Aage Bohr and Ben Mottelson (Nobel Prize, 1975.) This is NOT what the nucleus is doing!

Studies of the reduced electromagnetic transition probability B(E2) reveal that, indeed, these states have a transition strength equivalent to that of many, many single particles. They are indeed “collective” states.  All nucleons participate to some extent in the excitation of various nuclear states.

One of the most important developments in understanding the collective states of nuclei was the discovery of the Giant Dipole Resonance; it is usually excited by an energetic photon. Since the discovery of this collective 1^- state, many other giant resonances of many different types have been found. The most recent discovery, of a new kind of monopole spin-isospin excitation, was just a few years ago.  Density oscillations have not been seen, but isospin oscillations, where the proton distribution and neutron distribution swap places, are fairly common.

Monopole isovector spin resonance!

The more physics you know, the more surprising it might be that there are quite a few nuclei that exhibit a permanent deformation, breaking what one would expect to be a required symmetry under all rotations, for any system possessing a definite angular momentum quantum number! Well, that sounds like a job for the ever-useful concept of broken symmetry. In fact the rotational states can be considered the Goldstone Bosons that have to exist BECAUSE of the broken symmetry. However, the needed math is quite difficult and confusing, and gets about as ugly as the math of molecular vibrational/rotational spectra, especially because nuclei exhibit vibrations built on rotations, whereas molecules exhibit rotations built on vibrations!

A kindergarten level (undergraduate quantum physics) would describe a 3D quantum harmonic oscillator by E_ν = ℏω_ν[n_ν + (3/2)], where n is the number of phonons of order ν, and the rotational nuclei by Hamiltonian H = L²/(2I) leading to E_J = ℏ²J(J + 1)/(2I), where I is the rotational inertia.  In the diagram, K is the projection of J along the body-fixed symmetry axis.

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