Quasipinning and entanglement in the lithium isoelectronic series

The Pauli exclusion principle gives an upper bound of 1 on natural occupation numbers. Recently there has been an intriguing amount of theoretical evidence that there is a plethora of additional generalized Pauli restrictions or (in)equalities, of a kinematic nature, satisfied by these numbers [M. Altunbulak and A. Klyachko, Commun. Math. Phys. 282, 287 (2008)]. Here a numerical analysis of the nature of such constraints is effected in real atoms. The inequalities are nearly saturated, or quasipinned. For rank 6 and rank 7 approximations for lithium, the deviation from saturation is smaller than the lowest occupancy number. For a rank 8 approximation we find well-defined families of saturation conditions.