Recent Developments in Hyperspherical Harmonic Method
The infinite system of coupled differential equations of the hyperspherical harmonic expansion method is transformed in a single equivalent two variables integrodifferential equation. This equation is identical for 3 bosons in S state to the Faddeev equation written by Noyes for S state projected local potentials. The integrodifferential equation can be solved by an Adiabatic method. The Adiabatic eigenpotentials become asymptotically constant for large hyperradii. Each one is the total binding energy related to a definite asymptotic channel where clusters are at rest. Each eigenpotential is related to bound and/or scattering states. This method enables one to solve scattering.
KeywordsPartial Wave Adiabatic Approximation Infinite System Integrodifferential Equation Faddeev Equation
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