β−-Decay Half-Lives of Even-Even Nuclei Using the Recently Introduced Phase Space Recipe

Jameel-Un Nabi,Sabin Stoica,Mavra Ishfaq,Mihail Mirea,Ovidiu Niţescu

doi:10.3390/universe6010005

Abstract

In this paper, we present the    β   -decay half-lives calculation for selected even-even nuclei that decay through electron emission. The kinematical portion of the half-life calculation was performed using a recently introduced technique for computation of phase space factors (PSFs). The dynamical portion of our calculation was performed within the proton-neutron quasiparticle random phase approximation (pn-QRPA) model. Six nuclei (     20    O,      24    Ne,      34    Si,      54    Ti,      62    Fe and      98    Zr) were selected for the present calculation. We compare the calculated PSFs for these cases against the traditionally used recipe. In our new approach, the Dirac equation was numerically solved by employing a Coulomb potential. This potential was adopted from a more realistic proton distribution of the daughter nucleus. Thus, the finite size of the nucleus and the diffuse nuclear surface corrections are taken into account. Moreover, a screened Coulomb potential was constructed to account for the effect of atomic screening. The power series technique was used for the numerical solution. The calculated values of half-lives, employing the recently developed method for computation of PSFs, were in good agreement with the experimental data.

Highlights

In the last few decades, the β-decay process shaped our perspective of modern physics
We further explored the effect of pairing gaps on calculated phase space factors (PSFs) and β-decay half-lives
The associated nuclear matrix elements (NMEs) were calculated within the framework of the proton-neutron quasiparticle random phase approximation (pn-QRPA) model

Summary

Introduction

In the last few decades, the β-decay process shaped our perspective of modern physics. The typical approximation is to use the Dirac equation having an electrostatic potential instead of a plane-wave of β-particle [7] With this replacement, the half-life for nuclear β-decay is calculated after the computation of associated nuclear matrix elements (NMEs) and PSFs. In the literature, various approaches for β spectrum description and PSF calculation were reported [8,9,10,11]. We used β-particle exact radial wave functions for the construction of the Fermi function acquired by solving the Dirac equation numerically with realistic electrostatic potential In this approach, we included electrostatic finite-size corrections (finite size and diffuse nuclear surface) and atomic screening corrections by constructing an appropriate Coulomb potential.

Theoretical Framework

Results

Conclusions