The talmi transformation for different particles-A complete construction and new results

The transformation from single-particle coordinates to relative and center-of-mass coordinates for two particles moving in a common harmonic-oscillator potential well is generalized to include the case of different single-particle frequencies. The physical implications, particularly for hypernuclear structure calculations, are pointed out. Explicit expressions for the transformation matrix are obtained which show the group-theoretical structure of the transformation. A generalization to n-dimensional harmonic-oscillators is straightforward. As a by-product the Clebsch-Gordan series for a direct product of two symmetric SU(n) irreducible representations is derived.