Variational occupation numbers to a Müller-type pair-density

Based on a parametric point-wise decomposition, a kind of isospectral deformation, of the exact one-particle probability density of an externally confined, analytically solvable interacting two-particle model system we introduce the associated parametric ($p$) one-matrix and apply it in the conventional Müller-type partitioning of the pair-density. Using the Schrödinger Hamiltonian of the correlated system, the corresponding approximate ground-state energy $E_p$ is then calculated. The optimization-search performed on $E_p$ with such restricted informations has a robust performance and results in the exact ($ex$) ground-state energy for the correlated model system $E_p=E_{ex}$.

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