The dirac second-order equation and an improved quasirelativistic theory of atoms

A transformation decoupling the Dirac second-order equations for the large and small components of the radial atomic wavefunction has been derived. The decoupling procedure is exact for one-electron atoms and approximate, though very accurate, for a general case of an atomic spherical potential. Its connection with the quasirelativistic theory of atoms has been discussed. The transformation has been applied to deriving an optimized quasirelativistic equation and to establishing relations between the quasirelativistic and the Dirac wavefunctions. Formulas resulting from these considerations allow improvement of quasirelativistic expectation values of operators so that the error, relative to the Dirac values, is reduced by a factor of 10.