Low-velocity transient-field technique with radioactive ion beams: $g$ factor of the first excited 2${}^{+}$ state in ${}^{72}\mathrm{Zn}$

The $g$ factor of the first excited $2^{+}$ state in ${}^{72}\mathrm{Zn}$ has been measured using the transient-field (TF) technique in combination with Coulomb excitation in inverse kinematics. This experiment presents only the third successful application of the TF method to a short-lived radioactive beam in 10 y, highlighting the intricacies of applying this technique to present and future isotope separator on-line facilities. The significance of the experimental result, $g\left(2_1^{+}\right)=+0.47\left(14\right)$, for establishing the structure of the Zn isotopes near $N=40$ is discussed on the basis of shell-model and beyond-mean-field calculations, the latter accounting for the triaxial degree of freedom, configuration mixing, and particle number and angular momentum projections.

Figure 1

Sketch of the new target chamber which has been constructed for TF experiments using low-energy radioactive beams at REX-ISOLDE and HIE-ISOLDE.

Figure 2

Diagram of the geometry of the four MINIBALL cluster detectors used in the experiment. The surfaces of the MINIBALL detectors are shown as seen from the target position. The centers of the cluster surfaces were positioned at angles of $\pm$60${}^{\circ }$ and $\pm$120${}^{\circ }$ with respect to the beam axis close to the horizontal plane (out-of-plane angles $\pm$5${}^{\circ }$). In the lower part of the figure the classification of the segments into 14 segment groups on each side of the beam axis is indicated by different shades of gray.

Figure 3

(a) Energy vs strip number matrix for the horizontal strips of the Si detector placed above the beam axis. (b) Particle-$\gamma$-ray time-difference spectrum. The prompt and background time windows used to construct clean $\gamma$-ray spectra are indicated. (c) Particle energy spectrum obtained as projection of the matrix shown in (a).

Figure 4

(a) Prompt random-subtracted and Doppler-corrected $\gamma$-ray spectrum observed in the four MINIBALL detectors in Run II. (b) Prompt random-subtracted and Doppler-corrected particle energy vs $\gamma$-ray-energy matrix obtained in Run II.

Figure 5

Angular correlation functions for the $2_1^{+}\to 0_1^{+}$ transition in ${}^{72}\mathrm{Zn}$ observed in coincidence with C ions detected in one of the two Si detectors. Both experimental points (black circles) and fits (red curves) are normalized to $a_0=1$ for a better comparison.

Figure 6

Symmetric double ratios ${\rho }^c$ as a function of the angle $\theta$ for both runs and the three different analysis methods used.

Figure 7

Experimental precession angles $\Delta \Phi$ for both runs and the three different analysis methods used. The mean values (red) and their uncertainties (gray) are indicated by horizontal lines. The case of nonobservation of any effect ($\Delta \Phi =0$ mrad) is marked by black horizontal dashed lines. Dotted lines indicate the relative angle-dependent figure of merit, $M$ (see text for details). The values of $M$ have been scaled differently in each of the six cases to maximize the legibility of the figure.

Figure 8

Comparison between experimental and theoretical $g$ factors for the first excited $2^{+}$ state in even-even Zn isotopes. Experimental results for the stable isotopes are shown as black dots [4], the HVTF result for ${}^{72}\mathrm{Zn}$ [5] as a green diamond, the present TF result as a red square, and the average value of the TF and HVTF measurements for ${}^{72}\mathrm{Zn}$ as a blue dot. Shell-model calculations using the LNPS [24] (solid black line), JUN45 [25] (dotted line), and JJ4B [26] (dashed line) interactions are included. The thick black line represents the results of the beyond-mean-field calculations for ${}^{70,72,74}$Zn discussed in the text and the thin black line is the collective value $Z/A$.

Figure 9

Measured $g\left(2_1^{+}\right)$ values for ${}_{30}$Zn, ${}_{32}$Ge, ${}_{34}$Se, ${}_{36}$Kr, and ${}_{38}$Sr isotopes [4, 27] normalized to $Z/A$. The gray lines mark a 25% deviation from $Z/A$.

Figure 10

(Top panels) Contour lines in the ($\beta$,$\gamma$) plane of the potential energy surfaces of the ground states of the nuclei ${}^{70,72,74}$Zn in the PNAMP approach. The energy minimum has been set equal to zero for each panel. The contours are 1 MeV apart; only the odd ones have been labeled. (Bottom panels) Normalized collective wave functions of the ground states of the nuclei ${}^{70,72,74}$Zn in the ($\beta$,$\gamma$) plane. The contours are 0.0075 apart (dashed lines) from 0.03 to 0.1 and 0.01 apart from 0.01 to 0.03 (continuous lines).