Corrections to the formula for Compton rotation in

magnetic field

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

XIII Gomel School «Actual Problems of Microworld Physics» 03.08.2015

I. Introduction

Model of the process: photon is moving in spin polarized electron gas in strong MF (at NS

surface, for example). Rotation of the plane of polarization is possible (a kind of optical activity

of plasma). What kind of rotation dominates – the Faraday or Compton one?

Compton rotation was predicted by V.G. Baryshevsky and V.L. Luboshitz in 1965;

experimentally discovered in 1970s

Барышевский, В. Г. Ядерная оптика поляризованных сред / В. Г. Барышевский. – М. : Энергоатомиздат, 1995. – 320 с.

Лобашев, В. М. Экспериментальное наблюдение вращения плоскости линейной поляризации -квантов в намагниченных ферромагнетиках / В. М. Лобашев [и др.]. // Письма в ЖЭТФ. – 1971. – Т. 14. – С. 373–376.Lobashev, V. M. Rotation of the plane of polarization of quanta and leftright asymmetry of scattering by thick magnetized scatterers / V. M. Lobashev [et al.]. // Sov. Phys.·JETP. – 1975. – Vol. 41, No.4. – P. 606–609.Bock, P. Observation of the Faraday Effect with 230 keV and 330 keV Photons / P. Bock, P. Luksch // Lett. Nuovo cimento. – 1972. – Vol. 2, № 21. – P. 1081–1084.

The difference between Faraday and Compton rotation

Experiments for CR were carried out for the case when 2µBB/ħ << .

Astrophysical aspect is interesting because the effect is related to the study of the characteristics of circumstellar medium, the sources of X- and -radiation, and the case 2µBB/ħ ~ is

possible (the idea of V.G. Baryshevsky and V.V. Tikhomirov). .

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

The main task is to calculate the difference of the following constructions:

II. Results

If resonance widths on the intermediate Landau level 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 (the pole is removed from the real axis on the

complex energy plane)

Angle of rotation in pz=0 approximation at ne= 1022 cm-3 when 2µBB/ħ ~

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

for the integrals we have

for the integrals we have

for the integrals we have

for the integrals we have

Angle of Compton rotation

The difference between the previous and new results is very small (it is exactly zero at = 0;

see examples for =10-13,N = 200000 points for numerical integration):

III. Remarks and conclusions

If other conditions are equal then

Important remarksFor high degree of ionization, measuring the position of polarization plane at different , and estimating B (due to Zeemann splitting, gyrolines, etc.) , at low T (when kT/EF << 1), one can estimate ne (applying the formulae for Compton and Faraday rotation)The obtained formulae are useful in studying white dwarfs and neutron stars, namely, their magnetic fields and the structures of their atmospheres

Important remarks (continued)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)• The difference between the pz=0

approximation and the averaging on pz is small

• The contribution of =1,=3 and =3,=1 is negligibly small in comparison with the contribution of =1,=2 and =2,=1

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

Angle of Compton rotation

You can find the details of the calculations in the articles• 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.

• Серый, А. И. О некоторых поляризационных эффектах в астрофизической плазме / А. И. Серый // Веснiк Брэсцкага унiверсiтэта. Серыя 4 «Фiзiка. Матэматыка». – 2014. – № 1. – С. 30–43.

• Sery, A. I. To the Problem of Compton Rotation of Photons in a Strong Magnetic Field: Limit of Total Spin Polarization of Electrons / A. I. Sery // Nonlinear Phenomena in Complex Systems. – 2014. – Vol. 17, № 4. – P. 420–422.

Thank you for

your attention !