Resonance width consideration for Compton rotation in magnetic field

A.I. Sery, Brest State A.S. Pushkin University (Brest, Belarus)

XII Gomel School «Actual Problems of Microworld Physics» 31.07.2013

I. Introduction

Model of the process: photon is moving in spin polarized electron gas in strong

MF (at NS surface, for example)

The difference between Faraday and Compton rotation

Experiments were carried out for the case without magnetic fields. Astrophysical aspect is interesting because of much more

favourable conditions for electron spin polarization (the idea of V.G. Baryshevsky and V.V. Tikhomirov)

Compton rotation in different orders of perturbation theory

The algorithm from the following article has been used:

Фомин, П.И. Резонансное комптоновское рассеяние во внешнем магнитном поле /

П.И. Фомин, Р.И. Холодов // ЖЭТФ. – 2000. – Т.117, вып. 2. – С. 319–325.

Phomin, P.I. Resonant Compton scattering in external magnetic field / P.I. Phomin, R.I.

Kholodov // JETP. – 2000

Electron propagator contains the following expressions (multiplied by plane waves):

The functions Un are expressed through Hermitian functions

is substituted either for g ( transferred 4-momentum for r-scattering) or for f ( transferred 4-momentum for s-scattering)

i are Dirac matrices, i are expressed through

II. Results

If resonance widths are not considered then at total spin polarization of electrons we have

(here is the angle between k and B):

If ħ < mec2 then only R-resonance is considered

The following changes are made for R-diagram

If pz0, then the averaging procedure gives (T=0)

Rn is integrated numerically, but for Sn we have

For Sn we have (continued)

Angle of Compton rotation at ne= 1022 cm-3 (table; much greater than at B=0, ne= 1022 cm-3; the

angle at B~1010 Gs is also much greater than at B=0)

Angle of Compton rotation

III. Remarks and conclusions

I.e., if other conditions are equal then

At B0 the formula is not correct at least because Гn must remain finite

Important remarksMeasuring of polarization plane at different and estimating B (due to Zeemann splitting, gyrolines, etc.) and (at low T, when kT/EF << 1), one can estimate ne.

At finite T (it can be estimated by spectroscopic methods) another averaging procedure must be used, and it leads to another formula for the angle of rotation.

Important remarks (continued)

• Compton rotation exceeds Faraday rotation at B>109 Gs, when almost all the electrons become free. This is possible only in astrophysics.

• Photon splitting competes with Compton rotation at B ~ 1013 Gs. This is also possible only in astrophysics.

Conclusions

• the value of Compton rotation changes its sign at resonance (0 is the corresponding frequency)

• there are 2 peaks of the value of rotation - 1 at each side of 0

0 decreases with increase of (the angle between k and B)

0 increases with increase of B• the maximum value of Compton rotation at resonance

decreases with increase of either or B• Compton rotation dominates, at least, at B~1010 Gs (in

comparison with photon splitting and Faraday rotation)

Angle of Compton rotation

You can find the details of the calculations in the articles(http://www.brsu.by/science/vestnik-brgu)

• Серый, А.И. О комптоновском вращении при движении фотонов под произвольным углом к линиям индукции магнитного поля. / А.И. Серый // Веснiк Брэсцкага унiверсiтэта. Серыя 4 «Фiзiка. Матэматыка». – 2011. – № 2. – С. 43 – 48.

• Серый, А.И. О комптоновском вращении в магнитном поле с учетом ширины резонанса. / А.И. Серый // Веснiк Брэсцкага унiверсiтэта. Серыя 4 «Фiзiка. Матэматыка». – 2012. – № 2. – С. 30 – 36.

Thank you for

your attention !