Perturbed angular distributions with ${\mathrm{LaBr}}_3$ detectors: The $g$ factor of the first ${10}^{+}$ state in ${}^{110}\mathrm{Cd}$ reexamined

The time differential perturbed angular distribution technique with ${\mathrm{LaBr}}_3$ detectors has been applied to the $I^{\pi }={\frac{11}{2}}^{-}$ isomeric state ($E_x=846$ keV, $\tau =107$ ns) in ${}^{107}\mathrm{Cd}$, which was populated and recoil-implanted into a gadolinium host following the ${}^{98}\mathrm{Mo}$(${}^{12}\mathrm{C}$, $3n$)${}^{107}\mathrm{Cd}$ reaction. The static hyperfine field strength of Cd recoil implanted into gadolinium was thus measured, together with the fraction of nuclei implanted into field-free sites, under similar conditions as pertained for a previous implantation perturbed angular distribution $g$-factor measurement on the $I^{\pi }={10}^{+}$ state in ${}^{110}\mathrm{Cd}$. The ${}^{110}\mathrm{Cd}g\left({10}^{+}\right)$ value was thereby reevaluated, bringing it into agreement with the value expected for a seniority-two $\nu h_{11/2}$ configuration.

Figure 1

Partial level scheme of ${}^{107}\mathrm{Cd}$, showing the $11/2^{-}$ isomer of interest as well as the higher feeding $21/2^{+}$ isomer, and transitions for which the angular distributions were measured.

Figure 2

Excitation function for $\gamma$-ray energies from different channels for ${}^{12}\mathrm{C}$ beams on a ${}^{98}\mathrm{Mo}$ target with fits to guide the eye.

Figure 3

Out-of-beam $\gamma$-ray energy spectra recorded by (a) HPGe and (b) ${\mathrm{LaBr}}_3$ detectors following reactions of 48-MeV ${}^{12}\mathrm{C}$ on ${}^{98}\mathrm{Mo}$. The inset in (b) shows the region around the 640-keV transition of interest and indicates the peak and background regions used to project the time spectra in Fig. 4.

Figure 4

Time spectra for the 640-keV transition depopulating the $I^{\pi }={\frac{11}{2}}^{-}$ isomer in ${}^{107}\mathrm{Cd}$. (a) Group $N_1$ defined in Eq. (2), (b) group $N_2$ defined in Eq. (3). Fits to guide the eye show the oscillations in the two groups out of phase. The prompt peak is due to a prompt 632-keV transition in ${}^{106}\mathrm{Cd}$ which cannot be resolved from the 640-keV line by the ${\mathrm{LaBr}}_3$ detectors.

Figure 5

Angular distribution of the (a) 798-keV and (b) 956-keV transitions in ${}^{107}\mathrm{Cd}$ after population by the ${}^{98}\mathrm{Mo}$(${}^{12}\mathrm{C}$, $3n$) reaction. These stretched $E2$ transitions both feed the 846-keV isomer of interest and give a good indication of its spin alignment.

Figure 6

Ratio functions for ${}^{107}\mathrm{Cd}$ in gadolinium. (a)–(d) correspond to data sets I–IV in Table 1 and in the text. Data sets are arranged in order of collection. The missing data near $t=0$ is on account of only using data well away from the (contaminant) prompt peak.

Figure 7

Simulation of (a) $G_{22}\left(t\right)$ and (b) $R\left(t\right)$ from combined magnetic and electric interactions for the $I^{\pi }={\frac{5}{2}}^{+}$ state in ${}^{111}\mathrm{Cd}$ ($E_x=254$ keV, $\tau =121.9$ ns) in gadolinium. If the form of Eq. (6) is assumed for $R\left(t\right)$, $\kappa \approx 61$ ns. The $G_{22}\left(t\right)$ function corresponds to a polycrystalline source with no external field, whilst the $R\left(t\right)$ function is applicable to the present experiment with a polarizing external field at ${90}^{\circ }$ to the plane of detection.

Figure 8

A simulation analogous to Fig. 7, showing (a) $G_{22}\left(t\right)$ and (b) $R\left(t\right)$ for the $E_x=846$ keV, $I^{\pi }={\frac{11}{2}}^{-}$ ${}^{107}\mathrm{Cd}$ state in gadolinium. The solid line is for $\beta ={30}^{\circ }$, and the dashed for $\beta ={90}^{\circ }$. If the form of Eq. (6) is assumed for $R\left(t\right)$, $\kappa \approx 114$ ns. See also Fig. 7 caption.

Figure 9

Ratio functions from different field distributions: red solid line, Gaussian; blue dashed line, half-Gaussian; green dashed-dotted line, Lorentzian. (a) Fits of the ratio functions to data set II. (b) Field distributions, parameters specified in rows two to four in Table 2.

Figure 10

Fits to perturbed angular distribution data from Ref. [13]. A field distribution formed by taking a weighted average of the parameters extracted from data sets I and II was used (see the first two rows of Table 2). The $g$ factor was varied to obtain the best fit. The blue solid line is the perturbed angular distribution fit, the dotted red line is the unperturbed angular distribution.