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The dependence of the ultrasonic attenuation on the direction of magnetic field in an intermediate state of the very pure Gallium single crystal, in the case, when the magnetic field H is perpendicular to the wave vector k at the temperature T = 0.5 K, is found to be anomalously different from the dependence, observed at the same temperature and the magnitude of magnetic field equal to the critical magnetic field H=Hc in a normal state of superconductor. This new phenomenon can be explained, considering the anisotropy of the Fermi surface in the very pure Gallium single crystal.

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