Coulomb excitation of ${}^{74,76}\mathrm{Zn}$

The first experiment using radioactive beams post-accelerated by the HIE-ISOLDE facility has enabled to obtain a precise set of $B\left(E2\right)$ transition probabilities in neutron-rich ${}^{74,76}\mathrm{Zn}$ isotopes. The resulting $B(E2$; $2_1^{+}\to 0_1^{+}$) values are consistent with those determined in earlier REX-ISOLDE measurements. While the $B(E2$; $4_1^{+}\to 2_1^{+}$) transition probability in ${}^{76}\mathrm{Zn}$ is also in agreement with earlier Coulomb-excitation results, the value obtained for ${}^{74}\mathrm{Zn}$ is considerably lower. For the first time, a spectroscopic quadrupole moment of the $2_1^{+}$ state was measured for an exotic nucleus in this mass region. A detailed comparison is presented with large-scale shell-model and Monte Carlo shell-model calculations.

Figure 1

Systematics of $2_1^{+}, 4_1^{+}, 2_2^{+}$, and $0_2^{+}$ states and $B(E2$; $2_1^{+}\to 0_1^{+}$) values in even-even Zn isotopes from ${}^{66}\mathrm{Zn}$ ($N=36$) to ${}^{84}\mathrm{Zn}$ ($N=54$). Widths and labels of the arrows represent the measured $B(E2$; $2_1^{+}\to 0_1^{+}$) values, taken from ENSDF [25], with the exception of the values for ${}^{76,78}\mathrm{Zn}$ taken from Ref. [26], and expressed in Weisskopf units. Level energies, taken from ENSDF [25] and Refs. [27, 28, 29], are given in keV, and their uncertainties are plotted if they are larger than line width.

Figure 2

Total $\gamma$-ray energy spectra for (a) ${}^{74}\mathrm{Zn}$ and (b) ${}^{76}\mathrm{Zn}$ impinging on ${}^{208}\mathrm{Pb}$ at 4.0 MeV/nucleon, background-subtracted and Doppler-corrected for the projectile. The “safe” energy criterion was imposed on the selection of the events, see text for details.

Figure 3

Background-subtracted $\gamma$-ray spectra for ${}^{74}\mathrm{Zn}$ impinging on a ${}^{196}\mathrm{Pt}$ target, Doppler-corrected for the projectile. The spectrum plotted in blue was collected for a duration of 5 h at the beam energy of 4.0 MeV/nucleon. A spectrum obtained under the same experimental conditions, but at 2.85 MeV/nucleon and during 16 h of data collection is presented in red. The inset shows the 770–850 keV portions of the spectra, evidencing the enhancement of the $4_1^{+}\to 2_1^{+}$ transition at 4.0 MeV/nucleon. The “safe” energy criterion was imposed, see text for details.

Figure 4

Cross sections for Coulomb excitation of the $2_1^{+}$ and $4_1^{+}$ states in ${}^{74}\mathrm{Zn}$ on ${}^{208}\mathrm{Pb}$, calculated as a function of the beam energy assuming the values of matrix elements obtained in the present work. The integration was performed over the scattering angles covered by the particle detector, excluding those corresponding to nonsafe Coulomb-excitation process (see text for details). Dashed lines indicate the beam energies used in the present experiment.

Figure 5

$\gamma$-ray energy spectra for the $A=74$ beam impinging on ${}^{196}\mathrm{Pt}$ at 2.85 MeV/nucleon, background-subtracted and Doppler-corrected for the projectile. The spectrum in (a) was collected in laser ON mode, while that in (b) was collected during laser OFF periods.

Figure 6

Two-dimensional ${\chi }^2$ surfaces with respect to the $\langle 2_1^{+}\parallel E2\parallel 0_1^{+}\rangle$ and $\langle 2_1^{+}\parallel E2\parallel 2_1^{+}\rangle$ matrix elements, for (a) ${}^{74}\mathrm{Zn}$ and (b) ${}^{76}\mathrm{Zn}$, obtained in the final step of the analysis as explained in the text. A $1\sigma$ cut is applied with the condition that ${\chi }^2<{\chi }_{\min }^2+$ 1. The data are normalized to the excitation of a 2.0-mg/${\mathrm{cm}}^2{}^{196}\mathrm{Pt}$ target at a beam energy of 2.85 MeV/nucleon. The lines represent individual $1\sigma$ limits for each data set used for this analysis, listed in Tables 2 and 3: A—black dashed, B—blue dotted, C—green dotted-dashed, D—gray dotted-dashed, and E—magenta dashed.

Figure 7

Two-dimensional ${\chi }^2$ surface for ${}^{74}\mathrm{Zn}$ with respect to the $\langle 4_1^{+}\parallel E2\parallel 2_1^{+}\rangle$ and $\langle 4_1^{+}\parallel E2\parallel 4_1^{+}\rangle$ matrix elements. A $1\sigma$ cut is applied with the condition that ${\chi }^2<{\chi }_{\min }^2+$ 1. For this analysis, data collected with 4.0-MeV/nucleon ${}^{74}\mathrm{Zn}$ beam on ${}^{208}\mathrm{Pb}$ and ${}^{196}\mathrm{Pt}$ targets was used. The lines represent individual $1\sigma$ limits for each data set, see Table 2: A′—black dashed, B′—blue dotted, C′—green dotted-dashed, and D′—gray dotted-dashed lines.

Figure 8

Transition probabilities in even-even Zn isotopes from ${}^{66}\mathrm{Zn}$ ($N=36$) to ${}^{80}\mathrm{Zn}$ ($N=50$): a) $B(E2$; $2_1^{+}\to 0_1^{+}$) values, b) $B(E2$; $4_1^{+}\to 2_1^{+}$) values. For ${}^{66,68}\mathrm{Zn}$ only evaluated values are presented [25], while for heavier Zn isotopes the experimental results are plotted individually (REX-ISOLDE [26, 30, 44], Coulex LISE [37, 38], RDDS LISE [40], RDDS Legnaro [41], RDDS GANIL [42], DSAM Yale [39], DSAM RIKEN [27]). Some of the points are slightly offset on the $x$ axis for clarity. The experimental results are compared to the predictions of the large-scale shell model with the LNPS interaction (red dotted-dashed line), Monte Carlo shell model with the A3DA-m Hamiltonian (gray solid line) and large-scale shell model with the JUN45 interaction (blue dotted line).

Figure 9

T plots for the yrast states of ${}^{72,74,76,78}\mathrm{Zn}$ presenting the results of the MCSM calculations with the A3DA-m Hamiltonian. The distribution of the MCSM basis states is presented with the circles, whose sizes illustrate the importance of specific basis states in the total wave function. The circular lines of constant ${\beta }_2$ deformation correspond to ${\beta }_2$ values given on the $x$ axis.

Figure 10

Potential energy surfaces from constrained Hartree-Fock minimization in the shell-model basis for ${}^{74}\mathrm{Zn}$ (up) and ${}^{76}\mathrm{Zn}$ (bottom). Orange circles represent the amplitudes of the final ground-state wave functions in the DNO-SM basis.

Figure 11

$1\sigma$ contours in the $\beta \text{−}\gamma$ sextant for the ground states of ${}^{74}\mathrm{Zn}$ (top) and ${}^{76}\mathrm{Zn}$ (bottom) obtained from the analysis of the quadrupole invariants using the LNPS effective interaction. The red dots represent the effective $\beta$ and $\gamma$ values.

Figure 12

Spectroscopic quadrupole moments of the $2_1^{+}$ states in even-even Zn isotopes from ${}^{66}\mathrm{Zn}$ ($N=36$) to ${}^{80}\mathrm{Zn}$ ($N=50$). The result of the present measurement, plotted with a red filled circle, is compared to the literature values from electron scattering ([78], black filled circles) and Coulomb excitation ([32, 33, 34, 44], black open circles) as well as the predictions of the large-scale shell model with the LNPS interaction (red dotted-dashed line), Monte Carlo shell model with the A3DA-m Hamiltonian (gray solid line) and large-scale shell model with the JUN45 interaction (blue dotted line).