Nuclear spins, magnetic moments, and quadrupole moments of Cu isotopes from $N=28$ to $N=46$: Probes for core polarization effects

Measurements of the ground-state nuclear spins and magnetic and quadrupole moments of the copper isotopes from ${}^{61}\mathrm{Cu}$ up to ${}^{75}\mathrm{Cu}$ are reported. The experiments were performed at the CERN online isotope mass separator (ISOLDE) facility, using the technique of collinear laser spectroscopy. The trend in the magnetic moments between the $N=28$ and $N=50$ shell closures is reasonably reproduced by large-scale shell-model calculations starting from a ${}^{56}\mathrm{Ni}$ core. The quadrupole moments reveal a strong polarization of the underlying Ni core when the neutron shell is opened, which is, however, strongly reduced at $N=40$ due to the parity change between the $\mathit{pf}$ and $g$ orbits. No enhanced core polarization is seen beyond $N=40$. Deviations between measured and calculated moments are attributed to the softness of the ${}^{56}\mathrm{Ni}$ core and weakening of the $Z=28$ and $N=28$ shell gaps.

Figure 1

Experimental setup of the COLLAPS collinear laser spectroscopy beamline.

Figure 2

Production yield of radioactive ground states (solid symbols) and long-lived isomers (open symbols) during the experiments using the GPS (circles and squares) and using HRS (triangles). The limit for laser spectroscopy measurements before installation of the ISCOOL device is indicated with a solid line; the current limit is shown by a dashed line.

Figure 3

Fluorescence spectra for ${}^{72}\mathrm{Cu}$. (a) Before installation of the cooler/buncher, after 10 h of measurement. (b) With a bunched ion beam and photon gating, all six peaks are clearly resolved after 2 h of measurement.

Figure 4

Top: Hyperfine splitting of the ${}^2{S}_{1/2}$ and ${}^2{P}_{3/2}$ levels for a nuclear spin $I=1$. The hyperfine energy $E_F$ is given relative to the fine-structure energy. Bottom: Hyperfine spectra for ${}^{64}\mathrm{Cu}$ and ${}^{66}\mathrm{Cu}$. The sign of the magnetic and quadrupole moment is unambiguously determined by the positions and relative intensities of the resonances.

Figure 5

Ratio of the $A$ factors obtained from fitting the hyperfine spectra with their assigned nuclear spin. All values are in agreement within 2$\sigma$ with the literature value of 30.13(2) (horizontal bar).

Figure 6

Hyperfine spectrum for ${}^{68}\mathrm{Cu}$. The transition lines for the ground and isomeric state are shown. The zero of the frequency scale corresponds to the center of gravity of the ${}^{65}\mathrm{Cu}$ hyperfine structure.

Figure 7

The model space of the jj44b and JUN45 interactions consists of a ${}^{56}\mathrm{Ni}$ core, with copper isotopes having one proton outside the magic $Z=28$ shell. Beyond ${}^{57}\mathrm{Cu}$${}_{28}$ up to ${}^{79}\mathrm{Cu}$${}_{50}$, the negative parity neutron orbits $2p_{3/2}$, $1f_{5/2}$, and $2p_{1/2}$ and the positive parity $1g_{9/2}$ are filled, from the $N=28$ to the $N=50$ shell gap across the $N=40$ harmonic oscillator subshell gap.

Figure 8

Experimental $g$ factors (solid dots) compared with calculations (open symbols) using the jj44b and JUN45 interactions [17]. An effective spin $g$ factor of 0.7$g_{\mathrm{s},\mathrm{free}}$ was adopted.

Figure 9

Experimental and calculated energy levels of odd-$A$ Cu isotopes [30, 38, 39, 40, 41]. Only the lowest 1/2${}^{-}$, 3/2${}^{-}$, and 5/2${}^{-}$ states are shown.

Figure 10

The contributions to the spectroscopic quadrupole moment due to protons and neutrons separately, as given in Table . The neutron contribution is responsible for the observed core polarizing effect when moving away from $N=40$.

Figure 11

The measured spectroscopic quadrupole moments compared with shell-model calculations.

Figure 12

Experimental core polarization quadrupole moments compared to calculated core polarization moments with jj44b (top) and JUN45 (bottom). See text for details.

Figure 13

The experimental $g$ factors of the ground states of ${}^{58-74}\mathrm{Cu}$ (Table , solid circles) are compared with empirical $g$ factors using the additivity relation for simple proton-neutron configurations. The positive sign of the ${}^{66}\mathrm{Cu}$ value reveals a strongly mixed ground-state wave function.

Figure 14

Experimental and calculated lowest levels in the odd-odd Cu isotopes [24, 25, 30, 45]. Levels in bold have calculated moments in agreement with the experimentally measured magnetic and quadrupole moments of the ground state.

Figure 15

Experimental $g$ factors for the odd-odd Cu isotopes (solid dots) compared to calculations. The nuclear spin is added to distinguish between the different isomers in ${}^{64-70}\mathrm{Cu}$ (experimental values from Table ). Good agreement is obtained, except for the ${}^{66}\mathrm{Cu}$ 1${}^{+}$ ground state.

Figure 16

The experimental quadrupole moments for the odd-odd Cu isotopes compared with calculations [9].