Intrinsic crystal properties.

Next: Rates. Up: Appendix 1: Useful formulae Previous: Energy resolution. Contents

Intrinsic crystal properties.

The intrinsic properties of ideal single crystals can be calculated with an accuracy of a few percent within the framework of dynamical crystal theory [91]. The basic parameters are the rocking curve width $\omega$ , the peak reflectivity $P$ and the integrated reflectivity $R_{I}$ which are given here for plane crystals. The quantity $\omega$ is the divergence of an initially parallel beam of monoenergetic radiation after reflection on the lattice planes of a plane crystal. The peak reflectivity accounts for the maximum percentage of reflection and takes into account losses owing due to incoherent processes like photo effect in the crystal material. The integrated reflectivity is a measure for the intensity of the reflected radiation. These quantities are related by

$\begin{displaymath} R_{I}\sim \frac{4}{3}\cdot P\cdot \omega , \end{displaymath}$

(28)

where $R_{I}$ and $\omega$ are given in angular units.

Important in the case of high precision experiments is the change of the index of refraction inside the crystal material. The index of refraction shift $\Delta \Theta _{ind.}$ is almost always positive, i.e. the measured Bragg angle is given by $\Theta ^{vacuum}_{B}$ ( equation 14) plus $\Delta \Theta _{ind}$ . The value of $\Delta \Theta _{ind}$ is considered to be known with an accuracy of ( $2-5)$ % if the vicinity of absorption edges is avoided. As an example the correction for the $2\rightarrow 1$ transition in pionic hydrogen amounts to 38'' for the quartz crystal used in our experiment.

Next: Rates. Up: Appendix 1: Useful formulae Previous: Energy resolution. Contents

Pionic Hydrogen Collaboration
1998