Absolute determination of zero-energy eigenphase shifts: Applications to n-p, n-d, and p-d scattering

A generalization of Levinson’s theorem, relating the phase shift at zero energy to the number of bound states of the system, previously formulated to apply to the single-channel multiparticle scattering of a particle by a neutral system [L. Rosenberg and L. Spruch, Phys. Rev. A 54, 4978 (1996)] is further generalized to allow for multichannel scattering. An application to neutron-proton scattering with tensor forces leads to an extension of the existing version of Levinson’s theorem for this system by providing information on each of the eigenphases at zero energy rather than just their sum. The effect of the Pauli principle on the absolute determination of the phase shift is illustrated with applications of the method to the scattering of neutrons and protons by deuterons.