brown and ravenhall
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BORN–OPPENHEIMER APPROXIMATION FOR THE BROWN–RAVENHALL EQUATION

2001 ◽  
Vol 13 (08) ◽  
pp. 921-951
Author(s):  
VANIA SORDONI
Keyword(s):  
Semiclassical Limit ◽  
Energy Levels ◽  
Mass Ratio ◽  
Nuclear Mass ◽  
Oppenheimer Approximation ◽  
Brown And Ravenhall

In this paper we study the pseudo-relativistic Hamiltonian proposed by Brown and Ravenhall in the semiclassical limit when the mass ratio h2 of electronic to nuclear mass tends to zero. We show that the relativistic contribution of the nuclei on WKB-type expansions of the first energy levels are of order o(h2), as h→0.

scholarly journals On the evaluation of the norm of an integral operator associated with the stability of one-electron atoms

1998 ◽  
Vol 128 (5) ◽  
pp. 993-1005 ◽  
Author(s):  
V. I. Burenkov ◽  
W. D. Evans
Keyword(s):  
Integral Operator ◽  
Partial Wave ◽  
Nuclear Charge ◽  
Critical Value ◽  
Partial Wave Decomposition ◽  
The Stability ◽  
Wave Decomposition ◽  
Brown And Ravenhall

The norm of an integral operator occurring in the partial wave decomposition of an operator B introduced by Brown and Ravenhall in a model for relativistic one-electron atoms is determined. The result implies that B is non-negative and has no eigenvalue at 0 when the nuclear charge does not exceed a specified critical value.

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