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The problem of the elastic scattering of pions by a deuteron is considered using the separable representation of the two-body t-matrix. The Faddeev equations are reduced to a set of one-dimensional integral equations by separating the angular variables. The dependence of the π-d scattering length on the form of two-body interaction and on the values of the π-N scattering lengths is studied in the case of a one-term nonlocal potential with separable variables. The π-d scattering length proves to be practically independent of the two-body interaction form, and is essentially dependent on the values of the π-N scattering lengths.

Use of a separable expansion for the two-particle t -matrix reduces the problem of three particles with pair interaction to a set of one-dimensional integral equations. By the subsequent separable representation of kernels of such integral equations (based on the Bateman method) the problem of three identical particles is reduced to the solution of algebraic equations.

Various non-local interactions, including a tensor one, are employed in the calculation.

Polarization phenomena in the elastic neutron-deuteron scattering resulting from the spin-spin interaction between nucleons are considered. Numerical results are obtained on the basis of the exact solution of the three-nucleon problem in the case when the interaction between nucleons is described by a non-local separable potential. The results favour the phase shifts of Christian and Gammel.

On the basis of Faddeev integral equations the problem of the elastic scattering of π-mesons from deuterons is considered. The pion-deuteron scattering length is calculated under the assumption that there is only S-wave interaction between the particles.