Coulomb excitation of ${}^{96}\mathrm{Mo}$

The neutron-rich strontium, zirconium, and molybdenum nuclei have been observed to undergo a dramatic evolution, becoming strongly deformed around $N=60$, sometimes interpreted as a quantum phase transition between “normal” and intruder configurations. Key to understanding this evolution is to understand the configurations in isolation, in regions where interference can be neglected. A deformed coexisting configuration is inferred from the presence of a $0_2^{+}$ state which decreases in excitation energy with increasing neutron number, becoming the first-excited state at ${}^{98}\mathrm{Mo}$. We present here the results of a low-energy Coulomb-excitation measurement of the nucleus ${}^{96}\mathrm{Mo}$, extracting $B\left(E2\right)$ values and quadrupole moments. It is found that, while the $B\left(E2\right)$ values agree with those found in the literature, there is a significant disagreement with literature spectroscopic quadrupole moments. The results are compared with shell-model calculations using a ${}^{88}\mathrm{Sr}$ core with good agreement found, likely indicating that intruder structures do not significantly impact the ground-state structure, in contrast with the heavier molybdenum isotopes.

Figure 1

Charge detected in the rings of the downstream S3 detector. The laboratory angles are shown on the upper axis. The top band is the ${}^{96}\mathrm{Mo}$ scattered by the ${}^{196}\mathrm{Pt}$ in the target, the second band is the ${}^{196}\mathrm{Pt}$ which is scattered by the ${}^{96}\mathrm{Mo}$ in the beam. Additionally, ${}^{32}\mathrm{Si}$ and the corresponding ${}^{196}\mathrm{Pt}$ are seen due to the ${}^{32}\mathrm{Si}$ nuclei being the primary components in the beam. Note that bins containing less than five counts have been omitted from this figure for the purposes of presentation.

Figure 2

Doppler corrected $\gamma$-ray spectra for ${}^{96}\mathrm{Mo}$ (a) and ${}^{196}\mathrm{Pt}$ (b) obtained with SeGA. When correcting for the Mo recoils two peaks can be seen; $778\mathrm{keV}$ and 850 keV. Similarly for Pt three peaks are seen; $333\mathrm{keV}, 356\mathrm{keV}$, and $521\mathrm{keV}$.

Figure 3

A schematic view of levels and associated one- and two-step excitations and de-excitations. Where red arrows indicate those observed in this work and black arrows indicate literature values from Ref. [20] used to account for intruder states.

Figure 4

Figure displaying confidence in the matrix elements in this work, as seen in Table 2. The points in the center of each ellipse correspond to the matrix elements linked to respective ${\mathrm{P}}_3++,+-,-+,--$. The solid lines correspond to one standard deviation. For the $++$ and $--$ configurations, the ${\chi }^2$ surface is shown, cut off at the $1\sigma$ limit for both surfaces. The number of degrees of freedom was 22 in the fit, including both experimental data and literature constraints on ${}^{196}\mathrm{Pt}$ matrix elements.

Figure 5

$B(E2;0_1^{+}\to 2_1^{+}), Q_s\left(2_1^{+}\right)$, and $Q_s/Q_s^{rot}$ for molybdenum isotopes are shown in (a), (b), and (c), respectively. Results from this work are shown in black, results from Paradis et al. (1976) [5] are shown with hollow blue points, and adopted experimental values from ENSDF [20] are shown with red triangles. ${\mathrm{P}}_3++$ values are indicated by squares, ${\mathrm{P}}_3--$ values are indicated with circles. In addition to experimental data, shell model predictions using the jj45a interaction are indicated with the green line, and the IBM-2 based calculation indicated by the magenta line. In (a) the previous work on ${}^{96}\mathrm{Mo}$ aligns well with this work and follows the trend given using the shell model. In (b) it can be seen that values provided by the Paradis et al. (1976) paper [5] disagree with this work and differ somewhat from other works. In (c) this work shows a prolate deformation seen by the points being at the axially symmetric limit for prolate nuclei as outlined in Eq. (1). It is worth noting that for ${}^{94}\mathrm{Mo}$ and ${}^{96}\mathrm{Mo}$, Paradis et al. (1976) [5] is the primary or sole contributor to the ENSDF adopted values displayed.