Cluster decay half-lives and preformation probabilities

Abstract

An improved semi-analytic approach to the barrier penetration probability is developed in the frame work of the Wentzel-Kramers-Brillouin (WKB) approximation. It is used to calculate decay half-lives and preformation probabilities for a set of 304 cluster emitters in the range 87 ≤ Z ≤ 96 and a set of 390 α-emitters in the range 52 ≤ Z ≤ 120. For cluster decay, the validity of our approach is tested against Coulomb and proximity potential model (CPPM) by comparing decay half-lives and barrier penetration probabilities. Our results are found to be in a good agreement with CPPM calculations and with the available experimental data. In case of α-decay, our calculations are tested against the experimental data and also a very good agreement is achieved. In both cases, results are also compared with calculations of some other well known universal decay laws that are used in many recent studies. Our approach shows a better agreement with experimental data than most of the other models. Our study is extended to calculate the assault frequency and preformation probability of the cluster inside the parent nucleus. A strong correlation is obtained for all these parameters with each other. Neutron shell closures are found to be more important in the cluster decay process than proton shell closure. It is also noted that the odd–even staggering behavior dominates the decay processes involving the emission of clusters with odd neutron number.

Systematic calculations of cluster radioactivity half-lives with a screened electrostatic barrier*

“…The structure of this curve matches well with the other preformation probability values from Ref. [72]. Nevertheless, the results of their calculations vary greatly, which may have a model dependent reason.…”

Systematic calculations of cluster radioactivity half-lives in trans-lead nuclei*

“…Nevertheless, when the daughter neutron number at doubly magic daughter nucleus 208 Pb, the log 10 T 1/2 and log(P ) both take minimum and maximum values. Consequently, it confirms that neutron shell closure plays a more crucial role than proton shell closure in cluster radioactivity, revealing the neutrons paring effect is more influential than protons in this decay mode process [5].…”

“…where A i (i = c, d) are the mass number of the emitted cluster and daughter nucleus, respectively. R out is the outer turning point of the barrier satisfied the condition V (R out ) = Q c [5]. In this work, Q c can be obtained by…”

“…ǎ In nature, radioactive nuclei translate their unstable states to stable states, based on the minimum energy principle, by α, β, and/or γ emissions, or emitting particles heavier than α particles [1][2][3] but lighter than the lightest fission fragments, generally known as cluster radioactivity [4][5][6][7][8][9][10]. This subtle process, intermediate between α decay and spontaneous fission, undoubtedly involves vital nuclear structure information such as ground state half-life time, nuclear spin and parity, deformations of nuclear structure, and shell effects [11][12][13].…”

“…Soon afterwards, considering the cluster preformation factor as the charge-number dependence form, Ren employed the microscopic density-dependent cluster model (DDCM) where the realistic M3Y nucleon-nucleon interaction is used to investigate this exotic decay mode [14]. In 2009, extending the quasi-bound wave function, first used in α decay, to cluster radioactivity, based on the DDCM, Ni systematically studied the half-lives of cluster radioactivity [4]. In the latter, the cluster is assumed to be formed along with the emitted process, which is described as adiabatic with constant variations in geometric shape from the parent nucleus during its penetration through the nuclear barrier.…”