Mass Measurement of Upper $fp$-Shell $N=Z-2$ and $N=Z-1$ Nuclei and the Importance of Three-Nucleon Force along the $N=Z$ Line

Using a novel method of isochronous mass spectrometry, the masses of ${}^{62}\mathrm{Ge}$, ${}^{64}\mathrm{As}$, ${}^{66}\mathrm{Se}$, and ${}^{70}\mathrm{Kr}$ are measured for the first time, and the masses of ${}^{58}\mathrm{Zn}$, ${}^{61}\mathrm{Ga}$, ${}^{63}\mathrm{Ge}$, ${}^{65}\mathrm{As}$, ${}^{67}\mathrm{Se}$, ${}^{71}\mathrm{Kr}$, and ${}^{75}\mathrm{Sr}$ are redetermined with improved accuracy. The new masses allow us to derive residual proton-neutron interactions ($\delta V_{pn}$) in the $N=Z$ nuclei, which are found to decrease (increase) with increasing mass $A$ for even-even (odd-odd) nuclei beyond $Z=28$. This bifurcation of $\delta V_{pn}$ cannot be reproduced by the available mass models, nor is it consistent with expectations of a pseudo-SU(4) symmetry restoration in the $fp$ shell. We performed ab initio calculations with a chiral three-nucleon force (3NF) included, which indicate the enhancement of the $T=1$ $pn$ pairing over the $T=0$ $pn$ pairing in this mass region, leading to the opposite evolving trends of $\delta V_{pn}$ in even-even and odd-odd nuclei.

Figure 1

Part of the $m/q$ spectrum (a) and the corresponding scatter plot of $U$ versus $m/q$ (b). The spectrum is enlarged in the region of $m/q=1.889–1.975\mathrm{u}/\mathrm{e}$. The ion species are also indicated. Note that the unresolved ${{}^{57}\mathrm{Zn}}^{30+}$, ${{}^{62}\mathrm{Ge}}^{32+}$, ${{}^{66}\mathrm{Se}}^{34+}$, and ${{}^{70}\mathrm{Kr}}^{36+}$ in the $m/q$ spectrum are completely separated from ${{}^{38}\mathrm{Ca}}^{20+}$, ${{}^{31}\mathrm{S}}^{16+}$, ${{}^{37}\mathrm{Cl}}^{17+}$, and ${{}^{35}\mathrm{Ar}}^{18+}$, respectively, in the plot of $U$ versus $m/q$.

Figure 2

Experimental $\delta V_{pn}$ for $N=Z$ nuclei beyond $A=56$ and comparison to different mass model predictions [41, 42, 43, 44, 45, 46, 47, 48, 49]. Red lines are to guide the eye. Red symbols indicate that one of the masses given in Table 1 was used. $\delta V_{pn}$ of ${}^{58}\mathrm{Cu}$ using the binding energy of the $T=1$, $J^{\pi }=0^{+}$ excited state [33] is marked with open diamond. $\mathrm{ME}({}^{70}\mathrm{Br})=-52030(80)\mathrm{keV}$ is taken from [50, 51]. $\delta V_{pn}$ values obtained by using the extrapolated masses in AME’20 [33, 38] are connected by the black solid line.

Figure 3

Experimental $\delta V_{pn}$ for (a) $N=Z$ and (b) $N=Z+2$ nuclei beyond $A=56$ and comparison with the ab initio calculations. Data uncertainties are within the size of the symbols. $\delta V_{pn}$ values from ab initio calculations using $2\mathrm{NF}+3\mathrm{NF}$ and 2NF only are plotted as red and blue lines (solid lines for even-even and dashed lines for odd-odd), respectively.