$\beta$ Decay of ${}^{61}\mathrm{V}$ and its Role in Cooling Accreted Neutron Star Crusts

The interpretation of observations of cooling neutron star crusts in quasipersistent x-ray transients is affected by predictions of the strength of neutrino cooling via crust Urca processes. The strength of crust Urca neutrino cooling depends sensitively on the electron-capture and $\beta$-decay ground-state-to-ground-state transition strengths of neutron-rich rare isotopes. Nuclei with a mass number of $A=61$ are predicted to be among the most abundant in accreted crusts, and the last remaining experimentally undetermined ground-state-to-ground-state transition strength was the $\beta$ decay of ${}^{61}\mathrm{V}$. This Letter reports the first experimental determination of this transition strength, a ground-state branching of ${8.1}_{-3.1}^{+4.0}\%$, corresponding to a log $ft$ value of ${5.5}_{-0.2}^{+0.2}$. This result was achieved through the measurement of the $\beta$-delayed $\gamma$ rays using the total absorption spectrometer SuN and the measurement of the $\beta$-delayed neutron branch using the neutron long counter system NERO at the National Superconducting Cyclotron Laboratory at Michigan State University. This method helps to mitigate the impact of the pandemonium effect in extremely neutron-rich nuclei on experimental results. The result implies that $A=61$ nuclei do not provide the strongest cooling in accreted neutron star crusts as expected by some predictions, but that their cooling is still larger compared to most other mass numbers. Only nuclei with mass numbers 31, 33, and 55 are predicted to be cooling more strongly. However, the theoretical predictions for the transition strengths of these nuclei are not consistently accurate enough to draw conclusions on crust cooling. With the experimental approach developed in this work, all relevant transitions are within reach to be studied in the future.

Figure 1

Experimental (black) and fitted (red) total absorption spectrum (top), singles spectrum (bottom), and multiplicity distribution of the detector segment (inset). The $1\text{−}\sigma$ error band of the fit is shown in blue. The high-energy tail in the total absorption spectrum is due to a combination of the high-energy $\beta$ particles from low-energy entry states entering SuN and $\gamma$-decay cascades from high-energy entry states.

Figure 2

$B$ (GT) strength for the $\beta$ decay of ${}^{61}\mathrm{V}$ as a function of excitation energy in the daughter nucleus, deduced from the $\gamma$-ray data from this work (solid black line) and predicted by QRPA-fy (red, dashed line). Note that $\gamma$-ray data can only provide the strength function up to the neutron separation energy of 3.9 MeV.

Figure 3

The neutrino cooling contribution from individual mass chains for a neutron star crust made from rp-process ashes [14]. Predictions based on QRPA-fy (blue filled diamonds) are shown for the strongest cooling chains. For $A=61$, we also show the QRPA-fy prediction when assuming the predicted 10 keV daughter state in ${}^{61}\mathrm{Cr}$ populated by the $\beta$ decay of ${}^{61}\mathrm{V}$ is in fact the ground state (red open square, see text for more discussion). The $A=61$ cooling rates based on experimental transition strengths are shown without the contribution from the ${}^{61}\mathrm{Cr}\text{−}{}^{61}\mathrm{V}$ Urca pair Letter (orange circle) and with the new data on ${}^{61}\mathrm{Cr}\text{−}{}^{61}\mathrm{V}$ from this Letter (red error bar). Results shown are for a neutron star radius $R=12\mathrm{km}$ and a temperature $T=0.5$ GK and will scale with $R^2{T}^5$ for different physical parameters.