Cross section of the Coulomb excitation of $^{229m}$Th by low energy muons

TL;DR

This paper calculates the inelastic scattering cross section of low-energy muons with $^{229}$Th nuclei, revealing a significantly larger excitation probability of the isomeric state than electron interactions, relevant for future muon collider experiments.

Contribution

It provides the first detailed calculation of muon-induced excitation cross sections for $^{229}$Th, highlighting their potential for efficient isomer excitation in collider settings.

Findings

Muon excitation cross section reaches 10^{-21} cm^2 at ~10 eV.

Muon excitation cross section is 10^4 to 10^5 times larger than electron excitation.

Potential for efficient $^{229m}$Th excitation at muon colliders.

Abstract

The inelastic scattering cross section for muons, $\mu^-$, with energies $E$=9--100~eV from the $^{229}$Th nuclei is calculated in the framework of the second order of the perturbation theory for the quantum electrodynamics. The dominant contribution to the excitation of the low energy isomer $^{229m}$Th$(3/2^+,8.19\pm0.12$~eV) comes from the $E2$ multipole. The excitation cross section reaches the value of $10^{-21}$ cm$^2$ in the range $E\approx$10~eV. This is four to five orders of magnitude larger than the electron excitation cross section and enough for efficient excitation of $^{229m}$Th on the muon beam at the next generation of muon colliders.