Probing the ${}_{31}\mathrm{Ga}$ ground-state properties in the region near $Z=28$ with high-resolution laser spectroscopy

Magnetic-dipole and electric-quadrupole moments for ${}^{65,67,69,75,79\text{–}82}\mathrm{Ga}$ are reported using the Collinear Resonance Ionization Spectroscopy (CRIS) technique at the ISOLDE facility, CERN. The moments of ${}^{65}\mathrm{Ga}$ have been measured for the first time: $\mu =+1.775\left(3\right){\mu }_{\mathrm{N}}$ and $Q_s=+21.0\left(15\right)e{\mathrm{fm}}^2$. These results are compared to shell-model calculations using the GXPF1 and JUN45 interactions and the trends of the moments approaching the region of the doubly magic ${}^{56}\mathrm{Ni}$ are discussed. Additionally, new values for the change in mean-square charge radii for ${}^{65}\mathrm{Ga}$ and ${}^{67}\mathrm{Ga}$ allow investigation into the odd-even staggering in the region below $N=40$.

Figure 1

A diagram of the resonance ionization scheme used for neutral gallium, including the allowed hyperfine transitions (not to scale) for the 417.2-nm transition, assuming $I^{\pi }=3/2^{-}$.

Figure 2

Example hyperfine spectra for ${}^{65,67}\mathrm{Ga}$, using the $4p{}^{2}P_{3/2}\to 5s{}^{2}S_{1/2}$ transition. The solid lines are the best fit using an asymmetric Gaussian profile, assuming a spin assignment of $I=3/2^{-}$.

Figure 3

Isotope shift values from literature [4] plotted against this work. The green-dotted line represents consistency between the two data sets and the blue solid line represents the current relation between the two. Each data point is labeled according to the mass number involved.

Figure 4

A schematic representation of the model spaces involved for the GXPF1 and JUN45 interactions, shaded in blue and red respectively.

Figure 5

(a) The extracted $g$ factor for ${}^{65}\mathrm{Ga}$ (light-blue triangle), alongside tabulated values across the gallium isotope chain from Refs. [4, 25, 43] (dark-blue squares). Apart from ${}^{61}\mathrm{Ga}$, the error bars are smaller than the marker size. (b) $g$ factors for the odd-$A$ copper isotopes in the same mass range [15] (dark-blue squares). Values are compared to GXPF1 (black circles) and JUN45 (red diamonds) calculations. Effective $g$-factor values for the $\pi p_{3/2}$ and $\pi f_{5/2}$ orbitals are illustrated with dashed lines.

Figure 6

The extracted electric quadrupole moment for ${}^{65}\mathrm{Ga}$ (light-blue triangle), alongside literature values for the gallium [4, 38] and copper [17, 44] isotope chains (dark-blue squares). Values are compared to GXPF1 (black circles) and JUN45 (red diamonds) calculations.

Figure 7

Proton and neutron orbital occupations for odd-$A{}^{59\text{–}71}\mathrm{Ga}$, across the combined orbital space for the GXPF1 (black circles) and JUN45 (red diamonds) interactions. Proton occupancies (top) are viewed with respect to the occupancy of a single proton, while neutron occupancies (bottom) are viewed with respect to the total occupancy for a given orbital.

Figure 8

(a) Changes in the mean-square charge radii across the gallium isotope chain. Red circles represent new measurements for ${}^{65,67}\mathrm{Ga}$ ($N=34,36$) and blue circles denote literature values [4]. Statistical and atomic systematic uncertainty bounds are given by the shaded areas and black-dotted lines respectively. (b) Corresponding $D(N;\delta {\langle r^2\rangle }^{40,N})$ values representing the odd-even staggering, calculated from Eq. (3).