We discuss the influence of the Dzyaloshinskii-Moriya (DM) interaction in the Heizenberg spin chain model for the observables in the polarized neutron-scattering experiments. We show that different choices of the parameters of DM interaction may leave the spectrum of the problem unchanged, while the observable spin-spin correlation functions may differ qualitatively. Particularly, for the uniform DM interaction one has the incommensurate fluctuations and polarization-dependent neutron scattering in the paramagnetic phase. We sketch the possible generalization of our treatment to higher dimensions.