Eur. Phys. J. A (2006) 27: 269-276
https://doi.org/10.1140/epja/i2006-08-041-6

Nuclear Physics in Astrophysics II

Relation between proton and neutron asymptotic normalization coefficients for light mirror nuclei and its relevance for nuclear astrophysics

¹ Department of Physics, School of Electronics and Physical Sciences, University of Surrey, GU2 7XH, Guildford, Surrey, UK
² Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, CP 229, B-1050, Brussels, Belgium

Received: 20 June 2005
Accepted: 20 December 2005
Published online: 15 March 2006

Abstract

It has been realised recently that charge symmetry of the nucleon-nucleon interaction leads to a certain relation between Asymptotic Normalization Coefficients (ANCs) in mirror-conjugated one-nucleon overlap integrals. This relation can be approximated by a simple analytical formula that involves mirror neutron and proton separation energies, the core charge and the range of the strong nucleon-core interaction. We perform detailed microscopic multi-channel cluster model calculations and compare their predictions to the simple analytical formula as well as to calculations within a single-particle model in which mirror symmetry in potential wells and spectroscopic factors are assumed. The validity of the latter assumptions is verified on the basis of microscopic cluster model calculations. For mirror pairs in which one of the states is above the proton decay threshold, a link exists between the proton partial width and the ANC of the mirror neutron. This link is given by an approximate analytical formula similar to that for a bound-bound mirror pair. We compare predictions of this formula to the results of microscopic cluster model calculations. Mirror symmetry in ANCs can be used to predict cross sections for proton capture at stellar energies using neutron ANCs measured with stable or “less radioactive” beams.