Polarization factor

The polarization factor takes into account the angle dependence of the intensity in Thomson scattering (or angle dependence of the intensity emitted by a dipole ). It occurs primarily as a correction factor in X-ray structure analysis .

Necessity as a correction term

The polarization factor is:

{\ displaystyle {\ frac {1+ \ cos ^ {2} (\ alpha)} {2}}}

.

It is necessary as a correction term if the incident radiation is unpolarized in a scattering experiment, but the incident radiation is polarized. Thomson scattering occurs here because the energy of the X-ray quanta is not high enough to lead to inelastic ( Compton ) scattering. Photons are absorbed by the electron, which stimulate it to vibrate. As a result, it emits photons again as an oscillating dipole, which is known as scattering.

Derivation

The incident waves can be divided into a vertical and a parallel part:

{\ displaystyle I_ {0} \ propto E _ {\ perp} ^ {2} + E _ {\ parallel} ^ {2}}

In the case of unpolarized incident radiation:

{\ displaystyle E _ {\ perp} = E _ {\ parallel}}

The intensity of a radiating dipole also depends on the angle of radiation (in the Debye-Scherrer method , for example ). Since the radiation of the dipoles oscillating perpendicular to the direction of propagation always reaches the detector, the following results for the scattered waves: ${\ displaystyle \ cos ^ {2} (\ alpha)}$ ${\ displaystyle \ alpha}$ ${\ displaystyle \ alpha = 2 \ theta}$

{\ displaystyle I_ {1} \ propto {E _ {\ perp}} ^ {2} + {E _ {\ parallel}} ^ {2} \ cdot \ cos ^ {2} (\ alpha) = {E _ {\ perp }} ^ {2} \ cdot (1+ \ cos ^ {2} (\ alpha)) \ propto I_ {0} {\ frac {1+ \ cos ^ {2} (\ alpha)} {2}}}

If one observes the scattering at , the polarization factor is 1 and the full intensity is scattered. If the value is 90 °, the polarization factor is 0.5 and only half the intensity is scattered, so the scattered waves are polarized perpendicular to the direction of propagation. ${\ displaystyle \ alpha = 0 ^ {\ circ}}$ ${\ displaystyle \ alpha}$

Individual evidence

^ H. Neff: Fundamentals and Applications of X-ray Fine Structure Analysis 1962.
↑ Werner Massa: Crystal structure determination . 8th edition. Springer Fachmedien, Wiesbaden 2015, ISBN 978-3-658-09412-6 , pp. 96 f ., Doi : 10.1007 / 978-3-658-09412-6 .

[1] H. Neff: Fundamentals and Applications of X-ray Fine Structure Analysis 1962.

[2] Werner Massa: Crystal structure determination . 8th edition. Springer Fachmedien, Wiesbaden 2015, ISBN 978-3-658-09412-6 , pp. 96 f ., Doi : 10.1007 / 978-3-658-09412-6 .