Magnetic moment and lifetime measurements of Coulomb-excited states in ${}^{106}\mathrm{Cd}$

Background: The Cd isotopes are well studied, but experimental data for the rare isotopes are sparse. At energies above the Coulomb barrier, higher states become accessible.

Purpose: Remeasure and supplement existing lifetimes and magnetic moments of low-lying states in ${}^{106}\mathrm{Cd}$.

Methods: In an inverse kinematics reaction, a ${}^{106}\mathrm{Cd}$ beam impinging on a ${}^{12}\mathrm{C}$ target was used to Coulomb excite the projectiles. The high recoil velocities provide a unique opportunity to measure $g$ factors with the transient-field technique and to determine lifetimes from lineshapes by using the Doppler-shift-attenuation method. Large-scale shell-model calculations were carried out for ${}^{106}\mathrm{Cd}$.

Results: The $g$ factors of the $2_1^{+}$ and $4_1^{+}$ states in ${}^{106}\mathrm{Cd}$ were measured to be $g\left(2_1^{+}\right)=+0.398\left(22\right)$ and $g\left(4_1^{+}\right)=+0.23\left(5\right)$. A lineshape analysis yielded lifetimes in disagreement with published values. The new results are $\tau ({}^{106}\mathrm{Cd};2_1^{+})=7.0\left(3\right)\mathrm{ps}$ and $\tau ({}^{106}\mathrm{Cd};4_1^{+})=2.5\left(2\right)\mathrm{ps}$. The mean life $\tau ({}^{106}\mathrm{Cd};2_2^{+})=0.28\left(2\right)\mathrm{ps}$ was determined from the fully-Doppler-shifted $\gamma$ line. Mean lives of $\tau ({}^{106}\mathrm{Cd};4_3^{+})=1.1\left(1\right)\mathrm{ps}$ and $\tau ({}^{106}\mathrm{Cd};3_1^{-})=0.16\left(1\right)\mathrm{ps}$ were determined for the first time.

Conclusions: The newly measured $g\left(4_1^{+}\right)$ of ${}^{106}\mathrm{Cd}$ is found to be only 59% of the $g\left(2_1^{+}\right)$. This difference cannot be explained by either shell-model or collective-model calculations.

Figure 1

Single-particle spectrum. At the beam energy of 410 MeV, light particles dominate. The carbon peak is a result of Coulomb scattering of the beam projectiles in the carbon layer of the target.

Figure 2

Coincidence $\gamma$ spectra gated on the carbon peak in Fig. 1. The spectra show the Doppler-broadened and -shifted lines, including the distinct lineshapes observed in a backward- and in a forward-positioned detector segment at the indicated angle $\theta$ with respect to the beam direction.

Figure 3

Partial level scheme indicating the states in ${}^{106}\mathrm{Cd}$ that were excited in this experiment. The energies are taken from the National Nuclear Data Center (NNDC) [7]. The lifetime column shows the newly determined mean lives.

Figure 4

Simultaneous lineshape fit of (a) the $2_1^{+}\to 0_1^{+}\gamma$ line and (b) $4_1^{+}\to 2_1^{+}\gamma$ line in ${}^{106}\mathrm{Cd}$ as observed in a clover segment at ${68}^{\circ }$. The shaded area represents the feeding intensity from the $4_2^{+}\to 4_1^{+}\gamma$ line of 610.8 keV seen in panel (a).

Figure 5

lineshape fit of the 811.1 keV $4_3^{+}\to 4_1^{+}\gamma$ line and the 861.2 keV $4_1^{+}\to 2_1^{+}\gamma$ line in ${}^{106}\mathrm{Cd}$ as observed in a clover segment at ${112}^{\circ }$.