By Beskin et al.,
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Additional resources for Accretion Discs, Jets and High Energy Phenom. in Astrophysics
Since the dots are buried, only the transmitted wave inside the medium has to be considered, and the wave reﬂected at the surface and underlying interfaces is neglected for the diﬀuse scattering. 94) where ∆ denotes the diﬀerence between the electron density of the buried structure and that of the surrounding material. 93). However, this wave can also be scattered diﬀusely, leading to enhanced diﬀuse intensity in its vicinity. The inclusion of the specular beam in the framework of the DWBA was ﬁrst performed by Kaganer et al.
P. Ewald had already used the same ansatz for his dynamical theory of X-ray diﬀraction. 82) h where E[h,h] is the component of Eh perpendicular to Kh ≡ K 0 + h. 81) are the basic equations of the dynamical theory of X-ray diﬀraction, and they are generally valid. However, they cannot be solved exactly, and the Fourier expansion of the wave ﬁeld E(r) has to be truncated after a ﬁnite number of terms. e. h = 0) is considered, only one (plane) wave is present inside the crystal. This solution is, therefore, often referred to as the onebeam case.
This consideration makes it clear that a calculation of the scattering from the semi-inﬁnite substrate requires the consideration of four waves inside the crystal, and the DWBA coupling scheme provides us with 16 channels into which scattering can occur . However, when the diﬀuse scattering from free-standing islands calculated, only three vacuum waves have to be taken into account: the incident, the specularly reﬂected, and the diﬀracted wave. 102) (θB is the Bragg angle), and the diﬀerential scattering cross section is given by dσ (q) = r02 |A(q)|2 .
Accretion Discs, Jets and High Energy Phenom. in Astrophysics by Beskin et al.,