The Douglas-Kroll-Heß method: Convergence and block-diagonalization of dirac operators

Abstract

We show that the Douglas-Kroll block-diagonalization method for the Dirac operator with Coulomb potential is convergent in norm resolvent sense for coupling constant γ less than γ c = 0.37758 which corresponds to atomic number 51. Moreover, we give an explicit expression for the corresponding block-diagonalized Dirac operator. Communicated by Vincent Rivasseau.