Isomer Shift and Magnetic Moment of the Long-Lived $1/2^{+}$ Isomer in ${}_{30}{}^{79}{\mathrm{Zn}}_{49}$: Signature of Shape Coexistence near ${}^{78}\mathrm{Ni}$

Collinear laser spectroscopy is performed on the ${}_{30}{}^{79}{\mathrm{Zn}}_{49}$ isotope at ISOLDE-CERN. The existence of a long-lived isomer with a few hundred milliseconds half-life is confirmed, and the nuclear spins and moments of the ground and isomeric states in ${}^{79}\mathrm{Zn}$ as well as the isomer shift are measured. From the observed hyperfine structures, spins $I=9/2$ and $I=1/2$ are firmly assigned to the ground and isomeric states. The magnetic moment $\mu$ $({}^{79}\mathrm{Zn})=-1.1866(10){\mu }_N$, confirms the spin-parity $9/2^{+}$ with a $\nu g_{9/2}^{-1}$ shell-model configuration, in excellent agreement with the prediction from large scale shell-model theories. The magnetic moment $\mu$ $({}^{79m}\mathrm{Zn})=-1.0180(12){\mu }_N$ supports a positive parity for the isomer, with a wave function dominated by a $2h\text{−}1p$ neutron excitation across the $N=50$ shell gap. The large isomer shift reveals an increase of the intruder isomer mean square charge radius with respect to that of the ground state, $\delta ⟨r_c^2{⟩}^{79,79m}=+0.204(6){\mathrm{fm}}^2$, providing first evidence of shape coexistence.

Figure 1

Typical hyperfine spectra of the ground and isomeric states in ${}^{79}\mathrm{Zn}$, denoted by asterisks and diamonds, respectively. The three isomeric transitions were confirmed in separate scans around each of the three peaks, as highlighted in the insert. The blue solid lines show the fit with a Lorentzian line profile.

Figure 2

Measured $g$ factors of the ground state of ${}^{79}\mathrm{Zn}$ and its isomer ${}^{79m}\mathrm{Zn}$ together with the $g$ factors of ${}^{65,67,69m,71m}\mathrm{Zn}$ from Refs. [27, 29, 30]. Effective single-particle $g$ factors (dashed lines) are calculated for each orbit, of which the parity is marked in the square brackets.

Figure 3

Root-mean-square charge radii of ${}^{79,79m}\mathrm{Zn}$ obtained from this work, together with earlier data on other Zn [39] isotopes and calculated rms charge radii using a modern phenomenological model by Wang and Li [40].

Figure 4

(a) Ground and isomeric states in Zn isotopes suggested in Refs. [19, 44, 45, 46, 47]. (b) Odd-mass $N=49$ level systematics, partially adopted from Refs. [1, 17]. The levels with a thick solid line are the long-lived isomeric states, and the diamonds mark the $1/2^{+}$ and $5/2^{+}$ intruder states. The firm spin assignment for the ${}^{79}\mathrm{Zn}$ levels are from this work.