Kramers described the cross section of electron interaction with target atoms of atomic number Z by
![](//static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191018041259644-0610:S0376030800012908:S0376030800012908_inline1.gif?pub-status=live)
where Eo is the kinetic energy of impinging electrons, and E o S) the energy of x-ray photons of the continuum, Smith et al modified this equation, introducing an exponent x, so that
![](//static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191018041259644-0610:S0376030800012908:S0376030800012908_inline2.gif?pub-status=live)
We applied the cross-section σS, E to the evaluation of experimental results. The evaluation of the measured spectral responses of the x-ray signals nE was performed by
![](//static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191018041259644-0610:S0376030800012908:S0376030800012908_inline3.gif?pub-status=live)
where f(deff) describes the absorption of x-rays of energy E in the target, RE accounts for backscattering of electrons, DE quantifies the efficiency of x-ray detection within the solid angle Ω.