E. Baloitcha et Mn. Hounkonnou, Quantum description of five-particle systems in principal-axis hyperspherical coordinates, MOLEC PHYS, 98(6), 2000, pp. 387-396
To describe a 5-particle system, 'principal-axis hyperspherical' coordinate
s (made up of one hyperradius and eight angles as internal coordinates) and
three Euler angles as external (rotational) coordinates are used. A mathem
atical procedure to derive, in a systematic manner, the exact quantum mecha
nical Hamiltonian of the system in terms of these coordinates is presented.
A generalized angular momentum vector operator, which allows the generatio
n of a profitable standard representation for the angular part of the probl
em, is introduced.