Three-body problem. Generalized exponential expansion, arbitrary states in correlated basis and binding energy in the mesic molecule

A simple procedure for solving the three-body problem in the correlated basis for states with arbitrary L is presented. An effective correlated basis - a generalized exponential expansion, is proposed. It is shown that the respective function set is a complete one. Simple analytic formulas for the matrix elements of the hamiltonian and other typical operators in correlated bases are obtained for arbitrary L. The problem is reduced to a set of three-dimensional radial equations of a simple form. The rate of convergence of the expansions in correlated basis functions is studied for mesic molecular systems. Some general procedures for increasing the accuracy of the variational method are indicated. A generalization of the usual formulas for the matrix elements of irreducible tensor operators are presented