Ядерна фізика та енергетика Nuclear Physics and Atomic Energy   ISSN: 1818-331X (Print), 2074-0565 (Online)   Publisher: Institute for Nuclear Research of the National Academy of Sciences of Ukraine   Languages: Ukrainian, English   Periodicity: 4 times per year   Open access peer reviewed journal

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V. S. Vasilevsky¹, A. B. Nesterov¹, F. Arickx², J. Broeckhove<sup>2

1</sup>Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
²University of Antwerp, Antwerp, Belgium

Abstract: The reactions ³H(³H, 2n)⁴He and ³He(³He, 2p)⁴He are investigated within a fully microscopic cluster model featuring a three-cluster exit channel. A Hyperspherical Harmonics basis is used to describe the three-cluster continuum. The resulting astrophysical s-factor of both reactions is in good agreement with experimental data. Analysis of the low-energy scattering parameters reveals no evidence for a hidden resonance state would increase the cross-section of the reactions, and would help to resolve the solar neutrino problem.

1. Bahcall J. N. Solar neutrinos: What next? hep-ex/0002018 (1999).

2. Bahcall J. N. Solar neutrinos: Where we are, what we need. Nucl. Phys. A 631 (1998) 29. https://doi.org/10.1016/S0375-9474(98)00013-X

3. Haxton W. C. Topics in neutrino astrophysics, 1998 TASI summer school lectures. Nucl-th/0004052/ (1999).

4. Bahcall J. N, Davis R. Jr. The Evolution of Neutrino Astronomy. Publications of the Astronomical Society of the Pacific 112 (2000) 429. https://doi.org/10.1086/316545

5. Haxton W. C., Holstein B. R. Neutrino Physics. Am. J. Phys. 68 (2000) 15. https://doi.org/10.1119/1.19368

6. Adelberger E. G., Austin S. M., Bahcall J. B. et al. Solar Fusion Cross Sections. Rev. Mod. Phys. 70 (1998) 1265. https://doi.org/10.1103/RevModPhys.70.1265

7. The LUNA Collaboration. Cross section of ³He(³He, 2p)⁴He measured at solar energies. Nucl-ex/9707003 (1998).

8. Junker M., D'Aessandro E., Zavatarelli et al. The cross section of ³He(³He, 2p)⁴He measured at solar energies. Nuclear Physics B 70 (1998) 382. https://doi.org/10.1016/S0920-5632(98)00458-7

9. The LUNA Collaboration. First measurement of the ³He(³He, 2p)⁴He cross section down to the lower edge of the solar Gamov peak. Nucl-ex/9902004 (1999).

10. Bonetti R., Broggini C., Campajola L. et al. First Measurement of the ³He + ³He --> ⁴He + 2p Cross Section down to the Lower Edge of the Solar Gamow Peak. Phys. Rev. Lett. 82 (1999) 5205. https://doi.org/10.1103/PhysRevLett.82.5205

11. Vasilevsky V. S., Rubkin I. Yu. Astrophysical S-factor of the t(t, 2n)⁴He and ³H(³H, 2n)⁴He reactions. Sov. J. Nucl. Phys. 50 (1989) 411.

12. Langanke K., Typel S., Bluge G., Fowler W. A. Microscopic study of the low-energy ³He(³He, 2p)⁴He and ³He(³He, 2n)⁴He fusion cross sections. Z. Phys. A 339 (1991) 249. https://doi.org/10.1007/BF01284060

13. Descouvemont P. Microscopic analysis of the ³He(³He, 2p)⁴He and ³He(³He, 2n)⁴He reactions in a three-cluster model. Phys. Rev. C 50 (1994) 2635. https://doi.org/10.1103/PhysRevC.50.2635

14. Csoto A., Langanke K. Large-space cluster model calculations for the ³He(³He, 2p)⁴He and ³He(³He, 2n)⁴He reactions. Nucl. Phys. A 646 (1999) 387. https://doi.org/10.1016/S0375-9474(98)00638-1

15. Vasilevsky V. S., Arickx F. Algebraic model for quantum scattering: Reformulation, analysis, and numerical strategies. Phys. Rev. 55 (1997) 265. https://doi.org/10.1103/PhysRevA.55.265

16. Vasilevsky V. S., Nesterov A. V., Arickx F., Broeckhove J. Algebraic model for scattering in three-s-cluster systems. I. Theoretical background. Phys. Rev. C 63 (2001) 034606. https://doi.org/10.1103/PhysRevC.63.034606

17. Vasilevsky V. S., Nesterov A. V., Arickx F., Broeckhove J. Phys. Rev. C 63 (2001) 034607. https://doi.org/10.1103/PhysRevC.63.034607

18. Varga K., Suzuki Y. Precise solution of few-body problems with the stochastic variational method on a correlated Gaussian basis. Phys. Rev. C 52 (1995) 2885. https://doi.org/10.1103/PhysRevC.52.2885

19. Varga K., Suzuki Y., Lovas R. G. Microscopic multicluster description of neutron-halo nuclei with a stochastic variational method. Nucl. Phys. A 571 (1994) 447. https://doi.org/10.1016/0375-9474(94)90221-6

20. Faddeev L. D., Merkuriev S. P. Quantum Scattering Theory for Several Particle Systems (Kluwer Academic Publishers, Dordrecht, Boston, London, 1993). https://doi.org/10.1007/978-94-017-2832-4

21. Volkov A. B. Equilibrium deformation calculations of the ground state energies of 1p shell nuclei. Nucl. Phys. 74 (1965) 33. https://doi.org/10.1016/0029-5582(65)90244-0

22. Vasilevsky V. S., Nesterov A. V., Arickx F., Van Leuven P. Dynamics of the α+n+n channel in ⁶He and ⁶Li. Prepr. Nat. Ac. Sci. of Ukr. Institute for theoretical Physics ITP-96-3E (Kyiv, 1996) 19 p.

23. Vasilevsky V. S., Nesterov A. V., Arickx F., Van Louwen P. Dynamics of α+n+n channel in ⁶He and ⁶Li. Physics of Atomic Nuclei (Yad. Phys.) 60 (1997) 413.

24. Papp Z., Filikhin I. N., Yakovlev S. L. Integral Equations for Three-Body Coulomb Resonances. Few-Body Syst. 30 (2001) 31. https://doi.org/10.1007/s006010170016

25. Dwarakanath M. R., Winkler H. ³He(³He, 2p)⁴He Total Cross-Section Measurements Below the Coulomb Barrier. Phys. Rev. C 4 (1971) 1532. https://doi.org/10.1103/PhysRevC.4.1532

26. Серов В. И., Абрамович С. Н., Моркин Л. А. Измерение полного сечения рассеяния T(t,2n)⁴Не. Атомная энергия 42 (1977) 59.

27. Говоров А. М., Ли ГА Ен, Осетинский Г. М. и др. Полное сечение реакции Т + Т в интервале энергий 60 - 1140 МэВ. ЖЭТФ 42 (1962) 383.

28. Brown R. E., Jarmie N. Fusion-energy reaction ³H(³H,α)2n at low energies. Radiat. Eff. 84 (1986) 45.

29. Agnew H. M., Leland W. T., Argo H. V. et al. Measurement of the Cross Section for the Reaction T + T → ⁴He + 2n + 11.4 MeV. Phys. Rev. 84 (1951) 862. https://doi.org/10.1103/PhysRev.84.862

30. Krauss A., Becker H. W., Trautvetter H. P., Rolfs C. Astrophhysical S(E)-factor of ³He(³He, 2p)⁴He at solar energies. Nucl. Phys. 467 (1987) 273. https://doi.org/10.1016/0375-9474(87)90530-6