SU(2) approximation to the coupling of Morse oscillators

We show that the SU(2) vibron model automatically gives the correct coupling between Morse oscillators as long as they only interact via the dominant Δv=±1 selection rule. We compare the SU(2) approximation with the model introduced by Child and Lawton, where the coupling is harmonic. The well-known harmonically coupled anharmonic oscillator model (HCAO) can thus be modified to consistently incorporate anharmonicity maintaining an analytic framework. We also discuss the classical phase space for the Morse oscillator case and its relation to the harmonic and SU(2) approximations.