  We consider the energy level statistics of non-interacting electrons which
diffuse in a $ d $-dimensional disordered metallic conductor of characteristic
Thouless energy $ E_c. $ We assume that the level distribution can be written
as the Gibbs distribution of a classical one-dimensional gas of fictitious
particles with a pairwise additive interaction potential $ f(\varepsilon ). $
We show that the interaction which is consistent with the known correlation
function of pairs of energy levels is a logarithmic repulsion for level
separations $ \varepsilon <E_c, $ in agreement with Random Matrix Theory. When
$ \varepsilon >E_c, $ $ f(\varepsilon ) $ vanishes as a power law in $
\varepsilon /E_c $ with exponents $ -{1 \over 2},-2, $ and $ -{3 \over 2} $ for
$ d=1,2, $ and 3, respectively. While for $ d=1,2 $ the energy-level
interaction is always repulsive, in three dimensions there is long-range level
attraction after the short-range logarithmic repulsion.
