Magnetic Moments and Symmetries for even-even Argon Isotopes

In a single-j-shell calculation the spectra, g factors, and B(E2)'s of $^{40}$Ar and $^{44}$Ar are identical. Thus, deviations from this equivalence in the experimental data are due to configuration mixing. We do large-scale shell model calculations for the even-even Argon isotopes with the two interactions WBT and SDPF. The calculated g factors of the 2$_1^+$ states from A=38 to A=46 are, respectively, with WBT (.308,-.197,-.095,-.022,.100) and with SDPF (.319,-.228,-.084,-.040,.513). The two interactions agree very well except for $^{46}$Ar. For this nucleus the probability in the 2$_1^+$ wave function of the configuration where the neutrons form a closed f$_{7/2}$ shell, but a proton is excited from s$_{1/2}$ to d$_{3/2}$, is 2.5\% with WBT but 21.8\% with SDPF. This difference may be related to the rapid change with N of the J=(3/2)$^+$ - J=(1/2)$^+$ splittings in the odd-A Potassium isotopes. The respective calculated splittings from A=41 to A=49 in keV are with WBT (1106,1109,871,507,729) and with SDPF (854,672,345,-320,78), while the experimental ones are (980,561,474,-360,200). We see a crossover at A=47 which is given correctly by SDPF but not by WBT. This could help explain the large difference in the g(2$_1^+$) factors for $^{46}$Ar with these two interactions. It will be interesting to see what the experimental results will be.