Abstract
The thermal Green's functions are used to derive the thermal random phase approximation (TRPA) in open shell systems. The TRPA in the Sn isotopes is studied for a separable quadrupole interaction as a function of the temperature. The matrix elements of quadrupole particle-hole and two-particle operators as well as their energy-weighted sum rules are evaluated. The most noticeable features introduced by the temperature dependence are the big changes that happen when the superconductivity disappears.
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