[en] Sufficient conditions for the existence of a continuous translation operator are found in the case of a system of differential equations in which the matrix potential has the singularity of the centripetal term. The sufficient conditions are found in terms of moments of the nuclear potential. The method used employs the Riemann Green's function. Threshold energies introduce a threshold energy dependence into the translation kernel and lead to a requirement of an exponential decrease for terms of the matrix potential.