Time-dependent quantal treatment of muon-hydrogen collisions

Abstract

The interaction of free muons with hydrogen atoms is discussed within the framework of time-dependent Hartree-Fock theory. Both the muon and the electron are treated quantum mechanically. The incident muon energies considered are 2.7 and 0.27 eV, and we discuss the results for fixed muon wave-packet widths in this paper. At the lower energy, for our packet widths of 1.5 Å, the probability for muon capture is high (0.7), and the probability distribution as a function of principal quantum number peaks at n=14≃($m_{\mu }$/$m_e$ ${)}^{1/2}$, i.e., at the radius corresponding to the electron’s initial ground-state radius. At the higher energy, there is a sharp drop in the capture probability. The time development in this case is qualitatively similar to that for elastic scattering of the same muon wave function from the ‘‘frozen’’ ground-state hydrogen-atom potential. Radial probability distributions, principal quantum number distributions, probability density contours, etc., are examined and discussed, as are total cross sections and comparisons with other theoretical results.