A new study of the $N=32$ and $N=34$ shell gap for Ti and V by the first high-precision MRTOF mass measurements at BigRIPS-SLOWRI

Abstract

The atomic masses of $^{55}$Sc, $^{56,58}$Ti, and $^{56-59}$V have been determined using the high-precision multi-reflection time-of-flight technique. The radioisotopes have been produced at RIKEN's RIBF facility and delivered to the novel designed gas cell and multi-reflection system (ZD MRTOF), which has been recently commissioned downstream of the ZeroDegree spectrometer following the BigRIPS separator. For $^{56,58}$Ti and $^{56-59}$V the mass uncertainties have been reduced down to the order of $10\,\mathrm{keV}$, shedding new light on the $N=34$ shell effect in Ti and V isotopes by the first high-precision mass measurements of the critical species $^{58}$Ti and $^{59}$V. With the new precision achieved, we reveal the non-existence of the $N=34$ empirical two-neutron shell gaps for Ti and V, and the enhanced energy gap above the occupied $\nu p_{3/2}$ orbit is identified as a feature unique to Ca. We perform new Monte Carlo shell model calculations including the $\nu d_{5/2}$ and $\nu g_{9/2}$ orbits and compare the results with conventional shell model calculations, which exclude the $\nu g_{9/2}$ and the $\nu d_{5/2}$ orbits. The comparison indicates that the shell gap reduction in Ti is related to a partial occupation of the higher orbitals for the outer two valence neutrons at $N=34$.