Temperature antipairing effect over the energy weighted sum rule

We study the temperature dependence of the sum rules using the discontinuity of the first derivative of the Matsubara Green's functions of a bilinear particle-hole operator. Particularly we study the behavior of the dipole particle-hole operator. We applied the calculation to 114Sn, 138Ba, 154Gd and 170Yb. It is found that the energy weighted sum rule for the dipole operator changes as a function of the temperature depending on the square of the gap. This fact is related to the antipairing effect of the temperature over the nuclear system