The non-linear dependence <$E gamma ({k Vec} sup 2 )> of the halfwidth of a quasielastic incoherent neutron scattering peak in supercooled water on the square of the wave vector <$E k Vec> is investigated. It is shown that the standard dependence <$E gamma ({k Vec} sup 2 )~=~D{k Vec} sup 2>, where <$E D> is the self-diffusion coefficient of molecules, takes place only at <$E | k Vec |~symbol Г~10 sup 8~roman cm sup -1>. This follows from the asymptotic law <$E GAMMA (t)~=~6Dt> for the mean-square displacement <$E GAMMA (t)> applied at all times <$E t>. At <$E | k Vec |~>>~10 sup 8~roman cm sup -1>, deviations from <$E GAMMA (t)~=~6Dt> become determinative, which is caused, in the first place, by changes of molecular thermal motion due to the clusterization of supercooled water. It is shown that, in the interval <$E 1~symbol Г~{k Vec} sup 2~symbol Г~10 sup 16~roman см sup -2>, the halfwidth <$E gamma ({k Vec} sup 2 )> is practically a linear function of <$E | k Vec |>. The existence of a definitive invariant that connects the values of <$E gamma ({k Vec} sup 2 )>, temperature, shear viscosity, and <$E | k Vec |> is established. The full agreement between theoretical predictions and experimental data is demonstrated.

• Локотош Тетяна Володимирівна (фізико-математичні науки)

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