Muon capture rates: Evaluation within the Quasiparticle Random Phase Approximation

TL;DR

This paper evaluates muon capture rates using the QRPA method, demonstrating that the approach yields results consistent with experimental data without needing empirical adjustments to the axial coupling constant.

Contribution

It applies the QRPA framework with various model space sizes and muon wave treatments to accurately predict muon capture rates in nuclei relevant to double-beta decay.

Findings

Capture rates are consistent across different QRPA variants.

Most realistic variant matches experimental muon capture rates.

No empirical quenching of $g_A$ is necessary.

Abstract

The Quasiparticle Random Phase Approximation (QRPA) is used in evaluation of the total muon capture ratesfor the final nuclei participating in double-beta decay. Several variants of the method are used, depending on the size of the single particle model space used, or treatment of the initial bound muon wave function. The resulting capture rates are all reasonably close to each other. In particular, the variant that appears to be most realistic, results in rates in good agreement with the experimental values. There is no necessity for an empirical quenching of the axial current coupling constant $g_A$. Its standard value $g_A$ = 1.27 seems to be adequate.