Transition of dimuonium through foil

TL;DR

This study models how dimuonium, a bound state of muon and antimuon, passes through matter foils, analyzing state evolution, uncertainties, and convergence for different materials to inform future experiments.

Contribution

It introduces a detailed transport model for dimuonium passing through matter, including multiple atomic potential approximations and convergence analysis.

Findings

Atomic potential model uncertainties have minimal impact on low-lying state yields.

Transport equations converge well when truncated to a finite number of states.

Results vary across different foil materials like Beryllium, Aluminium, and Lead.

Abstract

This article presents a study of the passage of dimuonium through the foil of ordinary matter. First, we provide an overview of how dimuonium is planned to be produced for such a type of experiment and how it is expected to interact with the ordinary atoms -- predominantly electromagnetically via the screened coulomb potential of the atomic nuclei. Then, we describe the transport equations that represent the evolution of dimuonium states during the passage and their solution methods. Finally, for three different foils (Beryllium, Aluminium and Lead), we present the results of this study. To estimate impact of uncertainties in the potential of a target atom, we study 15 different approximations of the atomic potential and show that the corresponding atomic-potential-model-dependent error in the yields of the low lying states of dimuonium is quite small within the framework of the applied Born approximation. The convergence of the results after truncation of the infinite system of transport equations to the finite number of quantum states of dimuonium is also studied, and good convergence for the yields of low-lying states is demonstrated.