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Dielectric function:

To describe the inelastic scattering with the dielectric function, the relation between the cross section and the mean free path is required:

1/ is the inverse mean free path and N is the atomic density. To get the total inverse mean free path , the inverse mean free paths of all specific events has to be summed up:

To obtain the probability distribution of the deflection angle or the energy loss associated with a scattering process, one requires the differential inverse mean free path. In terms of the dielectric function, the differential cross section for inelastic scattering of an electron with kinetic energy E, an energy loss of and momentum transfer of is given by:

 

The term is called the function.

By integrating equation A.13 over both q and one obtains the total inelastic mean free path for electrons with incident energy E. Integrating over or q leads to the differential inelastic mean free path for energy loss and angular deflection, respectively.

A method to compute the energy loss function by use of i.e. , extending the function into the plane, thus permitting the calculation of the double differential inelastic mean free path using optical dielectric data, has been proposed by Penn [Pen87] and is applied in SESAME.



Horst Wagner
Tue Mar 19 10:24:55 MET 1996