The Leading Correction to the ThomasFermi Model at Finite Temperature
Abstract
The semiclassical approach leading to the ThomasFermi (TF) model provides a simple universal thermodynamic description of the electronic cloud surrounding the nucleus in an atom. This model is known to be exact at the limit of $Z\rightarrow\infty$, i.e., infinite nuclear charge, at finite density and temperature. Motivated by the zerotemperature case, we show in the current letter that the correction to TF due to quantum treatment of the strongly bound innermost electrons, for which the semiclassical approximation breaks, scales as $Z^{1/3}$, with respect to the TF solution. As such, it is more dominant than the quantum corrections to the kinetic energy, as well as exchange and correlation, which are known to be suppressed by $Z^{2/3}$. We conjecture that this is the leading correction for this model. In addition, we present a different free energy functional for the TF model, and a successive functional that includes the strongly bound electrons correction. We use this corrected functional to derive a selfconsistent potential and the electron density in the atom, and to calculate the corrected energy. At this stage, our model has a builtin validity limit, breaking as the L shell ionizes.
 Publication:

arXiv eprints
 Pub Date:
 December 2014
 DOI:
 10.48550/arXiv.1412.2402
 arXiv:
 arXiv:1412.2402
 Bibcode:
 2014arXiv1412.2402S
 Keywords:

 Condensed Matter  Materials Science;
 Astrophysics  Solar and Stellar Astrophysics;
 Condensed Matter  Other Condensed Matter;
 Physics  Atomic Physics
 EPrint:
 5 pages, 5 figures, 1 table