Mass measurements of As, Se, and Br nuclei, and their implication on the proton-neutron interaction strength toward the $N=Z$ line

Mass measurements of the nuclides ${}^{69}\mathrm{As},{}^{70,71}\mathrm{Se}$, and ${}^{71}\mathrm{Br}$, produced via fragmentation of a ${}^{124}\mathrm{Xe}$ primary beam at the Fragment Separator (FRS) at GSI, have been performed with the multiple-reflection time-of-flight mass spectrometer (MR-TOF-MS) of the FRS Ion Catcher with an unprecedented mass resolving power of almost $1000000$. Such high resolving power is the only way to achieve accurate results and resolve overlapping peaks of short-lived exotic nuclei, whose total number of accumulated events is always limited. For the nuclide ${}^{69}\mathrm{As}$, this is the first direct mass measurement. A mass uncertainty of 22 keV was achieved with only ten events. For the nuclide ${}^{70}\mathrm{Se}$, a mass uncertainty of 2.6 keV was obtained, corresponding to a relative accuracy of $\delta m/m=4.0\times {10}^{-8}$, with less than 500 events. The masses of the nuclides ${}^{71}\mathrm{Se}$ and ${}^{71}\mathrm{Br}$ have been measured with an uncertainty of 23 and 16 keV, respectively. Our results for the nuclides ${}^{70,71}\mathrm{Se}$ and ${}^{71}\mathrm{Br}$ are in good agreement with the 2016 Atomic Mass Evaluation, and our result for the nuclide ${}^{69}\mathrm{As}$ resolves the discrepancy between the previous indirect measurements. We measured also the mass of the molecule ${}^{14}\mathrm{N}{}^{15}\mathrm{N}{}^{40}\mathrm{Ar}$ ($A=69$) with a relative accuracy of $\delta m/m=1.7\times {10}^{-8}$, the highest yet achieved with an MR-TOF-MS. Our results show that the measured restrengthening of the proton-neutron interaction ($\delta V_{pn}$) for odd-odd nuclei along the $N=Z$ line above $Z=29$ (recently extended to $Z=37$) is hardly evident at the $N-Z=2$ line, and not evident at the $N-Z=4$ line. Nevertheless, detailed structure of $\delta V_{pn}$ along the $N-Z=2$ and $N-Z=4$ lines, confirmed by our mass measurements, may provide a hint regarding the ongoing $\approx 500$ keV discrepancy in the mass value of the nuclide ${}^{70}\mathrm{Br}$, which prevents including it in the world average of $Ft$ value for superallowed $0^{+}\to 0^{+} \beta$ decays. The reported work sets the stage for mass measurements with the FRS Ion Catcher of nuclei at and beyond the $N=Z$ line in the same region of the nuclear chart, including the nuclide ${}^{70}\mathrm{Br}$.

Figure 1

Proton-neutron interaction strength as a function of $Z$ for odd-odd $N=Z$ nuclei from the nuclide ${}^{58}\mathrm{Cu}$ to the nuclide ${}^{74}\mathrm{Rb}$. Black points are experimental data or AME16 [23] evaluations based on experimental data. The red point for the nuclide ${}^{74}\mathrm{Rb}$ is the AME16 evaluation based on systematics. $\text{Hoff}\_20$ refers to [22] and $\text{Davids}\_80$ refers to [10].

Figure 2

Left panel: Measured mass-to-charge ratio spectrum of singly charged ${}^{69}\mathrm{As}$ nuclides. The square points represent the histogram of the unbinned data, which is shown as well in the lower part of the plot. A hyper-EMG function with two exponentials on the left side and one exponential on the right side [hyper-EMG(2,1)] with a FWHM of 74 keV (mass resolving power of 870 000 FWHM) was used for fitting the un-binned data (‘rug’ graph below the histogram), the shape parameters of which were obtained from the calibrant data (red line). Right panel: Same as on the left, for the nuclide ${}^{70}\mathrm{Se}$, showing the results after the wMLE fit of a hyper-EMG(2,1) with a FWHM of 67 keV (mass resolving power of 970 000 FWHM) to a set of data containing 256 counts of the nuclide ${}^{70}\mathrm{Se}$.

Figure 3

Deviation of the measured mass-excess of this work (see Table 1), denoted by ‘FRS-IC’, and previous ones from the values given in AME16 [23]. [70Bo19] refers to [43], [77Ma22_1] and [77Ma22_2] refer to [44], which includes the published endpoint energies of the decays ${}^{69}\mathrm{As}(\beta +){}^{69}\mathrm{Ge}$ and ${}^{69}\mathrm{Se}(\beta +){}^{69}\mathrm{As}$, respectively, [98CH20] refers to [47], [01HA66] refers to [49], [02LI24] refers to [46], [09SA12] refers to [9], and [11HE10] refers to [48]. The gray band around the horizontal axis represents the AME16 uncertainty. Breaks in the $y$ axis with different scale widths are included in order to be able to see high-accuracy data as well as low-accuracy data. Note that if one of the borders of the error bar is out of the displayed region, then it is not shown.

Figure 4

Proton-neutron interaction strength as a function of $Z$ for odd-odd $N-Z=2$ and $N-Z=4$ nuclei from Cu isotopes to Rb isotopes. Solid symbols are experimental data or AME16 evaluations [23] based on experimental data. The open symbols for $\delta V_{pn}(N-Z=4$) of the As isotope are values based on the previous indirect mass measurements of the nuclide ${}^{69}\mathrm{As}$. [70Bo19] refers to [43], [77Ma22_1] and [77Ma22_2] refer to [44] that includes the published endpoint energies of the decays ${}^{69}\mathrm{As}\left({\beta }^{+}\right){}^{69}\mathrm{Ge}$ and ${}^{69}\mathrm{Se}\left({\beta }^{+}\right){}^{69}\mathrm{As}$, respectively. nuclide symbols near the points show the values which the measurement of this work had an impact on (the nuclide ${}^{69}\mathrm{As}$) or confirmed (the nuclides ${}^{70,71}\mathrm{Se},{}^{71}\mathrm{Br}$). Dotted lines are shown to guide the eye between $\delta V_{pn}$ points of the same $N\text{−}Z$ value.