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

Full text (en)

V. S. Olkhovsky, M. V. Romaniuk

Institute for Nuclear Research, National Academy of Sciences of Ukraine, Kyiv, Ukraine

Abstract: The non-relativistic particle tunneling and scattering through a spherical three-dimensional potential barrier (either rectangular, or Coulomb repulsion), containing a spherical potential rectangular well with a hard core inside, had been studied. The explicit analytical expressions for the S-matrix of elastic scattering and all probability amplitudes (external and internal reflections, tunneling inside and tunneling outside) for zero angular momentum and for relations between them had been firstly obtained. In conclusion, unlike to the typical simplified one-dimensional approximation, utilized for low-energy astrophysical nuclear-fusion reactions, we underline the necessity to consider the three-dimensional picture which brings to the multiple internal reflections from internal barrier wall and also to the more strict penetration factor.

Keywords: three-dimensional tunneling, scattering, barrier, potential well, hard core.

1. Olkhovsky V. S., Recami E. Recent developments in the time analysis of tunneling processes. Phys. Rep. 214 (1992) 339. https://doi.org/10.1016/0370-1573(92)90015-R

2. Olkhovsky V. S., Recami E., Jakiel J. Unified time analysis of photon and particle tunnelling. Phys. Rep. 398 (2004) 133. https://doi.org/10.1016/j.physrep.2004.06.001

3. Gamow G. Quantettheorie des Atomkernes. Zs. für Phys. 51 (1928) 204. https://doi.org/10.1007/BF01343196

4. Condon E. and Gurney J. G. Wave Mechanics and Radioactive Disintegration. Nature 122 (1928) 439. https://doi.org/10.1038/122439a0

5. Buck B., Merchant A. C., Perez S. M. New Look at α Decay of Heavy Nuclei. Phys. Rev. Lett. 65 (1990) 2975. https://doi.org/10.1103/PhysRevLett.65.2975

6. Sobiczewski A. Present view of stability of heavy and superheavy nuclei. Phys. Part. Nucl. 25 (1994) 295. https://doi.org/10.1070/PU1996v039n09ABEH000167

7. Olkhovsky V. S., Petrillo V., Jakiel J., Kantor W. Particle tunneling and scattering in a three-dimensional potential with a barrier. Central Europ. J. Phys. 6 (2008) 122. https://doi.org/10.2478/s11534-008-0071-8

8. Bonetti R., Broggini C., Campajola L. et al. First Measurement of the ³He(³He, 2p)⁴He 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

9. Spitaleri C., Aliotto M., Lattuada M. et al. "Trojan Horse" method applied to ²H(⁶Li, α)⁴He at astrophysical energies. Phys. Rev. C 63 (2001) 055801. https://doi.org/10.1103/PhysRevC.63.055801

10. Junghans A. R., Mohrmann E. C., Snoyer K. A. et al. ⁷Be(p, γ)⁸B Astrophysical S Factor from Precision Cross Section Measurements. Phys. Rev. Lett. 88 (2002) 041101. https://doi.org/10.1103/PhysRevLett.88.041101

11. Imbriani G., Constantini H., Formicola A. et al. Eur. Phys. J. A 25 (2005) 455. https://doi.org/10.1140/epja/i2005-10138-7

12. Lemut A., Bemmerer D., Bonetti R. et al. First measurement of the ¹⁴N(p, γ)¹⁵O cross section down to 70 keV. Phys. Lett. B 634 (2006) 483. https://doi.org/10.1016/j.physletb.2006.02.021

13. Winslow G. H. Alpha-Decay Theory and a Surface Well Potential. Phys. Rev. 6 (1954) 1032. https://doi.org/10.1103/PhysRev.96.1032

14. Preston M. A. Physics of the Nucleus (Addison-Wesley Publish. Company, 1962).

15. Кадменский С. Г., Фурман В. И. Альфа-распад и родственные ядерные реакции (Москва: Энергоатомиздат, 1985).

16. Давидовский В. В., Зайченко А. К., Ольховский В. С. Новые возможности одночастичной модели альфа распада. Зб. наук. праць Ін-ту ядерних досл. 6 (2005) 28. https://jnpae.kinr.kyiv.ua/06.1/Articles_PDF/jnpae-2005-06-1-028.pdf