A Search for $0^+$ States in $^{50}$Cr: Implications for the Superallowed $\beta$-decay of $^{50}$Mn

TL;DR

This study used a two-neutron pickup reaction to investigate excited states in $^{50}$Cr, leading to a reassignment of the first excited $0^+$ state and providing insights relevant to superallowed $eta$-decay in $^{50}$Mn.

Contribution

It provides the first experimental reassignment of the $0^+_2$ state in $^{50}$Cr and compares results with advanced theoretical models, improving understanding of nuclear structure and decay.

Findings

No evidence of the previously assigned $0^+_2$ state was found.

Reassigned $0^+_2$ state at 3895.0 keV in $^{50}$Cr.

Results align better with theoretical predictions for $0^+$ states.

Abstract

A $^{52}$Cr$(p,t)$$^{50}$Cr two-neutron pickup reaction was performed using the Q3D magnetic spectrograph at the Maier-Leibnitz-Laboratorium in Garching, Germany. Excited states in $^{50}$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 $^{50}$Cr. This reassignment directly impacts direct searches for a non-analogue Fermi $\beta^+$ decay branch in $^{50}$Mn. These results also show better systematic agreement with the theoretical predictions for the $0^+$ state spectrum in $^{50}$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.