Wigner-Kirkwood Expansion of the Quasi-Elastic Nuclear Responses and Application to Spin-Isospin Responses

Abstract

We derive a semi-classical Wigner-Kirkwood expansion ($\hbar$ expansion) of the linear response functions. We find that the semi-classical results compare very well to the quantum mechanical calculations. We apply our formalism to the spin-isospin responses and show that surface-peaked ${{\hbar }^{2}}$ corrections considerably decrease the ratio longitudinal/transverse as obtained through the Los Alamos $(\vec{p},{{\vec{p}}^{1}})$ experiment.