Hyperspherical harmonics for tetraatomic systems

A recursion procedure for the analytical generation of hyperspherical harmo nics for tetraatomic systems, in terms of row-orthonormal hyperspherical co ordinates, is presented. Using this approach and an algebraic Mathematica p rogram, these harmonics were obtained for values of the hyperangular moment um quantum number up to 30 (about 43.8 million of them). Their properties a re presented and discussed. Since they are regular at the poles of the tetr aatomic kinetic energy operator, are complete, and are not highly oscillato ry, they constitute an excellent basis set for performing a partial wave ex pansion of the wave function of the corresponding Schrodinger equation in t he strong interaction region of nuclear configuration space. This basis set is, in addition, numerically very efficient and should permit benchmark-qu ality calculations of state-to-state differential and integral cross sectio ns for those systems. (C) 2001 American Institute of Physics.