Identification of a new isomeric state in ${}^{76}\mathrm{Zn}$ following the $\beta$ decay of ${}^{76}\mathrm{Cu}$

Background: The evolution of nuclear shell structure far from stability can be explored by identifying and measuring the properties of isomers. Neutron-rich nuclei between the $Z=28$ and the $Z=50$ closed shells have been the subject of recent studies which have identified a number of $0.1–10\mu \mathrm{s}$ isomers and measured detailed spectroscopic properties.

Purpose: The purpose of this analysis was to identify and measure the properties of short-lived isomeric states populated following $\beta$ decay in $Z\approx 30,N\approx 50$ nuclei near the doubly magic nucleus ${}^{78}\mathrm{Ni}$.

Methods: Radioactive ions produced by beam fragmentation at the National Superconducting Cyclotron Laboratory were implanted into a ${\mathrm{CeBr}}_3$ scintillator coupled to a pixelated photomultiplier tube. Ancillary arrays of HPGe clover and ${\mathrm{LaBr}}_3$ detectors were positioned around the implantation detector to measure $\beta$-delayed $\gamma$ rays.

Results: The previously observed 2634-keV level in ${}^{76}\mathrm{Zn}$, populated following the $\beta$ decay of ${}^{76}\mathrm{Cu}$, was identified as isomeric with a half-life of 25.4(4) ns. A combination of timing and $\gamma$-ray spectroscopy was used to confirm this assignment. Shell-model calculations were performed and indicate that this state may be a negative-parity state formed by the occupation of the $\nu 0g_{9/2}$ orbital.

Conclusions: A new isomeric state in ${}^{76}\mathrm{Zn}$ has been identified, and its half-life was measured. Ambiguity about the structure of this state could be resolved with further experiments.

Figure 1

Particle identification plot of ions implanted in the ${\mathrm{CeBr}}_3$ detector. The ${}^{76}\mathrm{Cu}$ ions of interest are circled.

Figure 2

An example of a double-pulse signal from the PSPMT dynode recorded by DDAS. These signals are characteristic of an isomeric transition populated following $\beta$ decay. The best-fit detector response function described in Sec. 2 is shown in red. Features, such as the energies and the time difference between the two signals were determined from the fit.

Figure 3

Background-subtracted $\beta$-delayed $\gamma$ rays detected within 3.2 s of a ${}^{76}\mathrm{Cu}$ implant. The $\gamma$-ray transitions at 341, 599, 698, and 1337 keV are the strongest transitions observed in ${}^{76}\mathrm{Zn}$ following the $\beta$ decay of ${}^{76}\mathrm{Cu}$ from Refs. [15, 16]. The closed circles designate known transitions from ${}^{76}\mathrm{Ga},$ the granddaughter of ${}^{76}\mathrm{Cu}$, which are present due to ${}^{76}\mathrm{Zn}$ $\beta$ decay occurring within the 3.2-s correlation window.

Figure 4

The $E_1\text{−}{E}_2$ energy spectrum of double-pulse events separated by more than 20 ns identified following the procedure described in Sec. 2. A gating region identified for further analysis is given by the horizontal black lines. For more details, refer to Sec. 3.

Figure 5

$\gamma$ rays measured with the clover array (top) and the ${\mathrm{LaBr}}_3$ detectors (bottom) in coincidence with double pulses falling in the gating region shown in Fig. 4 where the coincident double pulses were separated by, at least, 20 ns in the dynode trace. The strongest transitions at 341, 599, 698, and 1337 keV have been observed previously in ${}^{76}\mathrm{Zn}$ following ${}^{76}\mathrm{Cu}$ $\beta$ decay and were used to place the isomeric transition in ${}^{76}\mathrm{Zn}$.

Figure 6

Previously unobserved 2225.4(3)-keV $\gamma$-ray transition in coincidence with the double-pulse gate in the $E_1\text{−}{E}_2$ spectrum shown in Fig. 4. This $\gamma$ ray is in coincidence with the isomeric transition in ${}^{76}\mathrm{Zn}$, however, it could not be placed in the level scheme due to insufficient statistics.

Figure 7

Distribution of time differences between the first ($E_1$) and second ($E_2$) pulses determined from the fit parameters of the model detector response (black). The time difference was fit with an exponential decay plus a constant background (red) resulting in a measured half-life of 25.4(4) ns. The contributions to the total fit from the exponential decay and constant background are shown in blue and green, respectively.

Figure 8

The distribution of time differences between the ${\mathrm{LaBr}}_3$ and PSPMT dynode signals for ${}^{76}\mathrm{Zn}$ double-pulse events where the first and second pulses in the dynode trace are separated by, at least, 50 ns. Prompt $\gamma$ rays which occur following the $\beta$ decay of ${}^{76}\mathrm{Cu}$ have a time difference centered around $t_{{\mathrm{LaBr}}_3}-t_{\mathrm{PSPMT}}=0$ whereas $\gamma$ rays which occur following the isomeric state are delayed and possess a time difference $t_{{\mathrm{LaBr}}_3}-t_{\mathrm{PSPMT}}>0$.

Figure 9

${\mathrm{LaBr}}_3$ $\gamma$-ray spectra in coincidence with the double pulses in the gating region shown in Fig. 4 for the peak centered around $t_{{\mathrm{LaBr}}_3}-t_{\mathrm{PSPMT}}=0\mathrm{ns}$ (top) and $t_{{\mathrm{LaBr}}_3}-t_{\mathrm{PSPMT}}>50\mathrm{ns}$ (bottom). The coincidence relationships were used to place the isomeric state in the ${}^{76}\mathrm{Zn}$ decay scheme below the 341-keV transition.

Figure 10

An anode energy distribution for a double-pulse event attributed to the decay of the isomeric state in ${}^{76}\mathrm{Zn}$. The two discrete local maxima located at approximately (4,6) and (6,13) are generated by a $\beta$-decay electron followed by a $\gamma$-ray scattering out of the ${\mathrm{CeBr}}_3$ crystal. This suggests that the isomeric state lies above a $\gamma$-ray cascade and explains the broadened $E_2$ distribution shown in Fig. 4.

Figure 11

Level scheme showing the states of interest and observed transitions in ${}^{76}\mathrm{Zn}$ for the current paper with energies given in keV. The assignment of $2^{+}$ and $4^{+}$ for the first two excited states is taken from Refs. [17, 18]. Spins and parities could not be assigned to other states observed in the present paper. The 2634-keV state which has been newly identified as isomeric in this paper is shown in red.

Figure 12

Comparison between the experimentally observed level scheme and partial level schemes determined using the shell-model calculations and their associated Hamiltonians described in Sec. 4. The experimental level scheme is presented the same as in Fig. 11. Negative-parity states with half-lives longer than 1 ns from the shell-model calculations are shown using blue dotted lines; their depopulating transitions are also shown in blue. Half-lives of isomeric states assuming a $B\left(E1\right)$ value of ${10}^{-8}{e}^2{\text{fm}}^2$ are given in parentheses to the left of the level spin and parity. Levels up to 4 MeV and $\gamma$ rays with branching ratios $>20\%$ which decay through the yrast 4-2-0 cascade are shown for the calculations.