Eur. Phys. J. D (2015) 69: 276
https://doi.org/10.1140/epjd/e2015-60427-6

Regular Article

Theoretical study of true-muonium μ ⁺ μ ⁻ formation in muon collision processes μ⁻ + μ⁺e⁻ and μ⁺ + pμ⁻

True-muonium μ⁺μ⁻ formation in μ⁻+μ⁺e⁻ and μ⁺+pμ⁻

Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan

^a e-mail: sakimoto@isas.jaxa.jp

Received: 21 July 2015
Received in final form: 30 September 2015
Published online: 15 December 2015

Abstract

Formation processes of true muonium (μ⁺μ⁻) atoms are investigated theoretically 1) for negative-muon (μ⁻) collisions with a muonium (Mu = μ⁺e⁻) atom (i.e., μ⁻ + μ⁺e⁻ → μ⁺μ⁻ + e⁻) and 2) for positive-muon (μ⁺) collisions with a muonic hydrogen (pμ⁻) atom (i.e., μ⁺ + pμ⁻ → μ⁺μ⁻ + p). The calculations are carried out by using two different types of approaches: one, applied to the μ⁻ + e⁻μ⁺ system where electron emission plays an important role, is a semiclassical (SC) method, in which the radial distance between the negative and positive muons is treated as a classical variable, and the remaining degrees of freedom are described by quantum mechanics. The other is a classical-trajectory Monte Carlo (CTMC) method, in which all the degrees of freedom are described by classical mechanics. The formation and ionization (or dissociation) cross sections and the state distributions of produced true-muonium atoms are presented.