Nucleon spectral function at finite temperature and the onset of superfluidity in nuclear matter

Nucleon self-energies and spectral functions are calculated at the saturation density of symmetric nuclear matter at finite temperatures. In particular, the behavior of these quantities at temperatures above and close to the critical temperature for the superfluid phase transition in nuclear matter is discussed. It is shown how the singularity in the thermodynamic $T$ matrix at the critical temperature for superfluidity (Thouless criterion) reflects in the self-energy and correspondingly in the spectral function. The real part of the on-shell self-energy (optical potential) shows an anomalous behavior for momenta near the Fermi momentum and temperatures close to the critical temperature related to the pairing singularity in the imaginary part. For comparison the self-energy derived from the $K$ matrix of Brueckner theory is also calculated. It is found that there is no pairing singularity in the imaginary part of the self-energy in this case, which is due to the neglect of hole-hole scattering in the $K$ matrix. From the self-energy the spectral function and the occupation numbers for finite temperatures are calculated.