Multiple Scattering and Dynamical Intensities

In this section, we show how multiple scattering can be considered in intensity calculations. It also shows that multiple scattering allows for diffraction spots, which are systematically cancelled in the (invalid) kinematic calculation of the structure factor. 

Of course, at r = i , the two wave functions must be continuous and continuously differentiable, that is. 

The quantity is the so-called phase shift for angular momentum I and must also be real to ensure flux conservation. Also, it must vanish for V(r) = 0 so that tit = = exp iko which allows to calculate Pi = 

The phase shifts are determined by the continuity request given in Eq. (3.2.1.46) 

In principle, an infinite number of angular momenta I and so phase shifts Si must be considered. Yet, as the extension of the potential is finite (r R), a finite number Imax is sufRcient, whereby a good estimation is Imax kR in agreement with intuition. So, as E ock, an increasing number of I must be considered with increasing energy. As an example, for E = 150 eV and platinum atoms with R 1.38 A a limit of l ax = 8.6 9 results. Also, the phase shifts 

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