  It has been suggested recently (Phys. Rev. Lett. 91, 232501 (2003)) that
charge symmetry of nucleon-nucleon interactions relates the Asymptotic
Normalization Coefficients (ANCs) of proton and neutron virtual decays of
mirror nuclei. This relation is given by a simple analytical formula which
involves proton and neutron separation energies, charges of residual nuclei and
the range of their strong interaction with the last nucleon. Relation between
mirror ANCs, if understood properly, can be used to predict astrophysically
relevant direct proton capture cross sections using neutron ANCs measured with
stable beams. In this work, we calculate one-nucleon ANCs for several light
mirror pairs, using microscopic two-, three- and four-cluster models, and
compare the ratio of mirror ANCs to the predictions of the simple analytic
formula. We also investigate mirror symmetry between other characteristics of
mirror one-nucleon overlap integrals, namely, spectroscopic factors and
single-particle ANCs.

Nuclear Theory