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We propose an algorithm for calculating matrix elements of the non-linearBoltzmann equation collision integral in isotropic case. These matrix elementsare used as starting ones in the recurrence procedure for calculating thematrix elements of the collision integral, which is non-isotropic with respectto velocities, as described in our previous paper. In addition, isotropicmatrix elements are of independent interest for the calculation of isotropicrelaxation in a number of problems of physical-chemical kinetics.  It is shown that the coefficients of the isotropic matrix elements expansionin terms of $ \Omega $ -integrals are connected by recurrence relations thatallow us to calculate them sequentially.

Isotropic matrix elements of the Boltzmann equation collision integral