Spectroscopy and excited-state $g$ factors in weakly collective ${}^{111}\mathrm{Cd}$: Confronting collective and microscopic models

Background: The even cadmium isotopes near the neutron midshell have long been considered among the best examples of vibrational nuclei. However, the vibrational nature of these nuclei has been questioned based on $E2$ transition rates that are not consistent with vibrational excitations. In the neighboring odd-mass nuclei, the $g$ factors of the low-excitation collective states have been shown to be more consistent with a deformed rotational core than a vibrational core. Moving beyond the comparison of vibrational versus rotational models, recent advances in computational power have made shell-model calculations feasible for Cd isotopes. These calculations may give insights into the emergence and nature of collectivity in the Cd isotopes.

Purpose: To investigate the nature of collective excitations in the $A\approx 100$ region through experimental and theoretical studies of magnetic moments and electromagnetic transitions in ${}^{111}\mathrm{Cd}$.

Method: The spectroscopy of ${}^{111}\mathrm{Cd}$ has been studied following Coulomb excitation. Angular correlation measurements, transient-field $g$-factor measurements and lifetime measurements by the Doppler-broadened line shape method were performed. The structure of the nucleus was explored in relation to particle-vibration versus particle-rotor interpretations. Large-scale shell-model calculations were performed with the SR88MHJM Hamiltonian.

Results: Excited-state $g$ factors have been measured, spin assignments examined, and lifetimes determined. Attention was given to the reported $5/2^{+}$ 753-keV and $3/2^{+}$ 755-keV states. The $3/2^{+}$ 755-keV level was not observed; evidence is presented that the reported $3/2^{+}$ state was a misidentification of the $5/2^{+}$ 753-keV state.

Conclusions: It is shown that the $g$ factors and level structure of ${}^{111}\mathrm{Cd}$ are not readily explained by the particle-vibration model. A particle-rotor approach has both successes and limitations. The shell-model approach successfully reproduces much of the known low-excitation structure in ${}^{111}\mathrm{Cd}$.

Figure 1

Observed level scheme of ${}^{111}\mathrm{Cd}$. Transition energies are given in keV and their intensities following Coulomb excitation with 90-MeV ${}^{32}\mathrm{S}$ beams are indicated by the arrow widths. The branching ratio for the dashed 622-keV line has been measured in Ref. [25] to be approximately twice that of the 867-keV transition. It was obscured in the present work by the much stronger 620-keV transition but could be resolved with poor statistics in particle-$\gamma \text{−}\gamma$ coincidences.

Figure 2

$\gamma$-ray spectrum measured at $+{65}^{\circ }$ to the beam in coincidence with backscattered beam ions. All data taken at $+{65}^{\circ }$ during the transient field precession measurement are included. The inset expands the 565–900 keV region which shows a single strong peak at 752.8 keV and no peak at 754.9 keV. Transitions labeled in red and with a star are decays from the 752.8-keV state.

Figure 3

Particle-$\gamma$ coincidence $\gamma$-ray spectrum at $+{65}^{\circ }$ to the beam for a natural Cd target from measurements reported in Ref. [27]. The red, starred transition corresponds to the single peak at 752.8 keV.

Figure 4

Particle-$\gamma$ angular correlations for the 342-keV (mixed $M1/E2$), 620-keV ($E2$), and 753-keV ($E2$) transitions, all of which are consistent with the multipolarities reported in the literature [24]. Note the similar shape of the correlation for the 620- and 753-keV $E2$ transitions and the contrast of those with the mixed multipolarity $M1/E2$ 342-keV transition with mixing ratio $\delta =+0.36$ [24]. Correlations for the 342- and 753-keV transitions have been vertically offset, respectively, by $-0.6$ and $+0.5$ for presentation.

Figure 5

Doppler-broadened line shape fit to the 725-keV transition in ${}^{114}\mathrm{Cd}$. The best-fit line is shown and corresponds to $\tau =2.26$ ps. The previously measured value is $\tau =2.00\left(12\right)$ ps [38]. Data from measurements reported in Ref. [27].

Figure 6

Doppler-broadened line shape fit to the 753-keV transition in ${}^{111}\mathrm{Cd}$. The line shown corresponds to $\tau =4.0$ ps.

Figure 7

Doppler-broadened line shape fit to the 681-keV transition in ${}^{113}\mathrm{Cd}$. The line shown corresponds to $\tau =9$ ps. Data from measurements reported in Ref. [27].

Figure 8

A comparison between the experimental and theoretical observables as a function of particle-vibration coupling parameter. Experimental data points are placed at the fitted particle-vibration coupling parameter value of $\xi =2.2$ (with some small displacements for clarity of presentation). (a) Level energies. Horizontal bars show experimental level energies; lines show the calculations. (b) Adopted $g$ factors. Dotted lines show experimental $g$ factors. Solid lines are calculated values. (c) Reduced transition strengths for the transitions to the ground state in Weisskopf units. Solid lines are calculated values. Data from Ref. [24].

Figure 9

Arrangement of the observed low-excitation energy, positive-parity levels in ${}^{111}\mathrm{Cd}$ into a particle-rotor level scheme.

Figure 10

(a) Nilsson model calculations of $g$ factors as a function of quadrupole deformation ${\epsilon }_2$. The theoretical $g$ factors of each state show a marked change with deformation moving towards the experimental values as deformation increases. (b) Positive-parity Nilsson scheme calculated for ${}^{111}\mathrm{Cd}$.