Nuclear response function at finite temperature

The static-path approximation is applied to the real-time response function of a nucleus at finite temperature. This approximation is shown to become accurate in the high-temperature limit for an appropriately energy-smoothed strength function. An additional local approximation to overlap integrals yields the familiar adiabatic approximation. These two approximations are compared with exact results for the Lipkin model. For a sufficiently large ratio of two-body interaction to single-particle energy, the static-path approximation accurately describes the exact strength function. For parameters characteristic of nuclear shape transitions, the static-path approximation is not reliable and the adiabatic approximation is qualitatively in error.