Exactly solvable models of delta(')-sphere interactions in relativistic quantum mechanics

We introduce and develop a systematic theory of delta'-sphere interactions formally given by the Hamiltonian H-{R} = H-D + Sigma(m=1)(N)<(alpha)over t ilde>(m)delta'(\x\-R-m); <(alpha)over tilde>(m) is an element of R,x is an element of R-3, R-m> 0,1 less than or equal to m less than or equal to N wi th boundary conditions of the second type, as a logical continuation of the work performed [J. Math. Phys. 40, 4255 (1999)]. First, we give the mathem atical definition of the model, self-adjointness of the Hamiltonian, the in dicial equation, and the useful scattering elements. Next, we extend the mo del by adding a Coulomb potential and provide useful mathematical definitio ns and corresponding stationary scattering elements. (C) 2000 American Inst itute of Physics. [S0022-2488(00)00704-0].