On the calculation of matrix elements of one body operators in many nucleon systems

TLDR: In this article, the connection between matrix elements of one body operators in odd nuclei and vertex functions is demonstrated and the renormalization of the external field, necessistated by configuration space limitations, is carried through for scalar, local fields, acting on the density and for radiation fields of the electric multipole type.

Abstract: We demonstrate the connection between matrix elements of one body operators in odd nuclei and vertex functions. The procedure is free of assumptions on the pole distribution of the two point functions and it does not use perturbation theory. The renormalization of the external field, necessistated by configuration space limitations, is carried through for scalar, local fields, acting on the density and for radiation fields of the electric multipole type using the requirement of gauge invariance. It is shown that this renormalization is possible, even if the renormalized field is strongly energy dependent due to configuration mixing.