Thomas Fermi model

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The Thomas-Fermi model is an atomic model in which the electron shell is treated like a gas of electrons . It was proposed by Llewellyn Thomas and Enrico Fermi in 1927 .

description

The electrons are bound in a potential well that is determined by the positive electrical charge of the atomic nucleus and the electrostatic repulsion of the electrons from one another. The potential well gives each electron a potential energy, the value of which varies locally. The electron density is adjusted in such a way that the maximum electron energy occurring in equilibrium is the same everywhere (constancy of the Fermi energy ). On the other hand, since the electron density itself determines the value of the potential energy, a self-consistent solution has to be found. This means that the location-dependent potential is determined in the Thomas-Fermi model by the fact that in the equilibrium state of the electron gas, the exact spatial distribution of the electron density is established which (together with the nucleus) produces this potential. The calculation uses the approximation that the Fermi energy of the electrons depends on their spatial density just as in an infinitely expanded electron gas.

The Thomas-Fermi model is the simplest way to take into account not only the Pauli principle but also the mutual electrostatic repulsion of the electrons in a multi-electron system, at least in a general way. The starting point is the only approximately correct idea that there is a fixed potential well and that it is the same for all electrons. The model therefore gives the same electron density curve for all atoms (according to their shape). The size of the atoms is shown correctly. The model cannot provide more precise ideas about the shape of the states of the individual electrons or more detailed information about the structure of the electron shell (e.g. atomic orbitals ). However, it is a good starting point for more precise calculations (e.g. using the Hartree-Fock method ). The basic idea of the Thomas-Fermi model is a method of self-consistent field (ger .: self consistent field "Thomas-Fermi method 'has also been applied to other many-body systems, SCF) or. The density functional theory is also a further development .

proof

  1. ^ LH Thomas: The Calculation of Atomic Fields . In: Mathematical Proceedings of the Cambridge Philosophical Society . tape 23 , no. 5 , 1927, pp. 542-548 , doi : 10.1017 / S0305004100011683 .
  2. ↑ E. Fermi: A statistical method for determining some properties of the atom and their application to the theory of the periodic system of elements . In: Journal of Physics . tape 48 , no. 1-2 , 1928, pp. 73-79 , doi : 10.1007 / BF01351576 . See also the Italian first publication by E. Fermi: Un metodo statistico per la determinazione di alcune priorieta dell'atome . In: Rendicondi Accademia Nazionale de Lincei . tape
     6 , no. 32 , 1927, pp. 602-607 .