Threshold behavior and analytical fitting of partial wave capture probabilities for attractive R−n potentials

Abstract

Numerically accurate analytical fittings for partial wave capture probabilities in the field of R(-n) potentials (n = 4 and 6) are presented across practically interesting ranges of probabilities. The results demonstrate the performance of the Bethe and Wigner threshold laws at low collision energies and should be useful for practical applications.

Electron capture by finite-size polarizable molecules and clusters

“…Eqn (2.6)-(2.8) with the parameters of Table 1, on the other hand, were found to be accurate within a few percent such as documented for l = 1-4 in ref. 15.…”

Quantum-reflection model for Penning ionization rate coefficients in cold collisions of metastable helium and rubidium

“…Dickinson (2007) combined this model with the analytic near-threshold results by Friedrich's group Trost, 2004, 2007) for quantum reflection on long-range inverse-power potentials. This provided a simple, closed-form expression, using only the C 6 dispersion coefficient and the reduced mass, for the ionization rate coefficient and reproduced the work of Stas et al (2006Stas et al ( , 2007 and McNamara et al (2007) (Dashevskaya et al, 2009;Quéméner and Bohn, 2010) for p-wave quantum reflection. For the He * -Rb system when this work started we were unaware of any published calculations of the C 6 dispersion coefficient and consequently a simple estimate of the value of this coefficient was made.…”

“…Note that the low-temperature limit of their expression differs by about 13% from the analytic result of Friedrich and Trost (2004). As Dashevskaya et al (2009) note 'tolerating an incorrect behavior of the small probability in the limit k → 0 allows one to achieve a better approximation in the region where the probability is noticeable. ' However at intermediate temperatures the value of K p (T ) can deviate by up to about 35% from the numerical values, k DLN T p (T ) based on the transmission probability results of Dashevskaya et al (2009).…”

“…More recently Dashevskaya et al (2009) have solved the Schrödinger equation numerically for the p-wave transmission coefficient, P p (k), k being the wavenumber, and provided an analytic fit to their results. While they don't compare their fit explicitly to their numerical values, the corresponding results for the 1/R 4 potential suggest the error should be no more than a few percent.…”

“…Guided by this temperature dependence we have attempted to fit our numerical result based on the transmission probability of Dashevskaya et al (2009):…”