Electromagnetic Decay of the 1-7- and 2.4J-Mev. Levels in ⁹Be Citation Purdom, Paul Walton (1966) Electromagnetic Decay of the 1-7- and 2.4J-Mev. Levels in ⁹Be. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/DAB0-KN61. https://resolver.caltech.edu/CaltechTHESIS:10192015-131229028 Abstract The 1.7- and 2.43-MeV levels in 9 Be were populated with the reaction 11 B(d, α) 9 Be* by bombarding thin boron on carbon foils with 1.7-MeV deuterons. The alpha particles were analyzed in energy with a surface-barrier counter set at the unique kinematically determined angle and the recoiling 9 Be nuclei at 90 o were analyzed in rigidity with a magnetic spectrometer, in energy by a surface-barrier counter at the spectrometer focus, and in velocity by the time delay between an alpha and a 9 Be count. When a pulse from the spectrometer counter was in the appropriate delayed coincidence with a pulse from the alpha counter, the two pulses were recorded in a two-dimensional pulse height analyzer. Most of the 9 Be* decay by particle breakup. Only those that gamma decay are detected by the spectrometer counter. Thus the experiment provides a direct measurement of Γ rad /Γ. Analysis of 384 observed events gives Γ rad /Γ = (1.16 ± 0.14) X 10 -4 for the 2.43-MeV level. Combining this ratio with the value of Γ rad = 0.122 ± 0.015 eV found from inelastic electron scattering gives Γ = (1.05 ± 0.18) keV. For the 1.7-MeV level, an upper limit, Γ rad /Γ ≤ 2.4 = 10 -5 , was determined. 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): Kavanagh, Ralph William Thesis Committee: Unknown, Unknown Defense Date: 1 January 1966 Record Number: CaltechTHESIS:10192015-131229028 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:10192015-131229028 DOI: 10.7907/DAB0-KN61 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 9228 Collection: CaltechTHESIS Deposited By: INVALID USER Deposited On: 27 Oct 2015 15:58 Last Modified: 07 Mar 2024 22:44 Thesis Files Preview PDF - Final Version See Usage Policy. 12MB Repository Staff Only: item control page

ELECTROMAGNETIC DECAY OF THE 1. 7- AND 2. 43-MeV LEVELS IN 9 Be Thesis by Paul Walton Purdom, Jr. In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1966 (Submitted January 1966) ii ACKNOWLEDGMENTS I wish to thank Dr. P. A. Seeger and Dr. R. W. Kavanagh for their great help in the conception, design and execution of the experiment. I wish to thank Mr. C. D. Zaidins for his assistance with the charge state measurements and Dr. F. C. Barker for helping in the calculation of the width of the 2. 43-MeV level in 9 Be. I am also indebted to the entire staff of the Kellogg Radiation Laboratory for creating an atmosphere in which the work could be carried out. iii ABSTRACT . 9 The l. 7 - and 2. 43-MeV levels in reaction Be were populated with the 11 B(d, a,) 9 Be *by bombarding thin boron on carbon foils with l. 7 - MeV deuterons. The alpha p a rticles were analyzed in energy with a surface -barrier counter set at the unique kinematically determined angle and the recoiling 9 Be nuclei at 90° were analyzed in rigidity with a magnetic spectrometer, in energy by a surface-barrier counter at the spectrometer focus, and in velocity by the time d e lay between an alpha · and a 9 Be count. When a pulse from the spectrometer counte r was in the appropriate . delayed coincidence with a pulse from the alpha counter, the two pulses were recorded in a two-dimensional pulse height analyzer. Most of the 9 Be * decay by particle . breakup. Only those that gamma decay are detected by the spectrometer counter. provides a direct measurement of r rad/r. events gives r ra d/r =( 1. 16 ± O. 14) x 10. · 4 Thus the e x periment Analysis of 384 observed for the 2. 43-Me V level. . · Combining this ratio with the value of r · d = 0. 122 ± 0. 015 eV found ra · from inelastic electron scattering gives r 1. 7 -MeV level, an upper limit, · = (1. 05 ± O. 18) keV. For the r ra d/ f -< 2, 4 = 10 - 5 , was determined. iv. TABLE OF CONTENTS Page I. Introduction l I I. Experiment and Apparatus 2 A. B. C. D. E. III. Analysis of Results A. B. c. D. IV. Recoil Ion Detection Alpha Detection Coincidence Detection Monitoring Equipment Experimental Procedure Counting Rate Factor {N*-B*) /N 0 Efficiency Factor Population Factor a ?<. /a 0 Calculation of r d/ r ra 3 5 6 7 7 11 11 13 14 15 Discussion 17 Appendix I Boron Foils 19 Appendix II Beryllium Charge-State Ratios 24 .Appendix III Calculation of Particle and Gamma Widths for the 2. 43-MeV Level in 9Be 27 References 33 Tables 35 Figures 50 1 I. INTRODUCTION The 2. 43-MeV, Jir = 5/2- excited state of 9 Be may decay in the following ways: 9 Be * -+ 8 Be(g. s.) + n -+la. + n -+ -+ -+ Decay through the £-wave neutrons. energies of 8 8 8 Be( 2 +) + n -+ 2a + n 5 He + a -+ 2a + n 9 Be + y Be ground state is greatly inhibited. since it requires The 2. 43-MeV level of 9 Be is below the nominal Be(2+) + n and of 5 He +a, but since these are broad levels, the decay may proceed at a reduced rate through their low-energy tails. The gamma decay is predominantly Ml. Previous investigators have measured several aspects of the decay. Inelastic proton scattering experiments limit the total width of the 2. 43-MeV level to less that 1 keV (Gossett 1955). Inelastic scattering indicates a gamma width of 0. 122 ± 0. 015 eV (Ml) (Edge 1962, Barber 1960) plus O. 0026 ± O. 0001 eV (E2)(Ngoc 1963). neutron scattering shows that the level decays by way of 0.12 ± 0.05 of the time (Marion 1959). Inelastic 8 Be(g. s.) + n So far, no experiment has been able to distinguish between decays through 8 Be(2+) + n and those through 5 He + a. Henley ( 1960) has calculated the partial widths for the various particle decay modes, using the· alpha model. His calculations indicate that the total width of the 2. 43-MeV level should be about t keV and that the primary decay mode should be 9 Be * -+ 5 He +a -+ 2a + n. 2 In addition to the 5/2- level at 2. 4 MeV, most nuclear models predict a i - level around 2 or 3 MeV (Kunz 1960, Nilsson 1955, 1- Such a z Kurath 1956). level has not yet been seen in 9 Be. There have been numerous investigations carried out in attempts to decide whether there is a resonance level near 1. 7 MeV, or whether the observed effects. can be accounted for in terms of phase space and potential scattering among the particles in the final state. An extensive summary of earlier work in this regard is given by Lucas et al. (Lucas 1964) and need not be repeated here. We consider it here to be a resonance state, with Jir = i+, as suggested by comparison of the inelastic electron scattering and photoneutron cross section (Lauritsen 1965). The width of the level observed in the 11 B(d,a) reaction is 224 ± 25 keV (Kavanagh 1958), and the gamma width is 4. 5 ± O. 6 eV (El) (Ngoc 1963). The decay proceeds primarily via 8 Be(g. s,) + n, The present work was undertaken to measure t he fraction r ra d/r of electromagnetic decays of the 2, 43-MeV level; an upper limit for the branching ratio of the 1. 7-MeV level was also found. II. EXPERIMENT AND APPARATUS The number of 9 Be",c recoil ions produced in the reaction 11 B(d,a) 9 Be* was measured by counting the alpha particles from the .. ~·t reaction with energy corresponding to the particular excited state. The recoil 9 Be >:< decays after traveling about 10 -9 cm or less. If the decay occurs by any of the non-electromagnetic modes, the 9 Be recoil is de_stroyed. The number of electromagnetic decays was measured by counting the number of 9 Be recoils of the proper energy to have 3 resulted from 9 Be * -+ 9 Be + y. The branching ratio, therefore, is the ratio of the number of 9 Be recoils detected to the number of 9 Be * recoils produced. For identification, the recoil ion was analyzed in rigidity, energy and velocity. This was done by sending the recoil along an 85-cm path through a low-resolution magnetic spectrometer to a surface-barrier detector (see Fig. 1). Furthermore, delayed coincidence was required between the recoil ion and the alpha particle from the formation reac- * tion 11 B( d, a) 9 Be . The recoil nucleus was observed at 90° in the iaboratory and the alpha particle was observed at the angle then determined by kinematics. experiment. Table 1 gives the kinematics relevant to the The alpha particles were identified by energy with a surface -barrier counter having a depletion depth thin enough that protons and deuterons gave pulse heights below the region of interest. A 0. 9-µA beam of 1. 70-MeV deuterons from a Van de Graaf£ accelerator was used to bombard a thin natural-boron target evaporated on a thin backing of natural carbon. (Carbon-backed targets are able to withstand several times higher beam intensity than self-supporting boron targets.) The boron and carbon content of each target used is given in Table 2. A typical impurity composition for the targets in . 17 2 16 units of 10 atom/cm was 0, 1.1; 25 <A< 30, 0. 3; 50 <A <70, - O. l; and 166 <A< 196, 0. 01. A. - - - (See Appendix I and Figure lQ) Recoil -ion Detection The alternating-gradient spectrometer indicated in Figure 1 has been described by Martin and Kraus (1957). The acceptance solid angle is 0. 011 sr, but the entrance aperture is elliptical with the major 4 axis vertical, so that the width in the reaction plane is only 2.4°. The center of rotation of the target, the beam spot on the target, and the focus of the magnet were adjusted to coincide by bombarding a natural boron target with 1. 17 -MeV protons and moving the beam, the target chamber, and the entrance slit of the magnet to the position of maximum transmission of alpha particles from the reaction 10 B(p, a) 7 Be >:c. The reaction rate was measured by counting gamma decays of the 7 Be * • The adjustment was complicated by the interaction of several of the adjustments and by the high accuracy required (moving vertically off center by 0. 8 mm would reduce the counting rate by a factor of two). Several times during the adjustment the momentum profile of the magnet was checked. The magnet operated at full efficiency over a range of only 2. 9% in ~ p/p compared to 5. 0% obtained by Seeger ( 196 3). There were no changes in the target chamber or magnet between this experiment and Seeger's experiment. Therefore, the difference in the mo- mentum range presumably came from errors in positioning the beam spot with respect to the magnet focus which permitted some particles in the momentum range to hit the sides of the magnet. however, was adequate for the recoil-ion detection. The range, The magnetic field is measured by a torsion-balance fluxmeter, the current setting of which is inversely proportional to the rigidity. The detector at the magnetic focus was an 11. 4-mm circular gold- silicon surface - barrier detector with a counting area defined by a 3. 2-mm slit. The pulse from the detector was amplified (as shown i..n the block diagram, Fig. 1) by a fast - amplifier system, clipped to 20-nsec width by a shorted length of 93 n cable, and fed to both a co- 5 incidence mixer and to the lower beam of a Tektronix type 555 dualbeam oscilloscope, used for checking the adjustment of various circuits. The pulse from the detector also went through a 1000 n resistor to a low-noise integrating preamp (Tennelec Model lOOA). The signal was further amplified and stored on the horizontal side of a Nuclear Data two-dimensfonal pulse-height analyzer. A typical spec- trum is shown in Fig. 2, corresponding to a magnet current setting of EM/Z 2 . =energy X mass/( charge) 2 = 4. 46 MeV. Particle groups with different values of E and therefore different values of M/Z rated on this spectrum. 2 are sepa- Figure 2 shows peaks for a + and a ++ ions. 'rhe positions where peaks from il B ++ and 9 Be ++ would appear with . longer runs are also shown. B. Alpha D e tection The chamber used in the experiment permits continuous vari- ation of the alpha angle, ea . A 1-mm X 5-mm. slit, .16 mm from th~ target,defines the solid angle of the alpha counter, a 6-mm gold- silicon surface - barrier detector. X 10-mm The long axes of the slit and counter are vertical. The fast amplifiers for the alpha channel (shown in Fig. 1) are similar to those in the recoil-ion channel. A variable delay, howeve r, has been added to delay the alpha pulse by the flight time required for the 9 Be recoil ion. The delay consisted of 77. 7 m of RGl 14/U cable, which could be switch-selected from 0 to 255 units of 30. 5 cm. 30. 5-cm unit of cable corresponds to a delay of 1. 2 nsec . Each The output of the fast amplifiers was fed to a coincidence mixer, the upper-beam input of the oscilloscope , and a biased amplifier. 6 Conventional slow electronics could not be used for the chamber-counter pulses since the intense flux of elastically scattered deuterons in tre chamber counter would give an unacceptably high rate of pile-up pulses. Hence the fast pulses were fed to a biased amplifier set to pass only pulses higher than the deuteron pulses. The biased amplifier also stretched the pulses for storing on the vertical side of the two-dimensional pulse -height analyzer. For identification of the various particle groups, the chamber counter spectrum was recorded with slow electronics (see Fig . 3). The groups were then identified by their energy (compared to a ThB alpha source). The counter bias was set such that protons with energy greater than 3. 2 MeV penetrated the depletion layer. After the various groups were identified, the biased amplifier was adjusted to pass pulses above about 2 or 3 MeV and the twodimensional analyzer was adjusted to record pulses between about 4 MeV and 8 MeV (see Fig. 4 for such a spectrum}. C. Coincidence Detection . A tunnel-diode coincidence mixer was used in this experiment. A tunnel-diode at each input of the mixer, also served as a discriminator, set so that input pulses of half a volt were sufficient to trigger the diode from the low voltage to the high voltage portion of the charac teristic curve . The ion and alpha pulses were clipped to 20 nsec. For a coincidence output, the ion and delayed alpha pulses had to occur within 20 nsec (for 0. 5-volt pulses) to 40 nsec (for pulses above 0. 7 volt). Both the 9 Be recoil ions and chamber alpha particles produced pulses of about one volt. 7 The fast rising coincidence output triggered the oscilloscope, and the "+ gate out" signal from the oscilloscope opened the coincidence gates of the multi-channel analyzer. When the coincidence gates were open, the two-dimensional analyzer stored the heights of the ion and alpha pulses. D. Monitoring Equipment An oscilloscope and five scalers monitored the operation of the electronics. The oscilloscope was used for making quick checks of the alpha and ion non-coincident spectra, to check amplifier gains and bias settings, and to check the coincidence circuit. The scalers counted the number of ion pulses through the slow electronics, the number of alpha pulses above about 6. 5 MeV, the number of pulses firing the ion side of the coincidence mixer, the number of pulses that fired the alpha side, and the number of coincidence pulses. E. Experimental Procedure The sub scripts 0, l, and 2 will refer to quantities pertaining to reaction 11 B{d,a) 9 Be where the 9 Be is in the ground state, 1. 7-MeV level, and 2. 43-Me V level respectively. placed by either subscript 1 or 2. The subscript * can be re - It is used to avoid repeating equations that hold for both the 1. 7 - and 2. 43-MeV levels. After positive identification of the prominent particle groups had been made on the basis of the non-coincident spectra (Figs. 2 and 4); the spectrometer current, the alpha-particle angle and delay were . varied to ·obtain the maximum counting rate of 9 Be +++ -a 0 coincidences. The counting rates were usually normalized to 100 µ.C of beam on the target. The maximum 9 Be ++.+- a o coincidence rate is called N , oc0 8 curring at the fluxmeter setting I , alpha angle e 0 The number N 0 0 , and the delay .e 0 • provides a measure of the coincidence efficiency which depends on the target thickness and on the slit defining the alpha counter acceptance. After optimizing, the thre.e parameters were changed to the appropriate values for 9 Be ++ - a 1 , 9 Be ++ - a 2 , or 9 Be ++++ - a 2 events as follows: 9B e ++ - a Fluxmeter curr·ent 0. 744 I Alpha delay j, 0 0 + 7 units (2. 14 m) e 0 - 2. 1° Alpha angle 9B ++ e - a2 9 Be ++++ 0.783 I 1. 566 I 1 j, 0 0 + 16 units (4. 87 . m) e0 - 3. 1° - a2 0 .e 0 + 16 units (4. 87 m) e 0 - 3. 1° The counting rate for any of these three groups of settings is called N*. The change of delay and alpha angle is relatively small. The linearity of the fluxmeter was checked to 0. 6% by observing vario,u s reaction groups from 1 - 6 Me V. Runs of 2 to 4 hours with O. 9-µA beam intensity were made. The alpha energy and ion energy of each pair of coincidence pulses were · stored in the two:..dimensional pulse-height analyzer. each run consisted of N 0 , The results of and of N*, determined from the analyzer out- put and from the integrated beam. Figures 5 and SA show the two -dimensional spectrum for a typical 9 Be ++ - a 2 run on target No. 1 (see Table 2). The most promi- nent group, with an alpha energy of 5. 3 MeV and ion energy of 1. 5 MeV, . llB++ - a co1nc1 . .dences f rom 13 C(d., a ) 11 B ( t h e peak f or t h e 11 B.ions is is shifted down from 1. 6 MeV, probably because of energy loss in the boron layer of the target). The long ridge with an ion energy of 1. 1 MeV .9 + is due to a, _ - a, coincidences from 10 . 11 B( d, a,) ---> 3a. and B( d,a,) ~ 3 a, + n. 11 B( d, a, ) 9 Be++, with alpha 2 11 energy 5. 3 MeV and ion energy 2. 0 MeV, lies just above the B recoil The small peak from the de sired reaction group. . b e t ween t h. e ll B reco1· 1 an d 9 B e reco1 , ·1 Th e separation groups from a longer run ~n target No. 1 is shown in Fig. 7, where the coincidences with alpha energy in the a, function of ion energy. 2 peak are summed and plotted as a Target No. l had the highest C to B ratio, so the separation of the peaks was even better for the other targets, The group in Fig. 5 with ion energy 2. 0 MeV and alpha energy 7. 0 MeV results from the reaction . 11 B(d,a, ) 9 Be ++where the 9 Be ion has lost 0 enough energy .in the target to go through the magnet. The separation between these stragglers and the desired group is shown in Fig. 8, for which seven runs totaling 21, 540 µC have been summed. The tail of the straggler peak results in a small background under the 9 Be - cx, 2 peak. , A measure of this background was made by setting the magnet for 2. 19 MeV 9 Be ++ions and counting ions near that energy in coincidence with various alpha energies (see Fig. 9). · The L7 - MeV l e vel in 9 Be should have contributed no more than one count to this run ( e stimated by multiplying the number· if 9 Be * (1. 7 -MeV level) produced at an angl e where they could enter the magnet times the branching ratio for g amma decay of the 1. 7 -MeV level; see Sections III and IV). Finally, ther e is a small peak with ion energy 2. 7 MeV and alpha energy 7. 0 MeV. This group is . 11 9 .. 9 presumed to be from B(d,a, ) Be with the Be ion undergoing chargeo . exchange collisions with gas molecules near the center of the magnet . that changed the charge of the 9 Be ion from++ to +++. 10 Figures 6 and 6A show the two -dimensional spectrum for the 11 B( d, a ) 9 Be++. 1 13 11 . Figure 6 is quite similar to Fig. 5 except the C(d, a) B group is sum of six runs totaling 34, 040µC with settings for quite weak and no (or perhaps one) count is in the The 11 11 B(d, a ) 9 Be ++group. 1 B(d,a ) 9 Be++++ runs are also similar to Fig. 5 except 2 the ridge of alpha coincidences is much stronger. The number of counts obtained and the length of running for the coincidence measurements is given in Table 3. 11 III. The ratio of r ANALYSIS OF RESULTS ra d/r is the ratio of the rate of 9 Be * surviving particle breakup (and hence observable) to the total rate of forming 9 Be *(which is the total rate of producing a* in the reaction). If B * is the background rate and €* is the efficiency of the system for detecting excited-state coincidences , then 9 r rad _ . (rate of observed Be-a* coincidences)-(background rate) ---r--~------------------€*--x--(~r-a_t_e __o~f~a--*~)---------------------( 1) = The efficiency € 0 for detecting ground state coincidences can be found directly by experiment, since in this case all recoils survive: € = o (rate of observed 9 Be-a 0 coincidences) rate of a 0 N = a0 ( 2) 0 By combing eqs. (1) and (2), we have r rad ( 3) r This equation requires the ratio of coincidences for the excited state to those for the ground state, the r a t i o of the alpha particl es associated with the two states, and the ratio of the detection efficiencies for the two states. A. Counting Rate Factor (N:.:. -B*) /N 0 The coincidence rates N * were measured during each run as described in Section II. The background rate B* is assumed proportional 12 to the number of counts in the straggler peak (see Section IIE and Figure 9 for the method of backgrouoo measurement). For the 2. 43- MeV state, the background correction was less than 1% except for the short run on the thickest target, No. 2, for which it was 45%. . at the beginning and end of each run, N average value was used. 0 N 0 0 was me a sured, and the The relative error for (N ,!< -B,:c)/N [ 1 /(N* expected + B ,:,) + (AN /N ) of N 0 2 0 .!. a where AN ] 0 was' not measured at the end of the run. 0 0 was then In several cases, In these cases , 30% was This is about 1± times the average value of AN /N 0 found on runs where N the run. 0 is half the difference measured at the beginning and end of the run. used for AN /N • Usually 0 0 was measured at both the beginning and end of It is presumed that AN /N 0 0 was so large because of changes in target wrinkling that affected counting efficiency. For about 5% of the runs, N 0 was measured by a scaler rather than with the two-dimensional analyzer. corrected by the ratio of N runs on the target where N correction changed N error of N • 0 0 0 0 In these cases, N 0 was (scaler) /N (analyzer) averaged over the 0 was measured by the analyzer. This by about 10% and contributed about 10% to the The difference between N (scaler) and N (analyzer) 0 0 came mainly from counts in the tail (which were counted by the scaler) that were not in the rectangle over which the peak was summed (when counted with the pulse -0.eight analyzer). For about 10% of the runs, the angle a 2 was not set correctly. The alpha acceptance angle was 3. 6°, and the error in the alpha angle . 0 was never more than 1. 2 • Since the coincidence rate for the ground state measured over a range of 6° each day, the effect of this small error in the alpha angle on efficiency was known. The correction to 13 the counting rate in these cases was about 10% with an error of about 6%. B. Efficiency Factor The efficiency factor = E 0 IE •.....-• was broken into two factors (~j(::) .• Here , t* is the fraction of the detected excited- state alpha particles whose accompanying 9 Be >;c recoils have momentum within the spectro- meter acceptance window; and similarly, t . 0 is the .fraction of the ground-state group of 9 Be recoils within the spectrometer window, associated with detected alpha particles. The fraction of excited-state recoil ions in the charge state observed (2+ or 4+) is c*, and the fraction of ground state recoil ions in the charge state observed ( 3+) is c . 0 To determine the charge state ratio of Be ions emerging from a boron foil, an elastic scattering experiment was done on a layer of boron and a layer of Be. foils having 9 Be ions from 9 Be(a, 9 Be)a emerg- ing through the B layer were observed with a 61-cm double-focusing magnetic spectrometer. The charge-state ratios from these measure- ments at 1. 78 and 2. 52 MeV is given in Table 4. ( 1965) Tombrello and Bacher have measured the charge-state ratios at higher energies. Table 4 also gives the values of the charge-state ratios for 1. 98, 2. 19, and 2. 7 3 MeV, interpolated by fitting Dmitriev functions to the data of this experiment and those of Tombrello and Bacher (Zaide ns 1965). error is estimated to be about 0. 02 on each point. More information on the charge-state measurements is given in Appendix II. The 14 The magnet efficiency as a function of rigidity was measured by observing 9 Be +++ - a; coincidences and varying magnet current. 0 . efficiency profile was trape.zoidal. The It had a steep rise on the low energy side, was 2, 9% wide on the top, and had a linear tail 2.1 % wide on the high energy side. When the momentum width of the recoil group was greater than 2. 9%, a correction was required to the counting efficiency. One source of momentum broadening was energy loss due to finite target thickness, which was measured for each target by elastic scattering. u .s ing the mean square charge of Be ions from Table 4, .the energy loss of the ions was calculated (see Table 2) from the relation that dE/dx will be 2 (Z ) times dE/dx for protons of the same velocity. Another source of momentum .width was kinematical or dE/d9 broadening, including the extra width caused by deflection from gamma emission of the recoil ions into the magnet's geometrical aperture. The final source was the longitudinal component of the momentum of the emitted gamma ray. Isotropic distribution of the gamma ray was assumed. The three distributions were folded together and integrated with the magnet's efficiency profile. t*/t 0 With all except target 2 (the thickest) the correction was less than 0.1% (see Table 5). If, due to wrinkling, the effec- tive target thickness had been twice the amount determined from the elastic scattering, . the the correction. t>:Jt 2o/o (except for target 2). 0 would have been less than However, measurements on the profile shape of the ground-state group showed the width to. be equal to the assumed width to within 50%. For infinite target thickness (or the worst possible case of wrinkling), t*/t 0 would be 1. 4. For the 1. 7 -MeV level, no correction was needed since all runs were on the thinnest target, No. 5. 14a C. Population Factor a,*/a, 0 To know the rate of producing recoil ions, the values of the 0 ratios Oz( 66 .4) to a. 0 ( 6 9.5) 0 0 0 • and a. ( 6 7.4) to a, ( 6 9.5) were required. 1 Figure 4 shows one of .the alpha spectra that 0 was used for measuring. 15 the ratios . . The ratio of counts in the a a 0 2 peak at 66. 4° to counts in the peak at 69. 5° was calculated with a least-square procedure which adjusted the height of three pairs of peaks c e ntered on a , a , the 2 1 next lower a peak {see Fig. 4) , and the height of a constant background to give the best fit to the spectrum from about 5 MeV to 6. 5 MeV. a 0 The peak from spectra at 69 . 5° {shifted down in energy an integer number of channels) were used to fit the three peaks. The a 0 peaks were used in pairs {one of which was shifted one more cha nnel than the other) to simulate the effect of shifting down a fractional number of channels. The ratio of counts in the a 1 peak at 67. 4° to counts in the a 69. 5° was calculated in a similar manner. 0 peak at The following values were found: a {66 . 4°) 2 a (69.5°) = 0. 97 ::l: 0. 07 ' 0 a {67. 4°) 1 a (69. 5°) = 0.15±0.02. 0 D. Calculations of r d/r , ra With all the terms of Eq. { 3) now m e asured or calculated, the data were combine d in the follo wing way. For al. l runs on a charge state, {N*-B,.<) /N 0 was calculated and corrected by th e thickness factor • It is permissible to correct by t 0 /t* before aver a ging (N.>;< -BJ>;< )/N 0 for all the runs on a target only because the error of t 0 It* was much less than the final. error of the experiment for all targets except target No. 2. The procedure is correct for target No. · 2 because only one run was made on it. The error in t 0 /t* was assumed to b e 1 - t * /t 0 • 16 These numbers were then averaged with weighing factors I/error for each term. 2 This average value of (N*-B*)t0 /N t* was corrected 0 by 1 I c*, one piece of the charge state factor. For the measurement on the 2. 43-MeV state (where measurements were made on two charge states) the values for the two charge states were now averaged with 2 weighing factors 1 / error . Finally, the result was multiplied by the population factor a 0 I a* and the other piece of the charge -state factor c . 0 The immediate results of each run on the 2. 43 MeV level are given in Table 6. Table 7 gives the intermediate calculations for the 2. 43-MeV level. Table 8 gives the intermediate calculations for the 1. 7 -Me V level. The results of the calculations are: (2. 43-MeV state) rrad -r= (1.1 6 ±0.14)xlO -4 ( 1. 7-MeV state) r rad < 2. 4 x 10 -5 . r 17 IV. The limit of r ra DISCUSSION d/r < 2. 4 x 10 - 5 ( 6 3% confidence) measured for the 1. 7-MeV level agrees with the value (2. 0 ± O. 3) x 10 -5 obtained by dividing the gamma width of 4. 5 ± O. 6 eV (Ngoc 1963) by the total width of 224 ± 25 keV (Kavanagh 1958). The branching ratio r ra dIr = (1. l 6 ± 0. 14) x 10 -4 obtained for the 2. 43-MeV 5/2- level may be combined with the gamma width of the level to obtain the total width. Inelastic electron scattering at 40 MeV indicates that the gamma width is O. 122 ± 0. 015 eV (Edge 1962, Barber 1960). Dividing this value by the branching ratio gives a total width of 1. 05 ± 0. 18 keV . The calculation of the gamma width from the inelastic electron scattering assumes that the 5/2- level is the only level in 9 Be near 2.43 MeV (within about 50 keV). On the other hand, the 1/2- level predicted by various models (Kunz 1960, Nilsson 1955, Kurath 1956) may be near the 5 / 2 - level. This level has not been seen but should show up in inelastic electron scattering. about 1/2 MeV. r ra It is expected to have a total width of Since the 1/2- level wouid have a very small value for 6 11 d/r (about 10- ) and since it has not been seen in B(d,a), it could not affect the measurement of r than 5%. ra d/r for the 2. 43-MeV level by more It would, however, lower the gamma width calculated from electron scattering by about 40%, and therefore lower the value we calculate for the total width. The Nilsson model predicts the gamma width of the 5/2- level to be 0 . 153 eV (see Appendix III), and intermediate coupling models predict th.e gamma width to be about O. 087 eV (Cohen 1965, Barker 1965). 18 This latter value for the gamma width combined with our value for r ra d/r gives a total width of 0. 7 5 keV. The value r = 1. 05. ± 0 . 18 keV obtained from the measured gamma width divided by the branching ratio is in agreement with the measured upper limit, r < 1 keV (Gossett 1955). The total width is larger than the value 1/4 keV predicted by the alpha model (Henley 1960) (see Appendix III). 19 APPENDIX I BORON FOILS The experiment used thin natural boron foils. The foils were required to pass 2-MeV 9 Be ions at 45° with an energy loss of no ·more than 3% in order that most of the 9 Be recoils accepted at the entrance of the spectrometer would be counted. Also, the foils were required to be thin enough that straggler events (see Section II, E, page 9) did not interfere with the experiment The foils were, however, made about as thick as the above considerations permitted, to maximize the counting rate. Targets that were 0. 2-0. 5 x 10 18 at/ cm 2 thick were best for measurements on the 2. 43-MeV level, while 0. 2 x 10 18 at/cm 2 was the best thi:ckness for the 1. 7 -MeV level. The procedure used to make thin boron foils by evaporating boron from a tantalum boat heated by electrical resistance is given below. The changes in procedure for making stronger foils with both a layer of carbon and a layer of boron follows. Finally, the boron-beryllium foils used for the Be charge state measurements are mentioned. Select several clean microscope slides and brush any dust off the slide with a wad of fresh cotton. slide (about 100 mg of BaC1 BaC1 2 ation. 2 Vacuum evaporate BaC1 in a boat 30 cm from the slide). 2 onto the If the is not dry, preheat it to 300°C in air before the vacuum evapor This will greatly reduce the amount of BaC1 2 that hops out of the boat during the evaporation. Now wipe the BaC1 2 out of the bell jar. pressure down during the boron evaporation. This will help keep the. Then mount a new, clean tantalum boat on the bell jar electrodes with copper hardware (a new 20 tungsten boat may also be used; experience in using both tantalum and tungsten boats for boron evaporation indicates that either type boat works as well as the other but that the tantalum boat is easier to make). The boat should be O. 25 mm by 8. 5 mm by 60 mm and depressed in the center so the boron won't flow out. From 50 to 100 mg of boron should be piled along the center of the boat with strips 1 to 2 mm wide along each edge of the boat left free of boron. Leaving the strips free of boron helps prevent the boat from breaking before the evaporation is complete. Place the slides with the BaC1 2 layer 10 cm above the boat and re-evacuate the bell jar. Shield the microscope slides from the boat. and heat the boat slowly to a dull red heat, driving the water off the boron. Then raise the temperature to a bright yellow white for two minutes to drive off additional impurities. five minutes. It is best to then let the boat cool for Finally, heat the boat to the evaporating temperature over a period of about one minute. The evaporating temperature produces a bright white light similar in color to a new 500-watt light bulb. At the evaporating temperature rapid eddies can be seen in the liquid boron (use dark goggles to look). As the boron alloys into the tantalum, it is necessary to continue raising the heating voltage in order to maintain the boat temperature. The evaporation should continue until enough or all of the unalloyed boron has been evaporated. When a ll of the unalloyed boron has evaporated, the color of the boat becomes brighter, bluer and more uniform. To minimize the chance of boat breakage, the evaporation should be completed fairly rapidly, with the boat remaining at the evaporation t e mperature no longer than two minutes. Once the slides have cooled they may be removed from the bell jar and stored until one wants to float the foils from the slides. No 21 difference in physical properties or chemica l composition was noticed in foils stored on the slides for up to six months. To float the foils from a slide, scribe lines dividing the foil into squares ( 1. 3 cm squares were used). Support .the slide at 10° in a dish and slowly syphon water into the dish. 1£ cracks appear in the foils as they float off, reduce the rate of rise of the water level. 1£ the foils do not float off with the water level rising at 2 mm/hr, it is best to make a new batch of foils. Once all the foils have floated off a slide, each foil may be pulled vertically out of the water with a clean tantalum holder. If the foil does not break upon drying, it will probably last until it receives some rough treatment. Perhaps one-quarter of the boron foils may be expected to survive the floating operation. The composition of the foils was measured by counting elastically scattered 1-MeV protons at elab = 150° with the 27-cm double-focusing spectrometer . 2 For this spectrometer the number of atoms/cm , A, is .determined by the number of counts from 9. 2811C of beam, N q , at r fluxmeter current I and by the elastic-scattering cross-section dtT/d n . The formula given by Seeger ( 196 3) is · A = 3. 43~· 10 dn 181 N (I) _q_ dI. I The following elastic-scattering cross sections were used: 10 B _: B 11 70 mb/ster (Overle y 1961) : 80 mb/ster (Tautfest 1955) c 12 : 188 mb/ster (Jackson 1953) 22 109 mb/ster (Tautfest 1955) 154 mb/ster (Eppling 1953) The Rutherford cross-section was used above mass 16, variations (in units of 10 17 The following 2 at/ cm ) of composion were found from mea- surements on 12 boron and carbon-boron foils : B: 5 12 C: 0.7 - 0.8 no carbon added C: 3 - 5 carbon layer added 0: 0.6 25 < A < 30 (presumably Si) : 50 < A < 70 (presuma bly F e ): 0.05 - o. 2 166 < A < 196 (presumably Ta) : 0 . 01 - 0 . 02. - 1. 8 0.02 - o. 3 No difference in impurity content was noted between the boron and carbonboron foils . Some foils may have shown a trace (less than 10 unless noted) of masses near the following masses : F, Na, S, Cl, and Ba. -15 N ( 5 x lo - at/cm 15 2 a t/cm 2 ), The composition and proton spectrum from one boron foil are shown in Fig. 10. Since the variation in the various im- purities w as too small to affect the branching ratio~ a surement, only the boron and carbon content of the foils used in the e x periment was measured. Most of the boron foils w ould break at beam currents of 0. 1 to 0. 2 µA of 1 M e V protons. The strength of foils with a carbon layer is much grea ter . Such targets are e a sier to float and will withsta nd 1-2 µA of 1-Me V protons for an 1-5-mm by 3-mm beam spot. · the floating procedure. At least 80% of them will survive 23 Targets with a carbon layer are made like those without one, except a layer of carbon is added either before or after the boron evaporation. The carbon should be deposited from a blue arc between spectroscopically pure carbon electrodes. If the carbon-boron foils are mounted on clean target holders, they will often curl up and roll off at the slightest touch. With a little finger grease on the target holder, the foils are somewhat harder to mount, but once dry they stick to the holder better. Foils were also .made with a layer of beryllium over a boron layer. These foils were made by evaporating beryllium onto the boron and then floating. The resulting foils were quite weak and would with- stand about a 30-nA beam of 10-MeV alphas for an 1. 5 mm by 3-mm · beam spot. 24 Appendix II BERYLLIUM CHARGE-STA TE RATIOS Since only two of the charge states of the 9 Be recoils were observed during the branching-ratio measurement, it was necessary to measure the probability of producing Be ions in these two charge states. This was done by bombarding beryllium-boron foils with 7. 07 -Mev· and 9. 74-MeV alpha particles from the C. I. T. tandem and counting the 9 Be recoils from the reaction 9 Be(a, 9 Be) at 55° with the 16-counter array in the 61 cm spectrometer. The target was positioned so that the Be recoils passed through the boron layer before going into the magnet. Measurements were made with recoil energies of 1. 78 MeV and 2. 52 MeV. The ions were produced at 1.98 MeV and 2. 73 MeV, but some energy was lost in the boron layer of the target. charge-state Usually, for each several runs were made that completely covered the recoil peak (see Figs. 11 and 12). Measurements were not made; however , fo·r the 1 + charge-state at 2. 52 MeV or the lower energy end of the 4 + charge-state peak at 1. 78 MeV because of diffi<tulty in operating the fluxmeter of the magnet. The combination of rigidity measurement by the magnetic spectrometer and energy measurement by the solid-state counters in the array permitted separation of the l+, 2+, and 4+ 9 Be recoils from other reaction products. The 3 + recoils, however, could not be separated from protons and alphas. From observations made a short distance either side of the 3+ recoil peak, it appeared that the peak sat on a constant background of about 5% of the height of the peak. background probably consisted of alpha stragglers. This is For analyzing the data, a method that compared the shapes of the various recoil peaks was used. The recoil peaks should all have . the same shape except for variations caused by such things as counting statistics, backgrounds from other reactions (important for the 3+ charge state), and erratic counter operation (it appears that a few of the points are lower than one would expect from statistics). The numbers A .. and B . . were adjusted to give the best least-squares fit lJ lJ to the relations Ni (E) ~ A .. N . (E) + B .. lJ (i and j run J lJ over all the charge states observed). The number of counts observed at recoil energy E for chargestate i times the counter efficiency factor is N. ( E). 1 The same quantity for charge state j is N. (E). The counter efficiency corrections {up to J ± 10%), measured by Lew Cocke (1964) are given in Table 9. The ratio of ions in charge-state i to those in charge-state j is then A .. lJ and the difference in any constant background unde r the two peaks is B... lJ A nonconstant background will increase the error calculated for A . . and B . . above that expected from counting statistics. lJ lJ obtained for ·A . . are given in Table 10. lJ The values The B .. were all zero except lJ when i or j was 3 . The fraction R. of ions in charge state i can be written as 1 R.1 = r. /Li r. , j .1 J 1 ri = ~ A .. j Jl The second equation gives the expected value of the charge-state ratio 26 when there is no error in the A . .. Jl The first equation requires that probability that the ion in one of the charge-states be one. The ~r. over 1 all charge states may not be exactly one when there are errors in the original data because in this case the· least-squares procedure does not, in general, give A .. = 1 /A... lJ . Jl This defect of the least-squares procedure is not serious so long as the errors are not large. The fraction of ions in each charge-state, along with the calculated error, is given in Table 4. The values for the charge-state ratios agree with those obtained by dividing the counts in each peak (after subtracting a constant background for the 3+ charge-state) by the number of counts in all the peaks. This simple procedure, however, permits calculation only of the errors from counting statistics, which are only about 0. 3%. Therefore, the more complicated method was used since it gave a better indication of the error in the experiment. 27 Appendix III CALCULATION OF PARTICLE AND GAMMA WIDTHS FOR THE 2. 43-MeV LEVEL IN 9 Be The gamma width of the 2. 43-MeV level of lated from the Nilsson model. 9 . Be may be calcu- First one uses the ground-state magnetic moment µ to calculate the g-value, gR' associated with the collective angular momentum, with the formula µ [st + J = J + 1 J gR + ! (gs - g l) 7 (a;, K- i -a~. K + t)] (Preston 1962}. For the calculation we use the ground-state spin, J= 3/2, the odd neutron orbital g-factor, gt= 0 , the neutron g-factor, gs =-3. 8263 (Preston 1962), and the Nilsson 9 Be wave function, at a 2 = 0 (Nilsson 1955) . Using µ 9 Be 312 _ 112 = 1 and all other 1. 177 ± 0. 001 nm (Preston 1962) and solving for gR we get gR = -0. 048 • The gamma width is given by r = T(Ml) = -169ir- k3 µoz (gK - gR)2 K2 (J-K)(J+K) J (2J + 1) (Preston 1962). Here T(Ml) is the transition probability per unit tim e for Ml d ecay, k = E ffic, the gamma dec ay energy divided b y -11.c, µ magneton, gK 0 is the nuclear = gt + iK (gs - gt) ( '7 (a2t,K -( i"> -az t,K + (!>) ( = -1. 27 54 for 9 Be), K = 3/2, the projection o f the total angular = 5/2, the total angular Using these values the formula gives r = O. 153 eV. 'Y momentum on the intrinsic nuclear axis, and J momentum. 28 The 2. 43-MeV level of 9 Be can decay into two alpha particles plus a neutron in the following ways: 8 9 Be* . . Be (g. s.) + n 8 Be(2+) 5 He _. 2a + n _. 2a + n +n _. 2a + n +a . 8 The decay through Be· (g. s.) + n requires £-wave neutrons . This decay is forbidden in the shell model but is permitted in the Nilsson m~del and in the alpha model (Henley 1960). Marion ( 1959) · has measured the branching ratio for tllis decay. and .finds that it ac 'counts for 0. 12 ± 0. 05 of the decay. The first excited sta·te of 8 Be + n .is 2. 1 MeV above the 2. 43-MeV level in 9 Be, but since the level is 1. 45-MeV wide, the decay may proceed through the tail of the level. The ground state of of 9 Be, and is He +a is 100 keV above the 2. 43-MeV level 577-keV wide, the tail of this level. (1965). 5 so the decay may also proceed through The energies and widths are from Lauritsen The decay through 8 + Be (2 } + n and if neutron recoil effects are neglected. 5 He +a become identical It is not safe, therefore, to consider these two decay modes as independent unless one of them gives a much larger decay probability than the other (Henley 1960). The partial width for .e ach decay mode can be estimated from E r = Jo avail 2y Joo - where E pt p (E) (E} p (E . - E} dE ava11 dE 00 . is the energy to go from the initial level to the final ava11 products, 1t (:8) is the penetrability of the first particle emitted (with angular momentum t and energy E, and p (E} is the density of s tates 29 8 5 available in the interm.e diate nucleus ( Be or He). The reduced width 2 'Y , can be expressed as 'Y 3 ii 2 2 2 = 2. -mR -:-zse sp where mis the reduced mass of the emitted particle, R is the interaction radius, s is the spectroscopic factor, and e 2 sp is the dimension- less reduced width. The spectroscopic factor for a nucleon or alpha decay of a pshell nucleus is given by 2 s ex(TJMT, TJMT) \ = a sp x L (a([A.]TSL) a ([X)TSL) x [A.]SL [X)SL (- )J s - s + x U(Ls x s, JS) ( lpn[A.)TSL I} U(SLJL, x L) x lpn[X)TSL, lpn - ii)) (Barker 1965, Lane 1960) Symbols with no bars refer to the initial nucleus, symbols with one · bar refer to the intermediate nucleus, and symbols with two bars refer to the nucleon or alpha particle. The number of p-shell nucleons is n, T is the isotopic spin, J is the total angular momentum, MT is projection of the isotopic spin ( (N - Z) /2 a is the coefficient in the 30 . LS expansion of the initial nucleus, [A.], L, Sare the partition, orbital angular momentum, and spin of a state S in which the initial nucleus is expanded, the U -coefficient is given in Rotenberg ( 1959), and the fractional parentage coefficient. ( I} ) is For Barker Is ( 1965) wave functions 8 s(9Be ~ Be (2+) + n) = 1.11. In the LS limit (where 11r <i~i) = 9 4 5 1 1 5 4 4 Be 1jr(ls lp [41] ZZ 2, z:)and1Jr (020) 1jr(ls lp [4]002,8 Be 5 9 2.)) s = 1. 2.5. The LS limit gives s( Be ~ He + a) = 7 /9.. Barker's = wave functions do not permit calculations of the decay through 8 Be (g.s.). Calculation of e 2 requires evaluation of the nuclear wave sp function at the nuclear surface. Since the simple models with infinite well depths do not provide a good value for e 2 , it is usually treated sp as a parameter and adjusted to fit the known decay widths. ( 1965) has fit many decays of light nuclei with e 2 sp Barker (p wave nucleon) 2 . 1/3 = 0. 3 and esp (£-wave alpha} = 0. 4 using 1. 45 (A + A 2 1/3) x 10 -13 1 cm as an interaction radius where A 1 and A 2 are the mass numbers of the two decay products. For the density of states factor one could use p (E) = sin 2 (o.t+cp.t) where 0,1, is the nuclear phase shift and <1>.e is the negative of the hard-sphere phase shift (for scattering of the two decay products of the intermediate level), except that the a - ad-wave and a-n P 312 phase shifts have not been measured at the energies important to this decay. energies o J, approaches At these low -cp.£ and therefore it is difficult to make a useful measurement of o.t + <Pr One can, however, fit the data at higher energies with a single-level formula. One then has (Barker 1962) 31 rt (E) p (E) = where r .£ (E) = 2')'.£ P.e (E) is the width of the intermediate level, .6.(E) is the coulomb level shift, and EJ, + A J, (Er) able for decay of the intermediate level. = Er is the energy avail- Since the 2. 43-MeV level of 9 Be is below the resonant energy for decay through both 5 He + n and 8 + Be ( 2 ) + n, the density of states function is quite sensitive to its parameters. Also, there are no phase-shift data in the relevant energy range to compare with. The width of the 9 Be 2. 43-MeV level was calculated using an interaction radius in 9 Be of 1.45 x (A for 5 He +a and 4. 78 f for 8 1 13 1 3 / + A 113 ) x locm (4. 35 f Be(2+) + n) with various sets of parameters for the single level formula. The results of calculations with para- meters from phase shift data and with parameters from the average of many measurements the m ergy and width of the intermediate levels are given in Table 11. For the parameters from the average values, various interaction radii for the decay of the intermediate levels were used in the calculation to show the sensitivity of the calculations to variations in this parameter. to variations of E r and r(E ) • r The calculated widths are also sensitive No reasonable variations of these parameters can raise the calculated width to the value of the measured width (1. 16 :I: 0. 14 keV). The alpha model (Henley 1960) for 9 Be interaction radii of 1. 45 (Al l/ 3 + A 2 1 3 3 / ) x l0-l cm predicts the following widths r = 7 eV, and r + Be(2 )+n The alpha-model 8 = 57 eV (see Table ). Be(g. s.) + n calculations use finite-depth nuclear wells. Henley ( 1960), therefore, 8 32 could evaluate the nuclear wave functions at the nuclear surface and did not have a parameter corresponding to e 2 . sp 33 List of References Barber, W. C., Berthold, F., Fricke, G., and Gudden, F. E. Phys. Rev. 120, 2081. Barker, F . C., and Treacy, P. B. 1960, 1962, Nuclear Phys. 38, 33. Barker, F. C. 1965, private communication. The wave functions Barker used for 9Be and 8Be will be published in Nuclear Phys. Cocke, C. L . 1964, private communication. Cohen, S. and Kurath, D. 1965 (to be published}. Dodder, D. C. and Gammel, J. L. 1952, Phys. Rev. 88, 522. Edge, R. D. and Peterson, G. A. 1962, Phys. Rev. 128, 2750. Eppling, F. J., et al. 1953, Phys. Rev. i!_, 438A. Gossett, C.R., Phillips, G. C., Schiffer, J.P., and Windham, l?. M. 1955, Phys. Rev. 100, 20 3. Henley, E.M. and Kunz , P.D. Jackson, H. L., et al. 1960, Phys. Rev. 118, 248. 1953, Phys. Rev. 89, 365. Kavanagh, R. W. and Barnes, C.A. 1958, Phys. Rev. 112, 503, and private communication. A re-examination of the original data has revealed a calculation error affecting the values quoted for the widths of the l. 7 5- and 3. 02-MeV states: The correct values are r 1. 5 224 ± 25 keV and r . 02 257 ± 25 keV. 7 3 = = Kunz, P. D. 1960, Ann. Phys . .!..!.• 275. Kurath, D. 1956, Phys. Rev. 10 l, 216. Lane, A. M. 1960 , Rev. Mod. Phys. 32 , 519 . Lauritsen, T. and Ajzenberg-Selove. Phys}. 1965 (to be published in Nuclear Lucas, B. T., Cosper, S. W., and Johnson, 0. E. 133, B963. Marion, J.B., Levin, J. S., and Granberg, L. 1584. 1964, Phys. Rev. 1959, Phys. Rev. 114, Martin, H.J. and Kraus, A.A. 1957, Rev. Sci. Inst, 28, 175; also, Martin, H.J. 1956, Thesis, California Instituteof Technology. 34 Nilsson, S. G. 1955, Kg. Dan. Vid. Selsk. Mat. Fys. Medd. 29, No. 16. Ngoc, H. N., Hors, M., and Perez y Jorba, J. 42, 62. Overley, J.C. 1963, Nuclear Phys. 1961, Thesis, California Institute of Technology. Preston, M.A. 1962 , Theor! of the Nucleus, Addison-Wesley, Palo Alto, pp. 62 , 15 ;-32:'9,""" 340. Renkin , J . H. 1963, Thesis , California Institute of Technology. Rotenberg , M., Bivins , R., Metropolis, N., Wooten, J. K ., Jr. 1959 , The 3-j and 6-j Symbols, the Technology Press, Cambridge, Mass . Russell, J . L. , Jr. , Phillips, G. C. , and Reich, C. W. Rev. 104, 135 . Seeger , P.A. 1963, The sis , California Institute of Technology. Tautfest, G. W. and Rubin, S. 1956 , Phys. Rev. 103, 196. Tombrello , T.A. and Bacher, A. D. Zaidins , C. S. 1956 , Phys . 1965 (to be published). 1965 (to be published in Ref. 21). 35 Table 1 Kinematics (S.ee Pg. 3) (Ed = 1. 7 MeV) Recoil Ion Ion Recoil Energy (MeV) .6.t (n sec) for 85 cm ea Alpha Energy (MeV) (deg) 9 Be (ground) 2. 7 30 111 6.997 69.5 9Be * ("l. 7 MeV) 2. 191 123 5.786 67 . 4 9Be * (2. 43 MeV) 1. 982 130 5.314 66 . 4 1. 604 159 5.263 66.2 11 B (ground) 36 Table 2 Tar et Thicknesses and Ener -loss Data for 9 Be Ions e e Pg s. 3 and •) Target Number B( 10 18 Thickness 2 2 18 at/cm ) C(lo at/cm ) .aE/E 1. 98 MeV 2. 7 3 MeV 1 0.42 10 o. 83% o. 58% 2 0.96 12 1. 89% 1. 33% 3 o. 39 0.50 o. 77% o. 54% 4 0.44 1. 28 o. 87% o. 61% 5 0.21 0.66 b. 41% o. 28% 37 Table 3 Summary of Experimenta l Results (See Pag e 10.) Coincidence Type 9 :Be Counts µ. Coulombs of beam on target ++ - a2 9B e ++++ - a 9 Be++ - al 2 361 615 30 23 32900 0 42040 38 Table 4 Charge-State Fractions for 9 Be (See Pgs. 13 and 24.) Calculated* Measured ' 1. 78 MeV 2. 52 MeV 1. 98 MeV 2 . 19 MeV 2.73MeV +l o. 0476 ± o. 005 0.013 o. 03 0.02 0.01 +2 0 . 467 ±0.012 o. 298 ± o. 013 0.40 o. 36 o. 27 +3 0.428 ± o. 009 o. 560 ± 0. 025 0. 47 0.51 0.55 +4 0. 057 ± 0. 01 o. 139 ± 0. 006 0. 10 0 . 11 o. 17 *Error of ± 0. 02 assumed for each point. 39 Table 5 Thickness Factors (See Pg. 14.) Target t 2 ( 1. 98 MeV) t 0 (2.73MeV) t.,. .J t 0 1 0.999 1.000 0.999 2 o. 971 0.992 0.981 3 0.999 1. 000 0.999 4 0.999 1. 000 0.999 5 1. 000 1. 000 1.000 Table 6 - Initial Data From Each Run (See Pgs. 11 and 41) Coincidences with 9Be in 2+ Charge-State N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 N l 2 3 4 5 DATE 5-07 5-08 5-09 5-10 5-13 5-13 5-14 5-14 5-28 5-30 6-04 6-04 6-05 6-05 6-05 6-05 7-02· 7-06 7-24 7-26 7-27 7-27 7-28 7-29 DATE 7-02 7-03 7-03 7-04 7-06 T c 1 23 1 6 1 14 1 11 1 24 1 53 1 28 1 71 2 18 3 13 4 11 4 8 4 13 4 7 4 12 4 10 4 15 4 6 5 5 5 4 2 5 5 l 5 3 5 3 T 4 4 4 4 4 c 8 4 2 4 5 BCCNT 5462 6811 13867 4420 3802 8262 4048 BE 90 AE 94 93 92 86 AV AV STR 59 7 22 49 25 51 42 54 762 2 46 190 105 116 123 176 133 45 0 2 6 4 3 8 RNLN 557A 30 40 56oA 478A 824A 554A lOOOA 375A 400A 326 290 290 290 290 348 320 171 400 800 400 440 240 800 STR 19 8 15 6 5 Coincidences with 9 Be in 4+ Charge-State RNLN BCCNT BE AE BCLN ECCNT AN AN AN 800 15653 40 11281 800 11242 s 400 s 40 480 14409 10509 11825 40 11577 810 s 92 s s BCLN 120A 10 ~o 69A 70A 135A 70A s 42114 18834 12509 19715 30604 24654 25129 19634 12358 11577 4710 4690 3886 727A 411A 30 58 58 58 58 58 58 58 40 40 40 5242 4237 40 40 s s ECCNT .6995 s s 11246 8262 14253 3900 8041 20282 7404 20446 24511 25037 25076 22741 19009 12181 EE s s 89 90 s s EA s s s s AV AV 89 72 82 s 40 40 40 40 40 40 R RER 22 72 47 58 27 78 47 33 91 19 14 107 88 18 120 12 47 49 37 90 97 37 52 54 85 30 46 55 30 89 38 70 21 0~ 139 100 38 110 39 66 49 57 87 40 149 52 108 39 85 ECLN AN 40 40 40 40 R 31 15 16 26 21 ECLN 87A s s 203A 135A 199A 63A 113A 407A 20A 67 58 58 58 58 58 58 s 4383 3364 2901 1459 3910 3198 EE EA RER 30 64 85 49 46 41 Table 6 Headings N DATE - Number to identify each run. Date of run . . T - Target number (See Table 2 for the thickness of each target). c - Number of coincidence counts with the correct energies for excited states events (See Fig. 5 and Pg. 8). STR - Number of coincidence counts with the correct energies for ground state straggler events (See Fig. 8 and Pg. 9). RNLN - Length of the run in which C and STR are measured. Thi$ run length is in units of lOµC. of beam unless A appears after the number. AE In the latter case the units are 10, 000 ex counts. - Percent correction for alpha angle error. DUring some runs the angle of the alpha counter wa.s O. 7° or 1. 2° too large while measuring excited state coincidences (the counter opening was 3. 6 °). (During the calibration run (Be 9 +++ -a ) the coincidence 0 efficiency was measured at 1° steps. · AE is 100 times the calibration coincidence rate at the correct angle O. 7 0 (or 1. 2°) divided by the calibration rate at the correct angle. B - All symbols starting with B refer to measurements of the calibration rate (counting Be 9 +++ -a ) made at the beginning 0 of the run (See Pg. 8). BCCNT - Number of coincidences for the calibration reaction. 42 I . BE - Percent efficiency for counting BCCN T. For the runs where BCCNT was counted with a scalar, it was necessary to correct BCCNT since some coincidences counted by the scalar did not have the correct energy for events from the calibration reac - . tlon (Be . 9+++ . - a0 )• A. t least once each day this ratio was checked by measuring the number of counts with the two dimensional analyzer and the scalar BE is 100 times the analyzer counts (which have the correct ion a nd alpha energy) divide.d by the scalar counts (all coincidences). BCLN Length of the run in which BCCNT was measured. This run ' length is in units of ·1 oµGunless A appears after the number. In: the latter case the units are l, 000 a counts. E - All symbols beginning with E refer to measurements of the calibration coincidence rate made at the end of the run. These symbols have the same meaning as the corresponding symbols starting with B. R - The ratio of the excited .. state coincidence counting rate to the ground-state coincidence counting rate after applying the corrections given in this table. (RNLN x (AE/100)). Let R * = (C-0. 0106xSTR)/ BR= BCCNT x (BE/100)/ BCCLN, ER= ECCNT x (EE/100)/BCCLN and GE =(BR+ ER)/2. Then R = R */GE. (See Pg. · 1.5). RER - The percent error in R ( see pg. 15 .for a discussion of error calculations). 43 Table 6 Symbols blank - The correction factor (SE, Be, or EE) was not needed. One may use 100% for its value in any formula. A - The length of the run was measured by counting the number of alphas with energy above about 6.5 MeV. Then the units are 10, 000 a for RNLN and l, OOOa for BCLN and ECLN. AN - No measurement of the calibration rate was made for this run. The average calibration rate from all other runs on this target was used for this run. AV - No measurement of the correction for the alpha angle was made this day. S The average of all other measurements was used - Use the value from the previous calibration run (the order is beginning calibration, run l; end calibration, run l; beginning calibration, run 2; etc.) . When the calibration was not checked at the end of the run, the calibration error was considered to be 1. 5 times the average of measured calibration variations. 44 Table 7 Calculations of 2. 43-MeV State (See Pg. 11.) +2 Charge State (N2 -B2> Target N 0 t 4 x ~ x 10 t2 Target (N2 -B2> N t -[!- x 10 x 4 2 0 1 0.76 ± o. 28 4 0.86 ± 0. 26 1 o. 63 ± o. 32 4 0.46 ± 0. 26 1 0.85 ± 0. 26 4 0.89 ± o. 27 1 o. 39 ± 0. 18 4 0.70 ± o. 27 1 1. 15 ± 0. 18 4 1. 39 ± o. 29 1 0.89 ± o. 16 4 1. 00 ± o. 39 1 1. 20 ± o. 15 5 1. 10 ± o. 42 2 0.49 ± 0. 23 5 0.49 ± o. 33 3 0.90 ± o. 33 5 0.57 ± 0. 50 4 0.97 ± 0.37 5 0 -. 40 ± o. 60 4 0.54 ± o. 28 5 1. 08 ± o. 57 5 o. 39 ± o. 33 (N2-B2) to average N t2 0 = (O. 825 ± 0. 063) x 10- 4 +4 Charge State Target 5 5 t (N2 -B2> 4 0 x 10 x N t2 0 o. 31 o. 15 average Target (N2-B2> N t x 0 ~ x 10 4 t2 ± o. 09 5 o. 16 ± o. 14 ± o. {)9 5 0.26 ± 5 0.20 = (O. 220 ± O. 047) x 10- o. 13 ± o. 10 4 45 Table 7 (cont'd.) charge rrad -r- N2-B2 t N t2 0 1 c2 0 - +2 20 . 5 ± 1. 9 +4 22.4 ± 6.6 average 20.6 ± 1. 8 x 10 4 a = 0 0:'2 = (20. 6 ± 1. 8) = ( 1. 16 ± o. 14 x 10 x 10-4 4 x (O. 55 ± O. 02) x (0. 972 x O. 072)-l 46 Table 8 Calculation of Limit on r . Target 11,) No • of Runs Total Length Be 7 42040µC 0 ± 10. 13 1 0 Be 9 Counts µC 0 10. 13 Counts µ.C 6 x = x fl"" x = (0 ± 2. 3) x 10 -6 x1 < 2 .4 x lo- 5 9* . ( 0 ± 2. 3) x 10 - x 42040 t rad (l.?) r d/r for 1. 7 MeV State (See Pg. 5 r ra . o. 55 ± o. 02 x (0. 15 ± o. 02) -1 o. 36 ± 0. 02 47 Counter Correction Factors t (See Appendix II, Pg. 21.) Counter Number Counter Number Factor 1 0.906 1.086 0. 9 31 o. 9 38 0. 948 0.974 0.990 1. 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Factor 1. 029 1. 048 1.066 1. 034 1. 096 1. 095 1. 093 1. 094* *Data from Counter 16 were unreliable and was therefore ignored. tThe counter correction factors, £. were measured by scattering . 3 1 He from a thick tantalum target and counting the number of scattered 3 He (per unit beam charge) with each counter and com- paring this to the number of 3 He (per unit beam charge) counted by counter 8 when the magnet current was adjusted so particles of the same rigidity fell on Counter 8. The factors f. are given by 1 £. = 1 where n . (r .) is the number o f 1 J 3 He counted by counter i when the magnet current was adjusted so particles of rigidity r . fell on . J counter i {Cocke 1964). 48 Table 10 Charge-State Ratios A .. (See Pg. 25.) 1 E ~ 9 Be = 2. 52 MeV + + + + +++ ++++ o. 505 ± o. 019 1 + + + 1. 857 ± o. 066 ++++ o. 439 ± o. 039 E 9 Be 1 2.26±0.09 3.77 ±0.07 o. 230 ± o. 001 1 = 1. 78 MeV ~· + ++ + 1 0.091 ±0.003 ++ 9• 50 ± o. 49 1 1. 094 ± o. 024 5. 52 ± o. 45 +++ 8. 7 5 ± o. 50 o. 899 ± o. 023 1 6. 39 ± o. 45 ++++ L 77 ± o. 98 : o. 149 ± o. 016 o. 137 ± o. 004 1 +++ ++++ o. 104 ± o. 004 o. 38 ± o. 04 49 Table 11 Calculated Particle Decay Widths (See Page 31.) 5 He+ er Decay Calculation r('He + er)( ev) 2.9 2.0 3. 0 3. 7 158 68 89 98 Alpha 4.0 5.0 2. 3 135 210 Calculation R(er+a)(f) PHe A He A He A He A He A He 111 P Be 5.0 24 A A A A A Be Be Be Be Be 4.2 14 4.6 5.0 24 5.8 30 39 Alpha ( 5. 0) 7 Calculation 18 5.4 E (MeV) r 0. 97 r(E ) MeV r 1. 81 PHe A He 0.96 o. 58 P Be A Be 3. 0 3. 0 1. 45 1. 45 P He: A He: 4 Data from er + p P31_2 phase shifts adjusted to fit He + n crosssection (Dodder 1952). 5 Data from average of measurements on He ground state (Lauritsen 1965). A Be: Data from er-er d-wave phase shift analysis (Russell 1956). 8 Data from average of measurements on Be(2+)(Lauritsen 1965). Alpha: Alpha model calculation (Henley 1960). P Be : 50 Figure 1 Experimental arrangement. Recoil 9 Be ions at 90° were ana - lyzed in momentum and detected with a surface -barrier counter. Alpha particles were detected with a surface-barrier counter in the target chamber. The alpha pulses were delayed by the time required for the 9 Be iOns to travel through the magnet. When- ever a pulse from the 9 Be counter was in coincidence with the delayed alpha pulse, the pulses were stored on a two-dimensional pulse-height analyzer. The boxes marked 417A are single- stage preamps using a type 417 A triode, the boxes marked hp A are Hewlett-Packard Type 460A wide band amplifiers , and the boxes hp B are Hewlett-Packard type 460B wide band amplifiers. (See Pg. 3.) 51 PLAN OF EXPERIMENT INCIDENT BEAM 1.7 MeV d ALTERNATING GRADIENT SPECTROMETER ~TARGET .~ or C FO I L I s Ii ts a-DETECTOR / ,/ ~__.11--~...1.. ~--- 417 A hp B VARIABLE DELAY 417A FAST ION SCALER INTEGRATING PREAMP SLOW ION SCALER FAST a SCALER ExtG Trig~ LOWER BEAM lf!. UPPER BEAM GATE OUT DUAL-BEAM SCOPE BIASED AMPLIFIER SLOW a SCALER COINCIDENCE SCALER AMPLIFIER x y COINCIDENCE TWO DIMENSIONAL ANALYZER Figure 1 . 52 Figure 2 Non-coincident ene_rgy spectrum at the magnetic-spectrometer focus. EM/Z The magnet current was set to admit particles with 2 = 4. 46 MeV . The channel number is a linear function of E, so particles with various values of M/Z The positions where peaks for 9 Be and with a longer run are indicated. 11 2 are separated. B recoils would appear (See Pgs. 5 and 7.) 53 1500 (f) 1000 t- z ::::> 0 (.) 500 ++ 119 +9 ++ Be 100 • 0 1.00 2 .00 3.00 PULSE HEIGHT Figure 2 54 Figure 3 Chamber counter spectrum with slow electronics. of peaks for various reactions are indicated. The positions Also the position of the peak from protons that penetrate the depletion layer is shown. There can be no peaks from protons above the depletion layer peak. (See Pg. 6.) 55 0 1,000,000 4U 'O "O NU - 100,000 • • -. "'": -.. N - .. - Q) 'O 'O 10,000 ~ C\J a a. CD - z ~ CD CD CJ) 0 0 a. CD a rt') • •• -.. Q) CD CJ) en CD CJ) .. a Q) - CD 'O - --. 0 ~ z :::> 0 Q) CD I'- 'O 1,000 • CJ) 'O 0 Q) 'O CD t Q) (.) ' ' 100 10 2 3 4 5 6 7 ENERGY(MEV) Figure 3 8 56 Fig·.ire 4 Non-coincident alpha spectrum.This spectrum was taken at a laboratory angle of 66. 4° and a bombarding energy of 1. 70 MeV. The spectrum is taken through the fast electronics with biased amplifier (See Figure 1) set to reject pulses below 2 MeV. lower curve shows the result of subtracting out the a 2 peak. (See Pgs .•. 6 and 14 .,) The ·57 2500 •a SPECTRUM 11 B(d,a) a ANGLE 66.40 o a SPECTRUM WITH 5.3- MeV PEAK SUBTRACTED OUT 2000 1500 (/') 1- z ::::> 0 (.) 1000 500 l \ I \ I I 5.3 5.8 7.0 ALPHA ENERGY MeV Figure 4 58 Figure 5 A plot of the two-dimensional analyzer output ~or a 9 Be ++ - a 2 run on Target .number i.· The magnet was set so that only ions with EM/Z 2 = 4.46 MeV could reach the ion counter. of each stick is proportional to the number of counts. The height The ion energy and alpha energy are determined by the position of the stick. - a 2 A black rectangle marks the position of 9 Be ++ ( 1. 98 MeV) (5. 3 MeV) coincidences. The total charge for this run was about 800µ C. See Figure 5A for the analyzer output in numerical · form. (See Page 8.) .59 ...~· .· . ., Figure 5 . . ·• ·' ·=··~. -\' ,·:. :- •' 60 Figure SA The data of Figure 5 ~e shown in numerical form. (See Fig. 5.) Alpha l 2 J ' Cb&Mtl lwlber 5 6 7 8 9 lO ll l2 lJ 14 15 16 lT lB 19 20 21 22 23 2• 25 26 21 26 29 JO 3l 32 J3 J4 J5 J6 JT JB 39 40 41 42 43 44 ' j 46 •r 48 09 50 51 52 5J 54 55 56 5T 58 59 6o Q 62 6J 6lo 6lo • 62 3,0 61 ~ ~ 58 ~ ~ " ~ . .•• 0 ~ ~ 2.5 ~ ~ ~ 48 " r ~ ... " I 7 ~ ~ ~ ~ ~ 2 l l • n ~ l l l l 2 .0 ( •• l l l y ) l TI ~ " l ~ n 1 2 1 l 32 3l 2 l 29 1 ~ • 21 ~ ~ ~ 23 ~ 1 1 l l J 2 3 8 4 J 2 2 2 10 8 ll 5 4 2 3 3 2 4 19 29 59 941<9 61 25 22 5 3 T 26 61105134160 91 ;S 21 18 5 6 14 50 T6ll5ll9 98 6lo 24 13 2 6 9 16 57 51 61 57 26 10 4 6 268221416 6 4 2 1 11 223456212 4 J ll J l JS 1,2 24 ; l l 5 5 1 1 l · 1 9 14 a lJ 6 11 9 i , 1 lo 1 4 J • s 6 e 1 6 3 3 5 2 5 i l i 9612~32Q"~~n~w~n2222nnm13"uw23d1w6 a 1 16 30 J6 20 3g 47 36 1,1, '•7 43 47 36 45 1,0 21 "" 29 30 i' 29 34 23 ie i3 6 4 J l u312d"n~n 29~• n3223d n22nmnu d12 ~12B63 l l ~ u 3 6 B 7 5 6 l2 T u 10 7 ll 10 6 ll 10 3 5 4 u 24lJl l 2 1 2 l 1. 5 l l 4 3 3 l 3 2 l l l 1 2 l 4 J l l l l l 2 2 l 1. 0 l d n d u D 1; l2 ll l l 3 l 2 2 3 ::>. 5 6 ~ ? 8 2 7 6 4 2 l l 2 1 6 l • 2 2 2 J l 1 J 3 2111212 l 2 l 1 3 1 2 3 l 2 2 l li e5 5. 0 5. 5 6.o Alpha 1nc...,. (HeT) 6.5 1.0 7.5 Figure SA .. 0-..... 62 Figure 6 A plot of the two-dimensional analyzer output summed over five runs ( 34, 040µC of beam) of 9 Be ++ - a 1 on Target number 5. magnet was set so that on:ly ions with EM/Z reach the ion counter. 2 The = 4. 9 3 MeV could A black rectangle marks the expected posi- tion .of 9 Be ++ (2. 19 MeV) - a 1 (5. 7 MeV) coincidences . Note that the scale and angle of view differ from those of Figure 5. See Figure 6A for the analyzer output in numerical form. (See Page 8.) 63 .. ......,.... . ~·· I . c;"< . - . .• · . ' . '· • • . . . •. l . •. . · . . · • . · . . · . , · . . · . . · . . · . -.· .-. · . . -.·.· .·.· .. ·.· .. · : . . · .· . ::·:."• :.'·:."·_' . . . . ... · ·. - ~ · • • . •. • .. . .. .. .. • .. i', .. .i . .. ·'. ." . _ I : . .. . ... . :;. ' ·. ~ ...'. . · ·-· . : ' . .. • • .. • " . .. • •. • . . • ~ • .. .. .. . • . . . . . . .. .. . .~ . ..• • .. .. .. . o~ c,,.,.· . •·.. .. • • .. ·~-crT'' , . .. 0 . . . (: ><·>: . !..:.... . • ' 1· · .• .....'................... ... . .. . ... · . . . ... . . .. . . . . . ... ... .. . . . .. ' I,·. ~ 01' . "-._·.:-. . ·-.··... _ . .·._··<····A·:.:- : -:·.:<·< <-.>~ ·.-. · . \ > •; _ .;_ .:·.:-:·. v:-::-:<:-:·.:-:·.·.:· . · _.·.·.·. '?lo "·. ·... ·,..............·........·..........·.. -.· ._ -.·.... .... . - . ·•. ·. .. . .·................. ...... ...... ... .... ........... . . .. ~1 . /. ~ ~t.."' ,· . . f: • ·... ., . ~."<«i>, · ~~t.·L.,t: .. . . .. .. · .. , . .:.;,- Figure 6 ·-::' .·. ~ .-...... .· • ., . .· ·:.. ·' t . . 64 Figure 6A The data of Figure 6 are shown in numerical form. (See Fig. 6.) Alpha Channel Number 1 2 3 4 5 . 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 3.0 31. 30 29 28 27 1 1 1 1 26 :I e 1 13 " c h a n n iT u l!I b e r 1 1 1 2 4 1 3 2 1 1 2 .5 1 23 22 21 20 19 18 17 16 15 14 0 3 1 25 2~ 1 I 0 n 2 1 I I 1 1 1 1 2 2 1 4 3 2 1 1 1 1 1 1 1 1 1 1 2 'E 2.0 n e :r: 1 2 g y .12 lJ. 1 3 1 1 3 10 1 2 9 . 59 32 6 14 15 11 18 8 259 119 55 50 51 51; 66 7 123 46 27 21 32 32 39 6 . 8 1 1 1 1 1 2 1 5 l: l 5 1 2 3 15 1 2 7 6 .8 7 10 10 2 1 1 1 1 ~~5 6 3 6 6 1 1 16 16 75 62 37 22 1 10 13 1 5.0 2 1 4 10 12 1 11 17 14 1 1 1 1 3 5 5 2 15 7 16 10 14 4 20 11 6 4 56 58 67 51 58 57 47 49 21 9 21 28 35 27 21 40 27 11 8 l; 1 1 1 2 3 2' 1 1 1 1 1 1 1 1 7 13 10 10 8 4 17 . 7 10 10 1 1 1 3 3 6.o 5.5 Al pho. Ene rr;y (MeV) Figure 6A 1 1.5 1 e 1 2 v 2 2 ) 1 1 1.0 1 9 15 2 3 1 6 i 4 6.5 1 5 10 10 1 6 7 ( M 5 7.0 5 "' 1.11 66 Figure 7 Spectrum of ions in coincidence with 5. 3 MeV alpha particles plotted against ion energy. The coincidences within the a have been summed and plotted against ion energy. was set for EM/Z 2. = 4. 46 MeV. (S~e Pg. 9.) 2 peak The magnet 67 100 llB (J) r- z 6 50 (.,) ~ ~ 0 L--~~~-.--~~~!::=::===~~....L---==-----J I. 5 2 .0 ION ENERGY (MEY) Figure 7 68 Figure 8 Spectrum of alpha particles in coincidence .with 1. 98 -MeV 9 Be ions plotted against alpha energy. The coincidences within the 9 Be peak from seven runs (21, 540µ.C of beam) on Target 4 have been summed and plotted against alpha energy. set for EM/Z 2 = 4. 46 MeV. (See Page 9.) The magnet was 69 ·150 - - - - - - - - - - - - - - - 100 (f) t- z :::::> 0 u en a:: w _J 50 <!> <!> <{ a:: ~ (/) *m Q) Q) m (1) O> ......~...:.::~--------::.1.....-i.......------~ o...-~ 4.0 5 .0 6.0 7.0 8.0 ALPHA ENERGY(MEV) Figure 8 70 Figure 9 The number of alpha particles in coincidence with ions of energy of 2. 19 MeV, taken in six runs (19140µC of beam) on Target 4, summed and plotted against alpha energy. EM/Z 2 = 4. 93 MeV. The magnet was set for The targ e t (No. 4) was moderately thick so that most of the counts in the region marked tail of the 9 Be straggler group. 9 Be >:< came from the About one count from the 1. 7-MeV * level in 9 Be should have come in the region marked 9 Be . This run, therefore, provides a . measure of the number of counts from stragglers (compare with Fig. 8). (See Page 9.) 71 200 150 CJ) 1- z :::::> 100 0 (.) en a:: w 50 _J <.!) <.!) <{ a:: ...... en *Cl) CD <n 5.0 6.0 7.0 8.0 ALPHA ENERGY(MEV) Figure 9 72 Figure 10 The momentum spectrum of elastically scattered protons of 1-MeV incident energy, as measured with a 25. 7 cm magnetic spectrometer at a laboratory angle of 150° is shown. has 1. 3 x 10 18 at/ cm 2 of boron. The target The atomic percent of other materials in the target is shown over their peaks. The lines at the top of the figure show where the front edge of the peaks for various elements should occur (See Pgs. 3 and 21.) 73 1e3w 285j !()SI 2951 9 .3% 1,000 6.3% 12.4% 0.7% 0.1% 1.4% • en rz ::> 0 (.) • • • •• • •• • • • • • 1 .76 .74 .72 • .70 . .68 • FLUXMETER CURRENT .66 .64 Figure 10 .62 74 Figure 11 The charge-state data for 2. 5-MeV 9 Be ions. The graph shows the number of counts (corrected by the counter correction factors in Table 9) for each observed charge state (2+, 3+, and 4+) plotted against the 9 Be ion energy measured by the magnetic spectrometer. (See Page 24. ) 75 4002+ 200- 0 3+ 600- .. - .. . 400Cf) !z :::> 0 (.) 200- 0 200 - . . : . . .. . . .... 0 2 .3 2.4 2.5MeV ... 2.6 4+ .. ." 2.7 F igur e 1 1 2.tj 76 Figure 12 The charge-state data for 1. 7-MeV 9 Be ions. The graph shows the number of counts (corrected by the counter correction factors in Table 9) for each observed charge state ( l+, 2+ , 3+ and 4+) plotted against the 9 Be ion energy measured by the magnetic spectrometer. (See Page 24.) 77 · 100- .. ,t ' I+ ,o 0 ..··.··... .·.·· 0-1---------.---------------------~---.........~~----------i • 0 • •· • • • I t 800- 2+ 600- 400- 200- - .. 0-+-------------.------------.---------~.------------T----------.....---------f en ~00 :::> 0 0 3+ . . ... 400- 200- - .. .... . ... . . . . . . 0-+-------------....-----------------.---------.......-------------~--t · IOO- .. .. ': ........... 1.6 1.7 MeV I. 8 F i g ur e 12 19 4+ 2.0