Assault frequency and preformation probability of theαemission process

Abstract

A study of the assault frequency and preformation factor of the α-decay description is performed from the experimental α-decay constant and the penetration probabilities calculated from the generalized liquid-drop model (GLDM) potential barriers. To determine the assault frequency a quantum-mechanical method using a harmonic oscillator is introduced and leads to values of around 10 21 s −1 , similar to the ones calculated within the classical method. The preformation probability is around 10 −1 -10 −2 . The results for even-even Po isotopes are discussed for illustration. While the assault frequency presents only a shallow minimum in the vicinity of the magic neutron number 126, the preformation factor and mainly the penetrability probability diminish strongly around N = 126.

Half-life of sphericalαemitters and intrinsic properties of nuclei

“…Since the interaction potential between the α particle and daughter nucleus plays an important role in the theoretical calculation of the penetration probability and half-life of α decay, the calculation of this potential becomes important in describing the decay process. In most cases, a one-dimensional potential is considered for the α decay process, and penetration probability is calculated using WKB approximation [1][2][3][4][5][6][7]. Among these, various models incorporating parent and daughter ground-state (GS) deformations are developed, such as the unified model for α decay and α capture [8], generalized density-dependent cluster model [9], and Coulomb and proximity potential model for deformed nuclei [10,11], which show the reduction of barrier height due to quadrupole deformation.…”

Properties of the alpha cluster states of [sup 212]Po from elastic scattering of alpha particles from [sup 208]Pb

“…The same potential is now used to calculate the inverse cross-sections. The D-preformation probability for the ground state of 212 Po has been calculated in a recent work and is found to be of 0.034 [7] that makes the alpha width calculated in the present work within a factor of 3 of the Buck result. However for the other excited positive parity states belonging to the cluster band the alpha formation probabilities are not available in the literature.…”

Signature of theN= 126 shell closure in dwell times of alpha-particle tunneling

“…As in the case of ν, we see that P α is, in general, also sensitive to the choice of G. However, as long as we restrict ourselves to even N the qualitative behaviour displaying a local minimum at N = 126 remains unchanged. We note that there is a clear model dependence in P α as far as the magnitude is concerned: we differ from Refs [7] by one order of magnitude. The order of magnitude of P α here is similar to that in [8].…”

“…Indeed, alpha decay was the very first application of the most exotic phenomenon of quantum mechanics, namely, tunneling as shown by Gamow [5] and Condon and Gurney [6] in their pioneering works in 1928. We have come a long way since the discovery of magic numbers and alpha-tunneling but the interest in the two phenomena taken together seems to be ever increasing [7]. For example, in [8] it was found that even if empirical laws are usually sufficient to explain the alpha decay half-lives without a consideration of the alpha cluster preformation problem, close to the neutron shell closure of N = 126, one must take into account the shell model and other effects [8].…”