THREE-BODY FORCE MODELS OF NONHYPERCENTRAL HARMONIC AND ANHARMONIC POTENTIALS IN THREE-DIMENSIONAL POTENTIALS

Abstract

We present a theoretical approach to the internal motion of a system based on three-body forces among particles in a special case, using three-body potentials. The three-body force models are more easily introduced and treated within the hyperspherical harmonic formalism. The internal particle motion is usually described by means of the Jacobian relative coordinates ρ, λ and R. The problems related to three-body nonhypercentral potentials in three dimensions are investigated. While the difficulties that arise in the study of nonhypercentral potentials are explicitly shown, we discuss some results obtained using nonhypercentral harmonic and anharmonic and some inverse power terms; however the potential can be easily generalized in order to allow a systematic analysis, which presents an exact solution to the wave function. The method is also applied to some other types of potentials.