Variable-phase methods and data for long-range scattering

Abstract

Long-range interactions play an important role in dark-matter phenomenology, affecting the relic abundance, indirect-detection signals, and structure formation on galactic scales. Reliable predictions often require nonperturbative solutions of the Schrödinger equation over broad parameter ranges and many partial waves. We present a numerical framework based on the variable-phase method, which recasts the radial Schrödinger equation as a system of first-order equations and allows both regular and irregular solutions to be computed efficiently. The former determine phase shifts and Sommerfeld factors, while the latter provide additional information relevant for the self-consistent unitarization of contact-like inelastic interactions. We discuss the numerical implementation, integration-domain selection, partial-wave convergence, and comparisons with analytic limits. We release the code together with tables for the Yukawa potential containing phase shifts, Sommerfeld factors, elastic and angularly weighted cross sections, and the irregular-solution information relevant for unitarization. These resources facilitate dark-matter studies without requiring repeated computationally intensive scans.