Distribution of r_(12) ? p_(12) in quantum systems

摘要

We introduce the two-particle probability density X(x) of x = r_(12) ? p_(12) = (r_1 ? r_2) ? (p_1? p_2). The fundamental equations involved in the derivation of this new intracule X(x), which we call the Posmom intracule, are derived and we show how to derive X(x) from the many-particle wave-function. We contrast it with the Dot intracule [Y.A. Bernard, D.L. Crittenden, and P.M.W. Gill, Phys. Chem. Chem. Phys. 10, 3447 (2008)] which can be derived from the Wigner distribution and show the relationships between the Posmom intracule and the one-particle Posmom density [Y.A. Bernard, D.L. Crittenden, and P.M.W. Gill, J. Phys. Chem. A 114, 11984 (2010)]. To illustrate the information provided by the Posmom intracule, we apply this new formalism to various two-electron systems: the three-dimensional parabolic quantum dot, the helium-like ions and the ground and excited states of the helium atom.