The ³He(α,γ)⁷Be Reaction at Low Energies Citation Osborne, John Lawrence (1983) The ³He(α,γ)⁷Be Reaction at Low Energies. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/jjbj-9188. https://resolver.caltech.edu/CaltechTHESIS:10222019-162722254 Abstract Cross sections for the 3 He(α,γ) 7 Be reaction have been measured at several energies from E cm = 165 to 1200 keV by counting prompt γ rays from a windowless, differentially pumped, recirculating, 3 He gas target. The cross-section factor S 34 ( E cm ) and branching ratio γ 1 /γ 0 were determined at each energy. Absolute cross sections were measured at E cm = 947 and 1255 keV by counting the γ rays from the 7 Be produced in a 3 He gas cell with a Ni entrance foil. The inferred zero-energy intercept of the cross-section factor is S 34 (0) = 0.52 ± 0.03 keV-barn. This value is in good agreement with the previous measurements of Parker and Kavanagh and Nagatani et al., but disagrees substantially with the recently published measurement of Kräwinkel et al. from Münster. The relationship between the present measurements and several theoretical calculations, and the effect of the extrapolated cross section on the solar neutrino problem are discussed. 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): Barnes, Charles A. Thesis Committee: Koonin, Steven E. (chair) Fowler, William A. Gomez, Ricardo Barnes, Charles A. Defense Date: 24 June 1982 Funders: Funding Agency Grant Number NSF PHY79-23638 Record Number: CaltechTHESIS:10222019-162722254 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:10222019-162722254 DOI: 10.7907/jjbj-9188 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 11844 Collection: CaltechTHESIS Deposited By: Mel Ray Deposited On: 22 Oct 2019 23:42 Last Modified: 07 Aug 2025 17:15 Thesis Files Preview PDF - Final Version See Usage Policy. 25MB Repository Staff Only: item control page

THE 3 He(cx;y) 7 Be REACTION AT LOW ENERGIES thesis by John Lawrence Osborne In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1983 (Submitted June 24, 1982) -ii- ACKNOWLEDGEMENTS It is difficult to find the words to express my sincere appreciation to ·the staff, students and faculty of the Kellogg Radiation Laboratory for providing a stimulating and encouraging atmosphere in which to work, to study and to play. In particular I wish to thank Professor C. A. Barnes for his patient instruction and guidance, Professor W. A. Fowler for his continuing interest in these experiments and Professor R. W. Kavanagh for his remarkable ability to draw unexpected amounts of beam from accelerators and knowledge from students. Special thanks go to Professor P. D. Parker of Yale University for the conception and design of the activity experiment and to Professor A. J. Howard of Trinity College, Dr. G. J. Mathews, Dr. J. L. Zyskind and R. M. Kremer for their invaluable assistance in the design, maintenance and operation of the experiments during the interminable hours of data collection. This work has greatly benefitted from many informative discussions with Professor S. E. Koonin, Professor T. A. Tombrello, Dr. H. S. Wilson, R. D. Williams and Dr. H. Friederich. Finally, I want to extend my sincere thanks to Dr. Martin Weiss of USC Medical School for his innovative skill which made the completion of this work possible. This research was supported in part by the National Science Foundation under Grant No. PHY79-23638. -iii- ABSTRACT Cross sections for the 3He(a,')')?Be reaction have been measured at several energies from Ecm = 165 to 1200 keV by counting prompt ')' rays from a windowless, differentially pumped, recirculating, 3 He gas target. The cross-section factor S 34 (Ecm) and branching ratio "hi !o were determined at each energy. Absolute cross sections were measured at Ecm =947 and 1255 keV by counting the')' rays from the 7 Be produced in a 3 He gas cell with a Ni entrance foil. The inferred zero-energy intercept of the cross-section factor is 5 34 (0)=0.52±0.03 keV-barn. This value is in good agreement with the previous measurements of Parker and Kavanagh and Nagatani et al., but disagrees substantially with the recently published measurement of Krawinkel et al. from Mlinster. The relationship between the present measurements and several theoretical calculations, and the effect of the extrapolated cross section on the solar neutrino problem are discussed. -iv- TABLE OF CONTENTS page ACKNOWLEDGEMENTS ii ABSTRACT iii I. INTRODUCTION A Solar Models 1 B. Solar Neutrino Problem 2 C. The 3_f.Ie(a,')'fBe Reaction 3 II. EXPERIMENTAL APPARATUS AND PROCEDURE A Windowless Gas Target System 11 1. Target 11 2. Detection 12 3. Procedure 13 B. Gas-cell Activity Measurement 15 1. Target 15 2. Detection 15 3. Procedure 16 III. DATAANALYSIS A Windowless Gas Target System 19 19 1. ')'-ray Yield 22 2. Angular Distribution Function 22 3. Number of Beam Particles 23 4. Target Density 24 5. Detector Efficiency 25 6. Calculation of errors 26 -v- TABLE OF CONTENTS (cont.) B. Gas-cell Activity Measurement 28 1. {-ray yield 30 2. Beam Energy 30 3. Current Integration 31 4. Target Density 31 5. Detector Efficiency 32 6. Calculation of errors 33 IV. RESULTS AND CONCLUSIONS 35 A Experimental Results 35 B. Relation to theory 37 C. Astrophysical Implications 38 Appendix A: Calorimeter 40 Appendix B: Integration of 'l-ray Yields 43 REFERENCES 45 TABLES 48 1. WINDOWLESS TARGET RUN PARAMETERS 48 2. EMPIRICAL EFFICIENCY FUNCTION 51 3. SYSTEMATIC ERRORS 52 4. ACTIVITY MEASUREMENT RUN PARA1'viETERS 54 5. RESULTS 56 6. THEORETICAL FITS 59 7. CALORIMETER CALIBRATION 61 -viTABLE OF CONTENTS (cont.) F1GURES 63 1. ENERGY LEVEL DIAGRAM 63 2. RESULTS OF PREV'lOUS EXPERIMENTS 65 3. THEORETICAL CALCULATIONS 67 4. WINDOWLESS GAS-TARGET SYSTEM 69 5. WINDOWLESS TARGET 71 6. PARTICLE SPECTRA 73 7. DETECTOR ELECTRONICS 75 8. WINDOWLESS TARGET BEAMLINE 77 9. GAS CELL 79 10. TARGET CEll GAS MANIFOLD 11. 24 12. 14 28 Mg (ex, 'Y ) Si FOIL THICKNESS MEASUREMENT 18 N(cx.,1) F FOIL THICI<NESS MEASUREMENT 81 83 85 13. DIRECT-CAPTURE 1-RAY SPECTRA 87 14. 1-RAY DETECTION EFFICIENCIES 89 15. TOTAL DETECTION EFFICIENCY 91 16. CATCHER FOIL SPECTRUM 93 17. PROMPT 1-RAY SPECTRUM 95 18. RESULTS 97 19. CALORIMETER 99 20. CALORIMETER CONTROLLER CIRCUIT 101 21. CALORIMETER CURRENT DECAY 103 I. INTRODUCTION A Solar Models Nuclear Astrophysics was born in 1939 with the pioneering work of Hans Bethe (Be39) in which he showed that the production of energy in our sun could come from the fusion of four protons into 4 He using 12 C as a catalyst in what has become known as the CNO cycle. The 1951 discovery of the reaction (I.1) by Fowler and Lauritsen (Fo51), provided the endpoint for the direct combination of protons into 4 He at a temperature below that required for the CNO cycle. In 1958 Holmgren and Johnston (Ho59) found the cross section for (I.2) to be "'100 times larger than the value being used in the solar model calculations of Salpeter (Sa52) and Burbidge, Burbidge, Fowler and Hoyle (Bu57). Fowler (Fo58) and Cameron (Ca58) independently calculated that, at solar temperatures, reaction (I.2) would compete with reaction (I.1) to complete the Proton-Proton Chain through either (I.3) or -2(1.4) Both Cameron and Fowler recognized that the energetic neutrinos from the decay of 6B in reaction chain (1.4) could provide an experimental test of solar models, if this branch were strong enough. Although the mean free path for particles and -y rays is far too short for information about the reaction processes in the interior of the sun to propagate to the outside, neutrinos, with their small interaction cross sections, will escape. Davis (Da55) had developed a sensitive neutrino detector based on the endoergic neutrino-capture reaction, (1.5) which has an interaction cross section proportional to the square of the neutrino energy minus the threshold energy, 0.81 MeV. For neutrinos with energy above 5.8 MeV, the superallowed transition to the isobaric analog state in 37Ar is possible, further enhancing the yield from 8 B neutrinos . B. Solar Neutrino Problem Using the neutrino-flux calculations from the 1963 solar model of Bahcall, Fowler, Iben and Sears (Ba63), Bahcall and Davis (Ba64 and Da64) demonstrated the theoretical and experimental feasibility of an experiment to measure the solar-neutrino flux. By 1968, the Brookhaven solar neutrino experiment, a 100,000 gallon tank of perchlorethylene, began collecting data in the Homestake mine at Lead, South Dakota, 4800 feet below the surface to reduce the background induced by cosmic rays . With improved measurements of the important cross sections for 3 He(a:,-y)1Be -3- improved solar model programs, a theoretical neutrino-capture rate of 7.5±3.0 SNU (Solar Neutrino Unit, 1 SNU = 10-36 captures per 37 Cl atom per second) was calculated by Bahcall et al. (Ba68). The discrepancy between this theoretical value and the <3 SNU that was reported by Davis, Harmer and Hoffman (Da68) has become known as the solar neutrino problem. Refinements in solar models and in the experimental technique have had little effect on the magnitude of this problem; the most recent theoretical and experimental capture rates are 7.6±3.3 (3-a error) (Ba82) and 2.2±0.3 SNU (Cl80). Most of the explanations that have been offered to resolve the problem fit into three categories; those which require modifications to the structure or evolution of solar models, such as Fowler's suggestion that the central temperature of the sun may oscillate, and that at the present time the temperature is at a minimum (Fo72); changes in the underlying particle physics, as in the quark catalysis of Libbey and Thomas (Li69) or neutrino oscillations, suggested by Gribov and Pontecorvo (Gr69), and errors in the measured nuclear reaction rates, as suggested by Fowler (Fo72) and others. C. The 3 He(a:,7) 7Be Reaction The energy level diagram for the 3He+ 4 He system is shown in figure 1. The entrance channel has a Q-value of 1586.4 keV relative to the ground state of 7 Be. Since 7 Be has no energy levels between the first excited stale at 429 keV and the ·F slate at 4.57 MeV, the capture reaction at energies below Ecm =2500 keV will proceed directly with the emission of a 7 ray (70 or 7 1) to either the ground or first excited stale. Because of the coulomb barrier, the cross section for 3 He(a:,7) 7 Be -4- decreases rapidly with energy below Ecm = 1000 keV. At solar energies, the capture cross section is too low to be measured: approximately 1000 particle coulombs of beam would be required to produce a single capture at Ea=40 keV. Measurements of the cross section must be made at higher energies and extrapolated theoretically to the region of interest. For these extrapolations, it is convenient to use an expression in which the coulomb effect has been factored out, such as the cross-section factor, (1.6) where 7] is the Sonunerfeld parameter, (I. 7) Z 1 and Z 2 are the projectile and target charges and v is their relative velocity. For the 3 He(o:,{) 7 Be reaction at low energies, the cross-section factor reduces to r 164. 125 S34(Ecm)=a(Ecm)Ecmexpl- ~ , -vEcm (I. B) with Ecm in keV. The first experimental measurement of the cross section for 3 He(o:,7) 7Be was made by Holmgren and Johnston (Ho59). Their apparatus consisted of a gas cell filled with 3 He which an ex beam from an electrostatic accelerator entered through a thin nickel foil. The cross section and S-factor were calculated from direct capture ganuna rays which were collected using a 3x5-in. well-type Nai(Tl) detector, and no attempt was made to distinguish between the ground state and first excited state -5transitions. Background was subtracted by performing the same experiment on the target filled with 4 He. The experimental uncertainty in this measurement was quite high, particularly at low energies, due to the large beam-energy spread (120 keV) caused by energy-loss straggling in the entrance foil and and energy loss in the target itself. Using a linear extrapolation from the cross-section factors measured at Ecm =200, 300 and 400 keV, they determined a zero-energy intercept of 5(0)=1.2 keV-b. Christy and Duck (Ch61) and Tombrello and Phillips (To61) independently developed the theoretical model for the calculation of nonresonant, direct, radiative capture reactions. Their calculations were based on the assumption that the process involves a direct electromagnetic transition from the initial state to a final bound state. The cross section for this type of reaction is then found by calculating the matrix element, between the initial and final state wavefunctions, of the electromagnetic interaction Hamiltonian, (I.9) where j is the nuclear current density and A is the vector potential of the photon field. Both calculations were simplified by considering only the electric-dipole component of the Hamiltonian; assuming that the capture would be dominated by a transition from an initial s-state to a fmal pstate. The initial-state was expressed in terms of coulomb wavefunctions for a hard-sphere potential with the nuclear radius adjusted to reproduce the experimentally observed elastic scattering phase shifts. Whittaker functions, adjusted to give the proper separation energies, were used for the final bound states. In both cases only the contributions to the -6integrals from outside the nuclear volume were used . These calculations made no estimate of the absolute cross section for the reaction, since no estimate is made of the reduced width of the 3 He+ 4 He cluster component of the 7 Be wavefunction. These reduced widths, which are independent of initial state energy, are left as fitting parameters to normalize the calculation to experimental data. Experimental data for total cross section and branching ratio are thus sufficient to define both partial widths and to establish a unique extrapolation to zero energy. The results of both of these investigations were consistent with the data of Holmgren and Johnston, indicating a negative slope in the cross-section factor at low energies. In 1963, Parker and Kavanagh (Pa63) reported a remeasurement of this cross section using detectors and apparatus similar to those used by Holmgren and Johnston. The accuracy of the experiment was improved by using thinner entrance foils and a shorter target cell. Using lineshape fits to the Nal(Tl) 1-ray spectra, the branching ratio was also calculated in this experiment. At this same time, Tombrello and Parker (To63) performed a more complete theoretical calculation. Using similar approximations for the initial- and final-state wavefunctions, they calculated not only the electric dipole part of the interaction Hamiltonian, but also the magnetic dipole and electric quadrupole components, fitting the initialstate wavefunction to the s-, p-, d- and f-wave phase shifts calculated from elastic scattering data. Again, the integrals were evaluated only in the extranuclear region. As shown in figure 2, the experimental data were in good agreement with this theoretical calculation, yielding a zeroenergy intercept for the cross-section factor S 34 (0)=0.47±0.05 keV-b . As in the Holmgren experiment, there was still considerable uncertainty in -7the low-energy measurements due to straggling and low count rate. An experiment performed by Nagatani, Dwarakanath and Ashery (Na69) was the first to use a "windowless" target, in which the beam enters the gas target through a narrow tube, thereby eliminating the problem of energy loss and straggling in an entrance foil. Since beam current could not be integrated directly due to ionization and charge exchange in the relatively poor vacuum upstream of the target, a two-cup calorimeter was used, which provided 6% accuracy with a maximum current of 4f.l,A. The measurements from this experiment, shown in figure 2, were combined with those from the Parker and Kavanagh work to give an intercept of S 34 (0)=0.61±0.07 keV-b using a polynomial fit. The continuing solar neutrino problem has prompted an experimental group in MD.nster (Kr79) to undertake a remeasurement of the lowenergy 3 He(o:.7)1Be cross section. Although their windowless target system is similar to that used by Nagatani et al., the use of high-resolution, lithium-drifted germanium 7-ray detectors can improve the accuracy of the measurement by allowing an independent measurement of beam energy, by resolving the three 7 rays of interest and by separating these 7 rays from beam-related background. Some measurements have also been made by this group using a high-pressure, supersonic-jet, gas target. providing a direct determination of 7-ray angular distributions . Early reports from this group (Ro80) indicated either an energy dependent branching ratio or an energy independent cross-section factor, in direct disagreement with both the early experimental results and the theoretical calculations. These reports motivated the present investigation of the cross section and branching ratio for this reaction and spawned a renewed interest in the theoretical calculation of direct-capture cross -8sections. Kim, Izum.oto and Nagatani (Ki81) employed three different techniques for their calculation of the 3 He(a,/') 7 Be cross section. The first method, involving a hard-core potential, was essentially the same as the previous calculation of Tombrello and Parker. For the partial widths, they used the same values obtained by Tombrello and Parker to fit the Parker and Kavanagh data. In the second calculation, the hard core potential was abandoned in favor of a more realistic, phenomenological Woods-Saxon potential, with the parameters adjusted to reproduce binding energies, elastic scattering data and the position and width of the f- state in 7 Be. In the third approach, the orthogonality condition model (Sa68) was used to construct properly antisymmetrized 3He+ 4He cluster wavefunctions in a local gaussian potential including a spin orbit term to split the ground state and the t- t first excited states of 7 Be. The results of these three calculations are shown in figure 3. It can easily be seen that, despite the different methods of calculation, these curves qualitatively agree with each other and with the earlier calculation of Tombrello and Parker. In a still more rigorous treatment, Uu, Kanada and Tang (Li81) have analyzed this reaction using a single channel (3He+ 4 He) resonating group calculation to obtain a correctly antisymmetrized seven-nucleon wavefunction in a non-local potential. In this calculation, only the electric-dipole component of the interaction was considered. The results of this calculation are shown in figure 3. Although there are no adjustable parameters in the cal~ulation, this curve should provide a reasonable upper limit on the cross section, since only the single cluster channel was - 9- considered. Williams and Koonin (Wi81) found that the integrals for the matrix element, using the extranuclear approximation, could be evaluated analytically for the logarithmic derivative [~ : J of the cross~section factor at zero energy. Their calculated value of -0.575 Mev-1, shown in figure 3 is also in good agreement with the previous theoretical calculations. Krawinkel et al. (Kr82) have now published the results of their windowless- and jet-target measurements which now agree with the previous experimental results for the energy dependence of branching ratio and cross-section factor. The normalization of their absolute measurements, however, gives a zero-energy intercept of 3 34 (0)=0.30±0.03 keV-b, 30-50% lower than the values presently adopted for solar-neutrino flux calculations. The objectives of the present experiment were to determine the absolute cross section for the 3 He(o:,7)1Be reaction at as low an energy as practical, and to make enough further measurements at higher energies to validate the theoretical extrapolation to solar temperatures. Because the entrance channel involves two isotopes of helium, it is necessary to use a gas target. Two independent measurements of the absolute cross section have been made. At low energies, the reaction cross section varies rapidly with energy (3.2% per keV at Ecm = 165 keV). For accurate measurements, a windowless target was used to avoid beam energy spread from energy-loss straggling in an entrance foil. The windowless target also allows higher beam currents and decreases beam-dependent background by eliminating the production of neutrons from the reaction - 1013 C(o:,n) on carbon deposits on the entrance foil. At higher energies (Ecm >900 keV) a gas cell target was employed. The problem of beamdependent background was eliminated by counting the residual 7 Be activity instead of the prompt capture -y rays to measure the production. This method allows a direct measurement of the angle-integrated total cross section. On the other hand, the branching ratio (u 1/ u0 ), needed for the theoretical fit, cannot be measured with this technique, and accurate measurements at lower energies are not possible . because of the low counting efficiency due to the 55-day half life and the 10% 7-ray branch of the decay of 7 Be. - 11- ll. EXPERIMENTAL APPARATUS AND PROCEDURE A Wmdowless Gas Target 1. Target The windowless, differentially pumped, recirculating gas-target system is show-n schematically in figure 4 and has been described previously by Dwarakanath and Winkler (Dw71). Although much of the apparatus is the same as that used in the measurement of Nagatani, Dwarakanath and Ashery (Na69), the use of a high-resolution -y-ray detector, low target pressure and a high current calorimeter significantly improves the experimental accuracy in the present measurement. The target system consists of three chambers separated from each other and from the beam-line by a series of canals. The first chamber (A) is connected to a -6-inch oil diffusion pump. This chamber is separated from the beam-line by a 9. 7-mm diameter water-cooled canal Chambers A and B are connected by a 10-cm long stainless-steel canal 5.4 mm in diameter. On the upstream side of the canal is an electrically isolated 3.2-mm diameter tantalum aperture, and the first 5 em of the canal contains a tantalum sleeve with an inside diameter of 4 .7 mm. The fore line of the diffusion pump is connected to the second chamber (B) which is pumped by a Heraeus model 1600 Roots pump. The output of this pump is compressed by a Heraeus model 152 two-stage Roots pump and fed - 12through a heat exchanger and a liquid nitrogen cooled zeolite trap for gas purification. The gas is then fed into the third chamber (C), which is the gas target. Gas pressure in the target cell is monitored with a Model FA160 Wallace and Tiernan pressure gauge, which reads 20 torr full scale. This gauge was calibrated against a mercury compound manometer. The target chamber (Figure 5) is 29-cm long from the upstream end of the entrance canal to the face of the calorimeter beamstop. The entrance canal to the gas target is a 3.2-cm long tantalum tube . The first 6 mm has a diameter of 4.3 mm, the remaining 2.6 rnm has a diameter of 4.6 mm. 2. Detection The -y-ray detector, a 100-cm3 lithium-drifted germanium crystal (Ge(Li)), Princeton Gamma-Tech serial number 1281, is located 13.3 em from the center of the entrance canal. The front face of this Ge(Li) detector is 25 mm from the beam axis at an angle of 90° to the beam. The detector and the target chamber are surrounded by 10 em of lead shielding to reduce -y-ray background. Between the detector and the target chamber is a 12-mm thick, 25-mm diameter lead aperture to limit the acceptance angle of the detector. The use of a high resolution -y-ray detector provides an accurate determination of beam energy since the capture -y-ray energy is dependent on the center of mass energy of the entrance channel. To obtain a homogeneous target and to isolate the detector from the entrance canal and beamstop requires an extended target and some of the advantage in using high-resolution -y-ray detectors is lost, since the 7-ray lines are broadened by a combination of beamenergy loss and doppler shift. - 13A 50-mrn3 , ruggedized, silicon surface-barrier detector, Ortec serial no. 19-452D, is located 13.6 em from the beam at an angle of 45°. The acceptance angle of this detector is defined by two 0.127-mm thick tantalum apertures, a 1.0-mrn vertical slit at 4. 7 em and a 0.62-mrn circular hole at 12.7 em from the center of the beam path. The particle detector was used to monitor gas contamination and to check beam current and target pressure. Typical particle spectra are shown in figure 6. A block diagram of the detector electronics is shown in figure 7. 3. Experimental Procedure At low energies (Ea= 401 to 1200 keV), 20 to 60 f,.LA 4He+ ion beams from the ONR-CIT JN Electrostatic Accelerator were used. The beams were energy analyzed with a 30° bending magnet. The layout of the beam line used in these measurements is shown in figure 8. The magnetic field strength of this magnet was monitored with a temperature stabilized Hall-effect probe. The energy resolution with this system was ±0.3% . Two additional measurements were made at Ea=1200 and 2740 keV, using a 90° double-focusing analyzing magnet, giving energy resolution within 0.1%. At 2740 keV, the 1-f,.LA 4 He+ beam was prepared with the ONR-CIT EN tandem accelerator. Beam energies were chosen at minima in the 13C(a,n) yield function to reduce neutron-induced background and to protect the Ge(Li) detector. Conventional current integration is not possible in windowless targets because of ionization of the low pressure gas in the target and upstream of of the entrance canal. Beam current was integrated using the calorimeter described in detail in appendix A. This calorimeter allowed higher beam currents than were used in the Nagatani experiment. As a result, gas-target pressure could be reduced, thereby - 14decreasing beam energy loss and straggling in the target. The low-energy measurements were made in groups of 2 to 4 different energies. During each group of measurements, the detector positions, bias voltages and the calorimeter base temperature and zero setting were not changed. Before and after each group of measurements, the 30° analyzing magnet hall probe was calibrated using the narrow resonances in 7 Li(o:,7) at Ea=401 and 819 keV (Be51), and 7-ray spectra of 152 Eu and 56 Co sources were accumulated for the purpose of energy cali- bration. One of the measurements in each group was made at Ea=819 keV for the purpose of normalization. Typical pressures in the target chamber during the runs were 2 to 3 torr. The measured pressures in the beam line, chamber A and chamber B were maintained below 4X 10-6 , 2x 10-5 and 0.02 torr respectively. Target pressure, calorimeter base temperature, analyzing-magnet current, hall probe reading, beam current and integrated charge were recorded at least once every hour. Every two hours, the accumulated 7-ray and particle spectra were written on magnetic tape, and a new particle spectrum was started. The extended target requires that the 7-ray detector efficiency be known both as a function of 7-ray energy and position in the target. This was accomplished by moving calibrated 56 Co, 152Eu and 7 Be sources along the axis of the target chamber, accumulating spectra at 1-cm intervals. - 15B. Gas-cell Activity Measurement 1. Target The gas target cell for the activation measurements is shown in figure 9. The beam is collimated with a pair of 3-mm tantalum apertures . An aluminum electron-suppression ring is connected to the beam-line and to the target cell by 2.5-cm sections of ceramic insulator. Two 4-mrn copper tubes provide increased pumping to the volume downstream of the apertures. The beam enters the cell through a window consisting of a 0.66-}Lm nickel foil on which 0.20 J.Lm of copper has been deposited. The purpose of the copper is to increase the thermal conductivity of the entrance foil, allowing a higher beam current. The entrance foils are attached to the foil holders with high-vacuum epoxy. The target cell is made of 0.4-mm thick stainless steel with an inside diameter of 12.7 mm. When the cell is placed on the foil holder, there is approximately 10 mrn between the entrance foil and the back of the cell. A 0.025-mrn platinum catcher foil was indium-soldered to the end of the target cell, and the sides of the cell were also lined with platinum foil. The cell was connected to a gas manifold (shown schematically in figure 10) by a 2-mrn stainless steel tube with a section of glass insulator. The beam current was integrated in the conventional manner, by collecting the current from the electrically isolated target. 2. Detection Prompt 1 rays from the target cell were monitored with a 3X3 Nai(Tl) scintillator, for the purpose of beam energy determination. The front face - 16- of the detector was 2 em from the center of the target cell at goo to the beam to eliminate doppler shift. The 100-cm3 Ge(Li) detector described in section B.2 was used to count the 7 Be activity. During the counting, the detector was surrounded by 10 em of lead to reduce background. The detector electronics were the same as those used for the windowless target experiment (Figure 7). 3. Experimental Procedure The target cell was filled to ""370 torr with gg.g% 3 He gas. Beams of 4 He+ ions from the ONR-CIT EN tandem accelerator were used for the two activation measurements at Ea.=2.2 and 3.4 MeV. The beams were analyzed with a goo double-focusing magnet stabilized by a digital NMR gaussmeter. Beam current was kept below 0.55JLA to protect the entrance foil and to limit target heating. During the runs, the end of the target cell was cooled by a stream of air. Beam current, total charge run, NMR frequency and target pressure were recorded at least once every hour, and gas was added when the pressure fell by more than 1%. The production was continued until the estimated number of 7 Be atoms produced exceeded 4 million. The suppression ring was maintained at -300 volts relative to the target cell and the beam-line to prevent secondary electrons produced on the apertures from reaching the target cell. Current flow from the suppressor was monitored with an ammeter, and was always less than 1% of the total beam current on target during the production runs. When the production was completed, the length of the target cell was measured using a depth micrometer. Additional target length from - 17bowing in the entrance foil caused by gas pressure was measured relative to the foil holder by using a calibrated microscope. The platinum catcher foil was then removed from the target cell and attached to a 3-mrn thick lucite source holder on the front face of the Ge(Li) detector. The beam spot on on the platinum catcher foil was aligned with a fiducial mark on the source holder so that it would be centered on the detector. The side and entrance foils were also counted in this manner to determine if any of the implanted beryllium had been sputtered out of the foil by the beam. The {-ray detection efficiency was measured by counting a weak calibrated 7Be source in this same geometry. Beam energy loss in the entrance foil was measured by observing the energy shift in narrow (a:,{) resonances with the beam passing through the foil. For the measurement at Ea=3400 keV, the Ea=3198 keV (Sm62) resonance in 24Mg(a:,{') was used. A metallic magnesium target was prepared by reducing and evaporating 99.94% enriched MgO onto a 0.25mrn, oxygen-free copper blank. This target was then indium-soldered to the end of the gas cell. The 11.0 and 12.7 MeV {-rays from this reaction were counted using a 3X3-in Nai(Tl) scintillator and excitation functions for the resonance (Figure 11) were produced, first with no entrance foil, then with the entrance foil and 95, 190 and 380 Torr of 3 He gas in the cell. The effect of beam heating on the target was also studied using this resonance. At 380 torr target pressure, the shift in beam energy at resonance was measured with 150, 300, and 450 na of beam current. It was found that the 450 na beam produced a 6% decrease in effective target thickness, more than the 3% predicted on the basis of energy loss in the gas. It is believed that the additional 3% decrease is caused by local heating of the gas in the region of the entrance foil. - 18For the Ea=2400 keV measurement, a resonance in 14 N(o::y) at Ea=2353 keV (Ro73) was used. Since the measurement was made using a N2 gas target, this resonance could not be observed without the entrance foil. Reaction 1 rays between 2.8 and 6.5 MeV were counted and the excitation functions for target gas pressures of 160 and 340 torr, shown in figure 12, were produced. - 19- ill. DATAANALYSIS A ·windowless Gas Target System The yield of l'i from a capture reaction with cross section ui (E) in an extended gas target can be written as an integral over the length of the target: (III. 1) where: Ji =total yield of 'li from the extended target fi (Ecm. 8)=angular distribution function of 'li N a=total number of beam particles nr=target number density c(En,z )=detection efficiency as a function of -y-ray energy and position. The calculation of these five quantities and their associated errors will be discussed below. Substituting, in equation (III.1), the expression for ui in terms of the cross-section factor (equation 1.6) gives, (III. 2) Making the assumption that the cross-section factor is constant over the range of energies in the target, the yield becomes, -20(III.3) The center-of-mass energy and the -y-ray energies in equation (III.3) will be functions of position due to doppler shift and energy loss in the target: (III.4) where 1 and {3 are the relativistic parameters for the recoiling 7 Be nucleus, Q 0 and Q 1 are the Q-values for the ground-state and first excited-state radiative captures and e is the angle to the center of the -yray detector. The energy loss, dE I dx, was calculated from the target density using the formulation of Ziegler (Zi77) for helium ions on helium gas. A computer program was written to soive the integral (h) in equation (III.3) and to calculate the energy centroid (E 0 ) of the -y0 distribution, (III.5) and Eo= I1 0 j ~expl E-ro r 164.1251 _ ~ f o(Ecm ,e) t;(E70 ,z) dz . em vEcm (III. 6) - 21 For each measurement, the incoming beam energy, Ea., was adjusted to reproduce the observed centroid, E 70 , of the /o yield. The S-factor was then calculated directly for each of the three {-ray transitions using the formula, (III. 7) where Et is the center- of-mass beam energy corresponding to the observed energy of the ground-state capture 1 ray, (III. B) The branching ratio is given by, for i =1 and 429. (III. 9) The total cross-section factor for the 3 He(a.,,)1Be reaction is equal to the sum of the cross-section factors for radiative capture to the ground state (S 0 ) and first excited state (S 1) of 7Be. The first excited state capture cross-section factor is the weighted average of the values calculated from the yields of the two cascade 1 rays, y 1 and 1 429 (see figure 1), S 34 =S 0 +aS 1 +bS 429 , (III.10) where a and b are the weighting factors, (III.ll) Similarly, the branching ratio is the weighted average of p 1 and p 429 , - 22(III.12) The total reaction cross section, Utot, can then be calculated from the total cross section factor using the inverse of equation (I.6). In the following discussions of the measured parameters, the notation !1x is used to indicate the probable error in the quantity x and the notation ox is used for the relative error, Ox =!1x I x. 1. {-ray yield Oi) Typical {-ray spectra for Ecm =165, 350, and 500 keV are shown in figure 13 with the capture {-ray peaks (/o and { 1 and { 429) indicated. Also shown are the important background -y-ray lines. The -y-ray yield ( Ji) and the statistical error (!1Ji) for each transition was calculated by integrat:ing the total number of counts under the peak and subtracting the number of counts below a straight-line least-squares fit to background regions above and below the peak, using the program described in detail in appendix B. This program also calculated the centroid of the {-ray distributions, E70 , from which the target energy (Equation IlLS) was calculated. Since the Q-value for the reaction is very accurately known, the error in the target energy (l1Et) was taken to be equal to the error :in the ro centroid (!1E10). 2. Angular Distribution Function (fi(Ecm•e)) The theoretical angular distribution functions of Tombrello and Parker were used in these calculations. Since only the P 0 and P 2 com- -23ponent have any significant value over the range of energies examined in this experiment, all other components were ignored, and the integrals in equations III.5 and III.6 were calculated using the angular distribution function (III.13) Since the theoretical P 2 coefficient is a slowly varying function of energy, it was assumed to be a constant for each of the measurements. The values of a 20 and a 21 used in these calculations are shown in table 1. The 'l-ray transition from the first excited state to the ground state of 7 Be is isotropic. 3. Number of Beam Particles (N a) The current Uc ), in microamperes, from the calorimeter controller (see appendix A) is equal to the temperature difference (T 2 -T 1), in Kelvins, between the beamstop and the water-cooled heatsink . The calibration constant for the calorimeter was found to be k =1.062±0.009 W/K. Because of the high thermal conductivity of helium, an additional calculated quantity, 0.065 W/K must be added to this constant. The temperature difference can be converted to beam power (p) by multiplying by k. This beam power is also given by the particle energy times the beam flux in particles per second, (III.14) where Ec is the energy of the beam at the calorimeter, calculated from the observed target energy Et and the additional beam-energy loss in the - 2413.6 em from the center of the target cell to the calorimeter beamstop Ec =2.327 Et -13.6 dE dx (III.15) He The number of beam particles is then found by integrating equation III.14, (III. 16) Equation III.16 was used to convert the integrated calorimetercontroller current into the number of beam particles . The random error inN a is given by, (III.17) where, assuming a 5% error in the energy loss calculation, (Me ) 2 is given by (b.Ec )2 =(2.327 b.Et )2 + (0.05 Ezoss )2, (III. 18) 6r is the relative calorimeter zeroing error (1%) and 61 is the current integration error (0.5%). In addition, the calorimeter calibration intraduces a 1% systematic error in the data. 4. Target Number Density (nT) The gas target density was calculated from the pressure, p, and temperature, T, of the gas which were assumed to be constant over the length of the target cell (not including the entrance canal) . The pressure of the gas is measured with an aneroid pressure gauge , which was calibrated against a McLeod compound manometer. The mean pressure was -25calculated from the values which were recorded hourly during the runs, and the error in the pressure, llP, was taken to be the calculated standard deviation of this mean pressure. The gas temperature can not be measured directly, since a radial temperature gradient exists in the target cell, but the temperature of the gas along the beam path can be estimated by assuming that all of the energy deposited in the target is conducted by the gas to the walls of the chamber, which act as an infinite, room-temperature heat sink. This assumption is reasonable, since the energy deposited was always less than 0.1 WI em. The temperature difference ( T') between two concentric cylindrical surfaces with a heat flow of H WI em was calculated with the expression T' =__l!__ln( b I a) 2rrk (III.19) where k is the thermal conductivity, b is the inner radius of the target chamber and a is the radius of the beam. This quantity was calculated for each run (See table 1) and added to the room temperature to give the effective target temperature, T. The decrease in target thickness as a function of energy deposition per unit length calculated in this manner agrees with the observations of Gorres et al. (Go80) , for a gas target of similar dimensions. The target density in atoms per cm3 is then given by, [__.E_] ' n _ No [273.15] .,.- 22,400 T 760 (III.20) where N 0 is Avogadro's number, Tis in Kelvins and p is in torr. The error in n.,. is simply given by, (III.21) - 26where the temperature error is assumed to be ±4 K. The calibration of the pressure gauge introduces an additional 2% systematic error. 5. Detector Efficiency (E:(E7 ,z )) Since the doppler broadening of ')'429 is very small and since the ')'-ray energy is independent of energy loss in the target, no energy dependence was included in the efficiency function for this transition. The integral in equation III.5 was numerically evaluated in 1-cm steps using discrete values interpolated from the detector efficiency curves measured for the 411-keV and 444-keV transitions in 152Eu. For the capture ')'-rays, the calibrated source efficiency data were fitted to an empirical function of the form: c(E.,,z) If = 1+ l_z_ r 'l (III.22) cEd7 Figure 14 shows the measured efficiency as a function of position for several energies corresponding to 1-ray lines from the calibrated 56Co and 152Eu sources. Also shown in figure 14 is the best fit of equation III.22 to these data. The parameters used in this fit are given in table 2. In figure 15, the sum, over the length of the target, of the measured efficiencies was compared to a corresponding sum over the efficiency function (Equation III.22) for several ~-ray lines between 1238 and 2598 keV; approximately the range of the observed 'Yo and 1 1 transitions in this experiment. The errors shown include only the statistical error in ,-ray yield and the error in source ')'-ray branching ratios. From the data in figure 15, an estimated 2% random error was assigned to the detection - 27 - efficiency. A systematic error of 3% is introduced by the "'j-ray source calibrations. 6. Calculation of errors The statistical errors in the individual cross sections were calculated from the relation, (III.23) The errors in the total cross section and branching ratio are more cornplicated due to correlated errors in the weighted averages and sums . From equation (III.10) the error in the total cross section is .to2 _ .to2 .to2 1 r 2 ( u..t2 Yo + u..t2l:o) u Utot- u n,. + u Na + ~O'o (III.24) tot Similarly, from equation (III.12), the error in the branching ratio can be written, (III.25) The error in the cross-section factors are then calculated from, 0zS =o2U + lro Ecm [ 1- 164.125] 2- rp;- ] 2 (III.26) VLcm A summary of the systematic errors in this measurement is given in table 3. - 28- B. Gas-cell Activity Measurement The gas cell activity measurement was divided into two phases; the production phase, in which the 7 Be is produced and implanted in the platinum catcher foil, and the counting phase, in which the 'i rays from the {3 decays of the 7 Be are counted using a Ge(Li) detector. The rate of production of 7 Be atoms is given by, dNse d1 (III.27) where ia. is the beam current in particles per second, nT is the target density and Ecm is a function of position due to energy loss in the gas, (III.28) and Efoil is the average beam-energy loss in the entrance foil. Over the range of energies in the target, Utot (Ecm) is very nearly linear and is constant to within 6%, so the integral in equation (III.23) can be approximated by a constant production rate, (III.29) where Et is the center-of-mass energy at the center of the target and NT is the total gas-target thickness. For a time period of duration t, with constant current ia. and target density nT, the number of 7 Be atoms produced will be (III.30) The production phase was divided into m time periods. For each period, - 29the duration (ti). average current (iai) and target density (nri) were calculated from the time, charge and pressure which were recorded approximately every hour during production. The estimated production rate (Pi) was calculated from these currents and target densities using an estimated cross section, Uest. The total estimated 7 Be production at the end of the production periods is given by, Nest l pi -)..t r i-1 =_2.:m ~( 1-e ) exp l-A. _2.: ti . ~~1 (III.31) ]~1 A The counting period begins at the end of the last run (t' =0) The estimated number of 7Be decays between t 1' and t 2 ' is given by, (III.32) The number of 7 Be decays during the counting period can be calculated from the yield of decay 1 rays ( Y478) d - y478 Be- 0.104 t: where t: (III.33) is the detector efficiency and 0.104 is the measured decay branch to the first excited state of 7Li. The total cross section . Utot (Et). can then be found by multiplying the estimated cross section by the ratio of the measured decays to the estimated decays, dse Utot =(Jest -d--. est (IIL34) The cross-section factor, S 34 (Et). was then calculated from Utot using equation I.6. - 301. /'-ray Yield ( Y47a) The catcher-foil -y-ray spectrum for the Ea=3400 keV activation measurement is shown in figure 16. The yield and probable error (6. Y478)in ilie yield of the 478 keV /' ray were calculated using the procedure described in appendix B. 2. Beam Energy (Et) For the Ea=3400 keV measurement, the center-of-mass beam energy was calculated from the centroid of the prompt /'-ray peak, using equation (III.8). Figure 17 shows the capture -y-ray spectrum and the 24 Na spectrum used to calibrate the /'-ray energy. The capture /'-ray energy and its probable error were calculated using the method described in appendix B. The /'-ray centroid, E70 =2834± 10 keV implies a beam energy of Et = 1247± 10 keV. This beam energy was also calculated from the incident beam energy and the energy loss in the foil and the target gas . These energy losses were measured by observing the shift in beam energy of the center of a narrow resonance with the beam passing through the entrance foil. Foil thickness was then calcus of .Ziegler (Zi77). For the foil used in this measurement, the observed en keV 24Mg(a./') 28 Si resonance was 410±5 keV, corresponding to a foil thickness of 0.86 f.-LID (0.66 f.-LID nickel + 0.20 f.-LID copper) . This implies an energy loss of 432±5 keV at the incident beam energy Ea=3400 keV. Including the 50±3 keV energy loss in the helithe calculated beam energy is Et =1255±4 keV in good agreement with the /'-ray calculation above. - 31- At Ea=2750 keV, only the energy-loss method was used to calculate target energy. An energy shift of 480±8 keVin the 2348 keV, 14N(a,,) 18F resonance was observed, corresponding to a foil thickness of 0.87 J.Lm. The calculated energy loss for an incident Ea=2750 keV beam is then 486±8 keV in the entrance foil and 62±3 keVin half the gas target, implying an average target energy of Et =947±6 keV. 3. Current Integration (ia) Since the beam consists of singly charged 4 He ions, the electrical current from the isolated target is equal to the beam particle current. Current flow from the secondary electron suppression ring was monitored, and amounted to less than 1% of the target current. The target current was integrated using a Brookhaven Nuclear Instruments model 1000 current digitizer, with a specified accuracy of 0.05%. Care was taken to accurately adjust the zero offset before each run, so the estimated relative error in the current is taken to be 1%. 4. Target Thickness (N-r) As in the windowless measurement, the target density, n-r, was calculated from the pressure and temperature of the gas target. The effective temperature was calculated from the current dependent shift in the energy of the 24Mg(a,')') resonance. The observed shift was -6±2% at the resonance energy with a beam current of 0.45±0.03 J.LA. and decreased linearly for currents of 0 .30 JLA and 0.15 J.LA. At Ea=3400 keV, the average current was 0.45 J.LA, so the effective temperature was taken to be T = (1.06±0.02) Troom , (III. 35) -32- or 316±6 K. For the Ea=2750 keV measurement, although the average beam current was lower, 0.33±0.03 f..lA, the energy loss, and therefore the beam heating of the entrance foil was 10% higher, giving an effective temperature T = (1.05±0.02) Troom, (III.36) or 313±6 K. The total target thickness is given by _ No NT- 22,400 [273.15][_E_]l T 760 ) (III.37) where l is the measured target length. The pressure error was taken to be the standard deviation of the mean target pressure during production combined with the calibration error of the Wallace and Tiernan gauge. The error in the target thickness will then be - .x-2 + .r:2 + .~:2 v.r:2N.,.v p v T v l . (III.38) 5. Detection Efficiency (c) A calibrated 7 Be source was counted in the same geometry as the catcher foil. The 'l-ray yield from the source, Ys, was calculated using the method described in appendix B. The counting efficiency is then given by; c=0.104at' (III.39) where 0.104 is the probability for the {3 decay of 7 Be to the first excited -33state of 7 Li, a is the calibrated source strength in disintegrations per second and tis the counting time in seconds. The strength of a calibrated source with an original activity a 0 and a decay constant A is a =a0 e-)..t, (III.40) where t is the elapsed time since the calibration. The error in this activity is (III.41) and the random error in the detection efficiency is (III.42) The branching probability error is not included in this calculation since this same value was used in the original calculation of source strength. 6. Calculation of errors Since the number of decays during production is small (about 1% of the total production) and since the counting began immediately after production, the error in A will have no appreciable effect on the error in Nest, and the total cross section is approximated by; (III.43) where N a is the total integrated beam. The relative error in N a is equal to the relative error in the current integration, so the relative error in the total cross section is - 34- (III.44) in which t' represents the elapsed time during counting and 0.02 is the relative error in the measured 10.4% decay branch (Aj74) to the first excited state in 7 Li. Values for all of the measured parameters and their probable errors are shown in table 4 for both of the gas cell activity measurements. -35- IV. RESULTS AND CONCLUSIONS A ExperlinentillResul~ Cross sections and branching ratios for the reaction 3 He(a:yfBe were calculated using the methods described in section III.A for each of the 19 windowless target measurements. The results of these calculations are shown in table 5. The efficiency calibration was performed immediately after, and in the same geometry as measurements C and D. Since small changes in detector geometry were possible between groups of runs, the cross section and S-factor data in each of the other four groups were normalized to measurement D through their corresponding Ea=820 keV measurements (F,K,N and Q). This normalization never amounted to more than 7%. Between the two high energy measurements (T and U), since the target system had been moved to another beam line, the detection efficiency was remeasured at several points using the 152Eu source. This calibration showed less than 1% change in the measured efficiency, so no normalization was applied to these points . Also shown in table 5 are the results of the two gas cell activity measurements. The absolute cross-section factor measurements for both experiments are shown graphically in figure 18 along with the results of the branching-ratio calculations from the windowless target. The results of these two experiments are in good agreement with each other and with the two-parameter fits of the Tombrello and Parker calculations to the data. The low-energy extrapolation of this fit gives an intercept of - 365 34 (0)=0 .52 keV-b. A x 2 analysis indicates an error for the fit of ±0.01 keV-b. Including the systematic errors in the two experiments, shown in table 3, the best value for the low-energy intercept of the cross-section factor is s34(0) = 0.52±0.03 keV-b (1-a error) I (IV.l) in good agreement with both the previous measurement of Parker and Kavanagh (5 34 (0)=0.47±0.05 keV-b), and that of Nagatani, Dwarakanath and Ashery (5 34 (0)=0.61±0.07 keV-b). Agreement with this second measurement is improved if the polynomial fit to the combined data which was used to obtain the extrapolated value is replaced with an independent fit of the Tombrello and Parker curve, giving an intercept of 5 34 (0)=0.58±0.07 keV-b. The significant discrepancy between these measurements and the recently published result, 5 34 (0)=0.30±0.03 keV-b, of Krawinkel et al. (Kr82) has been extensively studied and several possible sources of the disagreement have been uncovered . Because of the similarity between the experimental techniques used in the windowless, recirculating, gastarget measurements, the first impulse is to investigate the areas in which the two measurements differ. The most obvious difference between the two experiments is the method of beam-current integration. Whereas our experiment used the calorimeter described in appendix A, the Mimster collaboration integrated their beams by counting the scattered particles using ruggedized, silicon surface-barrier detectors at 30° and 45o to the beam. There is considerable uncertainty associated with this method; the high beam currents and low energies require very small collimators to reduce the counting rate to a manageable level; multiple - 37 - scattering between these apertures can alter the count rate, and, at low energies, the particle peaks are in the tail of the detector noise. A study of our particle spectra showed 10% deviations from the calculated Rutherford scattering yield in spite of the fact that we used lower beam currents and larger apertures and obtained better resolution of the scattered a-particle and recoil 3He peaks than the Milnster collaboration. However, it seems unlikely that any combination of these effects could be responsible for the energy independent 40% increase in apparent beam current which would be needed to produce the observed cross sections. On the other hand, for our calorimeter to produce a 60% decrease in measured beam flux would require 0.6 W/K to be convected away from the beamstop by the target gas and would mean that our highest-current measurement had an average current of more than 100 f.J.,A, even though no more than 75 f.1.,A of beam was observed on the tantalum beam viewer upstream of the target system (figure 8). In addition, some other mechanism would be needed to produce a similar increase in measured cross section in the gas-cell activity measurements. Perhaps the most likely source of the disagreement lies in the measurement of detection efficiency. In the Munster experiment, only a single commercially prepared 152Eu source was used to calibrate the low energy detection efficiency in the windowless target. At higher energies, reaction -y rays from 14N(p ,-y) and 160(p ,-y) were measured and normalized to the europium source at E 7 =1408 keV. In figure 5 of reference Kr82, the maximum absolute detection efficiency is plotted as a function of -y-ray energy. With an 80-cm3 Ge(Li) detector located 24 mm from the center of the beam, they measured an efficiency for detection of the 1408 keV transition from the 152Eu source C"'0.57%. In our experiment, using a 100-cm3 - 38Ge(U) detector at a distance of 25 mm from the beam, the peak efficiency was only c=0.46%, 20% less for a detector with a 25% larger volume. Depending on the relative geometry of the two detectors, this effect could certainly be responsible for the disagreement between the two experiments. Furthermore, in routinely checking the calibration of our commercially supplied 152Eu source against several other calibrated sources in the lab (6 °Co, 7Be, 137 Cs and 22 Na), it was found the the actual source activity was 30% less than that quoted by the supplier, an effect which would have further lowered our measured efficiency to 0.35%, so it is not implausible that a commercially prepared source could be miscalibrated by this amount. In 1981, a preprint was circulated reporting on a gas-cell activation experiment by Yolk, Krawinkel, Santo and Wallek (Vo81) in Munster. This short letter indicated a zero-energy S-factor intercept of 5 34 (0)=0.61±0.06 keV-b based on a single measurement at Ea=1577 keV. This preprint was later withdrawn from publication. B. Relation to theory Figure 18 shows the results of these experiments and the best fit of the Tombrello and Parker (To63) curve to the data. The reduced ·widths for the 3 He + 4 He cluster strength of the bound states used in these fits are er =1.29 and oS =1.33. This indicates a strong, nearly equal cluster 12 12 component in both the ground and first excited states of 7 Be, consistent with the picture of these states as a 3 He and 4 He in a relative p-state. In table 6, the zero-energy intercepts of the best fits to five different theoretical curves are compared. The value 5 34 (0)=0.523 was adopted on - 39- the basis of the three best fits to the Tombrello and Parker hard-core calculation, the Kim Izumoto and Nagatani (Ki81) Woods-Saxon phenomenological potential model and the Liu Kanada and Tang (Li81) resonating group method . The similarity of the curves calculated using several different models for the nuclear potential shows the validity of the extranuclear approximation in the original calculations; the capture cross section is quite insensitive to the details of the nuclear wavefunction. C. Astrophysical Implications The most recent theoretical calculation of solar-neutrino :flux was reported by Bahcall et al. (Ba82). The predicted 37 Cl capture rate in the calculation is 7.6±3.3 SNU (3-a error) adopting a value of 0.52±0.15 keV-b (3-a error) for the zero-energy intercept of the 3 He(a:;y)?Be cross-section factor . The only effect this present measurement will have on this calculation is to reduce the uncertainty in the calculated :flux. -40- APPENDJXA In previous experiments in this lab (N a69 and Dw74) beam current integration in a windowless, recirculating, gas-target was accomplished by using a two-cup calorimeter, in which the temperature of a dummy cup was matched to that of an identical beamstop by resistive heating . The integrated beam power is then equal to the power delivered to the dummy-cup heater. These calorimeters usually suffered from low accuracy (4-6% random error), and were designed for beam power less than 6 W. Using the principle that, over a relatively narrow range of temperatures, the heat flow in a metal rod is proportional to the temperature difference between the ends of the rod, we have designed a calorimeter which is capable of integrating up to 100-W beams. The body of the calorimeter, shown in figure 19, is turned from a single block of copper. It consists of a cylindrical beamstop (25-mm diam. by 12.5-mm long) connected by a 25-mm long by 10-mm diameter conduction rod to a large, cylindrical, water-cooled heatsink. The temperatures of the beamstop, T 2 , and the heatsink, T 1 , are measured by two Analog Devices model AD590 temperature transducers. These devices have the property that, with a potential between 5 V. and 30 V. applied across them, they pass a current in f.i,A equal to the Kelvin temperature. With the two transducers placed in the bridge circuit as shown in figure 20, the current in f.J,A flowing across the bridge, I, is equal to the temperature difference, ~T. between the ends of the conduction rod, and is therefore proportional to -41- the beam power. The integrated number of beam particles, n, can then be found from the relation n=(AI Ec) D where A is the calorimeter calibration constant in W/K, Ec is the beam energy at the calorimeter, and Dis the integrated calorimeter current D= f I dt =f D. T dt . If Ec is in eV, n will be in units of particle Coulombs, with Ec in joules, n will be the number of particles. To determine the calibration constant, A, the calorimeter was placed at the end of a faraday cup and the electrical integration was compared with calorimetric integration. During the calibration runs, the temperature of the water-cooled base of the calorimeter was maintained at 298± lK. Beam current energy and integration times were varied during the calibration to test the linearity and repeatability of the calorimetric integration. The results of the calibration are shown in Table 6. For two of the calibration runs, the current integrators measuring the beam and calorimeter current were switched to check for calibration errors. During the final run, the beam was turned on for 100 seconds, then turned off. The calorimetric integration was continued until the current fell below 0.01 J.LA (D.T < 0.01K). Figure 21 shows the beam current and D.T as a function of time . The logarithmic decay of D.T has a characteristic time constant of 25 seconds. Heat loss by convection was estimated by measuring the characteristic time constant of the calorimeter in nitrogen at atmo sphe ric pressure . -42Conduction in nitrogen gas for the calorimeter geometry is calculable , and amounts to less than 1% of the copper rod conduction. The time constant of 23 seconds at this pressure shows convection losses of about 8%. Since convection losses in this cylindrical geometry and in this temperature and pressure range are approximately proportional to the square root of the pressure (Mc54), they should be negligible at pressures below 10 Torr. -43- APPENDIX B 7-RAY YIELD CALCULATION Peaks in the 7-ray spectra were integrated using the interactive program TEKHIST. A multi-channel analyzer spectrum is displayed on a Tektronix graphics terminal, and the user defines the peak with three regions; one region containing the peak, and two background regions, usually on either side of the peak. A weighted, least-squares, linear fit to the background, of the form y =a+bx, is calculated using the formulas; l ~n~!__-~...!._L>, ·2 . (B.l) =~ l; ! i l;i -n l; ;i;j. (B.2) d=~-1 l:£_[l:~f Yi Yi Yi (B.3) a= Yi Yi and b where Yi is the number of counts in channel i, n is the total number of channels in both background regions and the summations are over all of the channels in both background regions. The x2 for the background linear fit is calculated from, (B.4) -44- The ?'-ray yield is then the sum of the counts in the peak minus the interpolated background, Y = 2: (Yi -a -b i) = 2: Yi -a 71p -b 2: i, peak peak (B.5) peak where 71p is the number of channels in the peak region. The error, oy, in the yield is given by, (B.6) The centroid of the peak is calculated from, C tr = 2: i (yi-a-bi)], (B.7) !Peak and the error in the centroid is approximated by, D.C=wD.Y Y, where w is the full width at half maximum of the ?'-ray peak (B.8) -45- REFERENCES Aj79 F . Ajzenberg-Selove, Energy Levels of Light Nuclei, A=~ 10, Nuclear Physics A320, 1( 1979). Ba67 A. D. Bacher, PhD. Thesis, California Institute of Technology, (1967). Ba63 J. N. Bahcall, William A. Fowler, I. Iben Jr. and R. L. Sears, Astrophysical Journal 137, 344(1963). Ba64 John N. Bahcall, Physical Review Letters 12, 300( 1964) . Ba68 J. N. Bahcall, N. A. Bahcall, W. A. Fowler and G. Shaviv, Physics Letters 26B, 359(1968). Ba82 John N. Bahcall, Walter F. Huebner, Stephen H. Lubow, Peter D. Parker and Roger K. Ulrich, Reviews of Modern Physics 54, (1982). Be51 W. E. Bennett, Paul A. Rays and B. J. Toppel, Physical Review 82, 20(1951) . Be39 H. A. Bethe, Physical Review 55, 434(1939). Bu57 E. Margaret Burbidge, G. R. Burbidge, William A. Fowler and F. Hoyle, Reviews of Modern Physics 29, 547(1957) . Ca58 A. G. W. Cameron, Bulletin of the American Physical Society Series II 3 , 227( 1958). Ch61 R. F. Christy and I. Duck, Nuclear Physics 24, 89(1961) . Cl80 B. T. Cleveland, R. Davis, Jr. and J. K. Rowley, Proceedings of the Neutrino Mass Mini-Conference, University of Wisconsin Report 186, 38( 1980) . -46Da55 R. Davis, Jr., Physical Review 97, 766(1955). Da64 R. Davis, Jr., Physical Review Letters 12, 303( 1964). Da68 R. Davis, Jr., D. S. Harmer and K. C. Hoffman, Physical Review Letters 20, 1205(1968). Dw71 M. R. Dwarakanath and H. Winkler, Physical Review C4, 1532(1971). Dw74 M. R. Dwarakanath, Physical Review C9, 804(1974) . Fo51 W. A. Fowler, Physical Review 81, 655(1951). Fo58 W. A. Fowler, Astrophysics Journal, 127, 551(1958) . Fo72 W. A. Fowler, Nature 238, 24(1972). Go80 J. Gorres, K. U. Kettner, H. Krawinkel and C. Rolfs, Nuclear Instruments and Methods 177, 295(1980). Gr69 V. Gribov and B. Pontecorvo, Physics Letters 28B, 493(1969). Ho59 H. D. Holmgren and R. L. Johnston, Physical Review 113, 1556(1959). Ki81 B. T. Kim, T. Izumoto, K. Nagatani, Physical Review C23, 33(1981). Kr79 H. Krawinkel, K. U. Kettner, W. E. Kieser, C. Rolfs, R. Santo, P. Schmalbrock, H. P. Trautvetter, R. E. Azuma and J. W. Hammer, Jahresbericht 1978, Universitat Munster, p. 35( 1979). Kr82 H. Krawinkel, H. W. Becker, L. Buchmann, J. Gorres,K. U. Kettner, W. E. Kieser, R. Santo, P. Schmalbrock, H. P. Trautvetter, A. Vlieks, C. Rolfs, J. W. Hammer, R. E. Azuma and W. S. Rodney, Zeitschrift fur Physik .A304, 307(1982). Li69 L. Marshall Libbey and F. J. Thomas, Nature 222, 1238(1969). Li81 Q. K. K. Liu, H. Kanada and Y. C. Tang, Physical Review C23, 645( 1981). -47Mc54 W. H. McAdams, Heal Transmission, McGraw-Hill, New York, p.176(1954). Na69 K. Nagatani, M. R. Dwarakanath and D. Ashery , Nuclear Physics A128, 325( 1969). Pa63 P. D. Parker and R. W. Kavanagh, Physical Review 131, 2578(1963). Pa66 P. D. Parker, Physical Review 150, 851(1966). Ro73 C. Rolfs, A. M. Charlesworth and R. E. Azuma, Nuclear Physics A199, 257(1973). Ro80 Claus Rolfs, Proceedings of The 1980 International Summer School on Nuclear Structure, to be published. Sa68 S. Saito, Progress of Theoretical Physics 40, 893(1968). Sa52 Edwin E. Salpeter, Physical Review 88,547(1952). Sm62 P. J. M. Smulders and P.M. Endt, Physica 28, 1093(1962) . To61 T. A. Tombrello and G. C. Phillips, Physical Review 122, 224(1961) . To63 T. A. Tombrello and P . D. Parker, Physical Review 131, 2582(1963) . Tr81 H. P. Trautvetter, Conunents on Nuclear and Particle Physics 10, 123(1981). Vo81 H. Volk, H. Krawinkel, R. Santo and L. Wallek, preprint, unpublished. Wi81 R. D. Williams and S. E. Koonin, Physical Review C23, 2773(1981). Zi77 J. F. Ziegler, Helium : Stopping Power and Ranges in AU Elemen- tal Matter, Pergamon Press, New York(1977) . -48- TABLE 1 WINDOWLESS TARGET RUN PARAMETERS The table on the next two pages shows the run parameters for each of the individual windowless target measurements. The groups of measurements described in section II.A.3 are separated by single horizontal lines. Four of the runs were not used in the final calculations, for the reasons given in the footnotes. In this and all of the following tables, the small italic numbers represent the probable error in the last digit of the preceding number (e.g. 1757.5 19 means 1757.5±1.9) . -49- TABLE 1 WINDOWLESS TARGET RUN PARAMETERS Run Ea Et E7o Ia keV keV keV J.LA 407 5 8303 171.1 355.7 1757.5 19 1942.112 20 30 4063 8262 166.6 346.6 1753.0 13 1933.1 9 28 33 5153 8202 6692 1069 3 212.7 343.6 279.5 450.9 1799.110 1930.0 8 1865.9 8 2037.3 13 22 33 38 23 4585 4693 8182 192.4 193.5 342.9 1778.8 22 1779.9 12 1929.3 9 31 41 61 8202 1172 3 817 3 343.7 496.1 342.6 1930.112 2082.5 12 1929.0 12 40 46 48 s 4045 4043 8043 1152 3 1036 3 165.5 165.8 336.7 486.1 437.0 1751.921 1752.2 11 1923.0 9 2073 .5 11 2023.412 33 45 40 24 32 T 12002 507.4 2093.8 8 25 u 273512 1169.0 2755.4 51 1 A* B* c D E F G H I J K L M N 0 p Q R • Preliminary investigation using 60 cm3 Ge(U) detector . Detection efficiency was not measured with this detector. -50- TABLE 1 {cont.) WINDOWLESS TARGET RUN PARAMETERS Run Charge F fj.T C. torr K A B 6.10 7 1.312 2.489 2.58 10 c 6.426 83 1.349 14 azo az1 5.8 9.9 -0.08 -0.02 -0.10 -0.03 2.72 g 2.67 11 8.9 11.3 -0.08 -0.02 -0.10 -0.03 H 3 .396 38 1.150 12 2. 143 22 0.263 3 2.73 8 2.745 2.56 8 2.89 3 7.6 11.5 12.6 8.0 -0.07 -0.02 -0.04 0.01 -0.08 -0.03 -0.06 -0.01 I J K 3.708 57 4 .920 5£} 1.450 16 1.35 15 2.72 4 2.86 3 5.2 13.6 22 .2 -0.07 -0.07 -0 .02 -0.09 -0.09 -0.03 L M N 0.694 at 0.476 5 0.696 7 2.67 3 2.62 4 2. 73 10 13.6 14.2 16.6 -0.02 0.03 -0.02 -0.03 0.01 -0.03 0 s 2.311 37.j: 9.98 12 1.330 14 0.7288 0.6117 2.75 6 2.78 4 2.75 3 2.69 4 2.80 3 10.8 14.8 14.1 7.5 10.7 -0.08 -0 .08 -0.02 0.02 0.01 -0.10 0.10 -0.03 0.01 -0.01 T 1.049 11 2.90 3 8.4 0.03 0.01 u 0.0504 6 3.30 5 0.2 0.09 0.09 D E F G p Q R t + Calorimeter cooling temporarily off. Run aborted due to calorimeter zero offset. -51- TABLE 2 EMPIRICAL EFF1CIENCY FUNCTION The data for the detection efficiency in the windowless target were fitted with a function of the form: e(E,z) = 1+ lf~t . zd cE where the constants a, b, c. d and f for the best fit are given in the table below. constant value a 2 .004 b -0.833 c 1.6672 d 0.08899 f 2.40 - 52TABLE 3 SYSTEMATIC ERRORS A summary of the systematic errors in the windowless target system and the gas-cell activity measurements is shown in this table . -53- TABLE3 SYSTEMATIC ERRORS Windowless Target Variable Beam current error Source 1% Calorimeter calibration 3% Conduction and convection loss Target pressure 2% Pressure gauge calibration Detection efficiency 3% Source calibration 2% Efficiency fit TOTAL 5.3% Gas-cell Target Variable error Source Current Integration 0.5% Integration error Pressure 1% Pressure gauge calibration Detection efficiency 3% Source calibration TOTAL 3.3% -54- TABLE4 ACTIVITY MEASUREMENT RUN PARAMETERS This table shows the run parameters for the two gas-cell activity measurements. -55- TABLE4 ACTIVITY MEASUREMENT PARAMETERS v w Eo. (keV) 3400 2750 p (torr) 368 6 3686 T (K) 316 6 313 6 l (mrn) 9.5610 9.39 10 foil 432 5 486 a' He gas 925 117 5 E, (keV) 1255 4 9476 Charge (mC) 30.36 22.31 (%) 5.76 10 5.65 10 y478 2227 86 2097 93 144 240 Parameter Etoss (keV) E Count time (h) -56- TABLE 5 RESULTS The table on the following two pages shows the results of both experiments . The normalization of each group t o run D has not been applied to these data. The normalized data are plotted in figure 18. -57- TABLE5 RESULTS Run ,-ray yields Et (keV) Yo yl y429 A B 171.119 355.7 12 490 31 191745 310 37 1029 43 682 46 2759 60 c 166.6 13 346.6 9 826 37 2719 54 393 43 1245 49 632 48 2644 61 212.710 343.6 8 279.5 8 450.913 1196 40 2424 51 2244 50 1317 38 61139 1167 45 1147 50 713 36 1154 49 2409 58 2126 54 1409 43 192.4 22 193.5 12 342.9 9 38925 17825 996 36 2697 54 49034 367 37 948 44 2831 60 343 .712 496.112 342.6 12 1539 41 2398 51 1346 38 s 165.5 21 165.8 12 336.7 9 486.111 437.012 24520 965 39 2468 51 3304 60 2182 48 467 46 1067 45 1570 57 1133 46 16023 869 47 2321 45 3652 71 2375 56 T 507.4 8 6651 84 3173 80 7210 98 u 1169.0 52 1091 44 512 51 1703 93 v w 1255. 4 947.5 D E F G H I J K L M N 0 p Q R 1409 50 76636 1095 46 69935 9318 1588 46 2659 59 1414 43 -58- TABLE 5 {cont.) RESULTS So s1 Ss4 Utat p keV-b keV-b keV-b nb a1/ ao A B * * * * * * * * * * c 0.39329 0.29416 0.144 11 0 . 116 5 0.536 38 0.410 20 7.70 175 0.365 31 H 0.32418 0.31116 0.339 16 0.309 13 0.139 7 0.127 5 0. 140 6 0.134 5 0.463 23 0.438 20 0.479 20 0.443 14 28.2 182 93.6 432 I J K 0.308 44 0.295 17 0.27110 0.123 21 0.124 7 0.119 4 0.431 60 0.419 20 0.390 11 16.2 16.3 161 0 .399 44 0.42125 0.439 16 L M N 0.323 13 0.27711 0 .292 16 0.137 4 0 .115 5 0.125 6 0.46014 0.392 12 0.417 20 192 497 171 0.425 19 0.41416 0.417 20 0 p 0 .10115 0.123 8 0.112 4 0.104 4 0.109 4 0.435 46 0.426 23 0.40412 0.40412 0.35110 0.359 10 7.57 7.49 156 421 320 0 .304 46 0.406 27 s 0.33438 0.303 19 0.29211 0 .247 9 0.250 9 T 0 .291 9 0 .1 20 3 0.41111 554 0.41112 u v w 0 .21011 0.095 5 0.305 14 2150 0.454 32 0.30416 2340 1850 Run D E F G Q R • 0.36424 Detection efficiency was nol measured for these runs . 0 . 39415 0.428 24 0.40816 0.414 16 0.434 20 0.420 15 0.435 17 -59- TABLE 6 THEORETICAL FTIS The fits of several different theoretical calculations to the present cross-section factor data are compared in this table . The ·i for each of the fits and the zero-energy intercept of the cross-section factor are tabulated . Also shown is the x2 and the zero-energy intercept for the best quadratic fit to the experimental data. - 60- TABLE6 TIIEORETICAL FITS S34(0) x2 0.522 11 24.1 Hard core 0.533 11 27.9 Woods-Saxon 0.51810 24.3 OCM 0.53210 26.2 Li81 0.522 10 24.2 Quadratic fit 0.52310 24.0 Reference To63 Ki81 - 61 TABLE 7 CALORllv.IETER CAIJBRATION The calorimeter calibration measurements are shown in this table. The beam current and calorimeter current were integrated using two different current digitizers. For two of the measurements, these two digitizers were exchanged. The calibration constant is calculated from nEe A=-D where n is in mC, Ec is in keV and D, the integrated temperature difference, is in Kelvin-seconds. -62- TABLE 7. CALORIMETER CAIJBRATION DIE Eo. fa n D MeV f.LA mC K-sec 0.819 14 1.996 1.519 1.855 1.076 0.819 35 3.000 2.320 2.833 1.059 0.819 35 3.000 2.293 2.800 1.071 0.819 35 3 .000 2.292 2.799 1.072 0.819 7 1.000 0.7716 0.9421 1.061 0.819 7 1.000 0.7709 0.9412 1.062 0.819 4 1.000 0.7592 0.9270 1.079 0.401 15 1.000 0 .3748 0.9346 1.070 0.401 15 1.000 0.3796 0 .9465 1.057 0.401 15 i.OOO 0.3777 0.9419 1.062 0.401 30 3.000 1.1382 2.838 1.057 0.401 30 3.000 1.1491 2.865 1.047 0.401 30 3.000 1.1461 2.858 1.050 0.401 30 2.641 * 1.000 2.494 1.059 0.401 30 13.228* 5.034 13.227 1.054 0.401 32t 3.444 1.299 3.239 1.063 avg. 1.062 7 • charge and calorimeter integrators switched t interrupted beam A w/K - 63- F1GURE 1 El'J"ERGY LEVEL DIAGRAM This diagram shows the energy levels and Q-values for the reaction 3 He(cx,)')1Be reaction, and for the subsequent decay of the 7Be. The I' rays (/'0 • )' 1 , )' 429 and )'478 ) referred to in the text are shown. The energy levels and {3-decay branching ratios are taken from Ajzenberg-Selove (Aj79). u WI E ~ - ~2 ~ ~ 3 He+4 He J1.586 1 " Yo 4.57 .429 312-' 'Y429'~ 0 1/2- 7/2- j Li 7 0'\ + - 65F1GURE 2 RESULTS OF PREVIOUS EXPERIMENTS The experimental cross-section factor and branching ratio data of Parker and Kavanagh (Pa63) and Nagatani, Dwarakanath and Ashery (Na69) are indicated by the square and triangular data points respectively. The solid line shown is the best fit of the Tombrello and Parker (To63) curves to the data of Parker and Kavanagh, using the reduced widths t.Jg;z=l.25 and ef;z=l.05. - 66 ~-----------------------------------------.----------------. 0 0 lD ....-l m c::J co co co C'J (1j 0.... o (1j 0 <J I z E--< 0 0 0 ....-l 8 () ~ 0 0 lD ~----------------------------~~--------------------------+ 0 lD 0 0 q-A~Dl (rno3:)S 0 0 - 67- FIGURE 3 THEORETICAL CALCULATIONS The theoretical calculations of the cross-section factor and branching ratio by Tombrello and Parker (To63), Liu, Kanada and Tang (Li81) and the three different calculations of Kim, Izumoto and Nagatani (Ki81) using a hard core potential (H-C), a Woods-Saxon potential (W-S) and the orthogonality condition model (OCM) are compared. - 68 0 0 um:::;s I I u I II ::r::~o C'J,....,......;......;,.....;..--i CDrororororo 0 . ..... I I I I I I .. I :t I :I I \ .. I I .. I I :I I I I :I I ·I·I I I ~I I : !I ~I II I 1/ . I :I I :~ I .J I I 1/ I .,I., ..: L() I I .. I :1 I :I I I . H I .'t .' I ~I .I ~ :I; I I I ! II .: I _I I 0 0 0 :. ~. I I CD 0 .: I I .I 0 :I.. I Cil :1 I Jl .. OJ s I If I ·f \ .. .'I ,, I ,.....; ~l I ·I I 0 0 0 :I .,III . ., I ,.....; :1 \ I I L() I .. ;I .I •..-1 ·~ · r l E--<:5~~~~ I I I :I II C\1 0 CD 0 0 C\1 0 0 0 - 69- F1GURE4 WINDOWLESS. DIFFERENTIALLY PUMPED. GAS-TARGET SYSTEM This figure is a schematic representation of the gas pumping, recirculating and purifying system for the windowless target . The canals, chambers, and apertures are described in detail in section II.A. l. - 70 - N 31 (l) '::J - '(1) ~-W----------- 0! <! <<< c o 0! E (/) :J ::JQ_ '+'+- 0 - 71- FIGURE 5 WINDOWLESS TARGET The windowless gas target is shown from the entrance canal to the calorimeter. During the runs, the target chamber and the Ge(Li) detector were surrounded with 10 em of lead shielding to reduce {-ray background. I I I 2 I 3 I 4 scale (em) I 0 I 5 Cooling Coils Calorimeter Detector Geli 1\) -.J -73- FIGURE 6 PARTICLE SPECTRA Two typical particle detector spectra for Ecm =166 and 347 keY are shown. The 165 keY spectrum represents 0.31 particle coulombs of beam, while the 350 keY spectrum was acquired for 0.29 particle coulombs . The indicated peak positions are: a: Scattered 4 He b : Recoil 3 He c : 4 He scattered from 14N d: 4 He scattered from 40Ar 0 ::::1 0 1=1 (/] ..,_) 10 1 10 I II I l 0 I I II I I 3 105 10 I 7 10 1 103 105 107 '- a 50 ~ b a \ d ~ c 100 I \ b Channel \ 150 200 d '\... ~ Ecm=347 keV ~-- . ,... . . c Ecm=166 keV 250 I + -J -75- F1GURE 7 DETECTOR ELECfRONICS The electronics for the particle detector and the lithium-drifted germanium (Ge(Li)) 7-ray detector used in the windowless-target measurements are shown in this block diagram. The gain of the 7-ray detector was adjusted to give approximately 1 keV per channel into 4096 channels. The same electronics were used for the counting phase of the gas-cell activity measurements, except that only 1024 channel spectra were used. - 76 - TENNELEC TC 945 Bias Supply Ortec 210 Bios Supply 4000 v. , IOOv. p G.T. Ge(Li) and Preamp (12 81) Ortec Sur fa ce-borrier Detector (19·4520) Canberra 2010 Amplifier (1276362) Canberra 808 Preamp (473311) Nuclear Data 88-0426 ADC (71-255) Canberra 2010 Amplifier (377439) Nuclear Data 4420 Multi- Channel Analyzer Nuclear Data 88-0426 ADC (71-235) - - 77- FIGURE 8 WINDOWLESS TARGET BEAMIJNE A scale drawing of the accelerator, bearnline, optics, pumping and energy regulation systems constructed for the low-energy. windowlesstarget measurements is shown. Current from the regulating slits was fed-back to the JN accelerator Corona control system to stabilize the terminal voltage. I 0 I I I I .5 I I I scale (m) I JN Electrostatic Accelerator I I 1 Target System Viewing Station ~gnetic QuadruP.oles CP ---.1 - 79- F1GURE 9 GAS CELL This draVving shows the gas-cell target used in the activity measurements. ARertures 2mm To II 1/4 CopP.er Tube 1-----1 lcm Aluminum Su PP.ressor + To Gas Manifold Foils 0 ()) - 81F1GURE 10 TARGET CEIL GAS MANIFOLD This figure depicts the gas manifold used with the gas-target cell shown in figure 9. For the two measurements, the cell was evacuated to below 0.02 torr and filled from a bottle containing 99.99% 3 He gas. In the foil thickness measurement using the 14N(a,-y) resonance, dry N2 gas was substituted. ~OUT GAUGE PRESSURE W-T VACUUM GAUGE THERMOCOUPLE VACUUM GAUGE TO TARGET CELL t RESERVOIR MECHANICAL VACUUM PUMP GAS t TO BEAMLINE t f0> - 83- F1GURE 11 2 These 4yg(o:;y) 28Si FOIL THICKNESS MEASUREMENTS curves show the excitation functions 24 Mg(o:,')') 28 Si with an ex beam on a for the reaction metallic magnesium target. Curve A is with no foil in the beam. Curves B, C and D were taken with the entrance foil and 90, 180 and 360 torr of 3He gas in the target cell respectively. The square points represent the excitation function of the resonance at 3198 keV. The diamonds, triangles, and bars represent the excitation function with the beam passing through the entrance foil and the target cell filled with 90, 180, and 360 torr of 3 He gas respectively. Extrapolation to zero pressure yields a foil thickness of 432± 5 keV. The additional loss in the gas at 360 torr with 0.15 J..LA of beam current is 96±5 keY. - 84 0 ~-------------------------------------------------rg ~ 1-H 1--H 1--<H 1-0-t ,--..... > Q) 0 0 1.[.) C":l - ~ -........- :>-. QD s... Q) ~ ~ 0 ~---------------+----------------~----------------Tg C":l 0 0 0 C":l 0 0 0 Cll 0 0 0 - 0 - 85- FIGURE 12 1 These ~(cx,/') 1 ~ FOIL THICKNESS MEASUREMENTS curves show the 14 N(o:,7) 18 F with an o: bean on a excitation functions for the reaction nitrogen target in the gas cell using the same entrance foil which was used in the Ecm =947 keV measurement. The two curves represent target pressures of 180 and 360 torr respectively. The vertical line represents the measured energy of the resonance (Ro73) . - 86 0 r--------------------------------------------------------------------. 0 L() C"J 00 roc.o riC') <> <J 0 0 0 C"J 1-<H 1-<H 1-<H 1-<H 1-<>-l 1-<>-l 1-<>-l 1-0-1 ,--.... tot ICC 101 <> > (J) 0 ~ <><> ............. <> :>., QQ l-. Q) c w 0 0 (J) () .......... ro ~ro ~ ....... s 0 ~ 0 UJ Q) z~ L() :>., C\1 QQ l-. Q) ~ w 0 r--------------------------------+---------------------------------+ 0 0 C\1 0 0 0 0 rl 0 0 0 l.{) 0 - 87- FIGURE 13 DIRECT-cAPTURE ~-RAY SPECTRA Spectra of the direct-capture 7 rays are shown for Ecm =166 keV (Run P), 347 keV (Run D) and 507 keY (RunT). The indicated 7-ray transitions are: a: 7 0 , direct capture to the ground state of 7 Be b: 7 429 , first excited state to ground state transition in 7 Be c: 7 1 , direct capture to the first excited state of 7 Be d: 511 keV, annihilation radiation e: 1460 keV, 4 °K decay background f: 2614 keV, first excited state of 208 Pb from the 232Th decay chain rJ) u 0 ;::i d -t..J 1 10 I I , ~-''" 1000 100 L I I bl d l I r ~ d h 1 10 100 1000 r 1 10 1000 ••r"" ,.-, 1000 I, · keV) Channel (Ey In - ~i'rr'Jw.r••!,,...Jilo.J 1.u..l.l~.. ~ a a \ ''j'l ,.~ •.• 1 I I 2000 .... ~ 11 ' ~ c Gamma Ray Spectra Ecm = Ecm = f I 500 keV f 350 keV E em = 165 keV l (X) (X) - 89- FlGURE 14 ~-RAY DETECTION EFF1CIENCIES These four curves show the 7-ray detection efficiency in the windowless target as a function of position along the beam axis, relative to the center of Ge(Li) detector (z=O). The solid lines represent the best fit of the empirical function (given in table 2) to the experimental measurements. >.. ~ ~ '+-1 Q) ...... () ...... '+-1 ~ () 56 Co E = 1238 keV I ~ 7<" -n- 56 E=l771keV E =1408 keV Co E =2035 keV 56 Co 152 Eu J Position (em) .01 ~----------------~----------------~----------------~----------------~ -10 0 10 .1 1 .1 L ll .1~ lr-~--~------~----~------~-+--~----~----~----~------~ .1 1~------~------~----------~--~--------------~--------------~ 0 \0 - 91- F1GURE 15 TOTAL DETECTION EFF1CIENCY The sum of the measured efficiencies at 1-cm intervals in the target is compared to the sum of the empirical efficiency function (see table 2) over the same positions . The resulting integrated efficiency is given in units of em-%. The data points are from the 56 Co (squares) and 152Eu (triangles) sources. - 92 - ,--.. > Q) ~ ,_... 0 0 0 C\l ::>.... 0.0 f-. Q) ~ Q) ttl a a ttl 0 ~---------4-----------+----------~----------+-----------+ 0 0 0 ..-1 0 l.() C"J C\l 0 C\l - 93- FIGURE 16 CATCHER FOIL SPECTRUM The Ge(Li)-detector spectrum of the 144-hour count of the platinum catcher foil used in the Ecm =1250 keV activity measurement is shown. The inset shows the 1 478 peak. The dotted line in the inset represents a 72-hour count of the entrance foil and the side foil. The total number of counts from the catcher foil is 2227±86. The number of counts in the side and entrance foil spectrum, using the same peak definition, is 27±40, consistent with zero. - 94 0 0 0 0 0 ....-! l{) ,......._ > s ::s (!) ~ ~ ...... H ~ 0 )o Q) ~ p. rn l{) 0 0 ..;:t< l{) 0 ....--1 • .-1 J..~ (!) ..0 a 0 !:;... 0 0 H Q) ..c:0 l{) 0 0 0 ....-! ....-! 0 0 0 ~ z l{) ......... (!) ~ ~ _...) (1j ro u u ..c::: ~--------~-----------+----------~----------~--------~ 0 0 0 0 l{) 0 0 0 ..q< 0 0 0 ("') 0 0 0 C\1 0 0 0 .....-4 0 - 95- FIGURE 17 PROMPT 7-RAY SPECTRUM = The prompt "j-ray spectrum from the Ecm 1250 keV gas-cell measurement is shown along with the 24 Na source spectrum which was used for energy calibration. tf) u 0 ;:::J c +! A . 24 Na Sour c e Capture Gammas ~ 0 500 Cha nnel 1000 1~----------~----~----~------r-----~----~----~~~~----~ 10 100 lOOJ L~ 10 100 1000 10000 Gamma Ray Spectra ~ \.() -97- FiGURE 18 CROSs-SECTION FACTOR AND BRANCHING RATIO RESULTS The results of these measurements are shown along with the best fit of the Tombrello and Parker (To63) calculation to the experimental data (solid curve) and the unnormalized resonating group calculation of Liu, Kanada and Tang (Li81, dashed curves). The normalized Tombrello and Parker branching-ratio curve is indistinguishable from that of Liu, Kanada and Tang. - 98 0 I I I j- 1- - I~ I I - 1 - I - I I lei I I I I I I I ,~ 1'- I I f- I Q) I I ~~ - -i- c5 0 • 0 -0 L[) I ' 0 w - I I, ~ u tel ~ w. ~ ~ ~ ~~~ I C\.1 • 0 -> -E Q) ~ I T co - I r I' 0 - 00 tit I 7"" I f- l[) I - co - 0 1 I Q). r0 Ir T -r N c5 0 0 . 0 -99- FIGURE 19 CALORIMETER This is a full scale drawing of the calorimeter used to integrate the beam current in the windowless target. The body of the calorimeter was turned from a single block of copper. - 100 - Beam stop Heatsink BNC Connectors {1:) TemQerature Transducers - 101 - FIGURE 20 C.ALORIMEI'ER CONTROLLER CIRCUIT With the two temperature transducers placed in the bridge circuit as shown, the current flowing across the bridge will be proportional to the temperature difference, T2 - T 1 , between the beamstop and the heatsink. The 1 kO variable resistor allows the circuit to be accurately zeroed. The 1 kO resistors in series with the transducers allow the temperatures of the beamstop and the heatsink to be monitored; the voltage drop across these resistors in mV is equal to the kelvin temperature of the corresponding transducer. - 102 - '-I ;·····-·............ ~I E -~I 0 ol 0 I .- -: l I I I ~ ................,_..... _...,.. ..... j I_ I \-I ol Q) ->E - ._c" > E --, I \- I gl I ..... 0 \-I Q) ~ Q)l E ·-<sl ~I I> w I+ I I I I I I I - 103- F1GURE 21 CALORIMETER CURRENT DECAY A 32 f..lA beam of 401 keV 4 He+ ions was turned on at t=O sec and off at t=106 sec. The resulting beam current and calorimeter current are plotted in this graph as a function of time. The calorimeter current shows the expected logarithmic decrease, with a characteristic time constant of 26 sec. .01 0 f-- .1 f-- .001 E-< N I E-< - ..........- ,--... ~ J * 10 f-- 100 * * *** * * 100 **************! Beam on ** ** *** * ** Time (Seconds) * ** Beam off *** ** ** 200 ** I Calorimeter Current Decay ** ** ** * ** ** * * * 300 - - - - +=" 0 1-'