On the muon transfer from protium to neon

Abstract

The rate of the muon transfer from the 1S-state of muonic protium to neon is calculated in the interval of collision energies from 10-4 eV to 15 eV. The basic idea of the present treatment is to describe the entrance channel of the transfer reaction at large interatomic separations as correctly as possible. Accordingly, the three-body Hamiltonian is written in the Jacobi coordinates of the entrance channel, and a problem of the muon motion in the field of two fixed Coulomb centers is formulated in these coordinates. Its eigenstates are used as a basis in which the three-body wavefunction is expanded. Finally, the radial functions describing the relative motion in the entrance and transfer channels satisfy a set of coupled ordinary differential equations. Its solution allows one to find diagonal S-matrix elements corresponding to the entrance channel and, as a result, to obtain the total transfer cross-section and the amplitude of the elastic scattering. In this approach the description of the entrance channel proves to be free of the well-known defects -- incorrect dissociation limits and spurious long-range interactions. These defects are manifested only in the transfer channel. However, their effect seems to be not very significant because of large energies of the relative motion in this channel (a few keV). The calculation made here with four two-center \(\sigma\)-states taken into account reasonably reproduces the experimental transfer rate measured in liquid hydrogen-neon mixtures. The situation at room temperatures is worse: the theoretical value of the transfer rate exceeds the experimental one by a factor of two. However, the calculation clearly indicates the existence of a well pronounced minimum of the transfer rate at thermal energies. This result corresponds qualitatively to the experimental fact of a strong suppression of the muon transfer at room temperatures. At collision energies of 0.3-0.5 eV a resonant peak in the transfer rate is predicted. It is due to a quasi-steady state in the D-wave. The elastic scattering of muonic protium by neon is also treated. The effect of the electron screening in the entrance channel is studied in detail. It is found to be very significant right up to collision energies of 1-2 eV.