Theory and measurement: comparison

V.A. Maisheev, IHEP, Protvino

For aims of comparison with the experimental data the calculations of

characteristics of the volume reflection process are presented.

The calculations are based on the analytical description of the process.

The obtained results are in a good agreement with experimental data

which take place now.

The our calculations of volume reflection are based onthe analytical description of the process in the accordance of

the paper: V.A. Maisheev, Archive: physics\0607009

The second peculiarity of our consideration is the using of the model of planar potentials for calculations which stands on experimental measurements of X-ray diffraction in single

crystals.The planar potentials are defined by the values of atomic form factors and rms of the thermal vibrations of atoms.

Fig. 1 illustates the quantities of the atomic form factors for silicon single crystalas a function of transfered momentum. Here the triangles are the results of measurements

of these values in electron beam (analog of x-ray difraction).One can see that green curve (approximation of experimental form factors) is

in better agreement with the measurements then Moliere atomic form factors (blue curve).

This difference corresponds to the difference in the planar potentials (fig. 2).

We calculated the third central momentum of the distribution of the scatteredparticles. This momentum shows the degree of distinction of real distribution from

the gauss one. This momentum as a function of radius are presented in Fig.5for (011) and (111) planes of the 2 mm silicon single crystal.

Theory and measurements: comparison (status on 15.03.07)

The mean angle of volume reflection ( in microradians)

QM1 –crystal Analytic prediction: 11.5

Experiment: 12.3 +-0.2 : 11.9 +- 0.4 R. Santacesaria

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QM2 –crystal Analytical prediction: 11.9

Experiment: 11.5+- 0.2; 12.2 +-0.4 R. Santacesaria

12.9 +-1.0 Yu. Ivanov

12.02+-0.06 S. Hasan

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ST4 –crystal Analytical prediction: 14.5

Experiment: 13.8+-0.2; 14.1+-0.2; 13.2 +-0.4 R. Santacesaria

13,83+-0.06 S. Hasan

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QM1-QM2 Analytical prediction: 23.4

Experiment: 23.8 +-0.2; 24.0+- 0.4 23.1+- 0.4 R. Santacesaria

23.22 +- 0.18 S.Hasan

• Calculations were done for planar potentials from x-ray measurements. The similar calculations for Moliere potentials give for mean volume reflection angle values which more on 0.7 microradian.One can conclude that calculated and measured volume reflectionangles are in a good agreement (on 15 March 07).

• Conclusions• 1 Calculations based on the analytical description of the process• and existing experimental results are in a good agreement.• 2 Calculations based on planar potentials from x-ray diffraction• give results more close to measurements.• 3 Complete picture of comparison will be possible after obtaining• experimental data for all crystals.