SMALL-AMPLITUDE VIBRATIONS AT A FINITE TEMPERATURE IN THE LIQUID-DROP MODEL

The ground state of a hot nucleus is studied in the classical limit. The equations of motion and boundary conditions of the liquid drop model are derived from the variational principle. The effect of the surface tension is taken into account. The temperature dependence of small-amplitude vibrations in the liquid drop model is investigated. It is shown that the breathing mode suffers a 6.3% decrease in energy when the temperature increases from 0 to 5 MeV. The present model allows for a description of surface modes with an A-1/2 dependence of the energy. It is also found that the surface modes will show an appreciable temperature dependence if a reasonable temperature dependence of the surface tension is postulated. It is shown that the model satisfies the energy-weighted sum rule and the inverse energy-weighted sum rule.