A g-factor puzzle for the N=38 nuclei:First measurement of the $^{70}$Ge 4$_{1}^+$ magnetic moment.

The transient field technique in inverse kinematics allows $g$-factor studies of short-lived states. This method gives information on both the sign and the magnitude of the $g$ factor. In a recent experiment, the $g$ factor of the 4$^+_1$ state of $^{68}_{30}$Zn$_{38}$ was measured to be -0.37(17) suggesting a significant neutron g$_{9/2}$ contribution to the wave function[1]. However, shell model calculations in the 0f$_{5/2}$,1p$_{3/2}$,1p$_{1/2}$,0g$_{9/2}$ space [1] predict a positive, nearly zero $g$ factor. To obtain more information on this region we measured the magnetic moment of the 4$^+_1$ in $^{70}_{32}$Ge$_{38}$. The measurement was performed at WNSL, Yale, using a 275 MeV $^{70}$Ge beam and a multilayered C+Gd+Cu target. A positive $g$ factor was obtained. The measured magnetic moment was compared to full $fp$ shell model calculations which we performed with the code ANTOINE using several effective interactions. The results were in good agreement with the experiment. The experiment and the implications of the new results will be discussed.\\ 1. J. Leske {\it et al.}, Phys. Rev C {\bf 72}, 044301 (2005).