The liquid drop model (LDM) is a macroscopic description of the nucleus that likens it to a droplet of uniform, incompressible fluid composed of nucleons. It captures bulk nuclear properties such as binding energy, stability, and fission behavior, but no details.

The “magic numbers” of the independent particle model show up clearly if you look closely at the detailed systematics of the curve of binding energy.

Niels Henrik David Bohr (1885 – 1962)

John Archibald Wheeler (1911 – 2008)

Carl Friedrich Freiherr von Weizsäcker (1912 – 2007)

George Gamow (1904 - 1968)

Hans Bethe (1906 - 2005)

Remember that molecules, atoms, and nuclei all have masses LESS than the summed total mass of the constituents, since the internal energy of a bound system is negative when we define the zero of energy as the state where all constituents are separated by an infinite distance. An atomic mass unit (symbolized  amu or au) is defined as precisely 1/12 the mass of an atom of ¹²C. Not used by nuclear physics!!

Equally spaced harmonic oscillator states.

Energy goes like J(J+1), rigid rotor.

Medium and heavy even-even nuclei have energy levels that unmistakably correspond to vibrational or rotational collective modes involving the entire nucleus and nearly every particle in the nucleus.