Electromagnetic Properties of the N=50 Isotones with the p35-i3 Hamiltonian

Abstract

The nuclei with 50 neutrons that lie between $^{78}$Ni and $^{100}$Sn have provided benchmark studies of the nuclear shell model for protons in the $\{0f_{5/2}, 1p_{3/2}, 1p_{1/2}, 0g_{9/2}\}$ model space. New Hamiltonians for this model space have recently been obtained based on valence-space in-medium renormalization-group (VS-IMSRG) methods with two- and three-nucleon interactions. The two-body matrix elements (TBME) obtained from these ab-initio methods served as the starting point for singular-value decomposition (SVD) method fits of the TBME to experimental binding energies and excitation energies, resulting in Hamiltonians called p35-i2, p35-i3 and p30-i3. In this paper, magnetic moments, quadrupole moments, $B(M1)$ and $B(E2)$ values obtained with these Hamiltonians are presented and compared to experiment. Results obtained from various Hamiltonians are compared to assess the theoretical uncertainties.