Ab initio calculation of muon capture on $^{24}$Mg

TL;DR

This paper presents a first-principles calculation of muon capture on magnesium-24 using chiral effective field theory and many-body methods, comparing results with phenomenological models and experimental data.

Contribution

It introduces a combined approach using chiral EFT and VS-IMSRG to compute muon capture rates, highlighting the effects of correlations and two-body currents.

Findings

Both models describe nuclear properties well.

Two-body currents significantly reduce capture rates.

Discrepancies remain for certain excited states.

Abstract

In this work we study ordinary muon capture (OMC) on $^{24}$Mg from a first principles perspective. Starting from a particular two- and three-nucleon interaction derived from chiral effective field theory, we use the valence-space in-medium similarity renormalization group (VS-IMSRG) framework to construct effective Hamiltonians and muon-capture operators which nonperturbatively account for many-body physics outside the valence space. The obtained nuclear matrix elements are compared against those from the phenomenological shell model. The impact of including the correlations from the nuclear shell model (NSM) as well as including the induced two-body part is studied in detail. Furthermore, the effects of realistic bound-muon wave function on the operators is studied. Finally, predictions for capture rates to the lowest excited states in $^{24}$Na are given and compared with available data. It is found that the spectroscopic properties of $^{24}$Mg and its OMC daughter $^{24}$Na are fairly well described by both the NSM and VS-IMSRG, and that the effect of the hadronic two-body currents significantly reduces the OMC rates. Both models have some difficulties in matching the measured OMC rates, especially for the $2^+$ final states. This calls for further studies in other light nuclei with available OMC data.