Past exam of the condensed matter physics major option course of the University of Oxford / 2016 / 1 / a

Away from an absorption edge, the scalar atomic scattering factor is the Fourier transform of an approximately spherical, real atomic electron density. Opposite points contribute conjugate phases, so their sum is real. In Thomson scattering the electronic response is also effectively in phase with the driving field in this nonabsorbing approximation. Near an absorption edge, resonantly driven electronic excitations introduce a phase lag and absorption. The atomic scattering factor becomes $f_0+f^{\prime }+i{f}^{\prime \prime }$, with $f^{\prime \prime }$ describing the absorptive component and $f^{\prime }$ its dispersive companion. The sign of the imaginary part depends on the time and scattering-phase conventions; here it is the source's $+i{f}^{\prime \prime }$ convention. This discussion concerns scalar charge scattering, without magnetic or tensor resonant contributions.