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In most nuclear many-body methods, observables are calculated using many-bodywave functions explicitly. The variational two-particle reduced density matrixmethod is one of the few exceptions to the rule. Ground-state energies of bothclosed-shell and open-shell nuclear systems can indeed be evaluated byminimizing a constrained linear functional of the two-particle reduced densitymatrix. However, it has virtually never been used in nuclear theory, becausenuclear ground states were found to be well overbound, contrary to those ofatoms and molecules. Consequently, we introduced new constraints in the nuclearvariational two-particle reduced density matrix method, developed recently foratomic and molecular systems. Our calculations then show that this approach canprovide a proper description of nuclear systems where only valence neutrons areincluded. For the nuclear systems where both neutrons and protons are active,however, the energies obtained with the variational two-particle reduceddensity matrix method are still overbound. The possible reasons for the noticeddiscrepancies and solutions to this problem will be discussed.

Revisiting the variational two-particle reduced density matrix for nuclear systems