Asymptotic normalization coefficients and continuum coupling in mirror nuclei

TL;DR

This paper investigates how the particle continuum affects asymptotic normalization coefficients (ANCs) in mirror nuclei using continuum shell models, confirming a previously proposed relation and highlighting differences between charged and neutral particles.

Contribution

It provides a detailed analysis of the impact of the continuum on ANCs in mirror nuclei, including validation of a known relation and exploration of effects in various physical scenarios.

Findings

ANCs exhibit different behaviors for charged and neutral particles.

The relation between proton and neutron mirror ANCs holds with minor modifications.

Strong coupling to decay channels can modify ANCs by up to 30%.

Abstract

Background: An asymptotic normalization coefficient (ANC) characterizes the asymptotic form of a one-nucleon overlap integral required for description of nucleon-removal reactions. Purpose: We investigate the impact of the particle continuum on proton and neutron ANCs for mirror systems from $p$- and $sd$-shell regions. Method: We use the real-energy and complex-energy continuum shell model approaches. Results: We studied the general structure of the single-particle ANCs as a function of the binding energy and orbital angular momentum. We computed ANCs in mirror nuclei for different physical situations, including capture reactions to weakly-bound and unbound states. Conclusions: We demonstrated that the single-particle ANCs exhibit generic behavior that is different for charged and neutral particles. We verified the previously proposed relation [N.K. Timofeyuk, R.C. Johnson, and A.M. Mukhamedzhanov, Phys. Rev. Lett. 91, 232501 (2003); Phys. Rev. Lett. 97, 069904(E) (2006); N. K. Timofeyuk and P. Descouvemont, Phys. Rev. C 72, 064324 (2005)] between proton and neutron mirror ANCs. We find minor modifications if the spectroscopic strength is either localized in a single state or broadly distributed. For cases when several states couple strongly to the decay channel, these modifications may reach 30%.