= Nuclear deformation
Departure of an intrinsic nuclear shape from <spherical symmetry>. Here intrinsic means referred to axes attached to a model <nuclear charge distribution>. A nuclear <quantum state> with definite <spin> need not have the same laboratory <charge density> as that intrinsic distribution. In particular, the <ground state> of a deformed <even-even nucleus> can have $I=0$, a spherical laboratory <expectation value>, and a nonzero <intrinsic nuclear quadrupole moment>.
For an illustrative uniform <charge density> inside a <spheroid>, let the semiaxes be $(a,a,c)$ and keep its <volume> equal to that of a sphere of radius $R$:
$$
a^2c=R^3,\qquad a=R\eta^{-1/3},\qquad c=R\eta^{2/3},\qquad\eta=\frac ca>0.
$$
Thus $\eta>1$ gives a <prolate spheroid>, $\eta=1$ a sphere, and $\eta<1$ an <oblate spheroid>. These are three-dimensional equal-<volume> shapes: equal areas of their drawn cross-sections would be a different constraint. Real <nuclear charge distributions> have diffuse surfaces and need not be uniform, axially symmetric or confined to one shape.
\Image[/nuclear-equal-volume-deformations.png]
{title=Equal-volume prolate, spherical and oblate intrinsic shapes}
{description=Original <spheroid> geometry with chosen axis ratios $\eta=1.8,1,1/1.8$. Each has $a^2c=R^3$. The surfaces illustrate shape coordinates, rather than literal arrangements or photographs of <nucleons>. The indicated signs refer to the <intrinsic nuclear quadrupole moment> of positive uniform <charge density>.}
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