- Email: [email protected]
Recent measurements of nuclear reaction cross-sections with ion beams at very low energies
Vacuum~volume44/numbers 3/4/pages 181 to 183/1993
0042-207X/9356.00+.00 © 1993 Pergamon Press Ltd
Printed in Great Britain
R e c e n t m e a s u r e m e n t s of nuclear reaction crosssections w i t h ion beams at very l o w energies F E C e c i l , H L i u a n d J S Yan, Department of Physics, Colorado School of Mines, Golden, CO 80401, USA
Recent measurements of radiative capture reactions of protons and deuterons on light nuclei at low energies are summarized. Applications of these measurements to various problems in astrophysical nucleosynthesis, fusion plasma diagnostics and near-surface quantitative analysis of low mass elements are described. The results of our investigation of the possible enhancement of deuteron-induced neutron-transfer reactions on light nuclei are presented.
1~. Introduction
2. Radiative capture reactions
The history of experimental nuclear physics over the past century has seen a constant increase in the energy and expense of the accelerators used to explore the atomic, nuclear and nucleonic structure of matter. The first charged particle accelerators fabricated by Cockcroft and W a l t o n were in the energy range of a few hundreds of kilovolts. The current generation of machines boast energies in excess of teravolts. In spite of this seeming monotonic increase in energy with time, there remain m a n y problems in pure and applied nuclear physics which can be investigated only with charged particle beams of very low energies, down to a few kilovolts. Over the past decade we have measured a fairly broad class of nuclear reactions at energies from a few to a few hundred kilovolts. This class includes the radiative capture of protons and deuterons by light nuclei. More recently we have examined a classic problem in nuclear physics. In 1935 Oppenheimer and Phillips ~ predicted an enhancement of (d,p) reactions (in which a neutron is transferred from the projectile deuteron to the target nucleus) by virtue of the elastic polarization of the deuteron in the C o u l o m b field of the target. We have investigated this prediction by measuring the yield of charged particles during the b o m b a r d m e n t of 2H, 6Li and ~°B by deuterons with energies between 6 and 180 keV. In this report, we summarize these reactions and discuss the applications of these measurements to a variety of problems.
Our measurements of the cross-sections for the radiative capture of protons and deuterons by 2H, 3H, 3He, 6Li, 7Li, 9Be and I°B are summarized in Table 1. The techniques used in these measurements are described in the references to the original work. The results of these measurements are most conveniently parameterized in terms of the astrophysical S-factors 7 which are used to compare the nuclear cross-section at a center-of-mass energy E (MeV) to the Coulomb barrier penetration probability ;
tr(E) = [S(E)/E] [exp ( - b/E t/2)],
(1)
where the constant b = 0.989 Z~ Z2A ~/2 (MeV)~/2 with Zj and Z2 being the charges of the projectile and target and A the reduced atomic mass of the system in amu. The S-factors in Table 1 represent the values extrapolated to E = 0. Over the range of energies from 0 to about 200 keV the S-factors are constant at the 10% level with the exception of the reaction ~lB(p,v) 12C for which there is a strong resonance in the p-~ ~B c o m p o u n d nuclear system for a proton bombarding energy of 163 keV (ref 8). In addition we have, for reference, used the S-factors listed in Table 1 and equation (1) generate the cross-sections for the reactions at a projectile laboratory bombarding energy of 100 keV. The cross-sections are also listed in Table 1. One area of application of the measurements is astrophysical
Table 1. S-factors and cross-sections for measured radiative capture reactions. The crosssections are evaluated for a projectile laboratory bombarding energy of 100 keV
No
Reaction
1 2 3 4 5 6 7 8 9
D(d,y)4He T(d,y)SHe D(3He,y)SLi 6Li(d,)') abe I°B(d,y) J2C 6Li(p,y)TBe 7Li(p,y)SBe 9Be(p,y) I°B
IIB(p,y)12C
Gamma energy (MeV)
S-factor (MeV-b)
Cross-section (b)
Ref
23.8 16.7 16.6 22.3 25.2 5.6 17.2 6.6 16.1
(6.0_ 1.2) × 10 9 (1.3+0.3) × 10-3 (3.6+0.9) × 10-4 (6.2+ 1.5) x I0 -6 (3.8_+1.0)×10 -3 (3.9__+0.8) x 10-5 (2.5_0.5)× 10-4 (9.2+2.5) x 10-4 (2.0+0.4) × 10 - 3
1.4 × 10 9 2.0× 10-4 8.6 × 10 - 7 1.4×10 -~° 1.1 × 10 tl 3.8 × 10-s
2 3 4 5 5 6 6 6 6
2 . 4 × 10 - 7
3.8 x 10-8 3.5 × 10-9
181
F E Cecil et al." Nuclear reaction cross-sections
nucleosynthesis. In the 'Big Bang' for example, the concentrations of deuterium, helium, and lithium are thought to have reached a maximum at a time of about 300 s (ref 9). At this time the temperature of the primordial fireball should have 'cooled' to about 5 × 108 K. This corresponds to a kinetic energy k T = 40 keV. The appropriate energy at which laboratory measurements of light ion cross-sections should be measured for application to primordial nucleosynthesis is therefore in the range of 0-200 keV. A number of the reactions listed in Table 1 are, therefore, directly applicable to primordial nucleosynthesis. Our measured cross-section for the reaction D(d,7)4He, for example, should allow the contribution of this reaction to the primordial synthesis of 4He to be evaluated. More recently, Rath e t a l ~° have proposed the reaction 7Li(3He,p)gBe as a mechanism for the primordial production of 9Be. Our measured value of the reaction 9Be(p,7 ) JOB, together with the recent measurement of the reaction ~°B(p,y)~ ~C (ref l l) and our measurement of the reaction ~B(p,7)~2C collectively provide a series of reactions resulting in the synthesis of ~2C and constitute an alternative source of this nucleus from the 'triple-alpha' process of Salpeter ~2. Another area of application of our measurements is the diagnostics of high-temperature fusion plasmas. The very high energy gamma rays from the reactions 1-3 in Table 1 provide the basis of a non-invasive diagnostic of the total reaction rate of the corresponding fusion plasmas ~3. In the case of the reaction D(3He,7) 5Li, the 16.6 MeV gamma ray will be the only escaping reaction product from a magnetically confined fusion plasma since the 3.5 MeV alpha particle and the 15 MeV proton from the reaction D(3He,p)4He will tend to be confined by the magnetic fields of the fusion device. This gamma ray producing reaction has thus been relied upon heavily by the diagnostics group at the large tokamak at JETt 4 in their studies of D-3He fusion plasmas. The (P,7) reactions on 6Li, 7Li, and ~B will similarly provide the basis for the diagnostics of these corresponding 'advanced fuel' fusion plasmas. The final area of application of our measurements of the reactions listed in Table 1 is the near-surface quantitative analysis of low mass elements and isotopes. The presence of any of the target nuclei listed in Table 1 can be detected by bombarding a sample containing the target with the appropriate beam of protons or deuterons and measuring the resulting gamma ray. From the Sfactors listed in Table 1 and equation (1) above, the cross-sections and the yields may be calculated in terms of the abundance of the target. Consider, for example, a 100 A layer of 7Li on an inert backing. From Table 1 and equation (1), the cross-section for the reaction 7Li(p,?) at a proton bombarding energy of 150 keV will be about 1 #b. For a 100 #A beam of 150 keV protons, there will thus be an easily measurable yield of about 60 17.4 MeV gamma rays emitted from the target per second. The range of a 150 keV proton in, for example, silicon is about 1 ym (ref 15). Consequently this technique is limited to depths of less than this range below the surface. Moreover, since the energy of the proton will decrease as it penetrates the material, the sensitivity of the technique will be correspondingly mitigated. For example, the energy loss of a 150 keV proton in, again, silicon is about 120 keV pm ~ (ref 15). Thus if the 100 A layer of lithium postulated above were buried in the silicon sample at a depth of 0.5 pm below the surface, then the energy of the proton beam would have dropped from 150 to about 80 keV by the time the proton reached the lithium layer. At this energy, again referring to equation (1), the cross-section would have dropped from 1 to 182
300
.
.
.
.
.
.
.
,
,
.
.
.
.
,
.
.
.
.
.
,
.
.
.
d e u t e r o n lab e n e r g y 7 k e V
o
200
"-
~
~
100
0
50
100 150 Channel
200
260
Figure 1. Energy spectrum of charged particles measured during bombardment of a deuterated-titanium target with a 7 keV deuteron beam.
about 0.1 pb and the yield would therefore be reduced by a factor of 10 compared with the yield from the surface layer. We would note that this analytical technique is isotope specific since, in the case of lithium, the gamma ray from the reaction 6Li(p,7)TBe is 5.6 MeV while the gamma ray from the reaction 7Li(p,7)SBe is 17.4 MeV. The application of the reactions in Table 1 to this analytical technique represents, of course, special cases of the more general technique of proton-induced-gammaemission (PIGE) which, in turn, is the nuclear analog of protoninduced-X-ray-emission (PIXE). 3. Oppenheimer-Phillips effect
The Oppenheimer Phillips (OP) effect postulates that a projectile deuteron encountering a charged target nucleus will become electrically polarized and that this polarization will enhance the probability for a (d,p) reaction induced by this deuteron. We have investigated this postulate by measuring the yield of charged particles from the D-D, D-6Li and D -~ °B reactions. In the case of the D - D reaction, we were able to compare the yield of the reactions D(d,p)T and D(d,n)3He by directly measuring the yields of the 1.01 MeV tritons and 0.86 MeV 3He ions (see Figure 1). By comparing these yields we are able to conclude that there is no enhancement of the D(d,p)T reaction relative to the D(d,n)3He reaction down to a center-of-mass energy of 3 keV (see Figure 2). Our measurements are compared with and agree 1.5 • present work • Brown and Jarmie • K r a u s s e t al. -Hale Koonin and Mukerjee v
!T
T +.~ I
t.o o
l
0.5 Center
10 of m a s s e n e r g y ( k e V )
100
Figure 2. Ratios of yield of D(d,p)T and D(d,n)3He. The solid symbols are present and previous measurements of the yield ratios while the lines are calculations.
jr E Cecil et al: Nuclear reaction cross-sections
with measurements at higher energies ~6 and with calculations of 1:he (d,p)/(d,n) ratio. Our measurements are in excellent agreement with the R-matrix calculations of Hale ~7 and in qualitative agreement with the D W B A calculations of K o o n i n and Mukerjee ~8. Similarly for the D-6Li and D-~°B reactions we compared the (d,p) and (d,c0 reactions and found no enhancement of the (d,p) reactions, There have been no reported ,zalculations of these ratios at low energies. An interesting application of these results lies in the recent zlaims of significant heat production from deuterium metal systems, 'cold nuclear fusion' ~9. Remarkable to these claims is the absence or near absence of the production of energetic neutrons concurrent with the production of heat. Specifically we would expect, based upon the near equality of the (d,p) and (d,n) branches of the D - D reaction at low energies as indicated in Figure 2, that if the d ~ t nuclear reactions were responsible for the heat production, then there would be about 10 j2 neutrons per watt of heat generated. We must conclude that either the (d,p) to (d,n) ratio for the D - D reaction changes by many orders of magnitude as the energy drops from a few kiloelectronvolts to r o o m temperature or that some other nuclear or non-nuclear reaction is responsible for the heat production.
4. Conclusion In conclusion, we have tried to summarize the results of many years of experimental effort. The astrophysical S-factors for the radiative capture reactions given in Table 1 may be used to generate the reaction cross-sections at energies up to a few hundred kiloelectronvolts. We have indicated, in turn, a few of the possible applications of these measurements. We would emphasize that any specific application of these measurements would involve considerably more detail than indicated in our discussion.
Nonetheless, the reaction cross-sections derived from the S-factors given in Table 1 will be important components of these applications.
Acknowledgement This work has been supported by United States Department of Energy Contract DE-FG02-87ER40342.
References J R Oppenheimer and M Phillips, Phys Rev, 48, 500 (1935). 2F J Wilkinson and F E CeciL, Phys Rev, C31, 2036 (1985). 3F E Cecil and F J Wilkinson, Phys Rev Lett, 53, 767 (1984). 4F E Cecil, D M Cole, R Philbin, N Jarmie and R Brown, Phys Rev, C32, 690 (1985). SF E Cecil, H Liu and J S Yan, Rev Scient Instrum, accepted for publication (1992). 6F E Cecil, H Liu, D Ferg, J S Scorby, J A McNeil and P D Kunz, Nucl Phys, A539, 75 (1992). 7C E Rolfs and W S Rodney, Cauldrons in the Cosmos, p. 157. University of Chicago Press, Chicago (1988). 8F Ajzenberg-Selove, Nucl Phys, A433, 1 (1985). 9 D N Schramm and R V Wagoner, A Rev Nucl Sci, 27, 37 (1977). t°D P Rath, R N Boyd, H J Hausman, M S Islam and G W Kolnicki, Nucl Phys, A515, 338 (1990). ~ M Weischer et al, Phys Rev, C28, 1431 (1983). ~2E E Salpeter, Phys Rev, 88, 547 (1952). 3S S Medley, F E Cecil, D Cole, M A Conway and F J Wilkinson III, Rev Scient lnstrum, 56, 975 (1985). 14D A Boyd et al, NuclFusion, 29, 593 (1989). 15H H Anderson and J F Zeigler, Hydrogen, The Stopping Powers and Ranges o f lons in Matter. Pergamon Press, Oxford (1977). 16A Krauss et al, Nucl Phys, A465, 150 (1987) ; R E Brown and N Jarmie, Nucl Instrum Meth, B40/41,405 (1985). 17G M Hale, Los Alamos National Labs, private communication (1991). ~8S E Koonin and M Mukerjee, Phys Rev, C42, 1639 (1990). 19M Fleischmann and S Pons, J l£lectroanalyt Chem, 261,301 (1989).
1 83
0042-207X/9356.00+.00 © 1993 Pergamon Press Ltd
Printed in Great Britain
R e c e n t m e a s u r e m e n t s of nuclear reaction crosssections w i t h ion beams at very l o w energies F E C e c i l , H L i u a n d J S Yan, Department of Physics, Colorado School of Mines, Golden, CO 80401, USA
Recent measurements of radiative capture reactions of protons and deuterons on light nuclei at low energies are summarized. Applications of these measurements to various problems in astrophysical nucleosynthesis, fusion plasma diagnostics and near-surface quantitative analysis of low mass elements are described. The results of our investigation of the possible enhancement of deuteron-induced neutron-transfer reactions on light nuclei are presented.
1~. Introduction
2. Radiative capture reactions
The history of experimental nuclear physics over the past century has seen a constant increase in the energy and expense of the accelerators used to explore the atomic, nuclear and nucleonic structure of matter. The first charged particle accelerators fabricated by Cockcroft and W a l t o n were in the energy range of a few hundreds of kilovolts. The current generation of machines boast energies in excess of teravolts. In spite of this seeming monotonic increase in energy with time, there remain m a n y problems in pure and applied nuclear physics which can be investigated only with charged particle beams of very low energies, down to a few kilovolts. Over the past decade we have measured a fairly broad class of nuclear reactions at energies from a few to a few hundred kilovolts. This class includes the radiative capture of protons and deuterons by light nuclei. More recently we have examined a classic problem in nuclear physics. In 1935 Oppenheimer and Phillips ~ predicted an enhancement of (d,p) reactions (in which a neutron is transferred from the projectile deuteron to the target nucleus) by virtue of the elastic polarization of the deuteron in the C o u l o m b field of the target. We have investigated this prediction by measuring the yield of charged particles during the b o m b a r d m e n t of 2H, 6Li and ~°B by deuterons with energies between 6 and 180 keV. In this report, we summarize these reactions and discuss the applications of these measurements to a variety of problems.
Our measurements of the cross-sections for the radiative capture of protons and deuterons by 2H, 3H, 3He, 6Li, 7Li, 9Be and I°B are summarized in Table 1. The techniques used in these measurements are described in the references to the original work. The results of these measurements are most conveniently parameterized in terms of the astrophysical S-factors 7 which are used to compare the nuclear cross-section at a center-of-mass energy E (MeV) to the Coulomb barrier penetration probability ;
tr(E) = [S(E)/E] [exp ( - b/E t/2)],
(1)
where the constant b = 0.989 Z~ Z2A ~/2 (MeV)~/2 with Zj and Z2 being the charges of the projectile and target and A the reduced atomic mass of the system in amu. The S-factors in Table 1 represent the values extrapolated to E = 0. Over the range of energies from 0 to about 200 keV the S-factors are constant at the 10% level with the exception of the reaction ~lB(p,v) 12C for which there is a strong resonance in the p-~ ~B c o m p o u n d nuclear system for a proton bombarding energy of 163 keV (ref 8). In addition we have, for reference, used the S-factors listed in Table 1 and equation (1) generate the cross-sections for the reactions at a projectile laboratory bombarding energy of 100 keV. The cross-sections are also listed in Table 1. One area of application of the measurements is astrophysical
Table 1. S-factors and cross-sections for measured radiative capture reactions. The crosssections are evaluated for a projectile laboratory bombarding energy of 100 keV
No
Reaction
1 2 3 4 5 6 7 8 9
D(d,y)4He T(d,y)SHe D(3He,y)SLi 6Li(d,)') abe I°B(d,y) J2C 6Li(p,y)TBe 7Li(p,y)SBe 9Be(p,y) I°B
IIB(p,y)12C
Gamma energy (MeV)
S-factor (MeV-b)
Cross-section (b)
Ref
23.8 16.7 16.6 22.3 25.2 5.6 17.2 6.6 16.1
(6.0_ 1.2) × 10 9 (1.3+0.3) × 10-3 (3.6+0.9) × 10-4 (6.2+ 1.5) x I0 -6 (3.8_+1.0)×10 -3 (3.9__+0.8) x 10-5 (2.5_0.5)× 10-4 (9.2+2.5) x 10-4 (2.0+0.4) × 10 - 3
1.4 × 10 9 2.0× 10-4 8.6 × 10 - 7 1.4×10 -~° 1.1 × 10 tl 3.8 × 10-s
2 3 4 5 5 6 6 6 6
2 . 4 × 10 - 7
3.8 x 10-8 3.5 × 10-9
181
F E Cecil et al." Nuclear reaction cross-sections
nucleosynthesis. In the 'Big Bang' for example, the concentrations of deuterium, helium, and lithium are thought to have reached a maximum at a time of about 300 s (ref 9). At this time the temperature of the primordial fireball should have 'cooled' to about 5 × 108 K. This corresponds to a kinetic energy k T = 40 keV. The appropriate energy at which laboratory measurements of light ion cross-sections should be measured for application to primordial nucleosynthesis is therefore in the range of 0-200 keV. A number of the reactions listed in Table 1 are, therefore, directly applicable to primordial nucleosynthesis. Our measured cross-section for the reaction D(d,7)4He, for example, should allow the contribution of this reaction to the primordial synthesis of 4He to be evaluated. More recently, Rath e t a l ~° have proposed the reaction 7Li(3He,p)gBe as a mechanism for the primordial production of 9Be. Our measured value of the reaction 9Be(p,7 ) JOB, together with the recent measurement of the reaction ~°B(p,y)~ ~C (ref l l) and our measurement of the reaction ~B(p,7)~2C collectively provide a series of reactions resulting in the synthesis of ~2C and constitute an alternative source of this nucleus from the 'triple-alpha' process of Salpeter ~2. Another area of application of our measurements is the diagnostics of high-temperature fusion plasmas. The very high energy gamma rays from the reactions 1-3 in Table 1 provide the basis of a non-invasive diagnostic of the total reaction rate of the corresponding fusion plasmas ~3. In the case of the reaction D(3He,7) 5Li, the 16.6 MeV gamma ray will be the only escaping reaction product from a magnetically confined fusion plasma since the 3.5 MeV alpha particle and the 15 MeV proton from the reaction D(3He,p)4He will tend to be confined by the magnetic fields of the fusion device. This gamma ray producing reaction has thus been relied upon heavily by the diagnostics group at the large tokamak at JETt 4 in their studies of D-3He fusion plasmas. The (P,7) reactions on 6Li, 7Li, and ~B will similarly provide the basis for the diagnostics of these corresponding 'advanced fuel' fusion plasmas. The final area of application of our measurements of the reactions listed in Table 1 is the near-surface quantitative analysis of low mass elements and isotopes. The presence of any of the target nuclei listed in Table 1 can be detected by bombarding a sample containing the target with the appropriate beam of protons or deuterons and measuring the resulting gamma ray. From the Sfactors listed in Table 1 and equation (1) above, the cross-sections and the yields may be calculated in terms of the abundance of the target. Consider, for example, a 100 A layer of 7Li on an inert backing. From Table 1 and equation (1), the cross-section for the reaction 7Li(p,?) at a proton bombarding energy of 150 keV will be about 1 #b. For a 100 #A beam of 150 keV protons, there will thus be an easily measurable yield of about 60 17.4 MeV gamma rays emitted from the target per second. The range of a 150 keV proton in, for example, silicon is about 1 ym (ref 15). Consequently this technique is limited to depths of less than this range below the surface. Moreover, since the energy of the proton will decrease as it penetrates the material, the sensitivity of the technique will be correspondingly mitigated. For example, the energy loss of a 150 keV proton in, again, silicon is about 120 keV pm ~ (ref 15). Thus if the 100 A layer of lithium postulated above were buried in the silicon sample at a depth of 0.5 pm below the surface, then the energy of the proton beam would have dropped from 150 to about 80 keV by the time the proton reached the lithium layer. At this energy, again referring to equation (1), the cross-section would have dropped from 1 to 182
300
.
.
.
.
.
.
.
,
,
.
.
.
.
,
.
.
.
.
.
,
.
.
.
d e u t e r o n lab e n e r g y 7 k e V
o
200
"-
~
~
100
0
50
100 150 Channel
200
260
Figure 1. Energy spectrum of charged particles measured during bombardment of a deuterated-titanium target with a 7 keV deuteron beam.
about 0.1 pb and the yield would therefore be reduced by a factor of 10 compared with the yield from the surface layer. We would note that this analytical technique is isotope specific since, in the case of lithium, the gamma ray from the reaction 6Li(p,7)TBe is 5.6 MeV while the gamma ray from the reaction 7Li(p,7)SBe is 17.4 MeV. The application of the reactions in Table 1 to this analytical technique represents, of course, special cases of the more general technique of proton-induced-gammaemission (PIGE) which, in turn, is the nuclear analog of protoninduced-X-ray-emission (PIXE). 3. Oppenheimer-Phillips effect
The Oppenheimer Phillips (OP) effect postulates that a projectile deuteron encountering a charged target nucleus will become electrically polarized and that this polarization will enhance the probability for a (d,p) reaction induced by this deuteron. We have investigated this postulate by measuring the yield of charged particles from the D-D, D-6Li and D -~ °B reactions. In the case of the D - D reaction, we were able to compare the yield of the reactions D(d,p)T and D(d,n)3He by directly measuring the yields of the 1.01 MeV tritons and 0.86 MeV 3He ions (see Figure 1). By comparing these yields we are able to conclude that there is no enhancement of the D(d,p)T reaction relative to the D(d,n)3He reaction down to a center-of-mass energy of 3 keV (see Figure 2). Our measurements are compared with and agree 1.5 • present work • Brown and Jarmie • K r a u s s e t al. -Hale Koonin and Mukerjee v
!T
T +.~ I
t.o o
l
0.5 Center
10 of m a s s e n e r g y ( k e V )
100
Figure 2. Ratios of yield of D(d,p)T and D(d,n)3He. The solid symbols are present and previous measurements of the yield ratios while the lines are calculations.
jr E Cecil et al: Nuclear reaction cross-sections
with measurements at higher energies ~6 and with calculations of 1:he (d,p)/(d,n) ratio. Our measurements are in excellent agreement with the R-matrix calculations of Hale ~7 and in qualitative agreement with the D W B A calculations of K o o n i n and Mukerjee ~8. Similarly for the D-6Li and D-~°B reactions we compared the (d,p) and (d,c0 reactions and found no enhancement of the (d,p) reactions, There have been no reported ,zalculations of these ratios at low energies. An interesting application of these results lies in the recent zlaims of significant heat production from deuterium metal systems, 'cold nuclear fusion' ~9. Remarkable to these claims is the absence or near absence of the production of energetic neutrons concurrent with the production of heat. Specifically we would expect, based upon the near equality of the (d,p) and (d,n) branches of the D - D reaction at low energies as indicated in Figure 2, that if the d ~ t nuclear reactions were responsible for the heat production, then there would be about 10 j2 neutrons per watt of heat generated. We must conclude that either the (d,p) to (d,n) ratio for the D - D reaction changes by many orders of magnitude as the energy drops from a few kiloelectronvolts to r o o m temperature or that some other nuclear or non-nuclear reaction is responsible for the heat production.
4. Conclusion In conclusion, we have tried to summarize the results of many years of experimental effort. The astrophysical S-factors for the radiative capture reactions given in Table 1 may be used to generate the reaction cross-sections at energies up to a few hundred kiloelectronvolts. We have indicated, in turn, a few of the possible applications of these measurements. We would emphasize that any specific application of these measurements would involve considerably more detail than indicated in our discussion.
Nonetheless, the reaction cross-sections derived from the S-factors given in Table 1 will be important components of these applications.
Acknowledgement This work has been supported by United States Department of Energy Contract DE-FG02-87ER40342.
References J R Oppenheimer and M Phillips, Phys Rev, 48, 500 (1935). 2F J Wilkinson and F E CeciL, Phys Rev, C31, 2036 (1985). 3F E Cecil and F J Wilkinson, Phys Rev Lett, 53, 767 (1984). 4F E Cecil, D M Cole, R Philbin, N Jarmie and R Brown, Phys Rev, C32, 690 (1985). SF E Cecil, H Liu and J S Yan, Rev Scient Instrum, accepted for publication (1992). 6F E Cecil, H Liu, D Ferg, J S Scorby, J A McNeil and P D Kunz, Nucl Phys, A539, 75 (1992). 7C E Rolfs and W S Rodney, Cauldrons in the Cosmos, p. 157. University of Chicago Press, Chicago (1988). 8F Ajzenberg-Selove, Nucl Phys, A433, 1 (1985). 9 D N Schramm and R V Wagoner, A Rev Nucl Sci, 27, 37 (1977). t°D P Rath, R N Boyd, H J Hausman, M S Islam and G W Kolnicki, Nucl Phys, A515, 338 (1990). ~ M Weischer et al, Phys Rev, C28, 1431 (1983). ~2E E Salpeter, Phys Rev, 88, 547 (1952). 3S S Medley, F E Cecil, D Cole, M A Conway and F J Wilkinson III, Rev Scient lnstrum, 56, 975 (1985). 14D A Boyd et al, NuclFusion, 29, 593 (1989). 15H H Anderson and J F Zeigler, Hydrogen, The Stopping Powers and Ranges o f lons in Matter. Pergamon Press, Oxford (1977). 16A Krauss et al, Nucl Phys, A465, 150 (1987) ; R E Brown and N Jarmie, Nucl Instrum Meth, B40/41,405 (1985). 17G M Hale, Los Alamos National Labs, private communication (1991). ~8S E Koonin and M Mukerjee, Phys Rev, C42, 1639 (1990). 19M Fleischmann and S Pons, J l£lectroanalyt Chem, 261,301 (1989).
1 83