Anatomy of an Inversion-46Ar

Two different interactions give very close results for properties of most even-even Ar isotopes, but for ${ }^{46}$Arthe results diverge. The interactions in question are a). WBT and b). SPDF-U. For ${ }^{42,44,46}$Ar the results are as follows : WBT E(2$_1 $+) (1.29,1.17,1.14) MeV E(2$_2 $+) (2.32,1.80,2.10) MeV g(2$_1 $+) (-.095,-.022,+.100 ) g(2$_2 $+) (.096,.045,-.070) SPDF-U E(2$_1 $+) (1.15,1.09,1.59) MeV E(2$_2 $+) (2.28,1.78,3.77) MeV g(2$_1 $+) (-.084,-.040,+.513) g(2$_2 $+) (+.075,+.346,+.514) To understand the big differences for A=46 we must look to the odd K isotopes. Consider the J=3/2$^+$---J=1/2$^+$ splitting.(MeV) EXPT/WBT/SPDF-U A=43 0.561,1.109,0.672 A=45 0.474, 0.871 ,0.345 A=47 -0.360,0.507,-0.320 A=49 0.200,0.729,0.078 We see that there is an inversion in the ``d$_{3/2} $ - s$_{1/2} $`` splitting for ${ }^{47}$K. The SPDF-U interaction successfully gives this inversion but WBT does not. Things are a bit different for B(E2,0$_1 $-2$_1 )$.The values in e$^2$fm$^4$ are WBT (338,425,541) /SPDF-U (351,357,525). Here the 2 interactions give very similar results. Both interactions yield a larger B(E2) for ${ }^{46}$Ar than for ${ }^{44}$Ar, as do previous calculations by others. This despite the fact that in single j A=46 has a closed shell of neutrons. Most experimental measurements had the opposite --larger B(E2) for A=44 than for A=46. But a most recent measurement by Mengone et al. disagrees with all previous measurements and agrees with the current shell model calculations.