New Precision Mass Measurements of Neutron-Rich Calcium and Potassium Isotopes and Three-Nucleon Forces

We present precision Penning trap mass measurements of neutron-rich calcium and potassium isotopes in the vicinity of neutron number $N=32$. Using the TITAN system, the mass of ${}^{51}\mathrm{K}$ was measured for the first time, and the precision of the ${}^{51,52}\mathrm{Ca}$ mass values were improved significantly. The new mass values show a dramatic increase of the binding energy compared to those reported in the atomic mass evaluation. In particular, ${}^{52}\mathrm{Ca}$ is more bound by 1.74 MeV, and the behavior with neutron number deviates substantially from the tabulated values. An increased binding was predicted recently based on calculations that include three-nucleon (3N) forces. We present a comparison to improved calculations, which agree remarkably with the evolution of masses with neutron number, making neutron-rich calcium isotopes an exciting region to probe 3N forces.

Figure 1

TOF-ICR resonances for ${}^{51}\mathrm{K}$, ${}^{51}\mathrm{Ca}$, and ${}^{52}\mathrm{Ca}$ with excitation times of $\approx 80\mathrm{ms}$. The applied radio frequency ${\nu }_{\mathrm{RF}}$ is given as the difference from the center frequency ${\nu }_{\mathrm{cent}}$ of the scan range. The solid lines are theoretical fits to the line shape [21].

Figure 2

Two-neutron separation energy $S_{2n}$ as a function of neutron number $N$ for the potassium (circles), calcium (square), and scandium (triangles) isotopic chains. Points enclosed by a circle are not based completely on experimental values in AME2003. The symbols connected by a dotted line are based on the TITAN mass values (mass values for ${}^{49,50}\mathrm{Ca}$ and ${}^{47–50}\mathrm{K}$ are taken from Ref. 19), while the symbols connected by solid lines are those from the AME2003.

Figure 3

Two-neutron separation energy $S_{2n}$ (top) and pairing gap ${\Delta }_n^{(3)}$ from three-point binding-energy differences (bottom) versus neutron number $N$ for the calcium isotopes. The TITAN mass values and the AME2003 values are shown by the symbols as in Fig. 2. The point labeled “$\mathrm{TITAN}+\mathrm{AME}2003$” is based partly on the TITAN mass values and complemented by the AME2003 value for ${}^{53}\mathrm{Ca}$. Theoretical predictions are shown based on chiral NN and 3N forces ($\mathrm{NN}+3\mathrm{N}$) in the extended $pf{g}_{9/2}$ valence space using empirical (emp) SPEs in ${}^{41}\mathrm{Ca}$ and consistently calculated MBPT SPEs (MBPT). For comparison, we also show results based on the $pf$-shell phenomenological KB3G [3] and GXPF1A [5] interactions, which have been fitted to spectra and gaps (KB3G) or spectra and masses (GXPF1A).