the liquid drop model

Picture the nucleus not as a swarm of individual particles but as a tiny drop of an incompressible, charged fluid. The nucleons are like molecules in a raindrop: densely packed, tugging on their immediate neighbours, held together by surface tension, all sitting at roughly constant density no matter how big the drop is. This deliberately classical, collective image is the liquid drop model, first developed by Gamow and Bohr, and it captures a surprising amount of a nucleus's bulk behaviour.

The model rests on two observations. First, nuclear matter is nearly incompressible: nuclear radius scales as R = r_0 A^(1/3) with r_0 approximately 1.2 fm, so volume grows in proportion to the number of nucleons and the density is roughly constant, exactly like a liquid. Second, the short-range nuclear force saturates, each nucleon interacting only with its nearest neighbours, which is why binding grows with volume while a surface term corrects for nucleons at the edge. These ideas translate directly into the volume and surface terms of the semi-empirical mass formula, with Coulomb repulsion added because the drop is charged.

Its greatest triumph is nuclear fission. Treat the drop as deformable: stretch it, and surface tension tries to pull it back to a sphere while the Coulomb repulsion of the elongated charge tries to drive it apart. For heavy nuclei the Coulomb term can win once the drop deforms enough, so the nucleus necks and splits, with a fission barrier set by the competition of the two effects. The model's honest limit is that it is purely collective; it says nothing about the single-particle shell structure, and magic numbers are invisible to it.