Edge localized modes of cold neutrons in periodic condensed media
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It is found that for certain energies of discreet cold neutrons, quasi-stationary eigen solutions of the corresponding Schrodinger equation, which are localized in the layer of a periodic medium, exist. The localization time of these solutions is strongly dependent on the layer thickness, being finite for a finite layer thickness and increasing indefinitely upon a infinite growth of the layer thickness as the third power of the layer thickness. The problem has been solved in the two-wave approximation of the dynamic diffraction theory for the neutron propagation direction coinciding with the periodicity axes (normal incidence of the neutron beam on the layer). The expressions for neutron eigenwave functions in a periodic medium, the reflection and transmission coefficients, and the neutron wavefunction in the layer as a function of the neutron energy incident on the layer have been determined. It turns out that for the certain discrete neutron energies, the amplitudes of the neutron wavefunction in the layer reach sharp maxima. The corresponding energies are just outside of the neutron stop band (energies forbidden for neutron propagation in the layer) and determine the energies of neutron edge modes (NEMs) localized in the layer, which are direct analogs of the optical edge modes for photonic crystals. The dispersion equation for the localized neutron edge modes has been obtained and analytically solved for the case of thick layers. A rough estimate for the localization length L is L ~(db N)–1, where b is the neutron scattering length, d is the crystal period, and N is the density of nuclei in the crystal. The estimates of the localized thermal neutron lifetime show that acheaving of a lifetime close to the free neutron lifetime seems nonrealistic due to absorption of thermal neutrons and requires a perfect large size crystal. Nevertheless, acheaving the localized neutron lifetime exceeding by ~104 times the neutron time of flight through the layer appears as experimentally attainable. The perspectives of the NEM observation are briefly discussed. It is proposed to use NEM for ultrahigh thermal neutron monochromatization by means of NEM excitation in perfect single crystals.
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