Constraining the trend of the $N = 50$ shell gap towards $^{100}$Sn with the masses of $^{96-98}$Cd

Abstract

We present the first determination of the $N = 50$ empirical shell gap at $Z = 48$ by precise mass measurements of the neutron-deficient cadmium isotopes $^{96-98}$Cd with the ISOLTRAP mass spectrometer at ISOLDE-CERN, including the first precise determination of the excitation energy of the $25/2^+$ isomer in $^{97}$Cd. Through the systematics of Coulomb Displacement Energies, we further deduce the empirical shell gap in the higher-$Z$ isotopic chains, tightly constraining the $^{100}$Sn mass-surface region. The new experimental data suggest an enhancement of the gap towards $^{100}$Sn, which is discussed in comparison to state-of-the-art calculations using energy-density functional and new ab initio approaches.