Analytical Expressions for the Hartree—Fock Potential of Neutral Atoms and for the Corresponding Scattering Factors for X Rays and Electrons

1964 ◽  
Vol 40 (6) ◽  
pp. 1686-1691 ◽  
Author(s):  
T. G. Strand ◽  
R. A. Bonham
Keyword(s):  
X Rays ◽  
Neutral Atoms ◽  
Hartree Fock ◽  
Analytical Expressions

X-ray Scattering Factors of Ions in Crystals

1979 ◽  
Vol 34 (12) ◽  
pp. 1471-1481 ◽  
Author(s):  
P. C. Schmidt ◽  
Alarich Weiss
Keyword(s):  
Gaseous Phase ◽  
Form Factors ◽  
Negative Ions ◽  
X Rays ◽  
Charged Sphere ◽  
Sphere Model ◽  
X Ray ◽  
Hartree Fock ◽  
X Ray Scattering ◽  
Atomic Scattering

AbstractThe atomic scattering factors for X - Rays are given for the ions Li⊕, Be2⊕, B3⊕, C4⊕, N5⊕, N3⊖, O2⊖, F⊖, Na⊕, Mg2⊕, Al3⊕, S2⊖, Cl⊖, K⊕, Ca2⊕, Sc3⊕, Ti4⊕, V5⊕, Ni, Cu⊕, Zn2⊕, Ga3⊕, Se2⊖, Br⊖, Rb⊕, Sr2⊕, Y3⊕, Pd, Ag⊕, Cd2⊕, I⊖, Cs⊕, and Ba2⊕ in the crystal. The crystal potential is simulated by a hollow charged sphere (Watson sphere model). The Hartree-Fock-Roothaan-method was used for the calculation. The crystal field affects most strongly the atomic form factors of the negative ions, especially the twofold and threefold ionized negative ions, which are unstable in the gaseous phase.

Analytical Hartree‐Fock wavefunctions for the neutral atoms from helium to xenon

1974 ◽  
Vol 60 (8) ◽  
pp. 3342-3342 ◽  
Author(s):  
Carla Roetti ◽  
Enrico Clementi
Keyword(s):  
Neutral Atoms ◽  
Hartree Fock

POTENTIAL OF NUCLEON INTERACTION WITH ODD NUCLEI IN THE HARTREE-FOCK THEORY

1999 ◽  
Vol 08 (02) ◽  
pp. 137-157 ◽  
Author(s):  
S. M. KRAVCHENKO ◽  
A. P. SOZNIK
Keyword(s):  
Optical Potential ◽  
Nucleon Nucleon ◽  
Effective Density ◽  
Nuclear Surface ◽  
Nucleon Interaction ◽  
Hartree Fock ◽  
Order Of Magnitude ◽  
Nucleon Nucleon Interaction ◽  
Analytical Expressions ◽  
Strong Spin

An expression for the real part of the optical potential of nucleon interaction with odd nuclei is derived in the Hartree-Fock approximation with effective density-dependent nucleon-nucleon interaction. It is shown for 13 C nucleus, as an example, that this potential contains the central interaction, as well as two spin-orbit forces connected with the spins of scattered nucleon and nucleus, and quite strong spin-spin and tensor interactions. The simple analytical expressions have been obtained for these potentials. The radial distributions of the interactions obtained and their energy dependences are investigated. It is shown that all potentials differ for neutron and proton scattering while the spin-spin and tensor forces in both cases have opposite signs, complicated radial dependences and are the same by an order of magnitude on the nuclear surface.

Nuclear Mass Dependence of the Dirac–Breit–Pauli Hamiltonian

1974 ◽  
Vol 52 (6) ◽  
pp. 536-540 ◽  
Author(s):  
Jacek Karwowski ◽  
Serafin Fraga
Keyword(s):  
Mass Effect ◽  
Mass Dependence ◽  
Neutral Atoms ◽  
Nuclear Mass ◽  
Specific Mass ◽  
Hartree Fock ◽  
Relativistic Mass ◽  
Mass Correction ◽  
Order Of Magnitude ◽  
Mass Dependent

The nuclear mass dependent (relativistic, specific, and normal) corrections for many electron atoms are discussed. Numerical values, determined from Hartree–Fock functions for all the neutral atoms from helium through nobelium, show that the relativistic mass correction, never included in actual calculations, is of the same order of magnitude as the specific mass effect.

Compton profiles from numerical Hartree–Fock wave functions

1976 ◽  
Vol 54 (21) ◽  
pp. 2155-2158 ◽  
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.

APPROXIMATE FORMULAS FOR THE INTENSITY AND ASYMMETRY OF THE HIGH-ENERGY ELECTRON BEAM AFTER TWO SCATTERINGS IN THE HARTREE-FOCK FIELD

1965 ◽  
Vol 43 (8) ◽  
pp. 1518-1524
Author(s):  
T. Tietz ◽  
L. S. Su
Keyword(s):  
Electron Beam ◽  
Born Approximation ◽  
High Energy ◽  
Energy Electron ◽  
High Energy Electron ◽  
Hartree Fock ◽  
Dirac Equations ◽  
Analytical Expressions ◽  
Approximate Formulas

In this paper, by using accurate approximations for the Hartree–Fock field as well as the Dirac equations and the second Born approximation, we have derived analytical expressions for the intensity and asymmetry of a high-energy electron beam after two scatterings.

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