  In this contribution we determine the exact solution for the ground-state
wave function of a two-particle correlated model atom with harmonic
interactions. From that wave function, the nonidempotent one-particle reduced
density matrix is deduced. Its diagonal gives the exact probability density,
the basic variable of Density-Functional Theory. The one-matrix is directly
decomposed, in a point-wise manner, in terms of natural orbitals and their
occupation numbers, i.e., in terms of its eigenvalues and normalized
eigenfunctions. The exact informations are used to fix three, approximate,
independent-particle models. Next, a time-dependent external field of finite
duration is added to the exact and approximate Hamiltonians and the resulting
Cauchy problem is solved. The impact of the external field is investigated by
calculating the energy shift generated by that time-dependent field. It is
found that the nonperturbative energy shift reflects the sign of the driving
field. The exact probability density and current are used, as inputs, to
investigate the capability of a formally exact independent-particle modeling in
time-dependent DFT as well. The results for the observable energy shift are
analyzed by using realistic estimations for the parameters of the two-particle
target and the external field. A comparison with the experimental prediction on
the sign-dependent energy loss of swift protons and antiprotons in a gaseous He
target is made.
