  The interpretation of observations of cooling neutron star crusts in
quasi-persistent 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 mass number $A=61$ 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
$^{61}$V. This work reports the first experimental determination of this
transition strength, a ground-state branching of 8.1$^{+2.2}_{-2.0} \%$,
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.
