Core polarization in the light of new experimentalgfactors offpshell,N=28,isotones

Precise experimental g factors of the first $2^{+}$ states of ${}^{50}\mathrm{Ti},$ ${}^{52}\mathrm{Cr},$ and ${}^{54}\mathrm{Fe}$ have been measured. They differ markedly from the g factors of the ${\mathrm{}(7/2)\mathrm{}}^{-}$ ground states of the odd-mass neighbors. The experimental results show that the g factors, ${g(2\mathrm{}}_1^{+})$ and $g\left({\mathrm{}(7/2)\mathrm{}}^{-}\right),$ lie approximately on straight lines as a function of Z albeit with different slopes. Shell model calculations were performed in which up to t nucleons were excited from the $f_{7/2}$ shell. The data are reproduced by calculations using the FPD6 interaction with $t=1.\mathrm{}$ However, the slope flattens out in the calculations with higher t. The sign of a key matrix element which allows for $f_{5/2}$ admixture is positive for the FPD6, zero for the KB3, and negative for the FPY interactions, respectively, indicating that a better understanding of the effective interaction in this region is needed.