Second Quantization with Coulomb potential

I am trying to understand how one can perform second quantization in the case of the Hamiltonian of the hydrogen atom, i.e. when the one particle Hamiltonian acquires an external coulomb potential. The problem arises on the fact that the spectra admits both discrete (bound) and continuum (scattering) eigeinvalues/states. Since, a complete basis of the one-particle Hamiltonian is needed in order to define creation/annihilation operators and build the occupation number representation how one can do it in the case of the coulomb potential?Have you even seen such formulation, for bosons or fermions?