New Phase Space Calculations for β-Decay Half-Lives

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

doi:10.1155/2016/8729893

Abstract

We revisit the computation of the phase space factors (PSF) involved in the positron decay and EC processes for a large number of nuclei of experimental interest. To obtain the electron/positron wave functions, we develop a code for solving accurately the Dirac equation with a nuclear potential derived from a realistic proton density distribution in the nucleus. The finite nuclear size (FNS) and screening effects are included through recipes which differ from those used in previous calculations. Comparing our results with previous calculations, performed with the same Q-values, we find a close agreement for positron decays, while, for the EC process, there are relevant differences. For the EC process, we also find that the screening effect has a notable influence on the computed PSF values especially for light nuclei. Further, we recomputed the same PSF values but using the most recent Q-values reported in literature. In several cases, the new Q-values differ significantly from the older ones, leading to large differences in the PSF values as compared with previous results. Our new PSF values can contribute to more reliable calculations of the beta-decay rates, used in the study of nuclei far from the stability line and stellar evolution.

Highlights

The phase space factors for beta decay and electron capture were calculated since a long time [1,2,3] and were considered to be evaluated with sufficient accuracy
We constructed a new code for computing phase space factors (PSF) values for positron decays and electron capture (EC) processes
Using the same Q-values, we compare our results with previous calculations where electron/positron w.f. were obtained in an approximate way

Summary

Introduction

The phase space factors for beta decay and electron capture were calculated since a long time [1,2,3] and were considered to be evaluated with sufficient accuracy In those works, the distortion of the electron wave functions (w.f.) by the Coulomb field of the nucleus was taken into account through Fermi functions which were expressed in terms of approximate radial solutions of the Dirac equation at the nuclear surface. The PSF for DBD were considered for a long time to be computed with enough accuracy and were used as such for predicting DBD lifetimes Recently, they were recalculated with improved methods, especially for positron and EC decay modes [17, 18], and several differences were found as compared to previous calculations where approximate electron/positron w.f. were used.

Formalism

Results and Discussion

Summary and Conclusion