Static Magnetic and Quadrupole Moments of Excited States of Nuclei

The gyromagnetic ratio $(g)$ is the ratio of $\mu$ to J. We have noticed that many isoscalar $g$ factors of excited states in both even-even and odd-odd nuclei have values close to 0.5 nuclear magnetons. It should be noted that both the collective model and the single $j$ shell model (in the limit of large orbital angular momentum $l$) predict this result. We also note the importance of the ``$l$ forbidden" $[Y^2 \sigma ]^1$ term for magnetic moments. For quadrupole moments we define the quadrupole ratio, $\frac {Q_0(S)}{Q_0(B)}$ i.e. the ratio between the intrinsic quadrupole moment deduced from $2^+$ states and from $B(E2)_{0 \rightarrow 2}$. Ideally, the rotational model predicts a value of one for the quadrupole ratio while the simple vibrational model predicts zero. The poster will show a graph plotting this ratio against mass number. There are small regions where the ratio is close to zero and $\frac{E(4)}{E(2)} $ is close to two. Also, there are regions where the quadrupole ratio is close to one and $\frac{E(4)}{E(2)}$ is close to $\frac{10}{3}$. Yet there are intermediate regions which lie in between these two limits. This theoretical analysis is of relevance to the experimental program of Prof. Noemie Koller at Rutgers University.