the 7 o 40 -Mev gamma ray from the So 37 -Mev resonance in o16 (a, )'}Ne 20 • together with the least squares fito The number of counts in the ene rgy window, 6o 56 to So 58 Mev for 600 j-LC of He+ are plotted against the cosine of the angle b etwe en the and the beam directiono Nai detector The upper data points are the uncorrected data included to show the ability of the apparatus to resolve a P 4 (cos 8} term in an angular distributiono The smooth curve through the corrected data points is a least squares fit which is: counts = 967 {1 + (Oo 439 ± 0., 052)P (cos 8} 2 - {Oo 243 ± Oo 057}P (cos 8} } 4 Further details ar·e given on page 30o - 144- 2000 -+ + <1> ::r::: 1600 u tl 0 0 (.() 1200 U1 rz :::> 0 u 800 0 CORRECTED DATA 400 0~------~------~--------~------~------~ 0 .0 Fig_ 15 0 .2 0.4 0 .6 cos 8 0 .8 1.0 0 16 Additional details are given on page 37 of the text. energy relationship of the two runs is shown on the excitation fun c tion in figUre 17. The (a., y)Ne The filled curve was made on resonance, and the dotted curve below resonance . . . . ments made on the 8. 64-Mev gamma ray from the 6. 93-Mev resonance m 20 • Figure 16 shows gamma-ray spectra obta ined during angular distribution measure- I I Ill 01 H>- 1-' I -;: 1 I } (\J 1'- > Q) ~ <.D 0 ¢ ~---~-·---1:1 .I g~ 00 0 <.D f'- -0 NO >Q) (j) 0 ~ ~t 1 ... ~ 1"0 c:i .., 7=.· ~ ~2 :~ 1::. II 0 (j) "'· 'lc• ~ '>C> .; : ~ ,.·~ i ~ <.0 w I oW I• II w u I ~ z w <t u z z 0 <! CJ) z w (\Jt (\J ,. . : a:: ~ 3: a:: g z w 0 0 1"0 (D I )C 0 ___...-__ ___ X _. )1(- ---•' } /" ./· 0 0 ;:y~ (''·'" .;;;· "'>e <.D ><"' • wJI'- . ! - ~... --: ~ -)It' t t -')C-- __.,. ~ ,/ .. • 0 ,-. " 00 - .,. .1': z <t • '· -)C: -)(" ~ I u ...,._;c.; " . ~-' • ................. w~- 0 <.D .r •' .... - - - - - - ><5x --... _ ·-----=--=·----------------- ... ..::."' --:~-' ..... "\.~·- ""_.-. t\1 -;( 0 "• ~·' _x___-.:_~~~--·ac_..-w-;:.--- _0 ¢ ......... .. .!---=~~~~~~~~~------~ ~,.-· ------ (\J _o I 0 ¢ I'() 0 1 (\J 0 0 (++aH 'JTI ~I£) l3NN't1H'J C:13d S.iNnO'J 0 <.0 -146a- Figure 17 shows the results of angular distribution measurements on the 8 . 64-Mev gamma ray from the 6. 93-Mev resonance in o16 (a; y)Ne 20 , together with the least squares fits. The cor- rected number of counts in the energy window, 6. 90 to 9. 07 Mev, for 240 !J.C of He ++ are plotted against the cosine of the · angle between the Nai detector and the beam direction. The smooth curve through the data points is the result of a least squares analysis which gave: counts= 1648 { 1 + (Oo475 ± Oo025}P {cos 0) 2 The lower curve marked "BACKGROUND" is the estimated back- ground obtained by interpolating between angular distribution measurements made below and above resonance. The energy relationship of the three measurements is shown on the excitation function for the 8. 64-Mev gamma ray inserted at the top of the figure. This back- ground has been removed from the corrected data at the top of the figure. Further details are given on page 38. -146- (f) ..... z :::> >-100 a: a: <( ..... 50 aJ a: <( 6 2400 o~~~_L__L_~~~ .....J w >- 6 .9 Ea(MeV) + + (1) 2000 I u ::l. ~ 1600 (\J (f) 1- z 1200 CORRECTED DATA ::) 0 0 800 400 BACKGROUND 0 0 .2 0.4 0.6 cos 8 Fig. l7 0 .8 1.0 0 2 (cos e) The theoretical values a re plotted 0 4 o < 0. the text. o are marked o > 0 Additional discussion is given on page 39 of The horizontal bands are the experimental values~ where the width of the band is the experimental uncertainty. and of the second Legendre polynomial that d epend on the sign ·of The two pas sible values for the coefficient o, which is defined as the ratio of the reduced rna trix elements for the E2 to Ml operators. against the mixing coefficient 20 16 from the 6. 93-~ev resonance in . o (a,y)Ne • 2 W{e) ::: 1 + a ja P (cos e) + aJ a P in the expression for the angular distribution for the 8. 64-Mev gamma ray: Figure 18 shows experimental and theoretical values for the L egendr e polynomials I I Pl -J .p.. f.-' w I0- 4 -.6 -.41 - .2 Fig . IS z :::::> ~ w n:: u - <! 0 .2r _J > .4 .6 <! _J :::::> .8 1.0 I0- 3 10-l ~- •~.\ y \ MIXING COEFFICIET; 8 I0- 2 - \ 10 10 2 o4/0o o4 ;o 0 (expl 3 10 ~ I I ..._, ~ - a3 11 X 3 11 Nal crystal; shown in B Show n in A is the s i ngles L ikewi se, spectrum D was • . More complicated cas cades starting at t he The transitions discussed on p age 44 details are given on pages 43 to 47 of the t ext. Probabl e sources fo r some of the l ow ene rgy gamma r ays h ave b een noted on B. Additional to the 2-, third excit ed state that is expected to have a full-energy peak i n channel 69. that i s expected to have a full - energy peak in channel 78, and the 5. 30 -Me v , El transition of the text are the 6. 02-Mev, E2 transition to the 4 + se cond excited state (see figure 1) in the high energy coincidence spectrum s how n i n C o 10. 27 -Mev leve l and going through the 1. 63-Mev first excit ed s t a t e do n ot show up cl early 20 The main f eatures of the coincide nce spectr a are the 8. 63 - 1. 63 - M ev cascade from the 10. 27 -Me v l evel in Ne ray above 3. 85 Mev. shlfted out of B on the condition tha t there was a coincidence w ith a high energy gamma with a low energy gamma r ay in the window shown i n B. The spectrum i n C was shifted out of A on the condition that there was a fast coincidence is the singl es spe ctrum for the l ow e nergy ga1nma r a y s d e t ec t ed in a 4 11 x 4 11 Nal crystal. spectrum for the high ene r gy gamma rays detected in 16 20 the radia tions from the 6. 93-Mev r es onance i~ o {u, y )Ne • Figure 19 shows gamma -ray s pectra obtained during coincidence measurements of I I Il-l 00 ~ ....... ~ 140 u I + +Q) 80 100 1- Fig. 19 u CHANNEL 200 160 J 40 80 120 u 160 :::> 0 40 Q. (f) :::> 0 z 10 20 30 40 50 60 5 240 u z \ C) 3X3-INCH Nor: COINCIDENCES I <{ z z w _j ~ 1- (f) a:: w Q. u I z z <{ w _j ~ \D (j) :::1._ INTEGRAL WINDOW (a, yl Ne 20 0 0 0 16 :::1._ 15 xl03 lx10 2 0 0 u I + +Q) 20~- 25 30 ~ - A) 3 X 3-INCH Nor: SINGLES 0 Xl02 I 1~3 ~ u (o,y)Ne w D) 4 X 4-INCH Nai: COINCIDENCES .... ~"'~04 X10 3 21 ) 160 .... . ...,.., .. .. -....~· ...'- ·: .. ''··· ..... ..... ~ 3 70 (cf(a,n) Ne -v.s.t 1.39 (d 8(o,n) Ni') 1 8) 4 X4-INCH No I: Sl NGLES I CX> ~ -149a- Figure 20 shows the results of a-'1-'1 triple angular correlation measurements made at the 6. 93-Mev resonance in the 0 16 (a, 'f )Ne 20 . reachon. A sketch of the experimental arrangement is shown at the top of the figure. The coincidence circuit biases · were arranged so that the 8. 64-Mev gamma rays were detected in the 4 11 x 4 11 Nai crystal, and the 1. 63 -Mev gamma rays were detected in the 2 11 X 2 11 Nai crystal. Plotted are the number of coincidence counts as a function of the cosine of the angle between the 4 11 crystal and .the beam direction. The smooth curves are the calculated patterns for various spin and gamma-ray multipolarities for the specific geometry of the counters. These curves have been adjusted in amplitude by least squares to the data points. quality of the fit has been judged by the X 2 The testp and the results are: Pattern Transition 2 _x_ P robability 1 O~{E2)2+{E2)0+ 90.0 << 1% 2 l-(El)2+(E2)0+ 60. 6 << 1 3 2+{M1)2+{E2)0+ 1. 57 96 4 2 +{E2)2+{E2)0 + 910 2 << 1 5 3-(El)2+{E2)0+ 17 s. << 1 6 4 +(E2)2 +(E2}0 + 6. 76 33 Additional discussions are given on page 47 of the text and in Appendix A. · -149- BEAM 2 X 2-1 NCH No I CRYSTAL (1.63-MeV y) + -- I I I I I 500 I +Q) --74x4-INCH Nal CRYSTAL (8 .64- MeV y) i~ e/ I (.) :::l 400 0 0 t0 ..._ (j) ~: 4 I 300 1-- z 5 ::::::) 0 u 200 w u z w 0 100 u z - 0 u Fig. 20 0 0.2 0.4 0.6 cos e 0.8 1.0 -150a- Figure 21 s how s gamma-ray spe ctra obta ined above, on, . 16 20 and b e low the 7. 94-Mev resonance 1n 0 (a, y}Ne o The energies were 8. 027-, 7. 953-, a n d 7. 910 -Me v bomba rding e n e r g yo The se three ene r g ies ar e indicated by arrow s on the excitation function for the 6. 83-Me v gamma ray shown in figure 22A. These spe ctra w e re obtained during ang ular distribution measurements on the 6. 83-Mev gamma ray; collimator. in Ne 20 the Nal crystal was equipped with a The small energy level diagram shows the cascade that gives rise to the 6o 83-Mev gamma rayo cussion on page 54 for further details. See the dis- -ISO- 12 0 ABOVE RESONANCE -E 0 =8.028 MeV 100 4.43 80 6 . 13 I I 60 6.92 I 7 .12 40 I 20 + + 0 Q) ::r: u ON RESONANCE- Ea =7.953 MeV 120 ::l 0 0 0 f'- 100 11 .08 _j w z z 1 80 <l: 83 ::r: u a:: 60 a... 40 4+ w 2+ - - 1.63 (/) o+ 1- z ::::> 0 4.25 20 20 Ne o 9.45 u I 0 BELOW RESONANC E -E 0 =7.91 0 MeV 100 80 60 40 20 0 Fig. 2 1 40 60 80 CHANNEL 100 120 140 -l5la- Figure 22 shows two excitation functions for the 6. 83 -Mev 20 16 radiation from the 7. 94-Mev resonance in o (a., '(}Ne o 22A is an excitation function obtained with the 4° x 4n Figure Nai crystal by summing the counts in the gamma-ray spectra falling in the energy window, 6. 29 to 7. 40 Mev. The resonance energy indicated by the half-way point on the low energy side is shown by an arrow on the abscissa. This excitation function was obtained prior to angular distribution measurements discussed on page 56. These measurements were made below, on and above resonance at energies indicated on the excitation function by arrowso The excitation function shown in figure 22B was an attempt to determine the resonance energy and find the total width of the 7. 94-Mev resonance. The resonance energy is marked on the abscissa; the l/4 to 3/4 rise of this excitation function is 3. 2 kevo The data was obtained with a 3 11 x 3 11 Nai crystalg and is the number of counts in the energy window 6. 29 to 7. 20 Mev. Additional details relating to figures 22A and B are given on page 55 of the text. 600 + +Q) 500 ON ~ I ~ 400 0 1.0 .__.. CJ) 300 1-- z :::J 0 200 0 8.00 7.90 Fig. 22A Ea (MeV) 8.06 -l52a- Figure .23 shows the results of angular distribution measure' ments on the 6o 83-Mev gamma r ay from the 7. 94-Mev resonance . m 0 16 (a~ y)Ne 20 , together with the least squares fits. The corrected number of counts in the energy window 5. 7 2 to 7 o 40· Mev for 500 J-LC of He ++ . are plotted against the cosine of the angle between the Nai detector and the beam direction. The smooth curve through the data points is the result of a l east squa r es analysis which gave: counts= 4989 { 1 + {0. 252 ± O.. Ol9)P {cos e) 2 - (Oo 033 ± o. 024)P {cos e)} 4 The lower curve marked 11 BACKGROUNDn is the estimated background obtained by· inte rpolating between angular distribution measurements made b e low and above resonanc e . The energy relationship of the three measurements is shown on the ·excitation function for the 6. 83-Mev gamma ray given in figure 22A. This background has been removed from the corrected data at the top of the figure. Further details are given on page 56. 6000 - + +Q) I 2-----2 4000 CORRECTED DATA u :::l 0 0 L() ___.. (}) I- z ::::J 0 BACKGROUND 2000 u 0 .0 Fig. 2 3 0.2 0 .4 cos 8 0 .6 0 .8 1.0 o16 (0:, y)Ne 20 o The th e oretical values ar e plotte d against taintyo Additional discussion is given on page 58 of th e texto bands are the experimental values, where the width of the b an d is t he expe rime ntal unc e r- The horizonta l The two possibl e values for the co efficie nt of the second Le gendre polynomial that depend on the sign of 6 are m a rked 6 > 0 and 6 < 0. the E2 to Ml operatorso the mixing coefficient 6, which is defined as the ratio of the r e duc ed mat rix e l ements for for the 7 o 94-Mev resonance in W {8) = 1 + a /a P (cos e) + a /a P (co s e) 2 0 2 4 0 4 in the expres sian for the angular distribution for the 6o 83 -M ev gamma r ay : Figure 24 shows the experimental and theoretical values for the L egendre polynomials I I Ill VJ 1--' (Jl Fig. 24 z :J ~ w 0: 4 I I I ! I I III 3 I I I !IIIII 2 I I I Ill! I 1 I I I !II I I I I I I 1 ! !!1 1 I I o4;oo 10 10 10- I MIXING COEFFICIENT; 10- 8 10 10 I !II I I I 2 I I I ! I I III 3 10 I <{ 0 I (J1 (>.1 -8' 2 ~7ZZZZZZZ!IZZZZZZZZZZZZZZZZ~ZZZZZZZ~77ZZZZOOZOZZZZZZ7zziizzomz~ o2jo0 (8 >0) _j > <{ _j :J w 4 6 -l54a- Figure 25 shows the results of a.-y-y triple angular cor- relation measurements made at the 7 o 94-Mev resonance in the 0 16 (a., y)Ne 20 . reactlono A sketch of the experimental arrangement is shown at the top of the figureo The coincidence circuit biases were arranged so that the 6o 83 -Mev gamma rays were detected in the 4 11 x 4n Nai crystal, and the 2o 62-Mev gamma rays were detected in ~the 2 :1 X 2rr Nai crystalo Plotted are the number of coincidence counts as a function of the cosine of the angle between the 4 11 crystal and the · beam directiono The smooth curves are the calculate d patterns for various spin and gamma-ray multipolarities for the specific geometry of the counterso These curves have been adjusted in amplitude by least squares to the data pointso of the fit has been judged by the X 2 The quality testg and the results are: '2 Patte rn Trans ition _x_ Probability: 1 4 +(M1 )4 +(E2)2 + E2 3.,46 74o/o 2 6 +(E2)4 +{E2)2 + 2 0 02 92 3 2 +{E2)4 +(E2 ) 2 + 3o05 81 4 3 -(El)4 +(E2)2+ 6. 90 33 . 5 5 - (El}4+(E2}2+ 13 . 0 4 The mixing coefficient used in calculating pattern 1 was the value determined from the, angular distribution measurements on the 6 .. 83Mev gamma ray that are discussed on pages 56 to 58 of the text. Additional discussions of the triple angular correlation measurement are given on page 59 ~ and in Appendix B., - 154 - BEAM 2 X 2-INCH Na I CRYSTAL (2 . 62- MeV y) --;- I I + I ...-- +Q) I : 100 I l (.) ::i_ 4 X 4-IN CH Nal CR Y STAL (6 .83-MeVy) ~ 80 e/ I 2 0 (j) ..__... (j) 60 5 I- z :::::> 0 u 40 w u z w 0 20 u z - 0 u 0 F ig. 25 0 .2 04 0 .6 cos 8 0.8 1.0 d 6 (a. a'y)d6• page 75. 13 (a, ny)d 6 reactiono Additional details are given on The cr-osses are an upper limit estimate for the contribution to the · 6.13-Mev radiation from the c 150 ~C of He++. The ordinate N is the number of counts in the energy window, 4. 91 to 6. 56 Mev, for Figure 26 is the excitation function for the 6.13-Mev radiation from ' ·su U1 U1 I ..... - 155 - 0 ------~~----~------~-------.------~6 + I.() (j) - > Q) ~ 0 w 0(J) co 0 0 o.. 0 0 1..() 0 0 0 0 0 0 .. ~ 0 0 0 0 .. f"() 0 0 0 0 0 0 .. C\J (++aH JTIO£ 1) N 0 0 ... 0 0 co <..0 C\1 0'1 ·~ . . .... 20 (19). the same height. 20 found in this experiment and the ground state of F Additional discussion is giv~n on page 79 of the text. 20 20 have The vertical scales, excitation energies in Mev, have been adjusted so the 10. 27 -Mev level in Ne and the energy levels of F Figure 27 is a comparison of the energy levels in Ne ,. 1\) . I "' U1 I ...... X w Fig. 27 10 II' "' "' <2 [ ~ ~ ~: I Ne2o t----------1 I 2+ - T =I 1'- 2+ (4~); (T=I) I ~ ·- c z I Ia+' ,-' 2+' 3-' 4+ I Q) C\J 0 I I I (3-, 4 +) o+, ,-' 2+' 3-, 4+ J7T I 12 r- 40 47 rem (KeV) F2o (i+) J ~2 C\J 0 I Q) w X ~ > c -- LL l .. J ~I I I J7T I I (J) U'1 - The labelled parts are: A) beam path, B) glass walled target chamber Not shown are the The scale is 1:1. the distance travelled in the lead. This figure is discussed in Appendix A on page 92. is 73o/o, and along path (2) it is 12%, where the a.ttenuation of o. 29 has been included for For gamma rays with energies of 8 Mev, the detection probability along path (1) shielding around the crystal. aluminum housing for the Nai crystal, the photomultiplier, or the cylindrical lead D) Faraday guard ring,_ E) lead collimator, ·F) 4" x 4" Nal{T.l) crystal. of the clean vacuum system (top view), C) target placed ~t 135° with res~ect to the beam, measurements. Figure 28 is a section drawing of the detector geometry used for angular distribution . , I Ill U1 -J ...... -15 7- IJ... -158aFigure 29 shows the numerical results of the unified model calculation discussed in Appendix B that compares the properties . 20 20 of the 10. 27 -Mev level 1n Ne and the F ground state beta decay. Plotted in a. b, and c for deformation parameters 11 = 6, 4, and 2, respectively, are the experimental values for the beta decay of the 20 F . ground state {13), and the Ml and E2 decay of the 10.27 -Mev level of Ne 20 • The three Ml lines, from top to bottom, are the upper limit, best value and lower limit of the experimental values. corresponding lines for the E2 decay are marked. The ordinate, ei. in these plots is related to the mixture of K = 1 and K in the initial state (either the F level in Ne 20 20 The = 2 bands g:t"ound state or the 10. 27 -Mev ), where e.= 0° makes the initial st~te a pure K ::z 2 1 . band, and e. = 45° makes a 50% mixture in intensity. Similarly, the abscissa, ef' is related to the mixture of K = 0 1 in the final state (the 1. 63-Mev level in Ne the initial state a pure K = 0 20 and K = 1 bands ), where e , = 0 0 makes 1 band. Figure 29d shows -the level_order associated with the K and K = 2 bands assumed in·the initial state of Ne 20 tur F subtracting 10. 27 Mev from the ordinate) as a function of e.. 1 are two solutions shown in this plot. I= 1 solution is to be used; for tion of this line is to be U:Sedc. 20 =1 by There For EK=l (I) < EK= 2 (I), the dotted EK=l{I) > EK= 2 (I) 1 the solid continuaThe energy scale has been adjusted ' to make the lower I = ·2 level correspond to the 10~ 27 -Mev level. -158- FIG 29 o FIG. 29 b i3 12 I I I= 2 (LO WER ) 10 7)=2 00 ~0------~~----~~~----~. --- --- -------5.0 F IG. 29 c 2.0 16 Ei-MeV FIG 29 d I0 --