Statistical Theory of the Atom in Momentum Space

H. Siedentop, V. von Conta

2015, v.21, №3, 433-448

ABSTRACT

We investigate the momentum energy functional for atoms found by
Englert \cite{Englert1992} who also discussed the relation to the
Thomas\tire Fermi functional. We prove that the momentum functional
yields upon minimization the same value as the well-known
Thomas\tire Fermi functional. In fact, we show an explicit relation
between the minimizers of the functionals. Moreover, it turns out
that the atomic momentum density converges on the scale $Z^{2/3}$ to
the minimizer of the momentum energy functional.

Keywords: statistical theory in momentum space, asymptotic behavior of the momentum density