Algebraic model for scattering in three-s-cluster systems. I. Theoretical background - art. no. 034606

A framework to calculate two-particle matrix elements for fully antisymmetr ized three-cluster configurations is presented. The theory is developed for a scattering situation described in terms of the algebraic model. This mea ns that the nuclear many-particle state and its asymptotic behavior are exp anded in terms of oscillator states of the intercluster coordinates. The ge nerating function technique is used to optimize the calculation of matrix e lements. In order to derive the dynamical equations, a multichannel version of the algebraic model is presented.