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The full relativistic KS equations
is be transformed into an equation for the large component only
and averaged over spin-orbit components. In atomic units
(Rydberg: 
 = 1, m = 1/2, e2 = 2):
 = 1, m = 1/2, e2 = 2):
| -  +   + M(r)  V(r) -    Rnl(r) |  |  |  | 
| -     +      = 0, |  |  | (12) | 
 
where 
 = 1/137.036 is the fine-structure constant,
 = 1/137.036 is the fine-structure constant,


 = - 1 is the degeneracy-weighted average value 
of the Dirac's
 = - 1 is the degeneracy-weighted average value 
of the Dirac's  for the two spin-orbit-split levels, M(r) is
defined as
The charge density is defined as in the nonrelativistic case:
 for the two spin-orbit-split levels, M(r) is
defined as
The charge density is defined as in the nonrelativistic case:
Filippo Spiga
2016-04-24