Treatment of large perturbations of the Hamiltonian and the boundary conditions in scattering and reaction calculations

Abstract

On the basis of an integrodifferential equation which was derived in a previous work for the $T$ matrix of nuclear reaction theory, we have developed a general formalism to treat large perturbations in both the Hamiltonian and the boundary conditions of a quantum mechanical system. As a result of this formalism, a set of first order differential equations, in terms of any of the physical parameters of the system, is given for the widths and poles of the collision $U$ matrix. The technique is illustrated by the conversion of a set of $R$-matrix resonance parameters into its equivalent set of $U$-matrix widths and poles, which corresponds to the passage from the $R$-matrix boundary conditions to the complex, momentum-dependent boundary conditions associated with the Kapur-Peierls reaction formalism. The case of large perturbations of the Hamiltonian is illustrated by the calculation of the elastic and inelastic scattering cross sections in a strongly coupled two-channel system which was proposed by Tobocman and has been widely used as testing grounds for reaction theories.