Exact Solutions for Pairing Correlations Among Protons and Neutrons

Using the nuclear shell model we are able to achieve, for the first time, exact solutions for pairing correlations for light to medium-mass nuclei, including the challenging proton-neutron pairs, while also identifying the primary physics involved. We utilize a new Hamiltonian with only two adjustable parameters. In addition to a single-particle energy term and the Coulomb potential, the shell-model Hamiltonian consists of isovector T=1 pairing interaction and average proton-neutron isoscalar T=0 interaction. The T=0 term describes the average interaction between non-paired protons and neutrons. This Hamiltonian is exactly solvable, but calculations represent a challenge, as they require highly non-linear equations to be computed. With this model, including from 3 to 7 single-particle energy levels, we can reproduce experimental data for 0 + state energies for isotopes with mass A=10 through A=62 exceptionally well including isotopes from He to Ge. These results provide a further understanding for the key role of proton-neutron pairing correlations in nuclei, which is especially important for waiting-point nuclei on the rp-path of nucleosynthesis.