Coulomb fourier transformation: application to a three-body Hamiltonian with one attractive coulomb interaction

For a three-body system consisting of one neutral particle and two charged particles the Hamiltonians are represented by matrix elements, called Coulomb-Fourier transforms. Any explicit appearance of the long-range Coulomb potential is disappearing, all Coulomb effects resides in the short-range potential matrices. The one consists of the short-range potential in the Coulomb representation, the other two are given as the Fourier-transformed short-range potentials multiplied by a function matrix of three-body type. This function matrix is universal, i.e. all elements are independent of the short-range potentials and need to be calculated only once and for all. The analytical expressions of the matrix elements behave as functions of the principal quantum numbers and have been found to decrease along the diagonal and along the sides of the matrix. Refs. 2 (nevyjel)