Identification of biphonons from prominent features of the angular and energy dependences of the inelastic-scattering cross section of biphonon-splitting neutrons

Abstract

The dispersion relations and wave functions of biphonon and dissociated two-phonon states of anharmonic crystals are used to determine the cross section of inelastic scattering of neutrons that split biphonons into unbound phonons, which scatter each other as a result of their anharmonicity. Prominent features are found of the angular and energy dependences of the cross section, useful for analyzing experimental data to identify biphonons; it is possible that these features can also be used for subsequent, potentially major modification of the system of existing criteria, based solely on energy-balance considerations for the classification of series of spectral resonances, supposedly corresponding to bound multiphonon states of various multiplicities. For a fixed, large loss of neutron energy, the cross section is a maximum in a “nonhead-on” neutron-biphonon collision with a lobe-shaped angular scattering diagram; for intermediate energy losses the cross section has the largest of all possible values at all collision angles; and, for small energy losses, the cross section is a maximum for “head-on” collision in a narrow range of angles. For a fixed angle the energy dependence of the cross section has a resonance peak, which exists at the low-energy edge of a finite energy band for large angles and, as the angle decreases, gradually increases as it shifts toward the high-energy edge of the band, which becomes narrower and shifts into the low-energy region. However, when the angle decreases below a critical value, the still-increasing resonance maximum changes direction and shifts back toward the low-energy edge. It is shown that, despite strong oscillations of the biphonon wave function in the presence of negative phonon dispersion, the cross section does not depend on the sign of the dispersion, i.e., the universal law of independence from this sign, established previously for the dispersion relation and the biphonon damping constant, appears to carry over to the cross section.