Characterizing resonances in positron-sodium scattering

TL;DR

This paper studies resonances in positron-sodium scattering using advanced computational methods, identifying various resonant states and comparing them with recent theoretical calculations to enhance understanding of scattering phenomena.

Contribution

It introduces a hyperspherical coordinate $R$-matrix approach to analyze resonances, including debated states, and compares results with complex-scaling calculations for the first time.

Findings

Identification of high partial-wave resonances up to Na(4f) threshold.

Observation of a dipole series of resonances consistent with ion-dipole interactions.

Discovery of quasi-dipole resonances near Na(4d) and Na(4f) degeneracy.

Abstract

We investigate resonances in positron-sodium scattering using the $R$-matrix propagation method formulated in hyperspherical coordinates. The interaction between the sodium core and the valence electron is described by analytical model potentials. High partial-wave resonances are calculated for collision energies up to the Na($4f$) threshold. Several resonant states of debated character are identified, and their behavior is analyzed through phase-variation studies, the associated structures in the calculated cross sections, and the characteristic patterns observed in the stability plots. The calculated dipole series of resonances, supported by the ion-dipole interaction between Na$^{\scriptscriptstyle+}$ and Ps($n=2$), shows good agreement with recent complex-scaling calculations. In addition, a sequence of quasi-dipole resonances is found to arise from the near degeneracy of the Na($4d$) and Na($4f$) states in the e$^{+}$-Na system, which accumulate geometrically toward the Na($4d$) threshold.