Selfadjoint extensions of Dirac operators for non spherically symmetric potentials in Coulomb scattering (Q1101932)

The paper is concerned with the construction of selfadjoint extensions of the Dirac operator \(\alpha_ jD_ j+P\) on domains with finite potential energy \(r^{-}Eu\in L^ 2({\mathbb{R}}^ 3)^ 4\), where the hermitean potential \(P=EP_ 1(x)E+P_ 2(r)F\) satisfies \[ P_ 1\in L^ 3_{loc}({\mathbb{R}}^ 3\setminus \{0\})^{4\times 4},\quad | P_ 1(x)| \leq \mu | x|^{-1} \] in a neighbourhood of \(x=0\), not demanding \(\mu <1\) as usual, and \(P_ 2\in L^ 1_{loc}(0,\infty)^{4\times 4}\) without any regularity at \(r=0\). F is the eigenprojector belonging to all eigenvalues \(| k| \leq \mu\) of the spin operator s and \(E+F=id.\) This result is also extended to multicenter potentials by reducing to one nucleus.