Muon-Induced Nuclear Magnetic Moments in Spinless Muonic Atoms: A Simple Estimate

TL;DR

This paper presents a simple semi-classical estimate of the nuclear magnetic dipole moment induced by a bound muon in heavy muonic atoms, linking it to nuclear polarisation effects and providing a practical method for estimating nuclear magnetic polarizability.

Contribution

It introduces a straightforward semi-classical approach to estimate muon-induced nuclear magnetic moments and relates it to nuclear polarisation calculations, offering a practical estimation method.

Findings

The simple estimate closely matches more complex nuclear polarisation calculations.

Effective nuclear magnetic polarizability values can be extracted from the estimate.

A practical back-of-the-envelope method for estimating nuclear polarisation is proposed.

Abstract

The magnetic field generated by a bound muon in heavy muonic atoms results in an induced nuclear magnetic dipole moment even for otherwise spinless nuclei. This dipole moment interacts with the muon, altering the binding energy of the muonic state. We investigate the relation of this simple, semi-classical-insriped approach to nuclear polarisation (NP) calculations. Motivated by the relative closeness of this simple estimate to evaluations of NP, we extract effective values for the nuclear magnetic polarisability, a quantity otherwise unknown, and put forward a simple back-of-the-envelope way to estimate the magnetic part of NP.