The Soliton and Bisoliton Input into the Elastic Scattering of Slow Neutrons

Abstract

The wide use of the Davydov soliton model [1] in bioenergetics [2] and superconductivity [3, 4] raises a question of direct experimental evidence for the existence of solitons and bisolitons in quasi-one-dimensional systems and investigation of their properties. As far as both solitons and bisolitons are localized electrons or intermolecular excitations [1] or their bound state [5], respectively, moving along the chain with its local deformation, it is natural to expect their influence on the scattering spectra of extra radiations, including slow neutrons. Here elastic coherent scattering of ultracold neutrons by the Davydov soliton or bisoliton propagating with velocity V along the chain of similar subunits (peptide groups, e.g.) is studied in the assumption of small role of thermal vibrations. If the neutron energy is of order 10⁻⁵−10⁻⁷ eV, then its de Broglie wavelength (10⁻⁷—10⁻⁸m) exceeds the (bi)soliton size, which is usually several chain units. That is why nuclei of the same isotope from different subunits scatter neutrons coherently provided the (bi)soliton velocity is small. The second important circumstance arises because the (bi)soliton kinetic energy is large compared with that of an ultracold neutron. So the (bi)soliton velocity change in the result of a collision with a neutron may be neglected, and one can study elastic coherent scattering only.