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

TL;DR

This paper models the energy dependence of muon transfer rates from protium to neon at low energies, proposing a new approach based on wave function derivatives to interpret experimental data and improve low-energy transfer calculations.

Contribution

It introduces a model assuming energy-independent wave function derivatives and applies it to analyze muon transfer rates, offering a method to refine low-energy transfer calculations.

Findings

The model fits experimental transfer rates at 20 and 300 K.

Different wave function derivative values affect transfer rates at a few kelvins.

Comparison with previous calculations helps select the appropriate derivative value.

Abstract

The direct muon transfer from protium to neon at low collision energies is considered. The question is discussed how the energy dependence of the transfer rate can be extracted from available experimental data. A model is suggested which is based on two assumptions. First, the muon transfer occurs within an interaction sphere out of which the entrance and transfer channels are not coupled. Secondly, for the s- and p-waves at low collision energies, the complex logarithmic derivatives of the radial wave functions of the entrance channel on the interaction sphere are energy-independent. With only the s-wave taken into account, two values of the logarithmic derivative were found, which agree with the transfer rates measured at the temperatures of 20 and 300 K. Within this temperature interval, the rates evaluated for these two values differ only slightly. Noticeable differences arise at temperatures of a few kelvins. The choice of the preferred value of the logarithmic derivative was made by the comparison of the energy dependence of the S-matrix with results of previous calculations. Thereby, the proposed procedure may be a way to correct calculations at low collision energies.