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Background: An asymptotic normalization coefficient (ANC) characterizes theasymptotic form of a one-nucleon overlap integral required for description ofnucleon-removal reactions. Purpose: We investigate the impact of the particlecontinuum on proton and neutron ANCs for mirror systems from $p$- and$sd$-shell regions. Method: We use the real-energy and complex-energy continuumshell model approaches. Results: We studied the general structure of thesingle-particle ANCs as a function of the binding energy and orbital angularmomentum. We computed ANCs in mirror nuclei for different physical situations,including capture reactions to weakly-bound and unbound states. Conclusions: Wedemonstrated that the single-particle ANCs exhibit generic behavior that isdifferent for charged and neutral particles. We verified the previouslyproposed 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 protonand neutron mirror ANCs. We find minor modifications if the spectroscopicstrength is either localized in a single state or broadly distributed. Forcases when several states couple strongly to the decay channel, thesemodifications may reach 30%.

Asymptotic normalization coefficients and continuum coupling in mirror nuclei