Influence of low-energy scattering on loosely bound states

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 16 O+n, 16 O+p and 12 C+α nuclear systems, with exotic nuclei and nuclear astrophysics applications in mind.

Precision calculation of the quartet-channelp−dscattering length

“…When effective ranges are calculated as well, one can extract near-threshold bound-state properties such as asymptotic normalization constants from scattering parameters with relations as given, e.g., in Refs. [9,10]. These constants can be used to determine the overall normalization of the S-factor for astrophysical nuclear reaction rates [11].…”

Reexamination of the astrophysicalSfactor for theα+d→6Li

“…In this procedure the elastic scattering phase shift is analytically approximated in the physical region with the subsequent analytical continuation to the bound state pole. This analytical approximation in the physical region can be done using different approaches: Pade approximation [2], effective range expansion [3][4][5]. There is also a possibility to solve N/D equations, which take into account the right unitary cut and the left dynamical singularities.…”

Analytic continuation as a bridge between continuum and bound states

“…This method was used in [8] to obtain the S wave VCs and ANCs for the process 6 Li → α + d, by Yu.V. Orlov et al [9] for the systems 3 H, 2,3,5 He, 5 Li, 8 Be, and by J.-M. Sparenberg et al [10] for the systems 16 O + n, 16 O + p, and 12 C + α.…”