Abstract

Formal solutions to the \ensuremath{\Delta}-hole and particle-hole coefficients describing nuclear coherent states are presented using the degenerate schematic model. These solutions are used to analytically solve for the momentum-dependent nuclear form factors in which the target is excited to a transition-spin-isospin, \ensuremath{\Delta}-giant resonance through the creation of coherent \ensuremath{\Delta}-hole states, whereas the projectile is excited to an ordinary spin-isospin giant resonance. The target then decays to its ground state emitting a pion. A more general model operator is proposed that leads to complete coherence for all momenta. The magnitudes of the nuclear form factors are calculated theoretically and the results coming from the completely coherent model are compared to the low-momentum coherent model. The calculation is then completed by introducing these models into the pion triple-differential cross section and energy distributions are calculated and compared. The importance of how the nuclear structure and coherence affect the magnitudes and shapes of the form factors and the pion-energy distributions is assessed.

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