A solvable version of the collisional random phase approximation

We derive the markovian limit of the collisional Random Phase Approximation (CRPA) by resort to the linearization of the Collisional Time-Dependent-Hartree-Fock (CTDHF) equation of motion for the one-body density matrix. The CRPA spectral problem is numerically solved in the frame of a model consisting of a finite fermion system with axial symmetry interacting by means of a separable force. Calculations are performed within a range of interaction strengths, temperature and size parameters and it is shown that both the centroids and the widths of the high energy collective modes exhibit the trend of experimental data. (orig.)