Energy resolution.

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Energy resolution.

For the geometry of the proposed experiment the main contributions to the relative energy resolution are:

1. Intrinsic width of the crystal (rocking curve width of a plane crystal,see 10.4) $\omega :$

$\begin{displaymath} \frac{\Delta E}{E}=cot\Theta _{B}\cdot \omega \end{displaymath}$

(25)

2. Finite width $b$ of crystal, where $\sigma =\frac{b}{2\cdot R_{c}}$ . The maximum energy shift along the coordinate x is given by:

$\begin{displaymath} \frac{\Delta E}{E}=\frac{\sigma ^{2}}{2}\cdot cot^{2}\Theta _{B} \end{displaymath}$

(26)

3. Height of source $\zeta =\frac{z}{R}$

$\begin{displaymath} \frac{\Delta E}{E}=\frac{\zeta ^{2}}{2\cdot sin^{2}\Theta _{B}} \end{displaymath}$

(27)

The need to avoid small Bragg angles again becomes obvious. With $\sigma$ and $\zeta$ being of the order of $10^{-2}$ the influence of these quantities has to be optimized during preparation experiments. The influence of the finite vertical extensions, however, disappears in this order because we measure the geometrical distribution of the reflection in the detector plane (curvature correction).

Next: Intrinsic crystal properties. Up: Appendix 1: Useful formulae Previous: Crystal and source dimensions. Contents

Pionic Hydrogen Collaboration
1998