Searching for 0 + states in Cr 50 : Implications for the superallowed β decay of Mn 50

A $^{52}\mathrm{Cr}(p,t)^{50}\mathrm{Cr}$ two-neutron pickup reaction was performed using the Q3D magnetic spectrograph at the Maier-Leibnitz-Laboratorium in Garching, Germany. Excited states in $^{50}\mathrm{Cr}$ were observed up to an excitation energy of 5.3 MeV. Despite significantly increased sensitivity and resolution over previous work, no evidence of the previously assigned first excited ${0}^{+}$ state was found. As a result, the ${0}_{2}^{+}$ state is reassigned at an excitation energy of ${E}_{x}=3895.0(5)$ keV in $^{50}\mathrm{Cr}$. This reassignment directly impacts direct searches for a nonanalog Fermi ${\ensuremath{\beta}}^{+}$ decay branch in $^{50}\mathrm{Mn}$. These results also show better systematic agreement with the theoretical predictions for the ${0}^{+}$ state spectrum in $^{50}\mathrm{Cr}$ using the same formalism as the isospin-symmetry-breaking correction calculations for superallowed nuclei. The experimental data are also compared to ab-initio shell-model predictions using the IM-SRG formalism based on $NN$ and $3N$ forces from chiral-EFT in the $pf$-shell for the first time.