Characterizing resonances in positron-sodium scattering

TL;DR

This study addresses resonances in positron-sodium scattering by applying an R-matrix propagation method in hyperspherical coordinates to a three-body e+Na model with analytic core–valence potentials. Resonances are identified through the eigenphase-sum and stabilization analyses across total angular momenta up to J = 4, and the results are benchmarked against prior theoretical work. The analysis reveals two distinct dipole resonance series: one converging toward the Ps2 threshold from Ps–Na+ coupling and a quasi-dipole series from near degeneracies of Na4d and Na4f, with universal scaling largely holding except near thresholds where interchannel coupling is strong; a broad F-wave resonance near 3.2 eV is also found. These findings provide quantitative benchmarks for theory and suggest signatures accessible to upcoming positron-beam experiments with enhanced energy resolution.

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.

Figures (6)

• Figure 1: (Color online) Stabilization plot of energy $E$ versus box size $R$ in the e$^{+}$ + Na system with $J=0-2$. The arrow marks the resonance position.
• Figure 2: (Color online) The eigenphase sums in the e$^{+}$-Na system with $J=0-2$. Arrows indicate the resonance positions.
• Figure 3: (Color online) The Ps($n=1,\,2$) formation cross sections for the e$^{+}$ + Na($3s$) $\rightarrow$ Ps($n=1,\,2$) + Na$^{+}$ process with $J=0-2$. Arrows indicate the resonance positions.
• Figure 4: (Color online) (a1), (b1), (c1) and (d1) Eigenphase sums; (a2), (b2), (c2) and (d2) Ps-formation cross sections for the e$^{+}$-Na system with $J=0-3$ at the Ps($n=2$) threshold. Arrows indicate the resonance positions near the Ps($n=2$) threshold. (a3), (b3), (c3) and (d3) Semilogarithmic plots of the resonance positions $E_{R}=E_{th}-E_{\nu}$ for Ps($n=2$)+Na$^{+}$ below the Ps($n=2$) threshold. Straight lines represent the fits using Eq. (\ref{['Ev']}).
• Figure 5: (Color online) (a1), (b1), (c1) and (d1)Eigenphase sums; (a2), (b2), (c2) and (d2) Ps-formation cross sections of the e$^{+}$-Na system with $J=0-3$ near the Na($4d$) threshold. Arrows indicate the resonance positions.