EXAMPLE:
Nuclear Stopping Power for Electrons in Silicon with Exponential form factor:
NOTE:
Output table and graph include the nuclear stopping power in units of Mev cm2/g (i.e., the mass nuclear stopping power).
In the present treatment, screening effects are factorized in the expression for the differantial cross section (Boschini et al. (2011)). However, it has to be remarked - as derived by Zeitler and Olsen (1956) - that for electron energies above 200 keV the overlap of spin and screening effects is small for all elements and for all energies; for lower energies the overlapping of the spin and screening effects may be appreciable for heavy elements and large angles.
User can suggest an "ad hoc" form factor by contacting us using This email address is being protected from spambots. You need JavaScript enabled to view it. . In fact (see discussion in Boschini et al. (2011)), a further work is likely to be needed for the most suited parametrization of the nuclear form factor, particularly for high-Z naterial.
Nuclear Stopping Power for compounds can be determined by means of Bragg's additivity rule, i.e., the overall Nuclear Stopping Power in units of MeV cm2/g (i.e., the mass nuclear stopping power) is obtained as a weighted sum in which each material contributes proportionally to the fraction of its atomic weight. An example for selection, with water (H2O) as target, follows:
or equivalently
The Total Cross Section is not affected by the Form Factor term. This because the Differential Cross Section is larger by several orders of magnitude with respect to the corresponding values at the very low angles, where the form factor is relevant. The effect of different form factors on differential cross section for 184 MeV electrons in In (Z=49) is in the following images, with the same experimental data set from B.Hahn et al. (1956). Our calculation is on the left and the graph from Fernandez-Varea et al. (1993) is on the right.:
However the transferred energy is several order of magnitude larger at high scattering angles.
The overall results is that the NIEL and the Nuclear Stopping power are affected by the form factor. Numerical results for 183 MeV electrons in In are presented in the following table:
or equivalently
However the transferred energy is several order of magnitude larger at high scattering angles.
The overall results is that the NIEL and the Nuclear Stopping power are affected by the form factor. Numerical results for 183 MeV electrons in In are presented in the following table:
