Scattering of charged particles within Efros method utilizing oscillator series expansion of wave functions

TL;DR

Addresses the accurate description of charged-particle scattering in ab initio nuclear theory, focusing on the Coulomb problem within the HORSE formalism. The authors integrate the Efros method with an oscillator-basis description to obtain phase shifts and cross sections using a small set of short-range functions, reducing the computational cost compared to full HORSE. Using Woods-Saxon nuclear potentials and a smoothing scheme, they demonstrate that the Efros-based approach reproduces exact solutions for several test cases, with small RMS deviations in the elastic cross sections and robust convergence for moderate SRF counts. The work provides a practical, scalable route to ab initio nuclear reaction calculations in combination with the No-Core Shell Model.

Abstract

We apply the version of the Efros method utilizing oscillator expansion of wave functions to the Coulomb scattering problem using our recent developments of the HORSE formalism. The approach yields accurate phase shifts and cross sections with significantly reduced computational cost compared to the full HORSE method, while maintaining agreement with exact solutions. These results demonstrate the efficiency of the Efros method and its prospect for applications in ab initio nuclear reaction calculations.

Figures (4)

• Figure 1: Phase shift $\delta_l(k)$ and elastic $p{-}\alpha$ scattering cross section $\sigma_l(k)$ dependences on relative motion energy $E$ in the $p_{3/2}$ partial wave obtained by different methods. Solid line: numerical integration of Schrödinger equation by Numerov method; crosses: HORSE methodYANIKOV2025100075; other lines: Efros method with different $v$ for SRFs $\bar{\beta}_{nl}(r) = \bar{\beta}_{nl}^{Eig}(r)$. For each method, $s_\sigma$ is the cross-section RMS deviation from the exact values. The results were obtained for truncation boundary $N=10$, $\hbar\omega = 27$ MeV and starting number $n_s = 200$ for calculating $S_{nl}(k)$ and $C_{nl}(k)$ using Eq. \ref{['TRR']}.
• Figure 2: Same as Fig. \ref{['figure_1']} but for SRFs $\bar{\beta}_{nl}(r)=\bar{\beta}_{nl}^{Osc}(r)$.
• Figure 4: Same as Fig. \ref{['figure_1']} but for $p_{1/2}$ wave and $\hbar\omega = 22$ MeV.
• Figure 5: Same as Fig. \ref{['figure_1']} but obtained in the $s_{1/2}$ wave for $p{-}^{15}N$ scattering with $\hbar\omega=18$ MeV.