Masses of neutron-rich ${}^{52-54}$Sc and ${}^{54,56}$Ti nuclides: The $N=32$ subshell closure in scandium

Abstract

Isochronous mass spectrometry has been applied in the storage ring CSRe to measure the masses of the neutron-rich ${}^{52-54}$Sc and ${}^{54,56}$Ti nuclei. The new mass excess values $ME$(${}^{52}$Sc) $=$ $-40525(65)$ keV, $ME$(${}^{53}$Sc) $=$ $-38910(80)$ keV, and $ME$(${}^{54}$Sc) $=$ $-34485(360)$ keV, deviate from the Atomic Mass Evaluation 2012 by 2.3$\ddot{I}ƒ$, 2.8$\ddot{I}ƒ$, and 1.7$\ddot{I}ƒ$, respectively. These large deviations significantly change the systematics of the two-neutron separation energies of scandium isotopes. The empirical shell gap extracted from our new experimental results shows a significant subshell closure at $N=32$ in scandium, with a similar magnitude as in calcium. Moreover, we present $ab$ $initio$ calculations using the valence-space in-medium similarity renormalization group based on two- and three-nucleon interactions from chiral effective field theory. The theoretical results confirm the existence of a substantial $N=32$ shell gap in Sc and Ca with a decreasing trend towards lighter isotones, thus providing a consistent picture of the evolution of the $N=32$ magic number from the $pf$ into the $sd$ shell.

6 pages, 5figures, accepted by Physical Review C