Comprehensive Table of Calculated Huff Factors

TL;DR

This paper provides a comprehensive and systematic calculation of the Huff factor for nuclei with atomic numbers 6 to 94, incorporating isotope dependence and nuclear structure effects, to improve the accuracy of muon capture rate analyses.

Contribution

It introduces the first unified set of Huff factors calculated with a microscopic nuclear model including pairing and deformation effects, extending previous atomic number-based estimates.

Findings

Huff factors decrease monotonically with increasing Z.

Isotope dependence of Huff factors is minimal.

Results agree well with previous calculations, validating the approach.

Abstract

We present a systematic calculation of the Huff factor for nuclei with atomic numbers ($ Z $) in the range of $ 6 \leq Z \leq 94 $. The Huff factor quantifies the increase in the partial lifetime of the decay-in-orbit (DIO) of the muonic atom and serves as an essential correction factor for extracting the nuclear muon capture rate from the measured lifetimes of the muonic atom. However, previous calculations typically provided only the atomic number dependence and neglected isotope dependence -- an assumption whose reliability had not been examined, despite its importance for a comprehensive understanding of the nuclear muon capture rate. In this work, we calculate the Huff factor using nuclear charge distributions obtained from a fully self-consistent microscopic nuclear structure model that incorporates pairing and deformation effects. The resulting Huff factors exhibit a monotonic decrease with increasing $ Z $, while the isotope dependence is found to be small. Our results also show good agreement with previous calculations, supporting the reliability of the present framework. The comprehensive set of Huff factors presented here constitutes the first unified values currently available and will serve as a basis for future evaluations of muon nuclear data.