The temperature dependence of the shell corrections

We have examined the dependence of the shell correction to the nuclear liquid drop energy at finite excitations on the excitation energy (temperature). For this we have calculated the shell correction to the energy and free energy in very broad region of nuclei and deformations starting directly from their formal definitions. We have found out that the dependence of the shell corrections on the excitation energy differ substantially from the widely used approximation $\delta E(E^*)=\delta E(0)\exp(-E^*/E_d)$ both at small and large excitations. In particular, below the critical temperature at which the pairing effects vanish, the shell correction to the free energy is rather insensitive to the excitation energy. We suggest a more accurate approximation for the temperature dependence of the shell correction to the energy and free energy that is expressed in terms of the shell correction to the energy of independent particles and the shell correction to the pairing energy at T=0 and few fitted constants.