  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.
