Theory of Transmission Coefficient of X-Rays Evanescent Wave for Grazing Incidence

  • Ino Shozo
    Department of Physics, Graduate School of Science, The University of Tokyo, Bunkyo–ku, Tokyo 113

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  • Theory of Transmission Coefflcient of X-Rays Evanescent Wave for Grazing Incidence.
  • Theory of Transmission Coefficient of X

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The nature of transmission coefficient |T(x)|2 of X-ray evanescent wave, x (=θ/θc) being normalized angle, for grazing incidence around the total external reflection angle is discussed. Refractive index n of X-ray is expressed by n = 1 - δ -I · β . A new equation which explains exactly the peak position xp of the function |T(x)|2 is presented. The value of xp2 is given as a solution of a cubic equation\n 4g3 + 3γ g2 + 6γ g + (4γ - 1)γ = 0, with γ = (β/δ)2 and g = 1 - xp2 . According to the equation, with increasing values of beta/δ, the peak position xp shifts to lower angle at first and increase again quickly. The peak heights |T(xp)|2 are also calculated. The nature of the cubic equation is investigated in details. The shapes of |T(x)|2$ are compared with the experimental values of an exit angle dependence of X-ray emission which are measured during RHEED observation.

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