Equations for low-energy elastic scattering of particles by nuclei

One-dimensional integral equations for elastic scattering of particles by nuclei at low energies (up to the rearrangement or disintegration threshold), which take into account the continuous spectrum of the nuclei, are obtained. The multiparticle channel Green's operator, which enters into the kernel of the equation for the transition operator, is decomposed into a sum of two operators, one of which is finite-dimensional while the other satisfies an equation that can be solved by iteration. One of the versions of our method of inclusion of the continuous spectrum is applied to calculation of the scattering lengths in a three-particle system. The solutions obtained are compared with the corresponding solutions of the Faddeev equations