Alternative treatment of the three-body problem

For solving the three-body problem with local potentials a model HamiltonianH ₀ containing an interaction between one particle and the centre-of-mass of the other two interacting particles is introduced. The total HamiltonianH is obtained byH=H _o +W whereW is a “residual interaction” in close analogy to the nuclear shell model. At a certain stage of the calculationsH ₀ has to be replaced by a new model Hamiltonian (tilde H_0 ) containing plane waves. The resolvent (and thereby theT-matrix) of the three-body problem is calculated by operator techniques. It is possible to draw some conclusions concerning three-body properties from these general expressions. Therefore this attempt may be considered as a supplementary treatment, in addition to the Faddeev-equations, of the three-body problem: it exhibits the discrete spectrum, the simple and the twofold continuum ofH arising from the corresponding states ofH ₀, and provides some approximation methods.