Matrix elements of potentials in the correlation-function hyperspherical-harmonic method

Matrix elements of two-body potentials and correlation functions between three- and four-body hyperspherical states, including their velocity-dependent parts, are calculated analytically for any value of the total orbital angular momentum. The resulting formulas contain explicitly written functions of the radial variable, and the Raynal-Revai coefficients. The latter are expressible through finite sums of 3-j and 9-j symbols. The formulas allow precise and fast evaluation of matrix elements of the effective potential in the correlation-function hyperspherical-harmonic method for atomic, molecular, and nuclear three- and four-body problems. The generalization to any number of particles is straightforward.