Influence of low energy scattering on loosely bound states

TL;DR

This paper derives algebraic relations linking binding energy and ANC of subthreshold states to scattering parameters, validated on nuclear models relevant for astrophysics.

Contribution

It introduces new algebraic equations connecting binding energy, ANC, and scattering data for charged and neutral particles, applicable in nuclear physics.

Findings

Relations accurately reproduce model data

Applicable to exotic nuclei and astrophysics

Validated on specific nuclear systems

Abstract

Compact algebraic equations are derived, which connect the binding energy and the asymptotic normalization constant (ANC) of a subthreshold bound state with the effective-range expansion of the corresponding partial wave. These relations are established for positively-charged and neutral particles, using the analytic continuation of the scattering (S) matrix in the complex wave-number plane. Their accuracy is checked on simple local potential models for the 16O+n, 16O+p and 12C+alpha nuclear systems, with exotic nuclei and nuclear astrophysics applications in mind.