Searching for $0^{+}$ states in ${}^{50}\mathrm{Cr}$: Implications for the superallowed $\beta$ decay of ${}^{50}\mathrm{Mn}$

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 $E_x=3895.0\left(5\right)$ keV in ${}^{50}\mathrm{Cr}$. This reassignment directly impacts direct searches for a nonanalog Fermi ${\beta }^{+}$ 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.

Figure 1

A comparison of the fresco calculated $L=0$ angular distributions (red curve) using shell-model generated two-nucleon amplitude files, to the experimental data for (a) the ground state, and excited states at (b) 3895.0(5) keV and (c) 4068.8(5) keV. Experimental errors are shown, however in most cases they are smaller than the data points. The curves are normalized to the data to provide a better shape comparison for the identification of the $0^{+}$ states. The inset in each panel shows the triton energy spectrum at ${10}^{\circ }$ for transfer to the respective states.

Figure 2

Experimental angular distributions for the observed levels at (a) 3697.9(6) keV, (b) 4368(3) keV, and (c) 4733(5) keV, shown with DWBA predictions for $L=0$ transfers (blue dashed line) and the $L$ transfer recommended from this work (red line). Experimental errors are shown, however in most cases they are smaller than the data points. Above each angular distribution panel is the triton energy spectrum at ${\theta }_{\mathrm{Q}3\mathrm{D}}={10}^{\circ }$ for the region of interest.

Figure 3

A comparison of the $0^{+}$ state excitation energies in ${}^{50}\mathrm{Cr}$ from (a) the evaluated data in Ref. [31], (b) this work, and shell-model calculations using (c) the GXPF1A interaction [28], (d) a modified GXPF1 interaction [36] (see text), and (e) ab-initio IM-SRG [48] (see text).

Figure 4

A partial schematic of the ${\beta }^{+}/\mathrm{EC}$ decay scheme for ${}^{50}\mathrm{Mn}$. The two lowest-lying $0^{+}$ states in ${}^{50}\mathrm{Cr}$ presented in this work indicate that nonanalog Fermi ${\beta }^{+}$ decay branches (red dashed) to these states would emit characteristic $E2\gamma$ rays at $E_{\gamma }=3111.7\left(5\right)$ and 3285.5(5) keV (green dot-dashed).