A new effective Hamiltonian for nuclei with 50 neutrons from 78Ni to 100Sn

The nuclei with 50 neutrons that lie between 78Ni and 100Sn have provided benchmark studies of the nuclear shell model. We invoke a model space involving 4 single particle orbits (0f5/2, 1p3/2, 1p1/2, and 0g9/2) which we will call the N50 model space. There are 65 two-body matrix elements (TBME) and 4 single-particle energies (SPE) involving these four orbitals. The singular-value decomposition (SVD) method was used to vary the best determined linear combinations of the 65 TBME and 4 single-particle energies. Within this method, the experimental data was separated into randomized batches of testing and training data to determine the predictability of the resulting Hamiltonian to (testing) data not used by the SVD. It was found that about 35 linear combinations were well determined from the data. TBME obtained from VS-IMSRG method with two and three nulceon interactions were used for the remaining 34 linear combinations. Several things motivate us to find a new Hamiltonian for the N50 model space. There are new data for nuclei near 78Ni, in particular for the low-lying levels of 79Cu that are described by 0f5/2, 1p1/2 and 1p1/2 single-particle states in the N50 model space. There are now better starting Hamiltonians obtained from modern renormalization methods that include three-body interactions. Our results will provide an improved starting point for understanding the structure of nuclei with N = 50 as well as being part of improved Hamiltonians for the larger jj44 and jj45 model spaces.