Exact integral relation between the triplet correlation function in the ground state of the completely polarized homogeneous electron fluid and the pair function: comparison with the classical liquid argon result

In a classical monoatomic liquid such as argon, there is a well-known relation between an integral over the triplet correlation function and the pair function, independent of the interparticle interaction. Here, we make a start on establishing a quantum-mechanical analogue by considering the ground state of the completely spin-polarised homogeneous electron fluid. Again, an exact relation is then established, but now at T = 0, for such a Fermion fluid, where only Pauli principle repulsions exist between all the electrons. A possible generalisation to embrace additional electron-electron Coulombic repulsions is thereby conjectured.