Rotationally Inelastic Collisions of Ground-State Helium or Argon with NaK ($A^{ ,1} Sigma^+$)

Abstract We have performed quantum mechanical scattering calculations that describe collisions between He or Ar and NaK $(A^{\,1}\Sigma^+)$ that change the rotational and magnetic quantum numbers, $j$ and $m$. These calculations involved determining {\it ab initio} potential energy surfaces by using the GAMESS electronic structure code. The coupled channel scattering formalism, developed by Arthurs and Dalgarno, was used with the potential surfaces to calculate $j$ and $m$-changing cross sections, along with the transfer of moments of the $m$ distribution. Our calculations show a propensity for transitions with even values of $\Delta j$; the strength of the propensity depends on the perturber. These results are in good agreement with experimental data measured by the Lehigh group. We identify a region of the potential that tends to diminish the propensity and develop a simple model to explain why such a region arises. We develop a semiclassical model that leads to closed form expressions for semiclassical $m$-changing cross sections (where $m$ is a continuous variable) and the distribution of final polar angles $\theta'=m'/\sqrt{j'(j'+1)}$. We compare our calculated semiclassical and quantum mechanical cross sections, and we identify special cases which admit analytic approximations to the polar angle distribution. One special case leads to a near-Lorentzian distribution, peaked where $\theta'=\theta$. Many results for He+NaK and Ar+NaK are well described by this case.