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Title: Momentum density and spatial form of correlated density matrix in model two-electron atoms with harmonic confinement

The detailed nature of the correlated first-order density matrix for the model atoms in the title for arbitrary interparticle interaction u(r{sub 12}) is studied. One representation with contracted information is first explored by constructing the momentum density {rho}(p) in terms of the wave function of the relative motion, say {psi}{sub R}(r{sub 12}), which naturally depends on the choice of u(r{sub 12}). For u(r{sub 12})=e{sup 2}/r{sub 12}, the so-called Hookean atom, and for the inverse square law u(r{sub 12})={lambda}/r{sub 12}{sup 2}, plots are presented of the above density {rho}(p) in momentum space. The correlated kinetic energy is recovered from averaging p{sup 2}/2m, m denoting the electron mass, with respect to {rho}(p). The second method developed is in coordinate space and expands the density matrix {gamma}(r{sub 1},r{sub 2}) in Legendre polynomials, using relative coordinate r{sub 1}-r{sub 2}, center-of-mass coordinate (r{sub 1}+r{sub 2})/2 and the angle, {theta} say, between these two vectors. For the Moshinsky atom in which u(r{sub 12})=(1/2)kr{sub 12}{sup 2} only the s term (l=0) contributes to the Legendre polynomial expansion. The specific example we present of the inverse square law model is shown to be characterized by the low-order terms (s+d) of the Legendre expansion. The Wigner function is finallymore » calculated analytically for both Moshinsky and inverse square law models.« less
Authors:
;  [1] ;  [2] ;  [1] ;  [3] ;  [4]
  1. Departamento de Fisica de Materiales, Facultad de Ciencias Quimicas, Universidad del Pais Vasco, Centro Mixto UPV-CSIC, and Donostia International Physics Center (DIPC), 20018 San Sebastian (Spain)
  2. (ETSF), Centro Joxe Mari Korta, Avenida de Tolosa, 72, 20018 San Sebastian (Spain)
  3. (Belgium)
  4. (United Kingdom)
Publication Date:
OSTI Identifier:
21015970
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 76; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.76.032510; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; CENTER-OF-MASS SYSTEM; CONFINEMENT; DENSITY MATRIX; ELECTRONS; EXPANSION; HELIUM; INTERACTIONS; KINETIC ENERGY; LEGENDRE POLYNOMIALS; MASS; WAVE FUNCTIONS; WIGNER DISTRIBUTION