Collective nature of low-lying excitations in ${}^{70,72,74}$Zn from lifetime measurements using the AGATA spectrometer demonstrator

Background: Neutron-rich nuclei with protons in the $fp$ shell show an onset of collectivity around $N=40$. Spectroscopic information is required to understand the underlying mechanism and to determine the relevant terms of the nucleon-nucleon interaction that are responsible for the evolution of the shell structure in this mass region.

Methods: We report on the lifetime measurement of the first 2${}^{+}$ and 4${}^{+}$ states in ${}^{70,72,74}$Zn and the first 6${}^{+}$ state in ${}^{72}$Zn using the recoil distance Doppler shift method. The experiment was carried out at the INFN Laboratory of Legnaro with the AGATA demonstrator, first phase of the Advanced Gamma Tracking Array of highly segmented, high-purity germanium detectors coupled to the PRISMA magnetic spectrometer. The excited states of the nuclei of interest were populated in the deep inelastic scattering of a ${}^{76}$Ge beam impinging on a ${}^{238}$U target.

Results: The maximum of collectivity along the chain of Zn isotopes is observed for ${}^{72}$Zn at $N=42$. An unexpectedly long lifetime of 20${}_{-5.2}^{+1.8}$ ps was measured for the 4${}^{+}$ state in ${}^{74}$Zn.

Conclusions: Our results lead to small values of the $B(E2;4_1^{+}\to 2_1^{+})/B(E2;2_1^{+}\to 0_1^{+})$ ratio for ${}^{72,74}$Zn, suggesting a significant noncollective contribution to these excitations. These experimental results are not reproduced by state-of-the-art microscopic models and call for lifetime measurements beyond the first 2${}^{+}$ state in heavy zinc and nickel isotopes.

Figure 1

Identification of Zn isotopes with PRISMA. Top: Energy loss in the two first ionisation chamber subsections versus total energy. Bottom: $A/Q$ distribution for Zn isotopes with a selected charge state $Q={24}^{+}$.

Figure 2

Left: Part of the Doppler corrected spectrum in coincidence with ${}^{76}$Ge ions identified in PRISMA, showing the $2_1^{+}\to 0_1^{+}$ transition. The two peaks corresponding to the gamma emitted before and after the degrader are well separated. The two small peaks at lower energy correspond to the $2_2^{+}\to 2_1^{+}$ transition. Right: $\gamma$-ray energies plotted as a function of the emission angle with respect to the direction of the recoiling ions.

Figure 3

$\gamma$-ray spectra in coincidence with ${}^{70}$Zn (top), ${}^{72}$Zn (center), and ${}^{74}$Zn (bottom). The spectra are Doppler corrected on an event-by-event basis for the velocities measured with the PRISMA spectrometer after the degrader foil. The shown spectra were measured with a target-to-degrader distance of 100 $\mu$m. Partial decay schemes including the observed transitions (energy in keV) are shown in the insets (see text for more details). Transition energies quoted on the spectra are for the slow component if existing, and for the fast component otherwise (for which the energy is smaller than in the level scheme). The broad structures localized at 550 keV, 650 keV, and slightly above 900 keV arise from the Doppler correction of the 511 keV line and neutron-induced Ge excitations in the AGATA clusters.

Figure 4

Partial spectra for ${}^{72}$Zn (upper part) and ${}^{74}$Zn (lower part) showing the $2_1^{+}\to 0_1^{+}$ (left) and $4_1^{+}\to 2_1^{+}$ transitions (right) for three different target-to-degrader distances as indicated. The measured spectra are shown as histograms and the Gaussian fits as full (blue) lines. The evolution of the fast and slow components as a function of distance is clearly visible.

Figure 5

Decay curves for the $2_1^{+}\to 0_1^{+}$ and $4_1^{+}\to 2_1^{+}$ transitions in ${}^{74}$Zn (left). The data points were fitted by a continuously differentiable function of piecewise defined second-order polynomials (splines). The right-hand side of the figure shows the resulting lifetimes obtained for different target-to-degrader distances. The horizontal line indicates the weighted mean value.

Figure 6

Results from the present experiment and systematics of experimental $B(E2;2_1^{+}\to 0_1^{+})$ and $B(E2;4_1^{+}\to 2_1^{+})$ values for the chain of Zn isotopes. Theoretical values were calculated with the shell model using the JUN45 interaction in the $p{f}_{5/2}{g}_{9/2}$ valence space (${}^{56}$Ni core, $e_p=1.5e$, and $e_n=1.1e$) [50], the LNPS interaction in the $pf{g}_{9/2}{d}_{5/2}$ valence space (${}^{48}$Ca core, $e_p=1.31e$, and $e_n=0.46e$) [17] and with a five-dimensional collective Hamiltonian using the Gogny D1S force [51].

Figure 7

The left panel shows experimental excitation energies of the $2^{+}$ (dot symbols) and $4^{+}$ states (square symbols) for the chain of Zn isotopes and a comparison with theoretical calculations. The right panel shows the ratio $R_{42}=E\left(4_1^{+}\right)/E\left(2_1^{+}\right)$. The theoretical calculations are based on the shell model (dotted and dashed blue lines) with the JUN45 [50] and LNPS [17] interactions (see text for details) and on a five-dimensional collective Hamiltonian (green line) used with the Gogny D1S force [51].

Figure 8

Experimental $B(E2;4_1^{+}\to 2_1^{+})/B(E2;2_1^{+}\to 0_1^{+})$ ratio for nuclei with $Z=20$ to $Z=40$. Zinc isotopes are represented by red dots.