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What does it mean for an atomic nucleus to have a shape? Can elemental isotopes have different isomers based on their shape?

I thought that atomic nuclei were defined the same exact way that an electron shell is; that is to say, just as electrons are parts of probability clouds, so are the nucleons. Just as electrons have specific shapes of probability clouds due to the electromagnetic force, nucleons would be bound to each other into a similar probability cloud by the residual strong nuclear force.

However, I only ever see the liquid drop model used, which (presumably erroneously) implies that nucleons are ball-like "molecules" in a "drop" and can jostle around to rearrange themselves in a semi-rigid fashion, which confuses me as to what is the "correct" description of nuclear models, because that would also imply that a whole new can of worms of nucleon arrangement isomers would be opened (such as a Ca-40 nucleus divided into a proton hemisphere and a neutron hemisphere, or a neutron core with a proton shell), which I have not seen mentioned anywhere.

I have seen nuclei described as not necessarily being spherical, but also as prolate, oblate, ellipsoidal, and even banana and pear/mushroom-shaped. What exactly does this mean, and what effect does it have on chemical and nuclear properties and how are they classified in terms of isomerism? Is the liquid drop model correct, or does the strong nuclear force allow for asymmetrical probability clouds? If not, what keeps nucleons ("molecules") in these configurations, i.e. why are the shapes of asymmetrical "drops" stable?
gpt
>I thought that atomic nuclei were defined the same exact way that an electron shell is; that is to say, just as electrons are parts of probability clouds, so are the nucleons. Just as electrons have specific shapes of probability clouds due to the electromagnetic force, nucleons would be bound to each other into a similar probability cloud by the residual strong nuclear force.

Yes, nuclei have a very similar structure, except the interactions between nucleons are very different than the interactions between electrons and a nucleus.

The liquid drip model is *one* way to think about nuclei, and it’s pretty simplistic. Another way is in terms of the nuclear shell model, which is similar to the atomic shell model that everybody studies in chemistry class.

When we talk about “shapes”, we’re talking about moments of the electric charge density of the nucleus. If the nucleus is a perfect sphere (as some are), they are pure electric monopoles, and all other moments are zero.

The next leading-order electric moment which isn’t highly suppressed by symmetry is the electric quadrupole moment. Any nucleus with a nonzero quadrupole moment has a shape which deviates from spherical. And most nuclides have nonzero quadrupole moments. These ones are either prolate or oblate, depending on the sign of the quadrupole moment (defined to be the Q*_zz_* element of the quadrupole tensor, where z is the spin axis).

It’s also been shown that some nuclides in their ground states have nonzero octupole moments. These nuclides are “pear-shaped”, and this is a big deal because electric octupole moments break parity and time-reversal symmetries.

Yes, nuclides can have isomers with different shapes than their ground states. There is a phenomenon called shape coexistence where two different shapes are close in energy.

And the basics liquid drop model is really just a model of the binding energies of nuclei, it doesn’t predict things like quadrupole moments. So the LDM doesn’t really know anything about nuclear shapes.