Calculation of the rate of muon transfer from a proton to neon on the basis of the two-center coulomb basis

Abstract

The results of improved calculations of the muon transfer rate from the 1S-state of muonic protium to neon are presented in the interval of collision energies from 10 −4 eV to 15 eV. The calculations have been made within the perturbed stationary states method in which the wavefunction of the three-body system (muon, proton and neon nucleus) is expanded in eigenfunctions of a two-centre Coulomb problem formulated in the Jacobi coordinates of the entrance channel. This approach provides the asymptotically correct description of the entrance channel. Namely, the correct dissociation limit is obtained, there are no spurious long-range interactions, the polarization attraction between muonic protium and neon appears naturally. Moreover, the electron screening, which is important at low collision energies, can be easily taken into account. The defects of the description are removed into the muon transfer channel in which their effect is not expected to be too significant because of large energies of the relative motion in this channel. The previous calculations carried out in this way allowed one to explain experimentally observed features of the temperature dependence of the transfer rate in hydrogen-neon mixtures. In the present work, a more perfect algorithm of constructing the basis eigenfunctions of the two-centre Coulomb problem has been realized and a better agreement with experimental data has been obtained.

On the reaction of muon transfer from protium to neon at low collision energies

“…The method used in Ref. [5] was based on a substantial difference of the energies of relative motion in the channels of the reaction (1). While the energy in the entrance channel [ µp (1s) + Ne ] is thermal, the energy gain in the transfer channel [ µNe * + p ] is a few keV [3].…”

“…The first one was performed in Ref. [5] within a version of the perturbed stationary states method suggested in…”

“…The values given in Table 1 were obtained for the case in which the electron screening was taken into account to a greater extent (the case C in Refs. [5,6]). The second calculation was performed in Refs.…”

“…Of course, it should be borne in mind that the electon screening in a liquid mixture may be more complicated than assumed in Refs. [5,6]. Moreover, the Maxwell distribution is a crude model in this case.…”

“…This model will be based on results of the calculation performed in Ref. [5]. Therefore, let us consider 1 A spread of theoretical results also exists for other elements with Z ≥ 6 .…”