Viola-Seaborg relation for α-decay half-lives: Update and microscopic determination of parameters

Basudeb Sahu and Swagatika Bhoi
Phys. Rev. C 93, 044301 – Published 1 April 2016

Abstract

Considering the emission process of α particles in the transition from an isolated quasibound state to a scattering state, a clear expression for the decay width derived in terms of regular Coulomb function, the quasibound state wave function, and the difference of potentials is analyzed. The Schrödinger equation with the effective potential representing the α + nucleus interaction consistent with the potential obtained in the relativistic mean-field approximation is solved exactly for the wave function. Using this exact wave function at resonance and the difference of the above potential from the point charge Coulomb interaction in the expression of decay width stated above, an analytic expression for the decay half-life is derived from the width. By invoking some approximations for different functions in this expression, a closed formula for the logarithm of half-life in terms of characteristic Q value equal to the resonance energy and the mass and charge numbers of the α emitter is obtained. The calculated results of half-life obtained by using the analytic expression of half-life or the closed formula for the logarithm of the half-life are shown to explain the corresponding measured data with values ranging from 106 s to 1022 y in the case of large numbers of α emitters that include heavy and superheavy nuclei. The results of the closed formula aligned in a straight line closely explain the rectilinear arrangement of the logarithm values of experimental results for decay half-lives as a function of a quantity that depends on Q values and charge numbers of the emitters. The analytic closed formula with all its terms defined is preferable to the empirical Viola-Seaborg rule of α-decay rate.

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  • Received 25 October 2015
  • Revised 10 February 2016

DOI:https://doi.org/10.1103/PhysRevC.93.044301

©2016 American Physical Society

Physics Subject Headings (PhySH)

Nuclear Physics

Authors & Affiliations

Basudeb Sahu1 and Swagatika Bhoi2

  • 1Department of Physics, College of Engineering and Technology, Bhubaneswar 751003, India
  • 2Department of Physics, Jyotivihar, Sambalpur University, Burla, 768019, India

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Issue

Vol. 93, Iss. 4 — April 2016

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