A set of hyperspherical harmonics especially suited for three-body collisions in a plane

The authors obtain a set of four-dimensional hyperspherical harmonics in closed form. These harmonics are not only quantized with respect to the rotation group (O2), but are an irreducible basis for the permutation group S3. An additional symmetry is found which allows the hyperspherical harmonics to be written, classified with respect to a 12 element group S3 X i X O2. A set of three mutually commuting operators is given, whose eigenvalues uniquely characterize each spherical harmonic with respect to degree, symmetry, and angular momentum in the plane. 6 refs.; 3 tabs