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The 17F(p, γ)18Ne direct capture cross section
Nuclear Physics A 746 (2004) 365c–369c
The
17
F(p, γ)18 Ne direct capture cross section
J.C. Blackmona , D.W. Bardayana , C.R. Bruneb , F. Carstoiuc , A.E. Champagned , R. Crespoe , T. Davinsonf , J.C. Fernandese , C.A. Gagliardig , U. Greifeh , C.J. Grossa , P.A. Hausladena , C. Iliadisd , C.C. Jewetth , R.L. Kozubi , T.A. Lewisa , F. Lianga , B.H. Moazeni , A.M. Mukhamedzhanovg , C.D. Nesarajai , F.M. Nunesj , P.D. Parkerk , D.C. Radforda , L. Sahind,a , J.P. Scotti , D. Shapiraa , M.S. Smitha , J.S. Thomasl , L. Tracheg , R.E. Tribbleg , P.J. Woodsf , C.-H. Yua a
Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831
b
Dept. of Physics and Astronomy, Ohio Univ., Athens, OH 45701
c
Institute of Atomic Physics, Bucharest, Romania
d
Dept. of Physics and Astronomy, Univ. of North Carolina, Chapel Hill, NC 27599
Dept. de F´isica, Instituto Superior T´ecnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
e
f
Dept. of Physics and Astronomy, Univ. of Edinburgh, Edinburgh EH9 3JZ, UK
g
Cyclotron Institute, Texas A&M Univ., College Station, TX 77843
h
Dept. of Physics, Colorado School of Mines, Golden, CO 80401
i
Physics Dept., Tennessee Technological Univ., Cookeville, TN 38505
j
National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824 k l
A. W. Wright Nuclear Structure Laboratory, Yale Univ., New Haven, CT 06511
Dept. of Physics and Astronomy, Rutgers Univ., New Brunswick, NJ 08903
The 17 F(p,γ)18 Ne reaction is important for understanding nucleosynthesis in novae. This reaction rate is expected to be dominated by the unmeasured direct-capture cross section at nova temperatures. We have measured cross sections for the proton-transfer reaction 14 N(17 F,18 Ne)13 C to determine 17 F+p asymptotic normalization coefficients for 18 Ne bound states and the 17 F(p, γ)18 Ne direct-capture cross section. Elastic scattering cross sections for the 14 N(17 F,17 F)14 N and 12 C(17 F,17 F)12 C reactions were also measured and used to determine reliable optical-model parameters within the framework of a microscopic double-folding model. Here we present the technique and some preliminary results. 0375-9474/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2004.09.054
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J.C. Blackmon et al. / Nuclear Physics A 746 (2004) 365c–369c
Nova explosions occur in binary star systems when matter is transferred from a companion star onto the surface of a white dwarf. The accreting hydrogen-rich gas mixes with the abundant carbon, oxygen, and neon on the surface of the white dwarf and ignites a thermonuclear runaway that ultimately ejects the stellar envelope and enriches the interstellar medium. A significant fraction of the envelope is converted into 17 F during the explosion by the 16 O(p, γ)17 F reaction [1]. The decay of the 17 F helps power the expansion and probably produces the majority of the fragile 17 O isotope found in the Galaxy. However, much of the 17 F may be destroyed by the 17 F(p,γ)18 Ne reaction. The ratio of the 17 F(p,γ)18 Ne reaction rate to the 17 F decay rate is important for understanding the galactic nucleosynthesis of the 17 O, 18 O and 15 N isotopes, as well as the flux of positron-annihilation gamma rays from novae [2]. The 17 F(p, γ)18 Ne reaction bypasses the production of 17 O and instead leads to the production of the long-lived 18 F isotope. The annihilation of positrons from the 18 F decay produces the greatest flux of potentially observable gamma rays from novae. Measurement of this gamma ray flux would provide an important test of nova models. The 17 F(p,γ)18 Ne cross section is dominated at Ecm < 1 MeV by direct capture and the contribution from a single resonance corresponding to the lowest energy 3+ state in 18 Ne. The energy and width of this 3+ state have been established via measurement of 17 F+p elastic scattering (Ex = 4525 ± 3 keV and Γ = 18 ± 2 keV) [3], but the resonance strength remains unknown experimentally (ωγ ≈ 20 meV). The direct-capture cross section depends upon the structure of states below the proton threshold in 18 Ne which is also uncertain. Estimates of the cross section based upon the properties of states in the 18 O mirror nucleus, nuclear shell model calculations, and microscopic cluster model calculations, predict that the 17 F(p, γ)18 Ne reaction rate will be dominated by direct capture to the two lowest energy 2+ states in 18 Ne for T < 5 × 108 K. Resonant capture to the first 3+ state is expected to dominate the rate at higher temperatures [3–5]. Measurements of the 17 F(p, γ)18 Ne capture cross section using a radioactive 17 F beam are desirable in order to determine both the resonant and direct contributions to the 17 F(p, γ)18 Ne reaction rate. The small cross sections expected at the energies most important for novae (σ ≈ 1 nb at Ecm = 300 keV) place measurements at these energies beyond the reach of radioactive ion beam facilities currently. However, it has been shown that direct-capture cross sections can be reliably determined by measuring Asymptotic Normalization Coefficients (ANC’s) for peripheral proton transfer reactions [6]. We have measured the 14 N(17 F,18 Ne)13 C reaction with the aim of determining ANC’s for 17 F+p for low-lying states in 18 Ne and hence the 17 F(p, γ)18 Ne direct-capture cross section. While the extraction of capture cross sections from ANC’s has reduced model dependence compared to other indirect approaches, the determination of reliable opticalmodel parameters is still important for obtaining an accurate direct-capture cross section. For this reason, we have also measured cross sections for the 14 N(17 F,17 F)14 N and 12 C(17 F,17 F)12 C elastic scattering reactions and used these cross sections to help determine the best optical-model parameterization for these channels. Here we describe the experimental approach and present results from the elastic scattering measurements and optical-model analysis. Some preliminary results from the 14 N(17 F,18 Ne)13 C measurement are also provided. A 170-MeV beam of isotopically-pure 17 F (1 − 2 × 106 s−1 ) from the Holifield Ra-
J.C. Blackmon et al. / Nuclear Physics A 746 (2004) 365c–369c
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Figure 1. The 14 N(17 F,17 F)14 N elastic scattering cross section, and the calculated cross section using the optical-model potential determined using the double-folding procedure described in the text.
dioactive Ion Beam Facility was used to bombard 1-mg/cm2 -thick targets of melamine (C3 N6 H6 ) and carbon. In one set of measurements, charged-particles were detected by two pairs of position-sensitive silicon-strip detector telescopes (25 cm2 area) covering θlab = 3◦ − 9◦ . Thin (65-µm) ∆E detectors were backed by 300-µm-thick detectors, allowing identification of the Z of the charged-particles. Both 17 F from elastic scattering and 18 Ne from proton transfer were easily identified, and the 18 Ne from the 14 N(17 F,18 Ne)13 C and 12 C(17 F,18 Ne)11 B reactions were distinguished by kinematics alone owing to the very different reaction Q values. However, the charged-particle energy resolution was not sufficient (due to the energy loss of the beam in the target) to distinguish transfer to each state of interest. Therefore, gamma-rays emitted by the recoiling 18 Ne nuclei were detected in coincidence using CLARION, an array of 11 segmented clover germanium detectors [8], providing a tag for transfer to the individual states in 18 Ne (except for the weakly-populated ground state). The efficiency of the silicon and germanium detectors was determined independently with calibrated sources, and the coincidence efficiency was calculated for each state by folding the individual detector efficiencies with the particlegamma angular correlations calculated from DWBA scattering amplitudes. We also performed a second set of measurements in order to extend the angular range of the elastic scattering measurements. An annular array of silicon-strip detectors, SIDAR [3], was arranged to cover laboratory angles of θlab = 7◦ − 18◦ in 16 angular bins. Data were collected on both the carbon and melamine targets, and 17 F scattering from the
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J.C. Blackmon et al. / Nuclear Physics A 746 (2004) 365c–369c
carbon and nitrogen in the melamine target could be distinguished at most of the angles covered in this measurement by kinematics. The 14 N(17 F,17 F)14 N elastic scattering cross section resulting from both sets of measurements is shown in Fig. 1. Similar results were obtained for the 12 C(17 F,17 F)12 C cross section, which was also used to determine the contribution to the 17 F scattering yield at forward angles resulting from carbon in the melamine target. Optical model parameters that are determined from phenomenological fits to limited data sets typically have significant ambiguities. However, a double-folding procedure has been shown to determine optical-model potentials that reliably reproduce elastic scattering data for a large number of systems involving loosely-bound p-shell nuclei [7]. We have used the measured 12 C(17 F,17 F)12 C and 14 N(17 F,17 F)14 N elastic scattering cross sections to test if this established technique for p shell nuclei could be applied to these systems involving 17 F. A standard spherical Hartree-Fock procedure was used to calculate singleparticle densities, with the parameters of the surface terms in the density functional being slightly adjusted to reproduce the experimental binding energies. The densities were then folded with a G-matrix effective nucleon-nucleon interaction [9,10]. The normalizations of the real and imaginary folding form factors were varied to fit the elastic scattering data. A best fit (χ2 = 4.9) to the 14 N(17 F,17 F)14 N elastic scattering data is also shown in Fig. 1, where the best-fit renormalization parameters for the real and imaginary folding form factors were found to be 0.61 and 0.91 respectively. A similar fit to the 12 C(17 F,17 F)12 C elastic scattering data was obtained with real and imaginary renormalization parameters of 0.53 and 1.03 respectively. The normalization of the imaginary form factors are in good agreement with those found for p-shell systems (1.00 ± 0.09). We find less suppression of the real form factor than that previously obtained for reactions involving light p-shell nuclei (0.37 ± 0.01), and our result is in closer agreement with that obtained for the 13 C(14 N,14 N)13 C reaction (0.456). For more tightly bound nuclei, the dynamic polarization potential tends to be dominated by exchange and nucleon transfer reactions which give less contribution at the nuclear surface. A phenomenological fit to the data was also performed using Woods-Saxon form factors, but only slightly improved fits to the data were obtained with substantial ambiguity in the fit parameters. We believe that the double-folding analysis provides the most reliable and unambiguous determination of the optical-model potentials, and we adopt the potentials generated in this manner for the analysis of the 14 N(17 F,18 Ne)13 C cross sections. A preliminary analysis of the 14 N(17 F,18 Ne)13 C data for the strongest transition, that populating the 3.376 MeV 4+ state in 18 Ne, is shown in Fig. 2. A DWBA calculation of the transfer cross section for a d5/2 proton to the 3.376 MeV state in 18 Ne is also shown, where optical-model parameters were determined by the double-folding procedure described above, and spectroscopic amplitudes were taken from microscopic model calculations [4,11] and are in good agreement with neutron single-particle amplitudes measured in the mirror nucleus 18 O [12]. The curve shown in Fig. 2 results from a completely parameter free calculation and indicates that the spectroscopic amplitudes for the 4+ state are about 30% bigger than expected. While this is the strongest transition in the protontransfer reaction, it is suppressed in 17 F(p, γ)18 Ne direct capture at low energies due to the centrifugal barrier for = 2 partial waves and has little influence on the 17 F(p, γ)18 Ne direct-capture cross section. Most important is capture to the first 2+ state at 1.887 keV.
J.C. Blackmon et al. / Nuclear Physics A 746 (2004) 365c–369c
369c
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Figure 2. Cross section for the cross section (solid curve).
14
N(17 F,18 Ne3376 )13 C reaction and the calculated DWBA
Analysis of the transfer to this state is complicated by cascade gamma rays from levels at higher energies, thus necessitating an accurate determination of the ANC’s for these states as well, particularly the strongly-populated 4+ level. Analysis of the data is still in progress, but we expect to be able to accurately determine the ANC’s for the 17 F+p vertex for both 2+ excited states and thus the 17 F(p, γ)18 Ne direct-capture cross section. ORNL is managed by UT-Battelle, LLC, for the U.S. Department of Energy under contract DE-AC05-00OR22725. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
S.A. Glasner, E. Livne, and J.W. Truran, Astrophys. J. 475 (1997) 754. C. Iliadis et al., Astrophys. J. Suppl. Ser. 142 (2002) 105. D.W. Bardayan et al., Phys. Rev. C62 (2000) 055804. M. Dufour and P. Descouvemont, submitted to Nucl. Phys. A. A. Garc´ia et al., Phys. Rev. C43 (1991) 2012. C.A. Gagliardi et al., Phys. Rev. C59 (1999) 1149. L. Trache et al., Phys. Rev. C61 (2000) 024612-1. C.J. Gross et al., Nucl. Instrum. Methods Phys Res. A 450 (2000) 12. J.P. Jeukenne, A. Lejeune, and C. Mahaux, Phys. Rev. C16 (1977) 80. E. Bauge, J.P. Delaroche, and M. Girod, Phys. Rev. C58 (1998) 1118. B.A. Brown, private communication. T.K. Li, D. Dehnhard, R. E. Brown, and P. J. Ellis, Phys. Rev. C13 (1976) 55.
The
17
F(p, γ)18 Ne direct capture cross section
J.C. Blackmona , D.W. Bardayana , C.R. Bruneb , F. Carstoiuc , A.E. Champagned , R. Crespoe , T. Davinsonf , J.C. Fernandese , C.A. Gagliardig , U. Greifeh , C.J. Grossa , P.A. Hausladena , C. Iliadisd , C.C. Jewetth , R.L. Kozubi , T.A. Lewisa , F. Lianga , B.H. Moazeni , A.M. Mukhamedzhanovg , C.D. Nesarajai , F.M. Nunesj , P.D. Parkerk , D.C. Radforda , L. Sahind,a , J.P. Scotti , D. Shapiraa , M.S. Smitha , J.S. Thomasl , L. Tracheg , R.E. Tribbleg , P.J. Woodsf , C.-H. Yua a
Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831
b
Dept. of Physics and Astronomy, Ohio Univ., Athens, OH 45701
c
Institute of Atomic Physics, Bucharest, Romania
d
Dept. of Physics and Astronomy, Univ. of North Carolina, Chapel Hill, NC 27599
Dept. de F´isica, Instituto Superior T´ecnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
e
f
Dept. of Physics and Astronomy, Univ. of Edinburgh, Edinburgh EH9 3JZ, UK
g
Cyclotron Institute, Texas A&M Univ., College Station, TX 77843
h
Dept. of Physics, Colorado School of Mines, Golden, CO 80401
i
Physics Dept., Tennessee Technological Univ., Cookeville, TN 38505
j
National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824 k l
A. W. Wright Nuclear Structure Laboratory, Yale Univ., New Haven, CT 06511
Dept. of Physics and Astronomy, Rutgers Univ., New Brunswick, NJ 08903
The 17 F(p,γ)18 Ne reaction is important for understanding nucleosynthesis in novae. This reaction rate is expected to be dominated by the unmeasured direct-capture cross section at nova temperatures. We have measured cross sections for the proton-transfer reaction 14 N(17 F,18 Ne)13 C to determine 17 F+p asymptotic normalization coefficients for 18 Ne bound states and the 17 F(p, γ)18 Ne direct-capture cross section. Elastic scattering cross sections for the 14 N(17 F,17 F)14 N and 12 C(17 F,17 F)12 C reactions were also measured and used to determine reliable optical-model parameters within the framework of a microscopic double-folding model. Here we present the technique and some preliminary results. 0375-9474/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2004.09.054
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J.C. Blackmon et al. / Nuclear Physics A 746 (2004) 365c–369c
Nova explosions occur in binary star systems when matter is transferred from a companion star onto the surface of a white dwarf. The accreting hydrogen-rich gas mixes with the abundant carbon, oxygen, and neon on the surface of the white dwarf and ignites a thermonuclear runaway that ultimately ejects the stellar envelope and enriches the interstellar medium. A significant fraction of the envelope is converted into 17 F during the explosion by the 16 O(p, γ)17 F reaction [1]. The decay of the 17 F helps power the expansion and probably produces the majority of the fragile 17 O isotope found in the Galaxy. However, much of the 17 F may be destroyed by the 17 F(p,γ)18 Ne reaction. The ratio of the 17 F(p,γ)18 Ne reaction rate to the 17 F decay rate is important for understanding the galactic nucleosynthesis of the 17 O, 18 O and 15 N isotopes, as well as the flux of positron-annihilation gamma rays from novae [2]. The 17 F(p, γ)18 Ne reaction bypasses the production of 17 O and instead leads to the production of the long-lived 18 F isotope. The annihilation of positrons from the 18 F decay produces the greatest flux of potentially observable gamma rays from novae. Measurement of this gamma ray flux would provide an important test of nova models. The 17 F(p,γ)18 Ne cross section is dominated at Ecm < 1 MeV by direct capture and the contribution from a single resonance corresponding to the lowest energy 3+ state in 18 Ne. The energy and width of this 3+ state have been established via measurement of 17 F+p elastic scattering (Ex = 4525 ± 3 keV and Γ = 18 ± 2 keV) [3], but the resonance strength remains unknown experimentally (ωγ ≈ 20 meV). The direct-capture cross section depends upon the structure of states below the proton threshold in 18 Ne which is also uncertain. Estimates of the cross section based upon the properties of states in the 18 O mirror nucleus, nuclear shell model calculations, and microscopic cluster model calculations, predict that the 17 F(p, γ)18 Ne reaction rate will be dominated by direct capture to the two lowest energy 2+ states in 18 Ne for T < 5 × 108 K. Resonant capture to the first 3+ state is expected to dominate the rate at higher temperatures [3–5]. Measurements of the 17 F(p, γ)18 Ne capture cross section using a radioactive 17 F beam are desirable in order to determine both the resonant and direct contributions to the 17 F(p, γ)18 Ne reaction rate. The small cross sections expected at the energies most important for novae (σ ≈ 1 nb at Ecm = 300 keV) place measurements at these energies beyond the reach of radioactive ion beam facilities currently. However, it has been shown that direct-capture cross sections can be reliably determined by measuring Asymptotic Normalization Coefficients (ANC’s) for peripheral proton transfer reactions [6]. We have measured the 14 N(17 F,18 Ne)13 C reaction with the aim of determining ANC’s for 17 F+p for low-lying states in 18 Ne and hence the 17 F(p, γ)18 Ne direct-capture cross section. While the extraction of capture cross sections from ANC’s has reduced model dependence compared to other indirect approaches, the determination of reliable opticalmodel parameters is still important for obtaining an accurate direct-capture cross section. For this reason, we have also measured cross sections for the 14 N(17 F,17 F)14 N and 12 C(17 F,17 F)12 C elastic scattering reactions and used these cross sections to help determine the best optical-model parameterization for these channels. Here we describe the experimental approach and present results from the elastic scattering measurements and optical-model analysis. Some preliminary results from the 14 N(17 F,18 Ne)13 C measurement are also provided. A 170-MeV beam of isotopically-pure 17 F (1 − 2 × 106 s−1 ) from the Holifield Ra-
J.C. Blackmon et al. / Nuclear Physics A 746 (2004) 365c–369c
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Figure 1. The 14 N(17 F,17 F)14 N elastic scattering cross section, and the calculated cross section using the optical-model potential determined using the double-folding procedure described in the text.
dioactive Ion Beam Facility was used to bombard 1-mg/cm2 -thick targets of melamine (C3 N6 H6 ) and carbon. In one set of measurements, charged-particles were detected by two pairs of position-sensitive silicon-strip detector telescopes (25 cm2 area) covering θlab = 3◦ − 9◦ . Thin (65-µm) ∆E detectors were backed by 300-µm-thick detectors, allowing identification of the Z of the charged-particles. Both 17 F from elastic scattering and 18 Ne from proton transfer were easily identified, and the 18 Ne from the 14 N(17 F,18 Ne)13 C and 12 C(17 F,18 Ne)11 B reactions were distinguished by kinematics alone owing to the very different reaction Q values. However, the charged-particle energy resolution was not sufficient (due to the energy loss of the beam in the target) to distinguish transfer to each state of interest. Therefore, gamma-rays emitted by the recoiling 18 Ne nuclei were detected in coincidence using CLARION, an array of 11 segmented clover germanium detectors [8], providing a tag for transfer to the individual states in 18 Ne (except for the weakly-populated ground state). The efficiency of the silicon and germanium detectors was determined independently with calibrated sources, and the coincidence efficiency was calculated for each state by folding the individual detector efficiencies with the particlegamma angular correlations calculated from DWBA scattering amplitudes. We also performed a second set of measurements in order to extend the angular range of the elastic scattering measurements. An annular array of silicon-strip detectors, SIDAR [3], was arranged to cover laboratory angles of θlab = 7◦ − 18◦ in 16 angular bins. Data were collected on both the carbon and melamine targets, and 17 F scattering from the
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J.C. Blackmon et al. / Nuclear Physics A 746 (2004) 365c–369c
carbon and nitrogen in the melamine target could be distinguished at most of the angles covered in this measurement by kinematics. The 14 N(17 F,17 F)14 N elastic scattering cross section resulting from both sets of measurements is shown in Fig. 1. Similar results were obtained for the 12 C(17 F,17 F)12 C cross section, which was also used to determine the contribution to the 17 F scattering yield at forward angles resulting from carbon in the melamine target. Optical model parameters that are determined from phenomenological fits to limited data sets typically have significant ambiguities. However, a double-folding procedure has been shown to determine optical-model potentials that reliably reproduce elastic scattering data for a large number of systems involving loosely-bound p-shell nuclei [7]. We have used the measured 12 C(17 F,17 F)12 C and 14 N(17 F,17 F)14 N elastic scattering cross sections to test if this established technique for p shell nuclei could be applied to these systems involving 17 F. A standard spherical Hartree-Fock procedure was used to calculate singleparticle densities, with the parameters of the surface terms in the density functional being slightly adjusted to reproduce the experimental binding energies. The densities were then folded with a G-matrix effective nucleon-nucleon interaction [9,10]. The normalizations of the real and imaginary folding form factors were varied to fit the elastic scattering data. A best fit (χ2 = 4.9) to the 14 N(17 F,17 F)14 N elastic scattering data is also shown in Fig. 1, where the best-fit renormalization parameters for the real and imaginary folding form factors were found to be 0.61 and 0.91 respectively. A similar fit to the 12 C(17 F,17 F)12 C elastic scattering data was obtained with real and imaginary renormalization parameters of 0.53 and 1.03 respectively. The normalization of the imaginary form factors are in good agreement with those found for p-shell systems (1.00 ± 0.09). We find less suppression of the real form factor than that previously obtained for reactions involving light p-shell nuclei (0.37 ± 0.01), and our result is in closer agreement with that obtained for the 13 C(14 N,14 N)13 C reaction (0.456). For more tightly bound nuclei, the dynamic polarization potential tends to be dominated by exchange and nucleon transfer reactions which give less contribution at the nuclear surface. A phenomenological fit to the data was also performed using Woods-Saxon form factors, but only slightly improved fits to the data were obtained with substantial ambiguity in the fit parameters. We believe that the double-folding analysis provides the most reliable and unambiguous determination of the optical-model potentials, and we adopt the potentials generated in this manner for the analysis of the 14 N(17 F,18 Ne)13 C cross sections. A preliminary analysis of the 14 N(17 F,18 Ne)13 C data for the strongest transition, that populating the 3.376 MeV 4+ state in 18 Ne, is shown in Fig. 2. A DWBA calculation of the transfer cross section for a d5/2 proton to the 3.376 MeV state in 18 Ne is also shown, where optical-model parameters were determined by the double-folding procedure described above, and spectroscopic amplitudes were taken from microscopic model calculations [4,11] and are in good agreement with neutron single-particle amplitudes measured in the mirror nucleus 18 O [12]. The curve shown in Fig. 2 results from a completely parameter free calculation and indicates that the spectroscopic amplitudes for the 4+ state are about 30% bigger than expected. While this is the strongest transition in the protontransfer reaction, it is suppressed in 17 F(p, γ)18 Ne direct capture at low energies due to the centrifugal barrier for = 2 partial waves and has little influence on the 17 F(p, γ)18 Ne direct-capture cross section. Most important is capture to the first 2+ state at 1.887 keV.
J.C. Blackmon et al. / Nuclear Physics A 746 (2004) 365c–369c
369c
1
dσ/dΩ (mb/sr)
10
0
10
−1
10
0
5
10
15
20
25
30
θcm (degrees)
Figure 2. Cross section for the cross section (solid curve).
14
N(17 F,18 Ne3376 )13 C reaction and the calculated DWBA
Analysis of the transfer to this state is complicated by cascade gamma rays from levels at higher energies, thus necessitating an accurate determination of the ANC’s for these states as well, particularly the strongly-populated 4+ level. Analysis of the data is still in progress, but we expect to be able to accurately determine the ANC’s for the 17 F+p vertex for both 2+ excited states and thus the 17 F(p, γ)18 Ne direct-capture cross section. ORNL is managed by UT-Battelle, LLC, for the U.S. Department of Energy under contract DE-AC05-00OR22725. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
S.A. Glasner, E. Livne, and J.W. Truran, Astrophys. J. 475 (1997) 754. C. Iliadis et al., Astrophys. J. Suppl. Ser. 142 (2002) 105. D.W. Bardayan et al., Phys. Rev. C62 (2000) 055804. M. Dufour and P. Descouvemont, submitted to Nucl. Phys. A. A. Garc´ia et al., Phys. Rev. C43 (1991) 2012. C.A. Gagliardi et al., Phys. Rev. C59 (1999) 1149. L. Trache et al., Phys. Rev. C61 (2000) 024612-1. C.J. Gross et al., Nucl. Instrum. Methods Phys Res. A 450 (2000) 12. J.P. Jeukenne, A. Lejeune, and C. Mahaux, Phys. Rev. C16 (1977) 80. E. Bauge, J.P. Delaroche, and M. Girod, Phys. Rev. C58 (1998) 1118. B.A. Brown, private communication. T.K. Li, D. Dehnhard, R. E. Brown, and P. J. Ellis, Phys. Rev. C13 (1976) 55.