Problem of Nuclear Decay by Proton Emission in Fully Quantum Consideration: Calculations of Penetrability and Role of Boundary Conditions

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 R_{form} 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.

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 R

KEYWORDS

Tunneling, Multiple Internal Reflections, Wave Packet, Decay by Proton Emission, Penetrability and Reflection, Half-Life

Tunneling, Multiple Internal Reflections, Wave Packet, Decay by Proton Emission, Penetrability and Reflection, Half-Life

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.

nullS. Maydanyuk and S. Belchikov, "Problem of Nuclear Decay by Proton Emission in Fully Quantum Consideration: Calculations of Penetrability and Role of Boundary Conditions,"

References

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[19] S. A. Gurvitz, G. K?lbermann, Decay width and the shift of a quasistationary state, Phys. Rev. Lett. 59 (3), 262-265 (1987).

[20] F. D. Becchetti, G. W. Greenlees, Nucleon-nucleus optical-model parameters, A > 40, E < 50 MeV, Phys. Rev. 182, 1190-1209 (1969).

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[22] S. A. Gurvitz, Phys. Rev. A38, 1747 (1988).

[23] B. Buck, A. C. Merchant, S. M. Perez, Ground state proton emission from heavy nuclei, Phys. Rev. C45 (4), 1688-1692 (1988).

[24] S. A. Gurvitz, P. B. Semmes, W. Nazarewicz, and T. Vertse, Phys. Rev. A69, 042705 (2004).

[1] S. Hofmann, in Particle emission from nuclei, edited by D. N. Poenaru and M. Ivascu (CRC, Boca Raton, 1989) Vol. 2, Chap. 2.

[2] S. Hofmann, Radiochim. Acta 70/71, 93 (1995).

[3] S. Hofmann, in Nuclear decay modes, edited by D. N. Poenaru and W. Greiner (IOP, Bristol, 1996).

[4] C. N. Davids, P. J. Woods, H. T. Penttila et al., Phys. Rev. Lett. 76, 592 (1996).

[5] S. ?berg, P. B. Semmes, and W. Nazarewicz, Spherical proton emitters, Phys. Rev. C56, 1762-1773 (1997).

[6] 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.

[7] 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), nucl-th/0407108.

[8] 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.

[9] 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].

[10] 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).

[11] J. H. Fermor, Quantum-mechanical tunneling, Am. Journ. Phys. 34, 1168-1170 (1966).

[12] K. W. McVoy, L. Heller, M. Bolsterli, Optical analysis of potential well resonances, Rev. Mod. Phys. 39 (1), 245- 258 (1967).

[13] A. Anderson, Multiple scattering approach to one-dimensional potential problems, Am. Journ. Phys. 57 (3), 230-235 (1989).

[14] S. Esposito, Multibarrier tunneling, Phys. Rev. E67 (1), 016609 (2003), quant-ph/0209018.

[15] 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).

[16] V.Yu. Denisov, H. Ikezoe, Alpha-nucleus potential for alpha-decay and sub-barrier fusion, Phys. Rev. C72, 064613 (2005); nucl-th/0510082.

[17] A. Sobiczewski, K. Pomorski, Description of structure and properties of superheavy nuclei, Prog. Part. Nucl. Phys. 58, 292-349 (2007).

[18] 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].

[19] S. A. Gurvitz, G. K?lbermann, Decay width and the shift of a quasistationary state, Phys. Rev. Lett. 59 (3), 262-265 (1987).

[20] F. D. Becchetti, G. W. Greenlees, Nucleon-nucleus optical-model parameters, A > 40, E < 50 MeV, Phys. Rev. 182, 1190-1209 (1969).

[21] D. F. Jackson, M. Rhoades-Brown, Ann. Phys. (N. Y.) 105, 151 (1977).

[22] S. A. Gurvitz, Phys. Rev. A38, 1747 (1988).

[23] B. Buck, A. C. Merchant, S. M. Perez, Ground state proton emission from heavy nuclei, Phys. Rev. C45 (4), 1688-1692 (1988).

[24] S. A. Gurvitz, P. B. Semmes, W. Nazarewicz, and T. Vertse, Phys. Rev. A69, 042705 (2004).