Decomposition of the scattering operator of the particle transport equation in a series of spherical tensors

A class of decompositions of the particle (i.g., neutrons, photons) scattering operator in a series of symmetric spherical tensors for analytical transformations and the numerical solution of the particle transport equation is proposed. The connection between symmetric spherical tensors and the class of polynomials is established. It is shown that in problems of radiation transport in a substance with predominant scattering forward or backward, it is advisable to use expansions in the Chebyshev tensor system. The system has a high speed of uniform convergence, which reduces the complexity of solving multidimensional particle transport problems.