A variation-iteration method for the three-body problem

We construct a practicable formulation of the variation-iteration method for the calculation of properties of a tri-nucleon system interacting via a modern potential. Our general approach is to take some integral form of the Schrödinger equation and reduce it to a set of simpler integral equations which may be solved by iteration. We concentrate particularly on the simplicity of the kernels which appear in this last set. The best method appears to be a two-step one, essentially equivalent to the Green function. In constructing the formalism, we are led to define a set of functions $\text{?}{}_{\mathrm{MN}}{}^{\mathrm{L}}\text{(k}{}_{12}\text{, k}{}_{23}\text{, k}{}_{31}\text{, r}{}_{12}\text{, r}{}_{23}\text{, r}{}_{31}\text{)}$ which play the role of iteration kernels. We give various properties of $\text{?}{}_{\mathrm{MN}}{}^{\mathrm{L}}$ and indicate very briefly how $\text{?}{}^{\mathrm{L}}{}_{\mathrm{MN}}$ may be reduced to a function of only two variables.