Distribution of r•p in atomic systems

We present formulas for computing the probability distribution of the posmom s = r • p in atoms, when the electronic wave function is expanded in a single particle Gaussian basis. We study the posmom density, S(s), for the electrons in the ground states of 36 lightest atoms (H-Kr) and construct an empirical model for the contribution of each atomic orbital to the total S(s). The posmom density provides unique insight into types of trajectories electrons may follow, complementing existing spectroscopic techniques that provide information about where electrons are (X-ray crystallography) or where they go (Compton spectroscopy). These, a priori, predictions of the quantum mechanically observable posmom density provide an challenging target for future experimental work.