Crystal and source dimensions.

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Crystal and source dimensions.

In the following the influence caused by crystal and source dimensions is discussed. We follow closely the paper by J. Eggs and K. Ulmer [90] which gives much more details. The horizontal and vertical opening angle of the crystal as seen from point O is denoted by $2\cdot \sigma$ and $2\cdot \varepsilon$ , respectively. The height of the source is given by the opening angle $\zeta =\frac{z}{R_{c}}$ with z being the geometrical height of the source. The change in angle $\Delta \Theta$ caused by the finite extension of source and crystal is given by

$\begin{displaymath} \Delta \Theta =\frac{\sigma ^{2}}{2}\cdot cot\Theta _{B}+\frac{\zeta ^{2}}{sin(2\cdot \Theta _{B})}. \end{displaymath}$

(23)

The angular offset caused by the height of the crystal is of the order

$\begin{displaymath} \Delta \Theta _{\varepsilon }=-cot^{3}\Theta _{B}\cdot \frac{\varepsilon ^{4}}{4} \end{displaymath}$

(24)

and therefore negligible for all practical purposes.

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

Pionic Hydrogen Collaboration
1998