Discrete and continuum spurious spectrum of distorted and reduced scattering equations

Certain versions of distorted and reduced scattering equations are found to admit continuum spurious solutions apart from the commonly known discrete spurious solutions. The spurious threshold corresponding to continuum spurious solutions may occur at an energy lower than the physical bound state energy and this may make the use of such equations questionable both for bound state and scattering problems. The spurious threshold, however, disappears in approximate calculation using bound state approximation. The origin of these spuriosities lies in a different type of factorization than that found by Newton in the context of the formulation of Weinberg and may shed light on the spurious spectrum of other formulations.