Dependence of nuclear $Z$ factor on the chemical potential

A simple microscopic formula is derived for the renormalization factor $Z$ of Green's function on the basis of the self-consistency relation of many-body theory and the Brueckner method. This formula involves the derivative of the Brueckner $G$ matrix with respect to energy. Based on the analysis of the properties of the $G$ matrix for a slab of nuclear matter, the $G$ matrix is approximately replaced by the off-mass-shell $T$ matrix taken for free $NN$ scattering at a negative energy $E$ equal to the doubled chemical potential $\mu$ of the nucleus under consideration. The $Z$ factor thus calculated depends strongly on $\mu$ and decreases with $|\mu|$. This effect is important for analyzing the properties of atomic nuclei near the drip line, where $\mu$ is zero.