The Pauli–Sommerfeld free electron model of a metal is remarkably successful in describing many of the properties of metals such as the linear behavior of the specific heat (C = γT) and the temperature-independent paramagnetic susceptibility. However, the energy associated with the Coulomb repulsion between electrons is of the same order as the kinetic energy and it is therefore not at all obvious that such a model should work at all.

Liquid He (at temperatures below 0.1 K) is another Fermi system which has some features in common with a Fermi gas. (He has no electronic spin and its statistics are governed by its I = 1/2 nuclear spin.) It may be thought of as having an even larger particle–particle interaction since the ‘empty volume’ for the atoms to move in is small; most of the liquid volume is occupied by the essentially impenetrable ‘hard core’ associated with the filled Is shell of the He atoms.

The long range of the Coulomb potential adds an initially unnecessary feature to understanding the success of the independent (or free) electron model so we will use (neutral) liquid He as our model Fermi ‘liquid’.

The success of the Pauli–Sommerfeld model rests on there being a sharp discontinuity separating the occupied from the unoccupied states at T = 0 which is associated with the Fermi occupation factor, n(ε).