Quantum systems of atoms with highly singular interaction potentials

Abstract Quantum statistical systems, composed of atoms or molecules interacting with each other through highly singular non-integrable potentials, are considered. The treatment of such systems cannot start with the standard approximations such as Hartree, Hartree–Fock or Hartree–Fock–Bogolubov approximations because of non-integrability of the interaction potentials leading to divergences. It is shown that the iterative procedure for Green functions can be rearranged so that the starting approximation takes into account regularizing atomic correlations. Then all the following approximation orders contain only the regularized interaction potential producing no divergences. The method of constructing the regularizing correlation function is suggested, based on the solution of the scattering equation in the form of asymptotic series at short distance, which can be extrapolated to arbitrary spatial variables by means of self-similar approximation theory. Regularizing correlation functions for several kinds of atomic systems are exemplified.