${16}^{+}$ Spin-Gap Isomer in ${}^{96}\mathrm{Cd}$

A $\beta$-decaying high-spin isomer in ${}^{96}\mathrm{Cd}$, with a half-life $T_{1/2}={0.29}_{-0.10}^{+0.11}\mathrm{s}$, has been established in a stopped beam rare isotope spectroscopic investigations at GSI (RISING) experiment. The nuclei were produced using the fragmentation of a primary beam of ${}^{124}\mathrm{Xe}$ on a ${}^9\mathrm{Be}$ target. From the half-life and the observed $\gamma$ decays in the daughter nucleus, ${}^{96}\mathrm{Ag}$, we conclude that the $\beta$-decaying state is the long predicted ${16}^{+}$ “spin-gap” isomer. Shell-model calculations, using the Gross-Frenkel interaction and the $\pi \nu (p_{1/2},g_{9/2})$ model space, show that the isoscalar component of the neutron-proton interaction is essential to explain the origin of the isomer. Core excitations across the $N=Z=50$ gaps and the Gamow-Teller strength, $B(\mathrm{GT})$ distributions have been studied via large-scale shell-model calculations using the $\pi \nu (g,d,s)$ model space to compare with the experimental $B(\mathrm{GT})$ value obtained from the half-life of the isomer.

Figure 1

$Z$ versus $A/Q$ identification plot. ${}_{48}{}^{96}\mathrm{Cd}$ and ${}_{47}{}^{96}\mathrm{Ag}$ nuclei are circled.

Figure 2

Gamma-ray spectra associated with the decays following implantation into the geometrically central DSSSD of the “active stopper.” (a) ${}^{96}\mathrm{Cd}$ events with $\gamma$-ray times restricted to be between 0 to 200 ns following the $\beta$-decay signal detected in the DSSSD. In the inset the time distribution of the 421 keV $\gamma$ ray with respect to the ${}^{96}\mathrm{Cd}$ implantation time is shown for the data (histogram) and the calculations (smooth curve) using $T_{1/2}=0.67\pm 0.15\mathrm{s}$. (b) Same as (a) except the $\gamma$-ray times are restricted to be between 200 ns to $4\mu \mathrm{s}$. The inset shows the combined correlation time distribution of the 470, 667, 1506 keV $\gamma$ rays which gives $T_{1/2}={0.29}_{-0.10}^{+0.11}\mathrm{s}$ for the ${16}^{+}$ isomer. (c) Same as (b) for all nuclei other than ${}^{96}\mathrm{Cd}$. In the above spectra, the 511 keV line arises from the positron annihilation while the remaining lines with labels correspond to the transitions in ${}^{96}\mathrm{Ag}$ (cf. Fig. 3). See text for details. The dashed lines are merely to guide the eye to particular energy coordinates.

Figure 3

Shell-model calculations for ${}^{96}\mathrm{Cd}$. ${}^{96}\mathrm{Cd}$, SM: All isovector $nn$, $pp$, $np$ and isoscalar $np$ interactions are included. ${}^{96}\mathrm{Cd}$, $T=0$: Only the isovector $np$ interaction is switched off. ${}^{96}\mathrm{Cd}$, $T=1$: Only the isoscalar $np$ interaction is switched off. Large-scale shell-model calculations for ${}^{96}\mathrm{Ag}$. ${}^{96}\mathrm{Ag}$, GDS $t=5$: Up to 5 ph core excitations across the $N=Z=50$ shell gap are included. Only the lowest states are shown for each spin. EX: Partial experimental scheme and the transitions observed in the decay of ${}^{96}\mathrm{Cd}$ [21, 37]. Here, $x$ and $y$ correspond to the unobserved transition energies.

Figure 4

Left: The proton and neutron occupations lined up in the sequence of increasing projection in the $p_{1/2}$ and $g_{9/2}$ orbitals representing the ${16}^{+}$ “spin-gap” isomer in ${}^{96}\mathrm{Cd}$ and the ${15}^{+}$ isomer in ${}^{96}\mathrm{Ag}$ [21]. The GT $\beta$-decay process ($\pi g_{9/2}\to \nu g_{9/2}$) is depicted by the arrow that receives the full GT strength within the $\pi \nu (p_{1/2},g_{9/2})$ space. Right: Decay branches are shown from the large-scale shell-model calculations with core excitations allowing different transitions including the one depicted on the left. Overlaps of the resonances, due to their $\simeq 2\mathrm{MeV}$ width, are not shown for the clarity. See text for details.