  The correlation energy in density functional theory can be expressed exactly
in terms of the change in the probability of finding two electrons at a given
distance $r_{12}$ (intracule density) when the electron-electron interaction is
multiplied by a real parameter $\lambda$ varying between 0 (Kohn-Sham system)
and 1 (physical system). In this process, usually called adiabatic connection,
the one-electron density is (ideally) kept fixed by a suitable local one-body
potential. While an accurate intracule density of the physical system can only
be obtained from expensive wavefunction-based calculations, being able to
construct good models starting from Kohn-Sham ingredients would highly improve
the accuracy of density functional calculations. To this purpose, we
investigate the intracule density in the $\lambda\to\infty$ limit of the
adiabatic connection. This strong-interaction limit of density functional
theory turns out to be, like the opposite non-interacting Kohn-Sham limit,
mathematically simple and can be entirely constructed from the knowledge of the
one-electron density. We develop here the theoretical framework and, using
accurate correlated one-electron densities, we calculate the intracule
densities in the strong interaction limit for few atoms. Comparison of our
results with the corresponding Kohn-Sham and physical quantities provides
useful hints for building approximate intracule densities along the adiabatic
connection of density functional theory.
