The Resonant-state-expansion Born approximation theory requires an alternative derivation of the Born approximation to the derivation approach of Max Born.
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The first two terms correspond to the standard Born approximation, the final summation term corresponds to the Resonant-state-expansion correction to the Born approximation.
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The first two terms correspond to the standard Born approximation, the final summation term corresponds to the Resonant-state-expansion correction to the Born approximation.
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The Born approximation is used to calculate the t-matrix, which simply means that { t _ i } is replaced with { v _ i }.
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The Born approximation assumes that the system-bath coupling is relatively weak, and the bath is very large, so that the bath is negligibly affected by the system.
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The nonrelativistic potential, which scatters in all directions with an equal amplitude ( in the Born approximation ), is one whose Fourier transform is constant a delta-function potential.
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Therefore combining all of these expressions and noting \ mathbf { r }, \ mathbf { r } " are far from the scatterer we arrive at the Resonant-state-expansion Born approximation
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In the Born approximation, corresponding to first order perturbation theory, one replaces this last \ psi ^ + with the corresponding eigenfunction \ phi of the free Hamiltonian " H " 0, yielding
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In the Born approximation the amplitude of the scattered wave corresponding to the scattering vector \ mathbf { q } is proportional to the Fourier transform \ textstyle \ psi ( \ mathbf { q } ).
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GISAXS also shares elements of the scattering technique of diffuse reflectivity such as the Yoneda / Vinyard peak at the critical angle of the sample, and the scattering theory, the distorted wave Born approximation ( DWBA ).
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