The large-Z behaviour of pseudo-relativistic atoms

Details The large-Z behaviour of pseudo-relativistic atoms The large-Z behaviour of pseudo-relativistic atoms

2004-08-30

arxiv.org/abs/math-ph/0408056v1

J. Math. Phys., 46, 052307 (2005)

Physics

Mathematical Physics

26 pages, 1 figure

Scientific paper

10.1063/1.1897645

In this paper we study the large-Z behaviour of the ground state energy of atoms with electrons having relativistic kinetic energy sqrt(p^2c^2+m^2c^4)-mc^2. We prove that to leading order in Z the energy is the same as in the non-relativistic case, given by (non-relativistic) Thomas-Fermi theory. For the problem to make sense, we keep the product Z*alpha fixed (here alpha is Sommerfeld's fine structure constant), and smaller than, or equal to, 2/pi, which means that as Z tends to infinity, alpha tends to zero.

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