CALCULATION OF THEORETICAL ISOTROPIC COMPTON PROFILE FOR MANY PARTICLE SYSTEMS

Theoretical isotropic (spherically symmetric) Compton profiles (ICP) have been calculated for many particle systems' He , Li , Be and B atoms in their ground states. Our calculations were performed using Roothan–Hartree–Fock (RHF) wave function, HF wave function of Thakkar and re-optimized HF wave function of Clementi–Roetti, taking into account the impulse approximation. The theoretical analysis included a decomposition of the various intra and inter shells and their contributions in the total ICP. A high momentum region of up to 4 a.u. was investigated and a non-negligible tail was observed in all ICP curves. The existence of a high momentum tail was mainly due to the electron–electron interaction. The ICP for the He atom has been compared with the available experimental data and it is found that the ICP values agree very well with them. A few low order radial momentum expectation values 〈pn〉 and the total energy for these atomic systems have also been calculated and compared with their counterparts' wave functions.

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Compton profiles from numerical Hartree–Fock wave functions

Canadian Journal of Physics ◽

10.1139/p76-255 ◽

1976 ◽

Vol 54 (21) ◽

pp. 2155-2158 ◽

Cited By ~ 5

Author(s):

Robert Benesch

Keyword(s):

Impulse Approximation ◽

Wave Functions ◽

Neutral Atoms ◽

Hartree Fock ◽

Hf Wave

Nonrelativistic Compton profiles, J(q)'s, calculated within the impulse approximation from numerical Hartree–Fock (HF) wave functions are reported for the neutral atoms As (Z = 33) through Yb (Z = 70). Comparison with results reported for relativistic HF wave functions indicates that the overall effect of using the relativistic functions is to produce total J(q)'s which are flatter at the centre than those computed from nonrelativistic HF wave functions.

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Quantitative treatment for extracting coherent elastic scattering from X-ray scattering experiments

Journal of Applied Crystallography ◽

10.1107/s0021889898014071 ◽

1999 ◽

Vol 32 (2) ◽

pp. 322-326 ◽

Cited By ~ 4

Author(s):

Khalid Laaziri ◽

J. L. Robertson ◽

S. Roorda ◽

M. Chicoine ◽

S. Kycia ◽

...

Keyword(s):

Impulse Approximation ◽

Coherent Scattering ◽

High Energy ◽

Compton Profile ◽

Detector Resolution ◽

X Ray ◽

Hartree Fock ◽

Fitting Procedure ◽

X Ray Scattering ◽

Peak Function

A fitting procedure for separating the inelastic and elastic contributions to the total scattering in diffuse-scattering experiments at high energy using energy-dispersive X-ray techniques is presented. An asymmetric peak function is used to model the elastic peak. The inelastic scattering peak is modeled using a theoretical Compton profile, calculated using the impulse approximation (Hartree–Fock wave functions were used), convoluted with the detector resolution. This procedure, which requires only two free parameters, is shown to be extremely effective in extracting the integrated elastic intensity of coherent scattering at each wave vector, even at low scattering angles where the Compton scattering is not well resolved.

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Perturbation theory for atomic systems

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1959.0108 ◽

1959 ◽

Vol 251 (1265) ◽

pp. 282-290 ◽

Cited By ~ 157

Keyword(s):

Wave Function ◽

Perturbation Theory ◽

Quantitative Assessment ◽

Atomic System ◽

The Other ◽

Atomic Systems ◽

First Order ◽

Hartree Fock ◽

Alternative Procedures ◽

Variation Iteration Method

The equations of the Hartree and Hartree-Fock formulations for a perturbed atomic system are discussed. It is pointed out that there are two alternative procedures, one of which is correct to first order in the error of the unperturbed wave function, but not the other, and explicit expressions are written down for the error in the derived perturbed energies in the two cases. A quantitative assessment of the accuracy of the two procedures is provided by the calculation of the dipole and quadrupole polarizabilities of helium, a variation-iteration method being used to solve the relevant equations.

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The Validity of the Hartree-Fock (HF) Picture in Diamagnetic Binuclear Transition Metal Compounds: trans[(η5 -C5H5)Fe(CO)2]2

Zeitschrift für Naturforschung A ◽

10.1515/zna-1982-0307 ◽

1982 ◽

Vol 37 (3) ◽

pp. 241-247

Keyword(s):

Wave Function ◽

Transition Metal ◽

Closed Shell ◽

Iron Complex ◽

Transition Metal Compounds ◽

Metal Compounds ◽

Hartree Fock ◽

Hf Wave ◽

Binuclear Iron

Abstract The Thouless instability conditions in the binuclear iron complex 1 have been investigated by means of a semiempirical INDO approach. The behaviour of the restricted Hartree-Fock (HF) wave function with respect to singlet, non-singlet and complex variations of the orbitals is studied. The existence of a spin decoupled solution near the diamagnetic closed shell groundstate is demonstrated. The nature of the correlation processes (angular vs left-right) for the various orbital fluctuations is discussed.

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Electron correlation in Li + , He, H − and the critical nuclear charge system Z C : energies, densities and Coulomb holes

Royal Society Open Science ◽

10.1098/rsos.181357 ◽

2019 ◽

Vol 6 (1) ◽

pp. 181357 ◽

Cited By ~ 3

Author(s):

Adam L. Baskerville ◽

Andrew W. King ◽

Hazel Cox

Keyword(s):

Wave Function ◽

Electron Correlation ◽

Correlation Energy ◽

Nuclear Charge ◽

Lithium Cation ◽

Charge System ◽

Hartree Fock ◽

Coulomb Hole ◽

Helium Hydride ◽

Hf Wave

This paper presents high-accuracy correlation energies, intracule densities and Coulomb hole(s) for the lithium cation, helium, hydride ion and the system with the critical nuclear charge, Z C , for binding two electrons. The fully correlated (FC) wave function and the Hartree–Fock (HF) wave function are both determined using a Laguerre-based wave function. It is found that for the lithium cation and the helium atom a secondary Coulomb hole is present, in agreement with a previous literature finding, confirming a counterintuitive conclusion that electron correlation can act to bring distant electrons closer together. However, no evidence for a tertiary Coulomb hole is found. For the hydride anion and the system just prior to electron detachment only a single Coulomb hole is present and electron correlation decreases the probability of finding the electrons closer together at all radial distances. The emergence of a secondary Coulomb hole is investigated and found to occur between Z = 1.15 and Z = 1.20. The FC and HF energies and intracule densities (in atomic units) used to calculate the correlation energy and Coulomb hole, respectively, are accurate to at least the nano-scale for helium and the cation and at least the micro-scale for the anions.

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PARITY-PROJECTED RESONATING HARTREE-FOCK APPROXIMATION TO THE LIPKIN MODEL

International Journal of Modern Physics E ◽

10.1142/s0218301399000306 ◽

1999 ◽

Vol 08 (05) ◽

pp. 443-460 ◽

Cited By ~ 2

Author(s):

SEIYA NISHIYAMA ◽

MORIYOSHI IDO ◽

KAZUHIRO ISHIDA

Keyword(s):

Wave Function ◽

Ground State ◽

Correlation Energy ◽

Energy Functional ◽

Hartree Fock ◽

Parity Symmetry ◽

Lipkin Model ◽

Model Hamiltonian ◽

Ground State Correlation ◽

Hf Wave

An exact eigenstate of the Lipkin-model Hamiltonian has a parity-symmetry. The resonating Hartree-Fock (Res-HF) ground-state wave function however breaks the parity-symmetry. To restore the parity-symmetry, we develop a parity-projected (P-P) Res-HF approximation to the Lipkin model. The P-P Res-HF wave function is superposed by two P-P Slater determinants. Self-consistent calculation is carried out so as to optimize the P-P Res-HF energy functional. A Res-HF ground state with definite parity brings us the ground-state energy much nearer to the exact one than that the Res-HF and explains most of the ground-state correlation energy. We also show behaviour of P-P Res-HF orbital energies and mixing coefficients calculated by the P-P Res-HF approximation and compare them with those calculated by the parity-unprojected Res-HF approximation. From this comparison, we find very interesting relations between them which have never been seen in the parity-unprojected Res-HF calculation.

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