Thomas–Fermi model

The Thomas-Fermi model is a model of the atom, electrons in the sheath such as a gas is treated by electrons. It was proposed in 1927 by Llewellyn Thomas and Enrico Fermi.

Description

The electrons are bound in a potential well, which is determined by the positive electric charge of the nucleus and the electrostatic repulsion between the electrons. The potential well gives each electron potential energy, whose value varies locally. The electron density adjusts itself so that in every place the maximum occurring at equilibrium electron energy is the same everywhere ( constancy of the Fermi energy). Other hand, since the electron density itself, the value of the potential energy determines a self-consistent solution must be found. That is, the position-dependent potential is determined by the Thomas - Fermi model that precisely adjusts the spatial distribution of the electron density in the equilibrium state of the electron gas, which ( together with the core ) produces this potential. In the calculation, the approximation is used, that the Fermi energy of the electrons from their spatial density just as dependent as in an infinite electron gas.

The Thomas-Fermi model is the simplest way to take into account in a multi -electron system not only the Pauli principle, but also the mutual electrostatic repulsion of the electrons, at least in the standard way. The starting point is only approximately correct idea that there is a fixed potential well and he was for all the electrons equal. The model thus obtained for all the atoms ( in shape ), the same profile of the electron density. The size of atoms is correctly reproduced. More detailed picture of the shape of the states of the individual electrons or more detailed information about the structure of the electron shell (eg atomic orbitals ) can not provide the model. But it is a good starting point for accurate calculations therefor ( for example, after the Hartree-Fock method ). The basic idea of the Thomas-Fermi model is as a method of self-consistent field: has also been applied or " Thomas-Fermi method" to other many-body systems (English self consistent field, SCF). A further development is the density functional theory.

Evidence

• Atomic physics
• Enrico Fermi