Numerical calculation of the Thomas-Fermi-von Weizsacker function for an infinite atom without electron repulsion

Technical Report · Thu Apr 01 04:00:00 EST 1982

DOI:https://doi.org/10.2172/5197412· OSTI ID:5197412

Lieb, E H; Liberman, D A

The Thomas-Fermi (TF) and Thomas-Fermi-von Weizsacker (TFW) theories of atoms and molecules with electron-electron repulsion are reviewed briefly. The main difference between the energies, E/sup TFW/ - E/sup TF/ (for large z), is a term D/sup TFW/z/sup 2/. (It is also believed that E/sup Q/ - E/sup TF/ approx. D/sup Q/z/sup 2/, where E/sup Q/ is the true quantum ground state energy). To calculate D/sup TFW/, it is necessary to find the positive solution to the differential equation: )- ..delta.. + vertical bar psi(x) vertical bar/sup 4/3/ - vertical bar x vertical bar/sup -1/) psi(x) = 0 in three dimensions. While this equation arises from TFW theory with electron-electron repulsion, it also has a second interpretation - namely as the TFW equation for an atom without electron-electron repulsion. The main content of this report is the numerical solution of this equation and the evaluation of D/sup TFW/.

• Research Organization: Los Alamos National Lab., NM (USA)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 5197412
• Report Number(s): LA-9186-MS; ON: DE82014123
• Country of Publication: United States
• Language: English

Related Subjects

640305* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Theory-- (-1987)
74 ATOMIC AND MOLECULAR PHYSICS
ATOMIC MODELS
ATOMIC NUMBER
DIFFERENTIAL EQUATIONS
ELECTRONIC STRUCTURE
ELECTRONS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
LEPTONS
MATHEMATICAL MODELS
NUMERICAL SOLUTION
THOMAS-FERMI MODEL