Asymptotic normalization of mirror states and the effect of couplings

TL;DR

This study investigates whether the ratio of asymptotic normalization coefficients of mirror nuclear states remains model-independent when deformation and core excitation are included, supporting indirect methods for astrophysical reaction rates.

Contribution

It extends previous assumptions by testing the Hamiltonian independence of ANCs ratio with deformation and core excitation in a phenomenological rotor + N model.

Findings

The ANC ratio is generally independent of coupling strength and multipolarity.

Exceptions occur with s-wave coupling to the core's ground state and loosely bound systems.

Results support the use of mirror symmetry in astrophysical reaction rate estimations.

Abstract

Assuming that the ratio between asymptotic normalization coefficients of mirror states is model independent, charge symmetry can be used to indirectly extract astrophysically relevant proton capture reactions on proton-rich nuclei based on information on stable isotopes. The assumption has been tested for light nuclei within the microscopic cluster model. In this work we explore the Hamiltonian independence of the ratio between asymptotic normalization coefficients of mirror states when deformation and core excitation is introduced in the system. For this purpose we consider a phenomenological rotor + N model where the valence nucleon is subject to a deformed mean field and the core is allowed to excite. We apply the model to 8Li/8B, 13C/13N, 17O/17F, 23Ne/23Al, and 27Mg/27P. Our results show that for most studied cases, the ratio between asymptotic normalization coefficients of mirror states is independent of the strength and multipolarity of the couplings induced. The exception is for cases in which there is an s-wave coupled to the ground state of the core, the proton system is loosely bound, and the states have large admixture with other configurations. We discuss the implications of our results for novae.