Precision measurement of $^{65}$Zn electron-capture decays with the KDK coincidence setup

$^{65}$Zn is a common calibration source, moreover used as a radioactive tracer in medical and biological studies. In many cases, $\gamma$-spectroscopy is a preferred method of $^{65}$Zn standardization, which relies directly on the branching ratio of $J \pi (^{65}\text{Zn} ) = 5/2^- \rightarrow J \pi (^{65}\text{Cu}) = 5/2^- $ via electron capture (EC*). We measure the relative intensity of this branch to that proceeding directly to the ground state (EC$^0$) using a novel coincidence technique, finding $I_{\text{EC}^0}/I_{\text{EC*}} = 0.9684 \pm 0.0018$. Re-evaluating the decay scheme of $^{65}$Zn by adopting the commonly evaluated branching ratio of $I_{\beta^+}= 1.4271(7)\%$ we obtain $I_{\text{EC*}} = (50.08 \pm 0.06)\%$, and $I_\text{EC^0} = (48.50 \pm 0.06) \%$. The associated 1115 keV gamma intensity agrees with the previously reported NNDC value, and is now accessible with a factor of ~2 increase in precision. Our re-evaluation removes reliance on the deduction of this gamma intensity from numerous measurements, some of which disagree and depend directly on total activity determination. The KDK experimental technique provides a new avenue for verification or updates to the decay scheme of $^{65}$Zn, and is applicable to other isotopes.