Springer Online Journal Archives 1860-2000
Abstract The generalized Faddeev-Yakubovsky equation is derived for the four-body system where three-body forces are included. There result twenty-two coupled equations which, in the case of four identical spinless particles, can be reduced to three. In addition, by using the hyperspherical-harmonics expansion in momentum space, as suggested by Dzhibuti and his collaborators, and the Raynal-Revai transformation, it is possible to write these as one-dimensional coupled integral equations. Numerical solutions are straightforward and, for sample potentials, suggest relatively fast convergence in the number of harmonics required. Results obtained so far offer fresh hope that this method may provide a means for quick and accurate computation of four-body scattering quantities.
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