The Resonant-state-expansion Born approximation theory requires an alternative derivation of the Born approximation to the derivation approach of Max Born.
12.
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.
13.
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.
14.
The Born approximation is used to calculate the t-matrix, which simply means that { t _ i } is replaced with { v _ i }.
15.
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.
16.
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.
17.
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
18.
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
19.
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 } ).
20.
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 ).
