Cross-shell excitations from the $fp$ shell: Lifetime measurements in ${}^{61}\mathrm{Zn}$

Lifetimes of excited states in the neutron-deficient nucleus ${}^{61}\mathrm{Zn}$ were measured employing the recoil-distance Doppler-shift (RDDS) and the electronic fast-timing methods at the University of Cologne. The nucleus of interest was populated as an evaporation residue in ${}^{40}\mathrm{Ca}({}^{24}\mathrm{Mg},n2p){}^{61}\mathrm{Zn}$ and ${}^{58}\mathrm{Ni}(\alpha ,n){}^{61}\mathrm{Zn}$ reactions at 67 and 19 MeV, respectively. Five lifetimes were measured for the first time, including the lifetime of the $5/2_1^{-}$ isomer at 124 keV. Short lifetimes from the RDDS analysis are corrected for Doppler-shift attenuation (DSA) in the target and stopper foils. Ambiguous observations in previous measurements were resolved. The obtained lifetimes are compared to predictions from different sets of shell-model calculations in the $fp$, $f_{5/2}p{g}_{9/2}$, and multishell $fp\text{−}{g}_{9/2}{d}_{5/2}$ model spaces. The band built on the $9/2_1^{+}$ state exhibits a prolate deformation with $\beta \approx 0.24$. Especially, the inclusion of cross-shell excitation into the $1d_{5/2}$ orbital is found to be decisive for the description of collectivity in the first excited positive-parity band.

Figure 1

Single-particle states above doubly-magic ${}^{40}\mathrm{Ca}$ with shell closures at $N=Z=20$, 28, and 50.

Figure 2

Partial level scheme of ${}^{61}\mathrm{Zn}$ including the first excited negative- and positive-parity bands. The reduced transition strengths of the 124-, 1141-, 1403-, 937-, and 1079-keV decays from the $5/2_1^{-}$, $9/2_1^{-}$, $9/2_1^{+}$, $13/2_1^{+}$, and $17/2_1^{+}$ states are the subject of this paper. Energies and spins are adopted from Ref. [20]. Dominating transitions are presented with thick arrows.

Figure 3

Simulated Doppler-shift attenuation correction factor $c\left(\tau \right)$ as a function of the lifetime (data points). A line is drawn to guide the eye.

Figure 4

$\gamma \gamma$ angular correlations fits. Experimental yields in the six correlation groups $({\theta }_1,{\theta }_2,\varphi )$ (data points) are compared to calculated angular-correlation functions $W({\theta }_1,{\theta }_2,\varphi )$ (lines) with the code corleone. (a) Fit of the well-known $4_1^{+}\stackrel{E2}{\to }{2}_1^{+}\stackrel{E2}{\to }{0}_1^{+}$ 1004–1454-keV cascade in ${}^{58}\mathrm{Ni}$. The spin hypothesis shows good agreement with the experimental data. (b) Fit of the $2_2^{+}\stackrel{\delta }{\to }{2}_1^{+}\stackrel{E2}{\to }{0}_1^{+}$ cascade in ${}^{60}\mathrm{Ni}$. The evaluated multipole-mixing ratio is reproduced within its error. (c) Fit of the 1161–1004-keV $4_2^{+}\stackrel{\delta }{\to }{4}_1^{+}\stackrel{E2}{\to }{2}_1^{+}$ cascade in ${}^{58}\mathrm{Ni}$. See text for details.

Figure 5

Extracted lifetimes (top row), intensity distributions of Doppler-shifted (second row) and unshifted peaks (third row), gated spectra of detectors at about ${45}^{\circ }$ for the different target-to-stopper distances, generated by a gate on the shifted peak of the feeding transition for the ($\mathrm{a},\mathrm{b},\mathrm{c},{\mathrm{d}}_{1–7}$) $9/2_1^{-}\to 5/2_1^{-}$, ($\mathrm{i},\mathrm{j},\mathrm{k},{\mathrm{l}}_{1–7}$) $13/2_1^{+}\to 9/2_1^{+}$, and ($\mathrm{m},\mathrm{n},\mathrm{o},{\mathrm{p}}_{1–7}$) $17/2_1^{+}\to 13/2_1^{+}$ transitions. The lifetime of the $9/2_1^{+}$ state is deduced from $\gamma$-ray spectra of the feeding $13/2_1^{+}\to 9/2_1^{+}$ transitions ($\mathrm{e},\mathrm{f},\mathrm{g},{\mathrm{h}}_{1–7}$), generated by a gate on the deexciting 1403-keV $\gamma$ rays. See text for details.

Figure 6

$\gamma \gamma$ angular correlations fits of the 1403–873-keV $9/2_1^{+}\stackrel{\delta }{\to }7/2_1^{-}\stackrel{E2/M1}{\to }5/2_1^{-}$ cascade in ${}^{61}\mathrm{Zn}$. The nomenclature is similar to that of Fig. 4.

Figure 7

Top: (a) Comparison of ${\mathrm{LaBr}}_3$:Ce and HPGe $\gamma$-ray spectra from the ${}^{58}\mathrm{Ni}(\alpha ,n){}^{61}\mathrm{Zn}$ fast-timing experiment. Note the limited energy resolution of the ${\mathrm{LaBr}}_3$:Ce scintillators. The $5/2_1^{-}\to 3/2_1^{-}$ transition at 124 keV is well resolved and separated from neighboring peaks in both spectra. Peaks from the other reaction and decay products ${}^{58,60,61}\mathrm{Ni}$ [42, 43] and ${}^{61}\mathrm{Cu}$ [45] are labeled. Solid triangles mark $\gamma$-ray transitions of ${}^{61}\mathrm{Zn}$. (b) ${\mathrm{LaBr}}_3$:Ce $\gamma \gamma$ projection with a gate on 124 keV in ${\mathrm{LaBr}}_3$:Ce. Bottom: Gated $\gamma \gamma$-delayed time distributions and final lifetime fits for the gating combinations (c) 1141 keV $9/2_1^{-}\to 5/2_1^{-}$ and 124 keV $5/2_1^{-}\to 3/2_1^{-}$, (d) 873 keV $7/2_1^{-}\to 5/2_1^{-}$ and 124 keV $5/2_1^{-}\to 3/2_1^{-}$, (e) 1531 keV $13/2_1^{-}\to 9/2_1^{-}$ and 124 keV $5/2_1^{-}\to 3/2_1^{-}$. Lifetimes are determined by exponential fits of the delayed component. The fit is drawn with a red solid line. Random background is determined separately and incorporated into the fit.

Figure 8

$\gamma \gamma$ angular-correlation fits to the 1141–124-keV cascade. Based on the known $E2$ character of the $9/2_1^{-}\to 5/2_1^{-}$ transition, two minima are found for the 124-keV transition, giving either $\delta =-0.007\left(33\right)$ (solid line) or $\delta =-3.7_{-6}^{+4}$ (dashed line). The dotted line corresponds to a $\delta =1$ hypothesis.

Figure 9

Comparison between experimental and theoretical level energies for ${}^{61}\mathrm{Zn}$ using various SM interactions. Negative- and positive-parity states are separated into different columns for better visibility. See text for details on the SM calculations.

Figure 10

Total energy surfaces for the (a) negative (natural) and (b) positive (unnatural) parity states in ${}^{61}\mathrm{Zn}$. Energy minima are indicated with white circles. (c) Electric intrinsic quadrupole moments for members of the band built on the $9/2_1^{+}$ state in ${}^{61}\mathrm{Zn}$. Spins $I$ on the horizontal axis are denoted as $2I$. Experimental values (black circles) are calculated assuming $K=1/2$. Calculated quadrupole moments with $K=1/2$ (red squares) and $K=9/2$ (blue diamonds) correspond to the decoupling limit and the strong coupling limit, respectively.