In the effective temperature given above, the temperature is used to construct an effective classical model. However, this form of the effective temperature does not correctly recover the specific heat and most other properties of the finite- T electron fluid even for the non-interacting electron gas. It does not of course attempt to include electron-electron interaction effects. A simple form for an effective temperature which correctly recovers all the density-functional properties of even the interacting electron gas, including the pair-distribution functions at finite T , has been given using the classical map hyper-netted-chain (CHNC) model of the electron fluid. That is T e f f E F = ( T 2 E F 2 + T q 2 E F 2 ) 1 / 2 where the quantum temperature T q is defined as: T q E F = 1 a + b r s + c r s where a = 1.594, b = −0.3160, c = 0.0240. Here r s is the Wigner–Seitz radius corresponding to a sphere in atomic units containing one electron. That is, if n is the number of electrons in a unit volume using atomic units where the unit of length is the Bohr, viz., 5.291 77 × 10 cm, then r s = ( 3 4 π π n ) 1 / 3 . For a dense electron gas, e.g., with r s ≈ ≈ 1 or less, electron-electron interactions become negligible compared to the Fermi energy, then, using a value of r s close to unity, we see that the CHNC effective temperature at T = 0 approximates towards the form 2 E F / 3 . Other mappings for the 3D case, and similar formulae for the effective temperature have been given for the classical map of the 2-dimensional electron gas as well.