Evidence for the microscopic formation of mixed-symmetry states from magnetic moment measurements

Using the transient field technique, the magnetic moments of the second excited $2^{+}$ states in ${}^{92,94}\mathrm{Zr}$ have been measured for the first time. The large positive $g$ factors, $g(2_2^{+};{}^{92}\mathrm{Zr})=+0.76(50)$ and $g(2_2^{+};{}^{94}\mathrm{Zr})=+0.88(27)$, which are in contrast to the known negative $g$ factors of the $2_1^{+}$ states, are found to be a consequence of weak proton-neutron coupling combined with the $Z=40$ subshell closure. From their large $M1$ transition strengths to the $2_1^{+}$ states, in earlier works an assignment to the $2_2^{+}$ states as proton-neutron symmetric and mixed-symmetry states has been made, which are now found to be polarized in their proton-neutron content. This fact allows to identify the underlying microscopic main configurations in the wave functions, which form the building blocks of symmetric and mixed-symmetry states in this region as valence nucleons are added and shell structure changes.

Figure 1

Particle-$\gamma$ coincidence spectra for ${}^{92}\mathrm{Zr}$ (bottom panel) and ${}^{94}\mathrm{Zr}$ (top panel) beams of 275 MeV.

Figure 2

Schematic IBM-2 calculation showing the dependence of energies (left) and $g$ factors (right) of the lowest $2^{+}$ states as a function of the $\mathit{pn}$ interaction strength. Proton and neutron boson numbers were chosen $N_{\pi }=N_{\nu }=1$.