Consistent Theory of Alpha-Decay
DOI:
https://doi.org/10.15407/ujpe66.5.379Keywords:
decay theory, alpha-decay, tunneling, scattering theoryAbstract
In the framework of the Goldberger–Watson decay theory, we consider the a-decay of nuclei as a transition between the initial bound state of the nucleus and scattering states of the continuum spectrum with a-particle. The scattering wave functions for the a-decay with arbitrary orbital angular momentum are derived in the quasiclassical approximation. The a-particle is described by the square-integrable wave packet formed by these functions, whose amplitude exponentially grows outside the nucleus up to the wave front. The Moshinsky’s distortions of the a-wave front are analyzed. The derived general expression for the decay rate is approximated by the quasiclassical formula.
References
D.M. Brink, M.C. Nemes, D. Vautherin. Eff ect of intrinsic degrees of freedom on the quantum tunneling of a collective variable. Ann. Phys. 147, 171 (1983).
https://doi.org/10.1016/0003-4916(83)90070-2
R.G. Lovas, R.J. Liotta, A. Insoliac, K. Vargaa, D.S. Deliond. Microscopic theory of cluster radioactivity. Phys. Rep. 294, 265 (1998).
https://doi.org/10.1016/S0370-1573(97)00049-5
S.G. Kadmensky, S.D. Kurgalin, Yu.M. Chuvilskii. Cluster states in atomic nuclei and cluster-decay processes. Phys. J. Part. Nucl. 38, 1333 (2007).
https://doi.org/10.1134/S1063779607060019
A. Sandulescu, W. Greiner. Cluster decays. Rep. Prog. Phys. 55, 1423 (1992).
https://doi.org/10.1088/0034-4885/55/9/002
D.S. Delion. Theory of Particles and Clusters Emission (Springer, 2010) [ISBN 978-3-642-14406-6].
R.G. Thomas. A formulation of the theory of alpha-particle decay from time-independent equations. Prog. Theor. Phys. 12, 253 (1954)
https://doi.org/10.1143/PTP.12.253
H.F. Zhang, G. Royer. A particle preformation in heavy nuclei and penetration probability. Phys. Rev. C 77, 054318 (2008).
https://doi.org/10.1103/PhysRevC.77.054318
A. Zdeb, M. Warda, K. Pomorski. Half-lives for a and cluster radioactivity in a simple model. Phys. Scr. T 154, 014029 (2013).
https://doi.org/10.1088/0031-8949/2013/T154/014029
A. Zdeb, M. Warda, K. Pomorski. Half-lives for a and cluster radioactivity within a Gamow-like model. Phys. Rev. C 87, 024308 (2013).
https://doi.org/10.1103/PhysRevC.87.024308
I. Silisteanu, W. Scheid, A. Sandulescu. Proton, alpha and cluster decay rates for nuclei with 52 ≤ Z ≤ 56 and 52 ≤ N ≤ 60. Nucl. Phys. A 679, 317 (2001).
https://doi.org/10.1016/S0375-9474(00)00336-5
Daming Deng, Zhongzhou Ren. Improved double-folding a-nucleus potential by including nuclear medium eff ects. Phys. Rev. C 96, 064306 (2017).
https://doi.org/10.1103/PhysRevC.96.064306
V.Yu. Denisov, A.A. Khudenko. a decays to ground and excited states of heavy deformed nuclei. Phys. Rev. C 80, 034603 (2009).
https://doi.org/10.1103/PhysRevC.80.034603
V.Yu. Denisov, A.A. Khudenko. Erratum: a decays to ground and excited states of heavy deformed nuclei. Phys.
Rev. C 80, 034603 (2009); Phys. Rev. C 82, 059902(E) (2010).
M. Ismail, A.Y. Ellithi, M.M. Botros, A. Abdurrahman. Penetration factor in deformed potentials: Application to
a decay with deformed nuclei. Phys. Rev. C 86, 044317 (2012).
Chang Xu, Zhongzhou Ren. Favored a-decays of medium mass nuclei in density-dependent cluster model. Nucl. Phys. A 760, 303 (2005).
https://doi.org/10.1016/j.nuclphysa.2005.06.011
Chang Xu, Zhongzhou Ren. New deformed model of a-decay half-lives with a microscopic potential. Phys. Rev. C 73, 041301(R) (2006).
https://doi.org/10.1103/PhysRevC.73.041301
D.F. Jackson, M. Rhoades-Brown. Theories of alpha-decay. Ann. Phys. 105, 151 (1977).
https://doi.org/10.1016/0003-4916(77)90231-7
T. Berggren, P. Olandes. Alpha decay from deformed nuclei:(I). Formalism and application to ground-state decays. Nucl. Phys. A 473, 189 (1987).
https://doi.org/10.1016/0375-9474(87)90142-4
T. Berggren, P. Olandes. Alpha decay from deformed nuclei: (II). Application to the decay of high-spin states. Nucl. Phys. A 473, 221 (1987).
https://doi.org/10.1016/0375-9474(87)90143-6
T. Berggren. Anisotropic alpha decay from oriented oddmass isotopes of some light actinides. Phys. Rev. C 50,
https://doi.org/10.1103/PhysRevC.50.2494
(1994).
Xiao-Dong Sun, Ping Guo, Xiao-Hua Li. Systematic study of a decay half-lives for even-even nuclei within a two-potential approach. Phys. Rev. C 93, 034316 (2016).
https://doi.org/10.1103/PhysRevC.93.034316
Xiao-Dong Sun, Chao Duan, Jun-Gang Deng, Ping Guo, Xiao-Hua Li. Systematic study of a decay for odd-A nuclei within a two-potential approach. Phys. Rev. C 95, 014319 (2017).
https://doi.org/10.1103/PhysRevC.95.014319
B. Sahu, S. Bhoi. Potential for a-induced nuclear scattering, reaction and decay, and a resonance-pole-decay model with exact explicit analytical solutions. Phys. Rev. C 96, 044602 (2017).
https://doi.org/10.1103/PhysRevC.96.044602
R.M. Clark, H.L. Crawford, A.O. Macchiavelli, D. Rudolph, A. Sеmark-Roth, C.M. Campbell, M. Cromaz, P. Fallon, C. Morse, C. Santamaria. a decay of high-spin isomers in N = 84 isotones. Phys. Rev. C 99, 024325 (2019).
https://doi.org/10.1103/PhysRevC.99.024325
G. Gamow. Zur Quantentheorie des Atomkernes. Z. Phys. 51, 204 (1928).
https://doi.org/10.1007/BF01343196
R.W. Gurney, E.U. Condon. Quantum mechanics and radioactive disintegration. Phys. Rev. 33, 127 (1929).
https://doi.org/10.1103/PhysRev.33.127
A.G. Sitenko. Lectures in Scattering Theory. Edited by P.J. Shepherd (Elsevier, 1971) [ISBN: 9781483486825].
https://doi.org/10.1016/B978-0-08-016574-5.50007-8
F.F. Karpeshin, G. LaRana, E. Vardaci, A. Brondi, R. Moro, S.N. Abramovich, V.I. Serov. Resonances in alpha-
nuclei interaction. J. Phys. G: Nucl. Part. Phys. 34, 587 (2007).
https://doi.org/10.1088/0954-3899/34/3/016
S.A. Gurvitz, G. Kalbermann. Decay width and the shift of a quasistationary state. Phys. Rev. Lett. 59, 262 (1987).
https://doi.org/10.1103/PhysRevLett.59.262
S.A. Gurvitz. Novel approach to tunneling problems. Phys. Rev. A 38, 1747 (1988).
https://doi.org/10.1103/PhysRevA.38.1747
S.A. Gurvitz, P.B. Semmes, W. Nazarewicz, T. Vertse. Modifi ed two-potential approach to tunneling problems. Phys. Rev. A 69, 042705 (2004).
https://doi.org/10.1103/PhysRevA.69.042705
M.L. Goldberger, K.M. Watson. Collision Theory, (J. Wiley, 1964) [ISBN: 978-0486435077].
https://doi.org/10.1063/1.3051231
A.Ya. Dzyublik. Integrable wave function, describing space-time evolution of alpha-decay. arXiv: 2001.09505v1[nucl-th]26Jan2020.
A.Ya. Dzyublik. Alpha decay of deformed even-even nuclei. Acta Phys. Polonica 10, 69 (2017).
https://doi.org/10.5506/APhysPolBSupp.10.69
M. Freer, M. Freer, H. Horiuchi, Y. Kanada-En'yo, D. Lee, Ulf-G. Meibner. Microscopic clustering in light nuclei. Rev. Mod. Phys. 90, 035004 (2018).
https://doi.org/10.1103/RevModPhys.90.035004
N.T. Zinner. Alpha decay rate enhancement in metals: An unlikely scenario. Nucl. Phys. A 781, 81 (2007).
https://doi.org/10.1016/j.nuclphysa.2006.10.071
A.Ya. Dzyublik. Infl uence of electronic environment on a decay. Phys. Rev. C 90, 054619 (2014).
https://doi.org/10.1103/PhysRevC.90.054619
R.G. Newton. Scattering Theory of Waves and Particles (Springer, 1982) [ISBN: 978-3-642-88128-2].
https://doi.org/10.1007/978-3-642-88128-2
A.S. Davydov. Quantum Mechanics. Edited by D. ter Haar (Elsevier, 1965) [ISBN: 9781483187839].
G. Esposito. A phase-integral perspective on a-decay. Eur. Phys. J. Plus 135, 692 (2020).
https://doi.org/10.1140/epjp/s13360-020-00719-8
R.E. Langer. On the connection formulas and the solutions of the wave equation. Phys. Rev. 51, 669 (1937).
https://doi.org/10.1103/PhysRev.51.669
M. Moshinsky. Boundary conditions and time-dependent states. Phys. Rev. 84, 525 (1951).
https://doi.org/10.1103/PhysRev.84.525
M. Moshinsky. Diff raction in time. Phys. Rev. Lett. 88, 625 (1952).
https://doi.org/10.1103/PhysRev.88.625
R.G. Winter. Evolution of a quasi-stationary state. Phys. Rev. 123, 1503 (1961).
https://doi.org/10.1103/PhysRev.123.1503
G. Garcia-Calder'on, A. Rubio. Transient effects and delay time in the dynamics of resonant tunneling. Phys. Rev. A 55, 3361 (1997).
https://doi.org/10.1103/PhysRevA.55.3361
W. van Dijk, Y. Nogami. Novel expression for the wave function of a decaying quantum system. Phys. Rev. Lett. 83, 2867 (1999). https://doi.org/10.1103/PhysRevLett.83.2867
W. van Dijk, F. Kataoka, Y. Nogami. Space-time evolution of a decaying quantum state. J. Phys. A 32, 6347 (1999). https://doi.org/10.1088/0305-4470/32/35/311
W. van Dijk. Numerical time-dependent solutions of the Schr¨odinger equation with piecewise continuous potentials. Phys. Rev. E 93, 063307 (2016). https://doi.org/10.1103/PhysRevE.93.063307
Handbook of Mathematical Functions. Edited by M. Abramovitz, I.A. Stegun (Nat. Bureau of Standards, 1972).
I.S. Gradshteyn, I.M. Ryzhik. Table of Integrals, Series, and Products. Edited by D. Zwillinger (Academic Press, 2007) [ISBN: 978-0-12-373637-6].
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.
.png){kind=small}
