Sensitivity of $\beta$-decay rates to the radial dependence of the nucleon effective mass

TL;DR

This paper investigates how the radial dependence of the nucleon effective mass in Skyrme energy-density functionals influences beta-decay rates in certain nuclei, highlighting the potential of decay rates to test nuclear models.

Contribution

It introduces a correction to the Skyrme EDF that modifies the radial shape of the nucleon effective mass and assesses its impact on beta-decay rates in magic nuclei.

Findings

132 Sn is significantly affected by the correction.

78 Ni and 100 Sn are moderately affected.

Beta-decay rates can serve as tests for different parts of the nuclear EDF.

Abstract

We analyze the sensitivity of $\beta$-decay rates in 78 Ni and 100,132 Sn to a correction term in Skyrme energy-density functionals (EDF) which modifies the radial shape of the nucleon effective mass. This correction is added on top of several Skyrme parametrizations which are selected from their effective mass properties and predictions about the stability properties of 132 Sn. The impact of the correction on high-energy collective modes is shown to be moderate. From the comparison of the effects induced by the surface-peaked effective mass in the three doubly magic nuclei, it is found that 132 Sn is largely impacted by the correction, while 78 Ni and 100 Sn are only moderately affected. We conclude that $\beta$-decay rates in these nuclei can be used as a test of different parts of the nuclear EDF: 78 Ni and 100 Sn are mostly sensitive to the particle-hole interaction through the B(GT) values, while 132 Sn is sensitive to the radial shape of the effective mass. Possible improvements of these different parts could therefore be better constrained in the future.