Description of $^{93}$Nb stellar electron-capture rates by the Projected Shell Model

TL;DR

This paper introduces the Projected Shell Model to accurately calculate stellar electron-capture rates for $^{93}$Nb by explicitly including excited nuclear states, improving understanding of nuclear processes in stellar environments.

Contribution

The work presents a novel application of the Projected Shell Model to include excited configurations in electron-capture rate calculations for medium-heavy nuclei.

Findings

PSM results agree with recent Gamow-Teller transition data.

Explicit inclusion of excited states affects EC rates at high temperature and density.

Comparison shows improvements over traditional shell model and QRPA calculations.

Abstract

Capture of electrons by nuclei is an important process in stellar environments where excited nuclear states are thermally populated. However, accurate treatment for excited configurations in electron capture (EC) rates has been an unsolved problem for medium-heavy and heavy nuclei. In this work, we take the $^{93}$Nb $\rightarrow$ $^{93}$Zr EC rates as the example to introduce the Projected-Shell-Model (PSM) in which excited configurations are explicitly included as multi-quasiparticle states. Applying the prevalent assumption that the parent nucleus always stays in its ground state in stellar conditions, we critically compare the obtained PSM results with the recently-measured Gamow-Teller transition data, and with the previous calculations by the conventional shell model and the quasiparticle random-phase approximation. We discuss important ingredients that are required in theoretical models used for stellar EC calculations, and demonstrate effects of the explicit inclusion of excited nuclear states in EC rate calculations, especially when both electron density and environment temperature are high.