Theoretical calculation of Penning-ionization cross sections for collisions of He(21,3S) with sodium atoms

Cross sections have been calculated for the Penning ionization of ground-state sodium atoms in collisions with metastable He(2 ${}_{}{}^1{}_{}{}^{}$,3S) atoms for the range of center-of-mass energies 0.01 eV ≤E≤1.0 eV. The cross sections were calculated with use of optical-model potentials. The real parts of the relevant potential-energy curves were determined by carrying out a configuration-interaction (CI) calculation on the NaHe molecule. The potentials were adjusted to yield the correct asymptotic van der Waals form. The imaginary parts of the potentials correspond to autoionization rates and were obtained from a Stieltjes moment analysis of a discrete ($L^2$) representation of the $e^{\mathrm{-}}$+${\mathrm{NaHe}}^{+}$ continuum, as represented by diffuse molecular orbitals generated by the CI procedure. The calculated cross section for He(2 ${}_{}{}^3{}_{}{}^{}S$) on Na at E=0.04 eV is in good agreement with stationary-afterglow measurements at room temperature. The singlet-to-triplet ratio of cross sections is in good agreement with that measured by beam techniques. Elastic differential cross sections for He(2 ${}_{}{}^1{}_{}{}^{}S$) scattered from Na have also been calculated. Satisfactory agreement is obtained with recent crossed-beam measurements.