Distribution of $r_{12}\cdot p_{12}$ in quantum systems

Abstract

We introduce the two-particle probability density $X(x)$ of $x={\mathbf{r}}_{12}\cdot {\mathbf{p}}_{12}=\left({\mathbf{r}}_1-{\mathbf{r}}_2\right)\cdot \left({\mathbf{p}}_1-{\mathbf{p}}_2\right)$. We show how to derive $X(x)$, which we call the Posmom intracule, from the many-particle wavefunction. We contrast it with the Dot intracule [Y. A. Bernard, D. L. Crittenden, 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, P. M. W .Gill, J.Phys. Chem.A, 114, 11984 (2010)]. To illustrate the usefulness of $X(x)$, we construct and discuss it for a number of two-electron systems.

17 pages, 8 figures, 5 tables, submitted to Mol. Phys. (Kutzelnigg Festschrift)

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Cited by in corpus (2)

• Distribution of xp in some molecular rotational states
• Measuring correlated electron motion in atoms with the momentum-balance density