be reproduced by solving the classical problem of scattering on $- C_n/r^n$ potential, assuming that all trajectories that fall on the collision center contribute to the total reaction cross-section $\sigma^{\mathrm}{re}$ with the probability of reaction $P^{\mathrm}{re}$ [@Langevin1905]. Then, $\mathcal{K}^{\mathrm}{re} = \sigma^{\mathrm}{re} v$, with $v = \hbar k/\mu$ denoting the mean relative velocity in the gas. We will call this classical result for the reaction rate constant $K^L$. For a general review of high temperature transition state theories, we refer the reader to [@fernandez2006].

Elastic rate
------------

In the case of the elastic rate constant the situation is not as straightforward, as each partial wave contributes to the elastic cross section. Inspired by the approach of Cote and Dalgarno [@Cote2000], we derived an approximate expression for the elastic rate constant in the limit of high collision energy. In this approach we consider separately two contributions $$K^{el} =K^{el,(1)} + K^{el,(2)}.$$ where $K^{el,(1)}$, and $K^{el,(2)}$ denote reactive rate from collisions well below the barrier and collisions close or above the centrifugal barrier, respectively. Some characteristic angular momentum $\ell_t$ separating the two regions can be defined such that $$\label{xitr}
\sin\xi(E,\ell_{\mathrm}{t})=\frac{1}{2}.$$ Since this value can be chosen with some flexibility, we decided to pick the 