Experimental ${}^{64}$Zn($\vec{d},t$)${}^{63}$Zn spectroscopic factors: Guidance for isospin-symmetry-breaking calculations

With the recent inclusion of core orbitals to the radial-overlap component of the isospin-symmetry-breaking (ISB) corrections for superallowed Fermi $\beta$ decay, experimental data are needed to test the validity of the theoretical model. This work reports measurements of single-neutron pickup reaction spectroscopic factors into ${}^{63}$Zn, one neutron away from ${}^{62}$Zn, the superallowed daughter of ${}^{62}$Ga. The experiment was performed using a 22-MeV polarized deuteron beam, a Q3D magnetic spectrograph, and a cathode-strip focal-plane detector to analyze outgoing tritons at nine angles between ${10}^{\circ }$ and ${60}^{\circ }$. Angular distributions and vector analyzing powers were obtained for all 162 observed states in ${}^{63}$Zn, including 125 newly observed levels, up to an excitation energy of 4.8 MeV. Spectroscopic factors are extracted and compared to several shell-model predictions, and implications for the ISB calculations are discussed.

Figure 1

A nucleus-by-nucleus comparison of the theoretical corrections in Eq. (1). The two ${\delta }_{C2}$ values for each case arise from the Woods-Saxon (WS) and Hartree-Fock (HF) treatment of the radial wave functions in the radial-overlap part of the ISB correction. The values included are taken from Refs. [1, 3].

Figure 2

Complete spectrum of observed tritons in this experiment at ${\theta }_{\mathrm{lab}}={30}^{\circ }$ resulting from 22-MeV “up” polarized deuterons on $99.3\left(1\right)\%$ ${}^{64}$Zn. Experimental limitations required states from 3.8 to 4.8 MeV to be shown at ${\theta }_{\mathrm{lab}}={25}^{\circ }$. In order to appropriately show the individual level detail, two inset panels are expanded on the regions of (i) 100–2580 keV and (ii) 2580–4800 keV, respectively. The wide feature at $\sim$4.1–4.3 MeV is the result of observing tritons from a ($\vec{d},t$) reaction on oxygen or carbon in the target. The two peaks shown within the red box near 1.6 MeV result from ($\vec{d},t$) transfer from a similar mass impurity within the target, as discussed in the text, and thus are not states in ${}^{63}$Zn.

Figure 3

Comparison of several global triton and deuteron OMP sets to experimental elastic scattering data of 22-MeV deuterons on ${}^{64}$Zn (left) and 12-MeV tritons on ${}^{57}$Fe($t,t$) [32] (right). All of the global OMP sets presented provide reasonable reproduction of the data; however, the optimal sets were determined to be those of An and Cai [30] and Li, Liang, and Cai [33] for deuterons and tritons, respectively. Experimental errors are shown; however, in most cases, they are smaller than the data points.

Figure 4

Angular distributions and vector analyzing powers for states populated in ${}^{63}$Zn from 0.0 to 1.7 MeV. The curves are a result of DWBA calculations, described in the text, for the various $j^{\pi }$ transfers indicated. The states with known $I^{\pi }=5/2^{-}$ are shown with the $J=5/2$ curves, despite the generally poor agreement with the vector analyzing power data. For the doublet at 1064 keV, the dashed curves represent the respective $L=1$ and $L=3$ components of the angular distribution, and the solid line shows the total. The 1435-keV state is shown with no curves, since the population of this $9/2^{-}$ state cannot be described by the one-step DWBA calculations for this reaction. Broad peaks in the spectrum at 1.6–1.9 MeV caused by light target impurities result in missing cross-section data for these states from ${10}^{\circ }$ to ${25}^{\circ }$. The state at 1435 keV is evaluated as a $9/2^{-}$ state in Ref. [25]. Other states of this nature were observed in this work and are described further in Sec. 4a.

Figure 5

Angular distributions and vector analyzing powers for states populated in ${}^{63}$Zn from 1.7 to 2.4 MeV. For some levels, ${10}^{\circ }$ data are not present due to large backgrounds caused by scattered beams within the target chamber. For states where multiple $L$ transfers are able to describe the data, both $L=1$ (red) and $L=3$ (green) DWBA calculations are shown. The state at 1978 keV is suggested here as populated in an $L=4$ (black) transfer; however, the $L=3$ (green) curve is also displayed with the data, for comparison.

Figure 6

Angular distributions and vector analyzing powers for states populated in ${}^{63}$Zn from 2.4 to 2.8 MeV. For states where multiple $L$ transfers are able to describe the data, both $L=1$ (red) and $L=3$ (green) DWBA calculations are shown. The strongly populated state at 2635 keV represents the single largest source of $1f_{7/2}$ strength of all the states observed in this work.

Figure 7

Angular distributions and vector analyzing powers for states populated in ${}^{63}$Zn from 2.9 to 3.1 MeV. For states where multiple $L$ transfers are able to describe the data, $L=1$ (red), $L=3$ (green), and $L=4$ (blue) DWBA calculations are shown.

Figure 8

Angular distributions and vector analyzing powers for states populated in ${}^{63}$Zn from 3.1 to 3.4 MeV. For states where multiple $L$ transfers are able to describe the data, both $L=1$ (red) and $L=3$ (green) DWBA calculations are shown.

Figure 9

Angular distributions and vector analyzing powers for states populated in ${}^{63}$Zn from 3.4 to 3.7 MeV.

Figure 10

Angular distributions and vector analyzing powers for states populated in ${}^{63}$Zn from 3.8 to 3.9 MeV.

Figure 11

Angular distributions and vector analyzing powers for states populated in ${}^{63}$Zn from 3.9 to 4.2 MeV.

Figure 12

Angular distributions and vector analyzing powers for states populated in ${}^{63}$Zn from 4.2 to 4.4 MeV. For states where multiple $L$ transfers are able to describe the data, both $L=3$ (green) and $L=4$ (blue) DWBA calculations are shown.

Figure 13

Angular distributions and vector analyzing powers for states populated in ${}^{63}$Zn from 4.4 to 4.6 MeV.

Figure 14

Angular distributions and vector analyzing powers for states populated in ${}^{63}$Zn from 4.6 to 4.8 MeV.

Figure 15

Experimental spectroscopic factors on a level-by-level basis for states populated via $J=1/2$, $3/2$, $5/2$, $7/2$, and $9/2$ transfers. Due to the concentration of $3/2$ and $5/2$ strength below 200 keV, the remaining region to 5 MeV is expanded in the two insets to show the fragmented strength distribution of weakly populated states. The summed single-particle strength for each orbital is shown in the inset, where the uncertainties quoted include the $30\%$ model-dependent systematic.

Figure 16

The multistep population process for (a) $9/2^{-}$ and (b) $11/2^{-}$ states observed in this experiment. The arrows show the observed $\gamma$-decay paths that are listed in the evaluated data from Ref. [25]. Where known, $B\left(E2\right)$ values are given for the respective transitions in Weisskopf units (W.u.); otherwise relative $\gamma$-ray intensities, $I_{\gamma }$, are listed. These values, for all ten decay paths, are taken from the evaluated data [25].

Figure 17

A running-sum comparison of the spectroscopic strengths measured here to the shell-model calculations described in Sec. 5. Each panel shows the accumulated spectroscopic strength as a function of ${}^{63}$Zn excitation energy for the five respective orbitals. The $1f_{7/2}$ orbital was not included in the TH02-MSDI3 shell-model calculation, and thus it is not present in the above panel. None of the shell-model calculations include the possibility for excitation of particles from the $1g_{9/2}$ orbital; therefore only the experimental data are shown. It should also be noted that the experimental curves represent a lower limit prediction, since only levels where definite $J$ values could be determined are included.