Structure of the electron momentum density of atomic systems

Abstract

The present paper addresses the controversial problem on the nonmonotonic behavior of the sphericallyaveraged momentum density γ(p) observed previously for some ground-state atoms based on the Roothaan-HartreeFock (RHF) wave functions of Clementi and Roetti. Highly accurate RHF wave functions of Koga et al. are used to study the existence of extrema in the momentum density γ(p) of all the neutral atoms from hydrogen to xenon. Three groups of atoms are clearly identified according to the nonmonotonicity parameter µ, whose value is either equal to, larger, or smaller than unity. Additionally, it is found that the function p −α γ(p) is (i) monotonically decreasing from the origin for α ≥ 0.75, (ii) convex for α ≥ 1.35, and (iii) logarithmically convex for α ≥ 3.64 for all the neutral atoms with nuclear charges Z = 1-54. Finally, these monotonicity properties are applied to derive simple yet general inequalities which involve three momentum moments p t . These inequalities not only generalize similar inequalities reported so far but also allow us to correlate some fundamental atomic quantities, such as the electron-electron repulsion energy and the peak height of Compton profile, in a simple manner.

Electron-momentum densities of singly charged ions

“…The 28 cations with [12][13][14][15][16][20][21][22]25,26,[32][33][34][38][39][40]43,[50][51][52]3,11,19,[21][22][23]37,40,41 have unimodal ⌸( p) with a maximum at pϭ0. Type II.…”

Hydrogen-like upper bounds to the electron momentum density of atoms

“…Apart from the quantum-mechanical non-negativity, only two other rigorous properties of (p) are known: the MacLaurin expansion for small momentum and the p −8 -behaviour at large momentum [6]. Numerically, this function has recently been investigated for the ground states of neutral atoms from H (Z = 1) to Lr (Z = 103), and for 97 singly charged ions, 54 cations from He + (Z = 2) to Cs + (Z = 55) and 43 anions from H − (Z = 1) to I − (Z = 53) [7][8][9][10]. According to (p) modalities three categories of atoms were clearly identified:…”

Relative Rényi entropy for atoms

“…The calculations have been performed for atomic numbers Z = 1–103 and for several values of α. The momentum space wave functions were computed using analytic expressions which where obtained by the three‐dimensional Fourier transformation of the finite superposition of Slater type functions 43–45 Note that the relative Rényi entropy is zero if f = g , and it measures the deviation of the density ϱ( r ) from ϱ asymp ( r ) or ϱ cusp ( r ) and γ( p ) from γ asymp ( p ) or γ cusp ( p ).…”