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Astrophysical S factors of reactions with light nuclei

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Abstract

The two-cluster model is a phenomenological semi-microscopic approach to the study of multinucleon nuclear systems. In the framework of this model, interaction of nucleon clusters is described by the local two-body potential determined from the condition of description of data on cluster scattering and properties of their bound states. In this case the many-body character of the problem is taken into account approximately in terms of Pauli-allowed and Pauli-forbidden states of the total nucleon system. Accounting for the dependence of cluster interaction potential on orbital Young schemes characterizing the properties of permutation symmetry in the nucleon system is an important ingredient of the model. This approach is used for examination of photonuclear processes for p 2H, p 3H, p 6Li, p 12C and 4He12C, 3He4He, 3H4He, 2H4He systems and corresponding astrophysical S factors. It is demonstrated that this approach provides fairly good description of the data available in the low-energy region, especially for systems with the number of nucleons A > 4 when errors for the phase shifts of cluster scattering extracted from experimental data are minimal.

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References

  1. Essays in Nuclear Astrophysics, Ed. by C. A. Barnes, D. Clayton, and D. Schramm (Cambridge Univ., Cambridge, 1982; Mir, Moscow, 1986).

    Google Scholar 

  2. E. Epelbaum, W. Glockle, and U. G. Meissner, “The Two-Nucleon System at Next-to-Next-to-Next-to-Leading Order,” Nucl. Phys. A 747, 362–424 (2005); A. Epelbaum et al., “Three-Nucleon Forces from Chiral Effective Field Theory,” Phys. Rev. C 66, 064001-1-064001-17 (2002); E. Epelbaum, “Four-Nucleon Force Using the Method of Unitary Transformation,” Eur. Phys. J. A 34, 197–214 (2007).

    ADS  Google Scholar 

  3. L. D. Faddeev, “Scattering Theory for a Three Particle System,” Zh. Eksp. Teor. Fiz. 39, 1459–1467 (1960) [Sov. Phys. JETP 12, 1014 (1961)].

    MathSciNet  Google Scholar 

  4. O. A. Yakubovskii, “On the Integral Equations in the Theory of N Particle Scattering,” Yad. Fiz. 5, 1312–1320 (1967) [Sov. J. Nucl. Phys. 5, 937 (1967)].

    Google Scholar 

  5. P. Grassberger and W. Sandhas, “Systematical Treatment of the Non-Relativistic N-Particle Scattering Problem,” Nucl. Phys. B 2, 181–206 (1967); E._O. Alt, P. Grassberger, and W. Sandhas, “Systematical and Practical Treatment of the Few-Body Problem,” JINR Report No. E4-6688 (Dubna, 1972).

    ADS  Google Scholar 

  6. A. Deltuva and A. C. Fonseca, “Four-Body Calculation of Proton — 3He Scattering,” Phys. Rev. Lett. 98, 162502-1–162502-4 (2007); “Ab Intio Four-Body Calculation of n-3He, p-3H, and d-d Scattering,” Phys. Rev. C 76, 021001-1(R)-0211001-4(R) (2007).

    ADS  Google Scholar 

  7. R. Lazauskas, “Elastic Proton Scattering on Tritium Below the n-3He Threshold,” Phys. Rev. C 79, 054007-1–054007-5 (2009).

    ADS  Google Scholar 

  8. Y. C. Tang, M. Lemere, and D. R. Thompson, “Resonating-Group Method for Nuclear Many-Body Problems,” Phys. Rep. 47, 167–223 (1978).

    ADS  Google Scholar 

  9. P. Navratil, J. P. Vary, and B. R. Barrett, “Properties of 12C in the Ab Initio Nuclear Shell Model,” Phys. Rev. Lett. 84, 5728–5731 (2000).

    ADS  Google Scholar 

  10. S. Quaglioni and P. Navratil, “Ab Initio Many-Body Calculations of n-3H, n-4He, p-3,4He, and n-10Be Scattering,” Phys. Rev. Lett. 101, 092501-1–092501-4 (2008).

    ADS  Google Scholar 

  11. A. Kievsky, M. Viviany, and S. Rosati, “Polarization Observables in p-d Elastic Scattering below 30 MeV,” Phys. Rev. C 64, 024002-1–024002-18 (2001).

    ADS  Google Scholar 

  12. O. F. Nemets, V. G. Neudatchin, A. T. Rudchik, et al., Nucleon Clustering in Nuclei and Nuclear Reactions of Multinucleon Transfer (Naukova Dumka, Kiev, 1988) [in Russian].

    Google Scholar 

  13. M. K. Baktybaev et al., “The Scattering of Protons from 6Li and 7Li nuclei,” in Proceedings of the 4th Eurasian Conference on Nuclear Science and its Application, Oct. 31–Nov. 3, 2006, Baku, Azerbaijan (2006), p. 62; N. Burtebaev et al., “The New Experimental Data on the Elastic Scattering of Protons from 6Li, 7Li, 16O and 27Al Nuclei,” in Proceedings of the 5th Eurasian Conference on Nuclear Science and its Application, Oct. 14–17, 2008, Turkey, Ankara (2008), p. 40.

  14. D. M. Zazulin et al., “Scattering of Protons from 12C,” in Proceedings of the 6th International Conference on Modern Problems of Nuclear Physics, Sept. 19–22, 2006, Tashkent, Uzbekistan (2006), p. 127; M. K. Baktybaev et al., “Elastic Scattering of Protons from 12C, 16O and 27Al,” in Proceedings of the 4th Eurasian Conference on Nuclear Science and its Application, Oct. 31–Nov. 3, 2006, Baku, Azerbaijan (2006), p. 56.

  15. V. G. Neudatchin et al., “Generalized Potential-Model Description of Mutual Scattering of the Lightest p + d, d + 3He Nuclei and the Corresponding Photonuclear Reactions,” Phys. Rev. C 45, 1512–1527 (1992).

    ADS  Google Scholar 

  16. S. B. Dubovichenko, “Photoprocesses in Nd and d 3He Systems on the Base of Cluster Models for Potentials with Forbidden States,” Yad. Fiz. 58, 1253–1259 (1995) [Phys. At. Nucl. 58, 1174 (1995)].

    Google Scholar 

  17. L. Wildermuth and Ya. Tang, A Unified Theory of the Nucleus (Vieweg, Braunschweig, 1977; Mir, Moscow, 1980).

    Google Scholar 

  18. W. A. Fowler, G. R. Caughlan, and B. A. Zimmerman, “Thermonuclear Reaction Rates, II,” Ann. Rev. Astron. Astrophys. 13, 69–112 (1975).

    ADS  Google Scholar 

  19. P. J. Mohr and B. N. Taylor, “CODATA Recommended Values of the Fundamental Physical Constants: 2002,” Rev. Mod. Phys. 77, 1–107 (2005).

    ADS  Google Scholar 

  20. C. Angulo et al., “A Compilation of Charged-Particle Induced Thermonuclear Reaction Rates,” Nucl. Phys. A 656, 3–183 (1999).

    MathSciNet  ADS  Google Scholar 

  21. S. B. Dubovichenko, Properties of Light Atomic Nuclei in the Potential Cluster Model (Daneker, Almaty, 2004) [in Russian]. http://xxx.lanl.gov/abs/1006.4944.

    Google Scholar 

  22. D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum (Nauka, Leningrad, 1975; World Sci., Singapore, 1988).

    Google Scholar 

  23. http://physics.nist.gov/cgi-bin/cuu/Value?mud|search_for=atomnuc!

  24. J. Eisenberg and W. Greiner, Nuclear Theory, Vol. 2: Excitation Mechanisms of the Nucleus, 3rd ed. (North Holland, Amsterdam, 1987; Atomizdat, Moscow, 1973).

    Google Scholar 

  25. S. B. Dubovichenko, Calculation Methods for Nuclear Characteristics (Kompleks, Almaty, 2006) [in Russian]. http://xxx.lanl.gov/abs/1006.4947.

    Google Scholar 

  26. G. R. Plattner and R. D. Viollier, “Coupling Constants of Commonly Used Nuclear Probes,” Nucl. Phys. A 365, 8–12 (1981).

    ADS  Google Scholar 

  27. G. I. Marchuk and V. E. Kolesov, Application of Numerical Methods for Calculation of Neutron Cross Sections (Atomizdat, Moscow, 1970) [in Russian].

    Google Scholar 

  28. Handbook of Mathematical Functions, Ed. by M. Abramowitz and I. Stegun (Nation. Bureau of Standards, New York, 1964; Moscow, Nauka, 1979).

    MATH  Google Scholar 

  29. A. Barnet et al., “Coulomb Wave Function for All Real η and ρ,” Comput. Phys. Commun. 8, 377–395 (1974).

    ADS  Google Scholar 

  30. S. B. Dubovichenko and L. S. Chechin, “Calculation Methods of Coulomb Functions and Scattering Phases,” Vestn. Kaz. NPU, Fiz. Mat., No. 1(7), 115–122 (2003).

  31. C. Itzykson and M. Nauenberg, “Unitary Groups: Representations and Decompositions,” Rev. Mod. Phys. 38, 95–101 (1966).

    MATH  MathSciNet  ADS  Google Scholar 

  32. P. E. Hodgson, Optical Model of Elastic Scattering (Clarendon, Oxford, 1963; Atomizdat, Moscow, 1966).

    MATH  Google Scholar 

  33. S. B. Dubovichenko, “Partial Wave Analysis of Elastic 4He4He — Scattering in the Energy Range 40–50 MeV,” Yad. Fiz. 71, 66–75 (2008) [Phys. At. Nucl. 71, 65 (2008)].

    Google Scholar 

  34. S. B. Dubovichenko, N. Zh. Takibaev, and L. M. Chechin, The Physical Processes in Distant and Near Cosmos (Daik-Press, Almaty, 2008) [in Russian]. http://xxx.lanl.gov/abs/1012.1705.

    Google Scholar 

  35. V. I. Kukulin et al., “Detailed Study of the Cluster Structure of Light Nuclei in a Three-Body Model: (I). Ground State of 6Li,” Nucl. Phys. A 417, 128–156 (1984).

    ADS  Google Scholar 

  36. L. A. Skornyakov, Elements of General Algebra (Nauka, Moscow, 1990) [in Russian].

    Google Scholar 

  37. B. A. Popov and G. S. Tesler, Computation of Functions on Electronic Computers, the Handbook (Naukova Dumka, Kiev, 1984) [in Russian].

    Google Scholar 

  38. G. Korn and T. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1967; Nauka, Moscow, 1973).

    Google Scholar 

  39. S. B. Dubovichenko and L. S. Chechin, “Method for Solving of the Generalized Problem on Eigenvalues,” Vestn. Kaz. NPU, Fiz. Mat., No. 1 (7), 110–115 (2003); S. B. Dubovichenko, “Some Methods for Solving of Bound States Nuclear Physics Tasks,” Vestn. Kaz. NPU, Fiz. Mat., No. 1, 49–58 (2008).

  40. S. G. Mikhlin and Kh. L. Smolitskii, Approximate Methods for Solving Differential and Integral Equations (Nauka, Moscow, 1965) [in Russian].

    Google Scholar 

  41. S. B. Dubovichenko and L. M. Chechin, “Modern Programming Methods of Actual Physical Tasks,” in Proceedings of the Conference on Modern Problems and Tasks of Informatization in Kazakhstan (KazNTU, Kazakhstan, Almaty) [in Russian].

  42. S. B. Dubovichenko, “Alternative Method for Solving of the Generalized Matrix Problem on Eigenvalues,” Izv. NAN RK, Fiz. Math., No. 4, 52–55 (2007).

  43. W. A. Fowler, “Experimental and Theoretical Nuclear Astrophysics: The Quest for the Origin of the Elements, Nobel Lecture (Stockholm, 8 Dec. 1983); Usp. Fiz. Nauk 145, 441–488 (1985).

    ADS  Google Scholar 

  44. K. A. Snover, “Solar p-p Chain and the 7Be(p, γ)8B S-Factor,” CEPRA. NDM03 1/6/2008 (Univ. of Washington, 2008).

  45. S. B. Dubovichenko and A. V. Dzhazairov-Kakhramanov, “Astrophysical S-Factor of the Radiative p 2H Capture,” Eur. Phys. J. A 39, 139–143 (2009).

    ADS  Google Scholar 

  46. R. Schiavilla, V. R. Pandaripande, and R. B. Wiringa, “Momentum Distributions in A = 3 and 4 Nuclei,” Nucl. Phys. A 449, 219–242 (1986).

    ADS  Google Scholar 

  47. Yu. N. Uzikov, “Backward Elastic p 3He Scattering and High Momentum Components of 3He Wave Function,” Phys. Rev. C 58, 36–39 (1998).

    ADS  Google Scholar 

  48. Yu. N. Uzikov and J. Haidenbauer, “3He Structure and Mechanism of p 3He Elastic Scattering,” Phys. Rev. C 68, 014001-1–014001-6 (2003).

    ADS  Google Scholar 

  49. P. Schmelzbach et al., “Phase Shift Analysis of p 2H Elastic Scattering,” Nucl. Phys. A 197, 273–289 (1972); J. Arvieux, “Analyse en Dephasages des Sections Efficaces et Polarisations dans la Diffusion Elastique p 2H,” Nucl. Phys. A 102, 513–528 (1967); J. Chauvin and J. Arvieux, “Phase Shift Analysis of Spin Correlation Coefficients in p 2H Scattering,” Nucl. Phys. A 247, 347–358 (1975); E. Huttel et al., “Phase Shift Analysis of p 2H Elastic Scattering below Break — Up Threshold,” Nucl. Phys. A 406, 443–455 (1983).

    ADS  Google Scholar 

  50. S. B. Dubovichenko and A. V. Dzhazairov-Kakhramanov, “Potential Description of the Elastic Nd, dd, Nα and dτ Scattering,” Yad. Fiz. 51, 1541–1550 (1990) [Sov. J. Nucl. Phys. 51, 971 (1990)].

    Google Scholar 

  51. G. M. Griffiths, E. A. Larson, and L. P. Robertson, “The Capture of Proton by Deuteron,” Can. J. Phys. 40, 402–411 (1962).

    ADS  Google Scholar 

  52. L. Ma et al., “Measurements of 1H(d, γ)3He and 2H(p, γ)3He at Very Low Energies,” Phys. Rev. C 55, 588–596 (1997).

    ADS  Google Scholar 

  53. G. J. Schimd et al., “The 2H(p, γ)3He and 1H(d, γ)3He Reactions Below 80 KeV,” Phys. Rev. C 56, 2656–2681 (1997).

    Google Scholar 

  54. C. Casella et al., “First Measurement of the d(p, γ)3He Cross Section down to the Solar Gamow Peak,” Nucl. Phys. A 706, 203–216 (2002).

    ADS  Google Scholar 

  55. S. B. Dubovichenko, “Astrophysical S-factor of Radiation p 2H Capture at Low Energies,” Doklady NAN RK 60(3), 33–38 (2008).

    Google Scholar 

  56. D. R. Tilley, H. R. Weller, and H. H. Hasan, “Energy Levels of Light Nuclei A = 3,” Nucl. Phys. A 474, 1–60 (1987).

    ADS  Google Scholar 

  57. D. R. Tilley, H. R. Weller, and G. M. Hale, “Energy Levels of Light Nuclei A = 4,” Nucl. Phys. A 541, 1–157 (1992).

    ADS  Google Scholar 

  58. D. A. Kirzhnits, “Does the Triton Contain a Deuteron?” Pis’ma Zh. Eksp. Teor. Fiz. 28, 479–481 (1978) [JETP Lett. 28, 444 (1978)].

    Google Scholar 

  59. L. D. Blokhintsev, I. Borbei, and E. I. Dolinskii, “Nuclear Vertex Constants,” Fiz. Elem. Chastits At. Yadra 8, 1189–1245 (1977) [Sov. J. Part. Nucl. 8, 485 (1977)].

    Google Scholar 

  60. M. Bornard et al., “Coupling Constants for Several Light Nuclei from a Dispersion Analysis of Nucleon and Deuteron Scattering Amplitudes,” Nucl. Phys. A 294, 492–512 (1978).

    ADS  Google Scholar 

  61. G. R. Plattner, M. Bornard, and R. D. Viollier, “Accurate Determination of the 3He-pd and 3He-pd* Coupling Constants,” Phys. Rev. Lett. 39, 127–130 (1977).

    ADS  Google Scholar 

  62. A. Kievsky et al., “The Three-Nucleon System near the N-d Threshold,” Phys. Lett. A 406, 292–296 (1997).

    Google Scholar 

  63. Z. Ayer et al., “Determination of the Asymptotic D- to S-State Ratio for 3He via (d, 3He) Reactions,” Phys. Rev. C 52, 2851–2858 (1995).

    ADS  Google Scholar 

  64. G. J. Schimd et al., “Effects of Non-Nucleonic Degrees of Freedom in the d(p, γ)3He and p(d, γ)3He Reactions,” Phys. Rev. Lett. 76, 3088–3091 (1996).

    ADS  Google Scholar 

  65. G. J. Schimd et al., “Polarized Proton Capture by Deuterium and the 2H(p, γ)3He Astrophysical S-Factor,” Phys. Rev. 52, R1732–R1732 (1995).

    ADS  Google Scholar 

  66. M. Viviani, R. Schiavilla, and A. Kievsky, “Theoretical Study of the Radiative Capture Reactions 2H(N, γ)3H and 2H(p, γ)3He at Low Energies,” Phys. Rev. C 54, 534–553 (1996).

    ADS  Google Scholar 

  67. S. B. Dubovichenko and A. V. Dzhazairov-Kakhramanov, “Electromagnetic Effects on Light Nuclei on the Basis of Potential Cluster Model,” Fiz. Elem. Chastits At. Yadra 28, 1529–1594 (1997) [Phys. Part. Nucl. 28, 615 (1997)].

    Google Scholar 

  68. J. B. Warren et al., “Photodisintegration of He3 near the Threshold,” Phys. Rev. 132, 1691–1692 (1963).

    ADS  Google Scholar 

  69. B. L. Berman, L. J. Koester, and J. H. Smith, “Photo-disintegration of 3He,” Phys. Rev. 133, B117–B129 (1964).

    ADS  Google Scholar 

  70. V. N. Fetisov, A. N. Gorbunov, and A. T. Varfolomeev, “Nuclear Photoeffect on Three-Particle Nuclei,” Nucl. Phys. A 71, 305–342 (1965).

    Google Scholar 

  71. G. Ticcioni et al., “The Two-Body Photodisintegration of 3He,” Phys. Lett. A 46, 369–371 (1973).

    Google Scholar 

  72. K. N. Geller, E. G. Muirhead, and L. D. Cohen, “The 2H(p, γ)3He Reaction at the Breakup Threshold,” Nucl. Phys. A 96, 397–400 (1967).

    ADS  Google Scholar 

  73. S. B. Dubovichenko, “Phase Shift Analysis of p 12C Scattering at Astrophysical Energies,” Izv. Vyssh. Uchebn. Zaved., Ser. Fiz., No. 11, 21–27 (2008).

  74. H. Berg et al., “Differential Cross Section, Analyzing Power and Phase Shifts for p 3He Elastic Scattering below 1.0 MeV,” Nucl. Phys. A 334, 21–34 (1980); R. W. Kavanagh and P. D. Parker, “He + p Elastic Scattering below 1 MeV,” Phys. Rev. 143, 779–782 (1966); L. Morrow and W. Haeberli, “Proton Polarization in p-3He Elastic Scattering between 4 and 11 MeV,” Nucl. Phys. A 126, 225–232 (1969).

    ADS  Google Scholar 

  75. S. B. Dubovichenko, V. G. Neudatchin, A. A. Sakharuk, and Yu. F. Smirnov, “Generalized Potential Description of Interaction of the Lightest Nuclei pt and pH,” Izv. AN SSSR, Ser. Fiz. 54, 911–916 (1990); V. G. Neudatchin, A. A. Sakharuk, and S. V. Dubovichenko, “Photodisintegration of 4He and Surermultiplet Potential Model of Cluster-Cluster Interaction,” Few Body System 18, 159–172 (1995).

    Google Scholar 

  76. S. B. Dubovichenko, “Photoprocesses in p 3H and n 3Ne Channels of 4He Nuclei on the Basis of Potential Cluster Models,” Yad. Fiz. 58, 1377–1384 (1995) [Phys. At. Nucl. 58, 1295 (1995)].

    Google Scholar 

  77. T. A. Tombrello, “Phase Shift Analysis for 3He(p, p)3He,” Phys. Rev. 138, B40–B47 (1965).

    ADS  Google Scholar 

  78. Y. Yoshino et al., “Phase Shift of p 3He Scattering at Low Energies,” Prog. Theor. Phys. 103, 107–125 (2000).

    ADS  Google Scholar 

  79. D. H. McSherry and S. D. Baker, “3He Polarization Measurements and Phase Shifts for p 3He Elastic Scattering,” Phys. Rev. C 1, 888–892 (1970).

    ADS  Google Scholar 

  80. L. Drigo and G. Pisent, “Analysis of the p 3He Low Energy Interaction,” Nuovo Cimento B 51, 419–436 (1967).

    ADS  Google Scholar 

  81. G. Szaloky and F. Seiler, “Phase Shift Analysis of 3He(p, p)3He Elastic Scattering,” Nucl. Phys. A 303, 57–66 (1978).

    ADS  Google Scholar 

  82. T. A. Tombrello et al., “The Scattering of Protons from 3He,” Nucl. Phys. 39, 541–550 (1962).

    Google Scholar 

  83. J. S. McIntosh, R. L. Gluckstern, and S. Sack, “Proton Triton Interaction,” Phys. Rev. 88, 752–759 (1952).

    ADS  Google Scholar 

  84. R. M. Frank and J. L. Gammel, “Elastic Scattering of Protons by 3He and T,” Phys. Rev. 99, 1406–1410 (1955).

    ADS  Google Scholar 

  85. R. Kankowsky et al., “Elastic Scattering of Polarized Protons on Tritons between 4 and 12 MeV,” Nucl. Phys. A 263, 29–46 (1976).

    ADS  Google Scholar 

  86. Yu. M. Arkatov et al., “Study of 4He(γ, p)3H Reaction at Maximum Energy of γ Radiation 120 MeV,” Yad. Fiz. 12, 227–233 (1970) [Sov. J. Nucl. Phys. 12, 123 (1970)].

    Google Scholar 

  87. K. Hahn et al., “3H(p, γ)4He Cross Section,” Phys. Rev. C 51, 1624–1632 (1995).

    ADS  Google Scholar 

  88. R. Canon et al., “3H(p, γ)4He Reaction below E p = 80 KeV,” Phys. Rev. C 65, 044008.1–044008.7 (2002).

    ADS  Google Scholar 

  89. S. B. Dubovichenko, “Astrophysical S-Factor of p 3H Radiative Capture at Low Energies,” Izv. NAN RK, Ser. Fiz.-Mat., No. 4, 89–92 (2008); S. V. Dubovichenko and A. V. Dzhazairov-Kakhramanov, “Astrophysical S-Factors of the p 2H and p 3H Radiative Capture at Low Energies,” Uz. J. Rhys. 10, 364–370 (2008).

  90. T. K. Lim, “3He-n Vertex Constant and Structure of 4He,” Phys. Lett. B 55, 252–254 (1975).

    ADS  Google Scholar 

  91. B. F. Gibson, “Electromagnetic Disintegration of the A = 3 and A = 4 Nuclei,” Nucl. Phys. A 353, 85–98 (1981).

    ADS  Google Scholar 

  92. J. E. Perry and S. J. Bame, “3H(p, γ)4He Reaction,” Phys. Rev. 99, 1368–1375 (1955).

    ADS  Google Scholar 

  93. F. Balestra et al., “Photodisintegration of 4He in Giant-Resonance Region,” Nuovo Cim. A 38, 145–166 (1977).

    ADS  Google Scholar 

  94. W. Meyerhof et al., “3He(p, γ)4He reaction from 3 to 18 MeV,” Nucl. Phys. A 148, 211he t s of Light Atomic Nuclei 211–224 (1970).

    ADS  Google Scholar 

  95. G. Feldman et al., “3H(p, γ)4He Reaction and the (γ, p)/(γ, n) Ratio in 4He,” Phys. Rev. C 42, R1167–R1170 (1990).

    ADS  Google Scholar 

  96. M. Skill et al., “Differential Cross Section and Analyzing Power for Elastic Scattering of Protons on 6Li below 2.2 MeV,” Nucl. Phys. A. A581, 93–106 (1995).

    ADS  Google Scholar 

  97. C. Petitjean, L. Brown, and R. Seyler, “Polarization and Phase Shifts in 6Li(p, p)6Li from 0.5 to 5.6 MeV,” Nucl. Phys. A 129, 209–219 (1969).

    ADS  Google Scholar 

  98. S. B. Dubovichenko, A. V. Dzhazairov-Kakhramanov, and A. A. Sakharuk, “Potential Description of Elastic N6Li and αt Scattering,” Yad. Fiz. 56, 90–106 (1993) [Phys. At. Nucl. 56, 762 (1993)].

    Google Scholar 

  99. D. R. Tilley et al., “Energy Levels of Light Nuclei A = 5,6,7,” Nucl. Phys. A 708, 3–163 (2002).

    ADS  Google Scholar 

  100. I. M. Kapitonov, B. S. Ishkhanov, and I. A. Tutyn’, Nucleosynthesis in the Universe (Librokom, Moscow, 2009); http://nuclphys.sinp.msu.ru/nuclsynt.html [in Russian].

    Google Scholar 

  101. V. G. Neudatchin, A. A. Sakharuk, and Yu. F. Smirnov, “Generalized Potential Description of Interaction of the Lightest Cluster Scattering and Photonuclear Reactions,” Fiz. Elem. Chastits At. Yadra 23, 480–541 (1992) [Sov. J. Part. Nucl. 23, 210 (1992)]; V. G. Neudachin, B. G. Struzhko, and V. M. Lebedev, “Supermultiplet Potential Model of Interaction between the Lightest Clusters and a Unified Description of Various Nuclear Reactions,” Fiz. Elem. Chastits At. Yadra 36, 888–941 (2005) [Phys. Part. Nucl. 36, 468 (2005)].

    Google Scholar 

  102. Z. E. Switkowski et al., “Cross Section of the Reaction 6Li(p, γ)7Be,” Nucl. Phys. A 331, 50–60 (1979); R. Bruss et al., “Astrophysical S-Factors for the Radiative Capture Reaction 6Li(p, γ)7Be at Low Energies,” in Proceedings of the 2nd Intern. Symposium on Nuclear Astrophysics, Nuclei in the Cosmos, Karlsruhe, Germany, 6–10 July, 1992, Ed. by F. Kappeler and K. Wisshak (IOP Publ., Bristol, UK, 1993), p. 169.

    ADS  Google Scholar 

  103. K. Arai, D. Baye, and P. Descouvemont, “Microscopic Study of the 6Li(p, γ)7Be and 6Li(p, α)3He Reactions,” Nucl. Phys. A 699, 963–975 (2002).

    ADS  Google Scholar 

  104. R. M. Prior et al., “Energy Dependence of the Astrophysical S Factor for the 6Li(p, γ)7Be Reaction,” Phys. Rev. C 70, 055801–055809 (2004).

    ADS  Google Scholar 

  105. F. C. Burker, “Neutron and Proton Capture by 6Li,” Austr. J. Phys. 33, 159–176 (1980).

    ADS  Google Scholar 

  106. F. E. Cecil et al., “Radiative Capture of Protons by Light Nuclei at Low Energies,” Nucl. Phys. A 539, 75–96 (1992).

    ADS  Google Scholar 

  107. S. B. Dubovichenko, “Astrophysical S-Factors of p 2H and p 3H Radiative Capture,” Izv. Vyssh. Uchebn. Zaved., Ser. Fiz., No. 3, 68–73 (2009).

  108. S. B. Dubovichenko and A. V. Dzhazairov-Kakhramanov, “Astrophysical S-Factor of p 6Li Radiative Capture,” Dokl. NAN RK, No. 6, 41–45 (2009).

  109. M. F. Jahns and E. M. Bernstein, “Polarization in pα Scattering,” Phys. Rev. 162, 871–877 (1967).

    ADS  Google Scholar 

  110. A. Barnard, C. Jones, and J. Well, “Elastic Scattering of 2–11 MeV Proton by 4He,” Nucl. Phys. 50, 604–620 (1964).

    Google Scholar 

  111. R. I. Brown, W. Haeberli, and J. X. Saladin, “Polarization in the Scattering of Protons by α Particles,” Nucl. Phys. 47, 212–213 (1963).

    Google Scholar 

  112. H. L. Jackson et al., “The 12C(p, p)12C Differential Cross Section,” Phys. Rev. 89, 365–369 (1953).

    ADS  Google Scholar 

  113. H. L. Jackson et al., “The Excited States of the 13N Nucleus,” Phys. Rev. 89, 370–374 (1953).

    ADS  Google Scholar 

  114. S. J. Moss and W. Haeberli, “The Polarization of Protons Scattered by Carbon,” Nucl. Phys. 72, 417–435 (1965).

    Google Scholar 

  115. A. C. L. Barnard et al., “Cross Section as a Function of Angle and Complex Phase Shifts for the Scattering of Protons from 12C,” Nucl. Phys. 86, 130–144 (1966).

    Google Scholar 

  116. V. G. Neudatchin and Yu. F. Smirnov, Nucleon Associations in Light Nuclei (Nauka, Moscow, 1969) [in Russian].

    Google Scholar 

  117. F. Ajzenberg-Selove, “Energy Levels of Light Nuclei A = 13,14,” Nucl. Phys. A 523, 1–116 (1991).

    ADS  Google Scholar 

  118. F. Ajzenberg-Selove, “Energy Levels of Light Nuclei A = 12,” Nucl. Phys. A 506, 1–186 (1990).

    ADS  Google Scholar 

  119. N. Burtebaev et al., “New Measurements of the Astrophysical S Factor for 12C(p, γ)13N Reaction at Low Energies and the Asymptotic Normalization Coefficient (Nuclear Vertex Constant) for p + 12C → 13N Reaction,” Phys. Rev. C 78, 035802–035813 (2008).

    ADS  Google Scholar 

  120. S. B. Dubovichenko and A. V. Dzhazairov-Kakhramanov, “Astrophysical S-Factor of p 12C → 13Nγ Radiative Capture,” Izv. Vyssh. Uchebn. Zaved., Ser. Fiz., No. 8, 58–64 (2009).

  121. E. E. Salpeter, “Nuclear Reactions in Stars,” Phys. Rev. 107, 516–525 (1957); E. E. Salpeter, “Nuclear Reactions in Stars without Hydrogen,” Astrophys. J. 115, 326 (1952); C. Rolfs, “Nuclear Reactions in Stars Far below the Coulomb Barrier,” Progress Part. Nucl. Phys. 59, 43 (2007).

    ADS  Google Scholar 

  122. D. Schurmann et al., arXiv:nucl-ex/0511050v1 (2005).

  123. S. B. Dubovichenko, “Phase Shift Analysis of 4He4He Scattering at 40–50 MeV,” Izv. Vyssh. Uchebn. Zaved., Ser. Fiz., No. 6, 74–79 (2007).

  124. C. M. Jones et al., “The Scattering of Alpha Particles from 12C,” Nucl. Phys. 37, 1–9 (1962).

    Google Scholar 

  125. S. B. Dubovichenko, “Photoprocesses in 4He12C Channel of 16O Nucleus on the Basis of Potential Cluster Model,” Yad. Fiz. 59, 447–553 (1996) [Phys. At. Nucl. 59, 421 (1996)].

    Google Scholar 

  126. R. Plaga et al., “The Scattering of Alpha Particles from 12C and the 12C(α, γ)16O Stellar Reaction Rate,” Nucl. Phys. A 465, 291–316 (1987).

    ADS  Google Scholar 

  127. D. R. Tilley, H. R. Weller, and C. M. Cheves, “Energy Levels of Light Nuclei A = 16−17,” Nucl. Phys. A 564, 1–183 (1993).

    ADS  Google Scholar 

  128. S. B. Dubovichenko, N. T. Burtebaev, A. V. Dzhazairov-Kakhramanov, and D. M. Zazulin, “Phase Shift Analysis and Potential Description of Elastic 4He12C Scattering at Low Energies,” Izv. Vyssh. Uchebn. Zaved., Ser. Fiz., No. 7, 55–62 (2009).

  129. S. B. Dubovichenko and A. V. Dzhazairov-Kakhramanov, “Astrophysical S-Factor of 4He12C Radiative Capture at Low Energies,” Dokl. NAN RK, No. 3, 30–36 (2009).

  130. K. U. Kettner et al., “The 4He(12C, γ)16O Reaction at Stellar Energies,” Z. Phys. A 308, 73–94 (1982).

    ADS  Google Scholar 

  131. P. Dyer and C. A. Barnes, “The 12C(α, γ)16O Reaction and Stellar Helium Burning,” Nucl. Phys. A 233, 495–520 (1974).

    ADS  Google Scholar 

  132. C. R. Brune et al., “Sub-Coulomb α Transfers on 12C and the 12C(α, γ)16O S Factor,” Phys. Rev. Lett. 83, 4025–4028 (1999).

    ADS  Google Scholar 

  133. R. E. Asuma et al., “Constraints on the Low — Energies E1 Cross Section of 12C(α, γ)16O from the β — Delayed α Spectrum of 16N,” Phys. Rev. C 50, 1194–1215 (1994).

    ADS  Google Scholar 

  134. P. Descouvemont and D. Baye, “12C(α, γ)16O Reaction in a Multi Configuration Microscopic Model,” Phys. Rev. C 36, 1249–1255 (1987).

    ADS  Google Scholar 

  135. G. Imbriani, “Underground Laboratory Studies of pp and CNO. Some Astrophysical Consequences. LUNA,” in Proceedings of the 3rd European Summer School on Experimental Nuclear Astrophysics, Oct. 2–9, 2005, S. Tecla, Catania, Sicily, Italy.

  136. A. Caciolli et al., “Ultra-Sensitive in-Beam γ-Ray Spectroscopy for Nuclear Astrophysics at LUNA,” Eur. Phys. J. A 39, 179–186 (2009).

    ADS  Google Scholar 

  137. V. I. Kukulin, V. G. Neudatchin, and Yu. F. Smirnov, “Composite Particle Interaction Relevant to the Pauli Principle,” Fiz. Elem. Chastits At. Yadra 10, 1236–1255 (1979) [Sov. J. Part. Nucl. 10, 492 (1979)].

    Google Scholar 

  138. S. B. Dubovichenko and A. V. Dzhazairov-Kakhramanov, “Photoprocesses on 7Li and 7Be Nuclei in Cluster Model for Potentials with Forbidden States,” Yad. Fiz. 58, 635–641 (1995) [Phys. At. Nucl. 58, 579 (1995)]; “Photoprocesses on 6Li Nucleus in Cluster Models for Potentials with Forbidden States,” Yad. Fiz. 58, 852–859 (1995) [Phys. At. Nucl. 58, 788 (1995)].

    Google Scholar 

  139. S. B. Dubovichenko and A. V. Dzhazairov-Kakhramanov, “Potential Description of Cluster Channels of Lithium,” Yad. Fiz. 56, 87–98 (1993) [Phys. At. Nucl. 56, 195 (1993)]; “Coulomb Form Factors of Lithium Nuclei in Cluster Model on the Basis of Potentials with Forbidden States,” Yad. Fiz. 57, 784–791 (1994) [Phys. At. Nucl. 57, 733 (1994)].

    Google Scholar 

  140. A. C. Barnard, C. M. Jones, and G. C. Phillips, “The Scattering of 3He by 4He,” Nucl. Phys. 50, 629–640 (1964).

    Google Scholar 

  141. R. Spiger and T. A. Tombrello, “Scattering of He3 by He4 and of He4 by Tritium,” Phys. Rev. 163, 964–984 (1967).

    ADS  Google Scholar 

  142. M. Ivanovich, P. G. Young, and G. G. Ohlsen, “Elastic Scattering of the Several Hydrogen and Helium Isotopes from Tritium,” Nucl. Phys. A 110, 441–462 (1968).

    ADS  Google Scholar 

  143. L. C. McIntyre and W. Haeberli, “Phase Shifts Analysis of d-α Scattering,” Nucl. Phys. A 91, 382–398 (1967).

    ADS  Google Scholar 

  144. L. G. Keller and W. Haeberli, “Vector Polarization Measurements and Phase Shift Analysis for d-α Scattering between 3 and 11 MeV,” Nucl. Phys. A 156, 465–476 (1979).

    ADS  Google Scholar 

  145. W. Gruebler et al., “Phase Shift Analysis of d-α Elastic Scattering between 3 and 17 MeV,” Nucl. Phys. A 242, 265–284 (1975).

    ADS  Google Scholar 

  146. P. A. Schmelzbach et al., “Phase Shift Analysis of d-α Elastic Scattering,” Nucl. Phys. A 184, 193–213 (1972).

    ADS  Google Scholar 

  147. S. B. Dubovichenko, “Tensor 2H4He Interactions in the Potential Cluster Model Involving Forbidden States,” Yad. Fiz. 61, 210–217 (1998) [Phys. At. Nucl. 61, 162 (1998)].

    Google Scholar 

  148. S. B. Dubovichenko, “Astrophysical S-Factors of Radiative 3He4He, 3H4He and 2H4He Capture,” Yad. Fiz., 73, (2010) [Phys. At. Nucl. 73, 1526 (2010)].

  149. L. D. Blokhintsev et al., “Determination of the 6α + d Vertex Constant (Asymptotic Coefficient) from the 4He + d Phase-Shift Analysis,” Phys. Rev. C 48, 2390–2394 (1993).

    ADS  Google Scholar 

  150. L. D. Blokhintsev et al., “Calculation of the Nuclear Vertex Constant (Asymptotic Normalization Coefficient) for the Virtual Decay 6Li → α + d on the Basis of the Three Body Model and Application of the Result in Describing the Astrophysical Nuclear Reaction d(α, γ)6Li at Ultralow Energies,” Yad. Fiz. 69, 456–466 (2006) [Phys. At. Nucl. 69, 433 (2006)].

    Google Scholar 

  151. T. K. Lim, “The 6Li-α-d Vertex Constant,” Phys. Lett. B 56, 321–324 (1975).

    ADS  Google Scholar 

  152. S. B. Igamov and R. Yarmukhamedov, “Modified Two-Body Potential Approach to the Peripheral Direct Capture Astrophysical α + A → B + γ Reaction and Asymptotic Normalization Coefficients,” Nucl. Phys. A 781, 247–276 (2007).

    ADS  Google Scholar 

  153. C. R. Brune et al., “Sub-Coulomb α Transfers on 12C and the 12C(α, γ)16O S Factor,” Phys. Rev. Lett. 83, 4025–4028 (1999).

    ADS  Google Scholar 

  154. S. B. Igamov, K. I. Tursunmakhatov, and R. Yarmukhamedov, “Determination of the 3He + α to 7Be Asymptotic Normalization Coefficients (Nuclear Vertex Constants) and their Application for Extrapolation of the 3He(α, γ)7Be Astrophysical S-Factors to the Solar Energy Region,” arXiv:0905.2026v3 [nucl-th] (2009).

  155. K. Langanke, “Microscopic Potential Model Studies of Light Nuclear Capture Reactions,” Nucl. Phys. A 457, 351–366 (1986).

    ADS  Google Scholar 

  156. T. Kajino, “The 3He(α, γ)7Be and 3He(α, γ)7Li Reactions at Astrophysical Energies,” Nucl. Phys. A 460, 559–580 (1986).

    ADS  Google Scholar 

  157. N. A. Burkova et al., “Is It Possible to Observe an Isoscalar E1-Multipole in 6Liγαd Reactions?,” Phys. Lett. B 248, 15–20 (1990).

    ADS  Google Scholar 

  158. C. R. Brune, R. W. Kavanagh, and C. Rolf, “3H(α, γ)7Li Reaction at Low Energies,” Phys. Rev. C 50, 2205–2218 (1994).

    ADS  Google Scholar 

  159. G. M. Griffiths et al., “The 3H(4He, γ)7Li Reactions,” Can. J. Phys. 39, 1397–1403 (1961).

    ADS  Google Scholar 

  160. U. Schroder et al., “Astrophysical S Factor of 3H(α, γ)7Li,” Phys. Lett. B 192, 55–58 (1987).

    ADS  Google Scholar 

  161. T. A. D. Brown et al., “3He + 4He → 7Be Astrophysical S Factor,” Phys. Rev. C 76, 055801.1–055801. 12 (2007).

    ADS  Google Scholar 

  162. F. Confortola et al., “Astrophysical S Factor of the 3He(α, γ)7Be Reaction Measured at Low Energy via Detection of Prompt and Delayed γ Rays,” Phys. Rev. C 75, 065803 (2007); arXiv:0705.2151v1 [nucl-ex] (2007).

    ADS  Google Scholar 

  163. G. Gyurky et al., “3He(α, γ)7Be Cross Section at Low Energies,” Phys. Rev. C 75, 035805 (2007).

    ADS  Google Scholar 

  164. N. Singh et al., “New Precision Measurement of the 3He(4He, γ)7Be Cross Section,” Phys. Rev. Lett. 93, 262503 (2004).

    ADS  Google Scholar 

  165. J. L. Osborn et al., “Low-Energy Behavior of the 3He(α, γ)7Be Cross Section,” Nucl. Phys. A 419, 115–132 (1984).

    ADS  Google Scholar 

  166. D. Bemmerer et al., “Activation Measurement of the 3He(α,γ)7Be Cross Section at Low Energy,” Phys. Rev. Lett. 97, 122502–122507 (2006); arXiv:nucl-ex/0609013v1 (2006).

    ADS  Google Scholar 

  167. H. Costantini, “The 3He(α, γ)7Be S-Factor at Solar Energies: The Prompt Experiment at LUNA,” arXiv:0809.5269v1 [nucl-ex] (2008).

  168. R. C. Robertson et al., “Observation of the Capture Reaction 2H(α, γ)6Li and Its Role in Production of 6Li in the Big Bang,” Phys. Rev. Lett. 47, 1867–1870 (1981).

    ADS  Google Scholar 

  169. P. Mohr et al., “Direct Capture in the 3+ Resonance of 2H(α, γ)6Li,” Phys. Rev. C 50, 1543–1549 (1994).

    ADS  Google Scholar 

  170. J. Kiener et al., “Measurements of the Coulomb Dissociation Cross Section of 156 MeV 6Li Projectiles at Extremely Low Relative Fragment Energies of Astrophysical Interest,” Phys. Rev. C 44, 2195–2208 (1991).

    ADS  Google Scholar 

  171. S. B. Igamov and R. Yarmukhamedov, “Triple-Differential Cross Section of the 208Pb(6Li, αd)208Pb Coulomb Breakup and Astrophysical S-Factor of the d(α, γ)6Li Reaction at Extremely Low Energies,” Nucl. Phys. A 673, 509–525 (2000).

    ADS  Google Scholar 

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  1. Fesenkov Astrophysical Institute NCSRT NSA RK, Almaty, Kazakhstan

    S. B. Dubovichenko

  2. Institute of Nuclear Physics NNC RK, Almaty, Kazakhstan

    S. B. Dubovichenko

  3. Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia

    Yu. N. Uzikov

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Original Russian Text © S.B. Dubovichenko, Yu.N. Uzikov, 2011, published in Fizika Elementarnykh Chastits i Atomnogo Yadra, 2011, Vol. 42, No. 2.

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Dubovichenko, S.B., Uzikov, Y.N. Astrophysical S factors of reactions with light nuclei. Phys. Part. Nuclei 42, 251–301 (2011). https://doi.org/10.1134/S1063779611020031

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