NUCLEON SPECTRAL-FUNCTION AT FINITE-TEMPERATURE AND THE ONSET OF SUPERFLUIDITY IN NUCLEAR-MATTER

Nucleon self-energies and spectral functions are calculated at the sat uration density of symmetric nuclear matter at finite temperatures. In particular, the behavior of these quantities at temperatures above an d close to the critical temperature for the superfluid phase transitio n in nuclear matter is discussed. It is shown how the singularity in t he thermodynamic T matrix at the critical temperature for superfluidit y (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 Fe rmi momentum and temperatures close to the critical temperature relate d to the pairing singularity in the imaginary part. For comparison the self-energy derived from the K matrix of Brueckner theory is also cal culated. It is found that there is no pairing singularity in the imagi nary 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 spe ctral function and the occupation numbers for finite temperatures are calculated.