Ground-state electromagnetic moments of calcium isotopes

Background: The neutron-rich calcium isotopes have gained particular interest as evidence of closed-shell structures has recently been found in two exotic nuclei, at $N=32$ and $N=34$. Additionally, the study of such neutron-rich systems has revealed new aspects of nuclear forces, in particular regarding the role of three-nucleon forces.

Purpose: We study the electromagnetic properties of Ca isotopes around the neutron number $N=32$.

Methods: High-resolution bunched-beam collinear laser spectroscopy was used to measure the optical hyperfine spectra of the ${}^{43-51}\mathrm{Ca}$ isotopes.

Results: The ground-state magnetic moments of ${}^{49,51}\mathrm{Ca}$ and quadrupole moments of ${}^{47,49,51}\mathrm{Ca}$ were measured for the first time, and the ${}^{51}\mathrm{Ca}$ ground-state spin $I=3$/2 was determined in a model-independent way. Our experimental results are compared with state-of-the-art shell-model calculations using both phenomenological interactions and microscopic interactions derived from chiral effective field theory.

Conclusions: The results for the ground-state moments of neutron-rich isotopes are in excellent agreement with predictions of interactions derived from chiral effective field theory including three-nucleon forces. Lighter isotopes illustrate the presence of particle-hole excitations of the ${}^{40}\mathrm{Ca}$ core in their ground state. Our results provide a critical test of modern nuclear theories, and give direct answer to the evolution of ground-state electromagnetic properties in the Ca isotopic chain across three doubly closed-shell configurations at $N=20$, 28, 32 of this unique system.

Figure 1

Examples of hfs spectra measured for the Ca isotopes in the 393 nm $4s{}^2{S}_{1/2}\to 4p{}^2{P}_{3/2}$ ionic transition. The lines show the fit with a Voigt profile. Frequency values are relative to the centroid of ${}^{43}\mathrm{Ca}$.

Figure 2

Ratio between the hfs constants $A{(}^2{P}_{1/2})$ and $A{(}^2{P}_{3/2})$. The continuous line shows the average value $A{(}^2{S}_{1/2})/A{(}^2{P}_{3/2})=25.92\left(3\right)$. Hyperfine structure spectra of ${}^{51}\mathrm{Ca}$ were fitted assuming different g.s. spin values of $I=3/2,5/2,7/2$.

Figure 3

Measured $g$ factors compared with literature values and effective single-particle values (lines) using $g_s^{\nu }=-3.041$ and $g_l^{\nu }=0.0$ $\left(g_{\text{eff}}^{\nu }=0.8g_{\text{free}}^{\nu }\right)$. The magnetic moment of ${}^{39}\mathrm{Ca}$ was taken from Ref. [45]. The experimental error bars are smaller than the symbols.

Figure 4

Measured magnetic and quadrupole moments of Ca isotopes. Results are compared with theoretical predictions from phenomenological interactions (KB3G, GXPF1A, SDPF.SM) and calculations including three-nucleon forces $\left(NN+3N\right)$. Experimental literature values (empty triangles) are given in Table 2. The open circles show the values calculated from the ratios $B{(}^{41}\text{Ca})/B{(}^{43}\text{Ca})=1.63\left(1\right),B{(}^{45}\text{Ca})/B{(}^{43}\text{Ca})=-0.94\left(27\right)$ [31] and relative to our value of $Q{(}^{43}\text{Ca})$.