Spectroscopic factors of magic and semimagic nuclei within the self-consistent theory of finite Fermi systems

A scheme is presented to find single-particle spectroscopic factors (SF) of magic and semimagic nuclei within the self-consistent theory of finite Fermi systems (TFFS). In addition to the energy dependence of the mass operator $\mathrm{\Sigma }$ induced by the surface-phonon coupling effects which are commonly considered in this problem, the in-volume energy dependence of the operator $\mathrm{\Sigma }$ inherent in the self-consistent TFFS is also taken into account. This dependence arises due to the effect of high-lying particle-hole excitations and persists in nuclear matter. The self-consistent basis of the energy density functional method by Fayans {\it et al.} is used. Both the surface and in-volume contributions to the SFs turned out to be of comparable magnitude. The results for magic ${}^{40,48}$Ca and ${}^{208}$Pb nuclei and semimagic lead isotopes are presented.