High-resolution ($p,t$) reaction measurements as spectroscopic tests of ab-initio theory in the mid-$pf$ shell

Detailed spectroscopic measurements of excited states in ${}^{50}\mathrm{Cr}$ and ${}^{62}\mathrm{Zn}$ were performed using 24-MeV $(p,t)$ transfer reactions on ${}^{52}\mathrm{Cr}$ and ${}^{64}\mathrm{Zn}$, respectively. In total, 45 states in ${}^{50}\mathrm{Cr}$ and 67 states in ${}^{62}\mathrm{Zn}$ were observed up to excitation energies of 5.5 MeV, including several previously unobserved states. These experimental results are compared to ab-initio shell-model calculations using chiral effective field theory with the valence-space in-medium similarity renormalization group method. This comparison demonstrates good agreement in the level orderings with these new theoretical methods, albeit with a slight overbinding in the calculations. This work is part of a continued push to benchmark ab-initio theoretical techniques to nuclear-structure data in $0^{+}\to 0^{+}$ superallowed Fermi $\beta$-decay systems.

Figure 1

Spectrum of observed states in ${}^{50}\mathrm{Cr}$ at ${\theta }_{\mathrm{lab}}={10}^{\circ }$ resulting from 24-MeV protons on $>99\%{}^{52}\mathrm{Cr}$. Experimental limitations required states from 2.8 to 3.4 MeV to be shown at ${\theta }_{\mathrm{lab}}={50}^{\circ }$. To appropriately show the individual level detail, two inset panels are expanded on the regions from 2800–4100 keV (top inset) and 4100–5600 keV (bottom inset). The wide features at $\sim 2.9$ and 4.5 MeV are the result of $(p,t)$ reactions on a light impurity within the target.

Figure 2

Spectrum of observed states in ${}^{62}\mathrm{Zn}$ at ${\theta }_{\mathrm{lab}}={15}^{\circ }$ resulting from 24-MeV protons on $>99\%{}^{64}\mathrm{Zn}$. Experimental limitations required states from 3.4 to 3.9 MeV to be shown at ${\theta }_{\mathrm{lab}}={20}^{\circ }$ and states from 4.4 to 4.9 MeV to be shown at ${\theta }_{\mathrm{lab}}={25}^{\circ }$. To appropriately show the individual level detail, two inset panels are expanded on the regions from 1800–3900 keV (top inset) and 3900–5600 keV (bottom inset). The wide feature at $\sim 2.8$ MeV is the result of a $(p,t)$ reaction on a light impurity within the target.

Figure 3

Comparison of several global OMP sets with experimental data, for (left and middle panels) 24-MeV proton elastic scattering from ${}^{52}\mathrm{Cr}$ and ${}^{64}\mathrm{Zn}$. The right panel includes a comparison of 12-MeV triton scattering off ${}^{57}\mathrm{Fe}(t,t)$ data from Ref. [17], which are the energies closest to those needed for this work. All of the examined sets effectively reproduce the observed data; however, the sets of Varner et al. [18] and Li, Liang, and Cai [19] were chosen as the optimal sets for protons and tritons, respectively. The DWBA calculated curves obtained using the optimal sets are shown in black.

Figure 4

Experimental angular distributions for all (a) $0^{+}$ states and (b) $2^{+}$ states observed in ${}^{50}\mathrm{Cr}$. The dashed lines for states at 2924 and 3161 keV indicate DWBA calculations performed using the known spin and parity from the evaluated data (not assigned from this work) and are shown for reference. All energies listed are in keV.

Figure 5

Experimental angular distributions for all (a) $4^{+}$, (b) $6^{+}$, (c) $1^{-}$, (d) $3^{-}$, and (e) $5^{-}$ states observed in ${}^{50}\mathrm{Cr}$. The dashed line for the 3324-keV state indicates a DWBA calculation performed using the known spin and parity from the evaluated data (not assigned from this work) and is shown for reference. The dashed line for the 4052-keV state results from the DWBA calculation for a $2^{+}$ state, shown against the assigned $3^{-}$ state calculation for comparison. All energies listed are in keV.

Figure 6

Experimental angular distributions for all observed (a) $0^{+}$ states and (b) $2^{+}$ states observed in ${}^{62}\mathrm{Zn}$. All energies listed are in keV.

Figure 7

Experimental angular distributions for all (a) $4^{+}$, (b) $6^{+}$, (c) $1^{-}$, (d) $3^{-}$, and (e) $5^{-}$ states observed in ${}^{62}\mathrm{Zn}$. All energies listed are in keV.

Figure 8

Experimental angular distributions for the six strongest unassigned states in (a) ${}^{50}\mathrm{Cr}$ and (b) ${}^{62}\mathrm{Zn}$. The relatively flat angular distributions likely result from a multistep transfer of the two neutrons which removes the detail of the final-state nuclear structure. All energies listed are in keV.

Figure 9

Comparison of the experimental $0^{+}$ (black), $2^{+}$ (blue), $4^{+}$ (red), and $6^{+}$ (green) states to the VS-IMSRG theoretical calculations for both ${}^{50}\mathrm{Cr}$ (left panel) and ${}^{62}\mathrm{Zn}$ (right panel). Only the $2_1^{+}$ state in ${}^{62}\mathrm{Zn}$ has a connection line between experiment and theory to provide better clarity of the figure.