TEMPERATURE BEHAVIOR OF THE THOMAS-FERMI STATISTICAL MODEL FOR ATOMS,

Abstract

The usual theoretical calculations of equations of state and specific heats, particularly at high temperatures and pressures, are dependent on the Thomas-Fermi statistical model of the atom. The mathematical description of this model involves complicated nonlinear differential equations, for which there have been an inadequate number of solutions available in the past. A number of solutions sufficiently extensive to determine the thermodynamic properties of all elements over an exceedingly wide range of temperatures and densities were obtained with the aid of an IBM 701 Defense Calculator. The results are presented in graphical form. In addition, some of the analytic properties of the Thomas-Fermi equations were investigated and certain approximate analytic solutions have been derived for limiting cases. (Author)

Document Details

Document Type
Technical Report
Publication Date
Apr 25, 1955
Accession Number
AD0604704

Entities

People

  • Richard Latter

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Calculators
  • Differential Equations
  • Equations
  • Equations Of State
  • High Temperature
  • Linear Differential Equations
  • Mathematical Analysis
  • Mathematics
  • Nonlinear Differential Equations
  • Specific Heat
  • Thermodynamic Properties

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Quantum spin resonance or Electron Paramagnetic Resonance spectroscopy.
  • Systems Analysis and Design