Intrinsic Quadrupole Moments and Shapes of Nuclear Ground States and Excited States

A new method of determining nuclear shapes is proposed which avoids the assumption of a specific nuclear model. The concept of an equivalent ellipsoid, whose charge and moments equal those of the nucleus, is employed. But the method is equally valid for spherical, deformed, and intermediate nuclei. It can be employed for any nucleus (evev-evevn, odd-$\mathbf{A}$, or odd-odd) provided enough $E2\mathrm{}$ matrix elements are available. The example of ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$ is discussed.