Mass measurements of ${}^{60\text{–}63}\mathrm{Ga}$ reduce x-ray burst model uncertainties and extend the evaluated $T=1$ isobaric multiplet mass equation

We report precision mass measurements of neutron-deficient gallium isotopes approaching the proton drip line. The measurements of ${}^{60\text{–}63}\mathrm{Ga}$ performed with the TITAN multiple-reflection time-of-flight mass spectrometer provide a more than threefold improvement over the current literature mass uncertainty of ${}^{61}\mathrm{Ga}$ and mark the first direct mass measurement of ${}^{60}\mathrm{Ga}$. The improved precision of the ${}^{61}\mathrm{Ga}$ mass has important implications for the astrophysical $rp$ process, as it constrains essential reaction $Q$ values near the ${}^{60}\mathrm{Zn}$ waiting point. Based on calculations with a one-zone model, we demonstrate the impact of the improved mass data on prediction uncertainties of x-ray burst models. The first-time measurement of the ${}^{60}\mathrm{Ga}$ ground-state mass establishes the proton-bound nature of this nuclide, thus constraining the location of the proton drip line along this isotopic chain. Including the measured mass of ${}^{60}\mathrm{Ga}$ further enables us to extend the evaluated $T=1$ isobaric multiplet mass equation up to $A=60$.

Figure 1

Mass spectra acquired at $A=60$ with mass-selective retrapping turned off (top) and on (bottom). The intensities of peaks outside the retrapping TOF gate (gray-shaded area) were suppressed by up to two orders of magnitude, enabling a 50-fold increase of the incoming rare isotope beam intensity and resulting in the observation of the minute ${}^{60}\mathrm{Ga}$ signal. The solid red lines mark maximum-likelihood fits obtained using a hyper-EMG model function [61] with two positive and two negative exponential tails. Colored dashed lines indicate the fit components associated with each peak. For clarity, only for every second bin is the Poisson counting uncertainty indicated by an error bar. The total measurement durations are given in the respective mass spectra.

Figure 2

Mass spectra acquired at $A=61$ with the ionizing laser beam blocked (top) and unblocked (bottom). The laser-induced increase of the relative intensity of the lower mass peak provided additional verification of the gallium peak assignment. For both spectra mass-selective retrapping was used to suppress contaminant peaks outside the shown mass range. The solid red lines mark maximum-likelihood fits obtained using a hyper-EMG model function [61] with two positive and one negative exponential tails. Colored dashed lines indicate the fit components associated with each peak. For clarity, error bars are only shown for every second bin. The total measurement durations are given in the respective mass spectra.

Figure 3

Trend of the proton separation energies along the gallium chain. The inset shows $A=60$ and $A=61$ with expanded ordinate scale. For clarity, the $S_p{(}^{60}\mathrm{Ga})$ values of Mazzocchi et al. [83] and Orrigo et al. [85] are only shown in the inset and were slightly offset horizontally. Due to the small proton separation energies of ${}^{60}\mathrm{Ga}$ and ${}^{61}\mathrm{Ga}$, global mass models (dashed lines), and estimates from systematic trends of experimental CDEs (open circle) or the mass surface (open square) cannot reliably predict the location of the proton drip line. Because of the associated uncertainties, drip line predictions from theoretical CDEs (dotted lines) from FL-MAC-NP [35] and Brown et al. [29] are likewise insufficient. Only precision measurements (dark blue and magenta dots) can establish ${}^{60}\mathrm{Ga}$ to be proton bound and constrain the location of the drip line along this isotopic chain.

Figure 4

Trends of the IMME $b$ and $c$ coefficients for the lowest-lying $T=1$ multiplets in the $pf$ shell. The directly measured mass value for ${}^{60}\mathrm{Ga}$ from this work completes the experimental data on IMME triplets up to $A=60$. The updated experimental coefficients (blue dots) improve on an earlier evaluation [32] (red triangles) and exhibit fair agreement with shell-model predictions obtained with the cdGX1A Hamiltonian (green squares). Unfilled blue circles indicate fit results based on semiempirical input data (see text for details).

Figure 5

Dispersion of predicted x-ray burst light curves resulting from $3\sigma$ variation of the improved ${}^{60\text{–}61}\mathrm{Ga}$ mass data from this work (blue solid lines) in comparison to AME2020 (red dashed lines). The areas between the obtained light curves were filled for clarity. The more precise ${}^{61}\mathrm{Ga}$ mass value significantly constrains the predicted light curve.

Figure 6

Ratio of the two light curves obtained from $3\sigma$ variation of the ${}^{60\text{–}61}\mathrm{Ga}$ mass data (ratio of the envelopes in Fig. 5) from this work (blue solid line) and from AME2020 (red dashed line), respectively. The narrow peaks at 5 and 50 s arise from small discontinuities in the light curves, when the model switches between different opacity descriptions. The new mass data reduces the mass-induced prediction uncertainties in the x-ray burst light curve by more than a factor of 2.