ABSTRACT We develop a new fully quantum method for determination of widths for nuclear decay by proton emission where multiple internal reflections of wave packet describing tunneling process inside proton-nucleus radial barrier are taken into account. Exact solutions for amplitudes of wave function, penetrability T and reflection R (estimated for the first time for decay problem) are found for n -step barrier (at arbitrary n) which approximates the realistic barrier. In contrast to semiclassical approach and two-potential approach, we establish by this method essential dependence of the penetrability on the starting point Rform in the internal well where proton starts to move outside (for example, for Ta the penetrability is changed up to 200 times; accuracy is T+R-1|<1.5.10-15 ). We impose a new condition: in the beginning of the proton decay the proton starts to move outside from minimum of the well. Such a condition provides minimal calculated half-life and gives stable basis for predictions. However, the half-lives calculated by such an approach turn out to be a little closer to experimental data in comparison with the semiclassical half-lives. Estimated influence of the external barrier region is up to 1.5 times for changed penetrability.
Cite this paper
nullS. Maydanyuk and S. Belchikov, "Problem of Nuclear Decay by Proton Emission in Fully Quantum Consideration: Calculations of Penetrability and Role of Boundary Conditions," Journal of Modern Physics, Vol. 2 No. 6, 2011, pp. 572-585. doi: 10.4236/jmp.2011.26067.
 S. Hofmann, in Particle emission from nuclei, edited by D. N. Poenaru and M. Ivascu (CRC, Boca Raton, 1989) Vol. 2, Chap. 2.
 S. Hofmann, Radiochim. Acta 70/71, 93 (1995).
 S. Hofmann, in Nuclear decay modes, edited by D. N. Poenaru and W. Greiner (IOP, Bristol, 1996).
 C. N. Davids, P. J. Woods, H. T. Penttila et al., Phys. Rev. Lett. 76, 592 (1996).
 S. ?berg, P. B. Semmes, and W. Nazarewicz, Spherical proton emitters, Phys. Rev. C56, 1762-1773 (1997).
 V. S. Olkhovsky, S. P. Maydanyuk, Method of multiple internal reflections in description of tunneling evolution through barriers, Ukr. Phys. Journ. 45 (10), 1262-1269 (2000), nucl-th/0406035.
 S. P. Maydanyuk, V. S. Olkhovsky, A. K. Zaichenko, The method of multiple internal reflections in description of tunneling evolution of nonrelativistic particles and photons, Journ. Phys. Stud. 6 (1), 1-16 (2002),
 S. P. Maydanyuk, V. S. Olkhovsky, S. V. Belchikov, The method of multiple internal reflections in description of nuclear decay, Probl. At. Sci. Tech. (Voprosi atomnoi nauki i tehniki, RFNC-VNIIEF, Sarov, Russia) 1, 16-19 (2002), nucl-th/0409037.
 S. P. Maydanyuk, Time analysis of tunneling processes in nuclear collisions and decays, Ph. D. dissertation (Supervisor: Prof. V. S. Olkhovsky, Kiev, 2003), p. 147 [in Ukrainian].
 F. Cardone, S. P. Maidanyuk, R. Mignani, V. S. Olkhovsky, Multiple internal reflections during particle and photon tunneling, Found. Phys. Lett. 19 (5), 441-457 (2006).
 J. H. Fermor, Quantum-mechanical tunneling, Am. Journ. Phys. 34, 1168-1170 (1966).
 K. W. McVoy, L. Heller, M. Bolsterli, Optical analysis of potential well resonances, Rev. Mod. Phys. 39 (1), 245- 258 (1967).
 A. Anderson, Multiple scattering approach to one-dimensional potential problems, Am. Journ. Phys. 57 (3), 230-235 (1989).
 S. Esposito, Multibarrier tunneling, Phys. Rev. E67 (1), 016609 (2003), quant-ph/0209018.
 B. Buck, A. C. Merchant, S. M. Perez, Half-lives of favored alpha decays from nuclear ground states, At. Dat. Nucl. Dat. Tabl. 54 (1), 53-74 (1993).
 V.Yu. Denisov, H. Ikezoe, Alpha-nucleus potential for alpha-decay and sub-barrier fusion, Phys. Rev. C72, 064613 (2005); nucl-th/0510082.
 A. Sobiczewski, K. Pomorski, Description of structure and properties of superheavy nuclei, Prog. Part. Nucl. Phys. 58, 292-349 (2007).
 L. D. Landau and E. M. Lifshitz, Quantum mechanics, course of Theoretical Physics, Vol. 3 (Nauka, Mockva, 1989), p. 768 - [in Russian; eng. variant: Oxford, Uk, Pergamon, 1982].
 S. A. Gurvitz, G. K?lbermann, Decay width and the shift of a quasistationary state, Phys. Rev. Lett. 59 (3), 262-265 (1987).
 F. D. Becchetti, G. W. Greenlees, Nucleon-nucleus optical-model parameters, A > 40, E < 50 MeV, Phys. Rev. 182, 1190-1209 (1969).
 D. F. Jackson, M. Rhoades-Brown, Ann. Phys. (N. Y.) 105, 151 (1977).
 S. A. Gurvitz, Phys. Rev. A38, 1747 (1988).
 B. Buck, A. C. Merchant, S. M. Perez, Ground state proton emission from heavy nuclei, Phys. Rev. C45 (4), 1688-1692 (1988).
 S. A. Gurvitz, P. B. Semmes, W. Nazarewicz, and T. Vertse, Phys. Rev. A69, 042705 (2004).