Decoupling a collective degree of freedom from a model for tunneling in many-particle systems

The theory of large amplitude adiabatic motion is applied to a recently proposed model of tunneling in many body systems. We construct the corresponding collective Hamiltonian and study the applicability of the decoupling procedure, both by comparing the results of the large amplitude theory with exact results and by studying different measures of the decoupling procedure, including the stability of the collective motion against noncollective vibrations. We also analyze briefly another approximation scheme especially suited for the problem at hand. The theory of large amplitude collective motion provides an extremely accurate description of the collective motion and of the tunneling process.