DETERMINATION OF 2-BODY POTENTIALS FROM N-BODY SPECTRA

We show how a two-body potential may be uniquely determined from n-bod y spectra in cases where the hypercentral approximation is valid. We i llustrate this by considering a harmonic-oscillator potential which ha s been altered by changing the energy or normalization constant of the ground state of the n-body system and finding how this modifies the t wo-body potential. It is shown that, with an increasing number of part icles, the spectrum must be known more precisely to obtain the two-bod y potential to the same degree of accuracy.