Recurrence relations between transformation coefficients of hyperspherical harmonics and their application to Moshinsky coefficientsĬlosed formulae and recurrence relations for the transformation of a two-body harmonic oscillator wave function to the hyperspherical formalism are given. The results indicate that the method is a viable calculational tool. The method is tested by calculation of a matrix element for knockout scattering for a simple three-body-system. The coefficients in such an expansion are generalized Talmi- Moshinsky coefficients. With the help of our method the multidimensional integral which must be performed to evaluate a few-body matrix element can be transformed into a sum of products of three dimensional integrals. This result is a generalization of the Talmi- Moshinsky transformation for two equal-mass particles to a system of any number of particles of arbitrary masses. We show that these harmonic oscillator functions can be chosen in a manner that allows such a product to be expanded as a finite sum of the corresponding products for any other set of Jacobi coordinates. These basis states are products of harmonic oscillator wave functions having as arguments a set of Jacobi coordinates for the system. International Nuclear Information System (INIS)Ī set of basis states for use in evaluating matrix elements of few-body system operators is suggested. A generalized Talmi- Moshinsky transformation for few-body and direct interaction matrix elements
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