The Effect of Local and Non-Local Potentials on BCS Solutions for Some Even-Even Nuclei

We study the like-particle pairings using the BCS approximation applied for different even-even nuclear isotopes using different realistic potentials for the NN interaction. First we solve the Schrodinger equation using a deformed axially symmetric Woods-Saxon potential. For the pairing interaction the interaction G-matrix is calculated using local potentials (Argonne V18 and Nijmegen II) and non-local potentials (Bonn-CD and Nijmegen I). A study of the effect of these different realistic potentials on the pairing strengths, average pairing gaps, Fermi energies, and occupation probabilities of protons and neutrons is introduced. We find that the pairing strength values calculated by the local potentials are greater than that calculated by the non-local potentials. We find that only one of the BCS outputs, the pairing energy gap, is slightly affected by using different types of realistic potentials.