Resonances with natural and unnatural parities in positron-sodium scattering

Abstract

We present an investigation of resonances in positron-sodium scattering using the complex scaling method. For the target sodium atoms, the interaction between the core and outer electron is treated using two different types of analytical model potentials. Explicitly correlated Gaussian wave functions are used to represent the correlation effects between the outer electron, the positron, and the ${\text{Na}}^{+}$ core. $S\ensuremath{-}, P\ensuremath{-}$, and $D\text{-wave}$ resonances with natural parity have been calculated for energies extending up to the positronium $n=2$ formation threshold. Resonance states for unnatural parities ${P}^{e}$ and ${D}^{0}$ have been calculated for energies extending up to the positronium $n=3$ threshold. Below both positronium thresholds we have for each symmetry identified a dipole series of resonances, with binding energies scaling in good agreement with expectations from an analytical calculation. The presented results are compared with other theoretical calculations.