Response function of hot asymmetric nuclear matter

An approximated expression for the response function of hot asymmetric nuclear matter to small external perturbations was calculated. A general expression for the four channels (scalar, isovector, spin and spin-isovector) was obtained and the results for the isovector channel are presented in this letter. Two possible prescriptions for the neutron and proton density fluctuations are considered leading to different results. In the case of a realistic Skyrme-type force, SGII, for an asymmetry coefficient corresponding to that of the lead nucleus, a damped zero sound was found at zero temperature for small momentum transfer in the case of the first (second) prescription. For a higher asymmetry coefficient the mode becomes either more or less collective, depending on the ansatz for the density fluctuations. Although both prescriptions yield strength functions which satisfy the energy-weighted sum rule sufficiently well, it is argued that the prescription leading to a more collective mode as the asymmetry increases has a sounder physical meaning. As temperature increases collectivity weakens making the zero sound disappear whenever it occurs.