Abstract

Based on an experimental result on disappearance of the Laue spots of the downward x-ray diffraction (2 θB∼90°. Hereafter, abbreviated as DXD.) in solid helium a radically modified Debye-Waller factor and a modified Bragg law, considering the recoil scattering and its Doppler effect, could be obtained. Since kBΘD≪ER (recoil energy) in solid helium in contrast with the reverse inequality in almost all materials, the fraction of recoil-free diffraction is extremely less than one which is one of main causes of disappearance of the Laue spots of the DXD. The difference of wave-length in Pendelloesung beat 1.4 · 10−6 Aby using Kato-Lang’s fomula from the (200) plane in GaAs which occurs by slight frequency shifts of incident X-ray becomes in order of 0.5· 10−6 A derived from a modified Bragg law. This agrees very well with the experimental values of GaAs [1].

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