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Releevskoe rasseyanie

- chastnyi sluchai kogerentnogo rasseyaniya izlucheniya na atomah, molekulah ili chasticah mezhzvezdnogo veshestva, kogda chastota rasseivaemogo izlucheniya sushestvenno men'she osn. sobstv. chastot rasseivayushei sistemy.

Klassicheskaya f-la dlya polnogo effektivnogo secheniya izlucheniya (sm. Vzaimodeistvie izlucheniya s veshestvom) na garmonich. oscillyatore s massoi m i zaryadom e (prosteishaya model' sistemy rasseivayushih zaryadov) imeet vid:
$\sigma={8\pi\over 3} \left( {e^2\over{mc^2}} \right)^2 {\nu^4\over {(\nu^2-\nu_0^2)^2+(\gamma_0\nu)^2(2\pi)^{-2}}}$ , (1)
gde $\nu_0$ - sobstvennaya chastota oscillyatora, $\gamma_0=8(\pi e\nu_0)^2/3m c^3$ - klassich. postoyannaya zatuhaniya. Pri $\nu \ll \nu_0 i \gamma_0 \ll \nu_0$ (t.e. dlya dostotachno nizkih chastot) iz (1) sleduet vyrazhenie dlya secheniya R.r.
$\sigma_P={8\pi\over 3} \left( {e^2\over{mc^2}} \right)^2 \left( {\nu\over{\nu_0}} \right)^4$ , (2)
analogichnoe sootnoshenie, vpervye poluchennomu angl. fizikom Dzh. Releem (v 1871 g.). Zametim, chto pri $\nu\gg\nu_0 ,\; \gamma_0$ iz (1) sleduet vyrazhenie dlya secheniya tomsonovskogo rasseyaniya (tomsonovskoe sechenie): $\sigma_T={8\pi\over 3} \left( {e^2\over{mc^2}} \right)^2$ . Real'nuyu sistemu svyazannyh zaryadov (atom, molekula ili chastica veshestva) nel'zya opisyvat' uproshennoi model'yu garmonich. oscillyatora, i poetomu f-ly (1) i (2) dlya nee neposredstvenno ne primenimy. Vmesto (1) ispol'zuetsya vyrazhenie, v k-rom summiruetsya vklad vseh elementarnyh oscillyatorov. Odnako osn. osobennost' R.r. - proporcional'nost' secheniya velichine $\nu^4$ (ili $\lambda^{-4}$ ) vsegda sohranyaetsya.

Dlya dielektrich. makrochastic (pylinok) summarnoe deistvie ogromnogo chisla elementarnyh oscillyatorov opisyvaetsya tenzornoi velichinoi $\hat{\alpha}$ , k-raya zavisit ot polyarizuemosti veshestva pylinki, a takzhe ot ee formy i opredelyaet komponenty navedennogo v elektricheskom pole volny $\bf{E}$ dipol'nogo momenta $\bf{d}=\hat{\alpha} \bf{E}$ . Po poryadku velichiny:
$\pi a^2\sigma_P \sim \pi a^2 {8\pi\over 3} \left( {2\pi\over{\lambda}} \right)^4 |\alpha |^2$ , (3)
gde a - harakternyi razmer pylinki, $\alpha$ - harakternoe znachenie komponentov $\hat{\alpha}$ . Dlya izotropnoi sfery:
$\alpha={n^2-1\over{n^2+2}} a^3$ , (4)
zdes' a - radius sfery, n - pokazatel' prelomleniya. Iz (3) i (4) imeem
$\sigma_P={128\pi^5\alpha^6\over{3\lambda^4}} \left| {n^2-1\over{n^2+2}}\right|^2$ , esli $a<0,05\lambda$ . (5)
Vyrazhenie (5) legko obobshaetsya na sluchai ellipsoidal'nyh chastic. Ochevidno, chto releevskii predel dlya makrochastic sootvetstvuet usloviyu $2\pi a/\lambda\ll 1$ .

Differencial'noe sechenie R.r. zavisit ot ugla rasseyaniya $\theta$ mezhdu napravleniyami padayushei i rasseyannoi voln:
$d\sigma_P(\theta)={3\over 8} \sigma_P (1+\cos\theta^2) \sin\theta d\theta$ . (6)

Rasseyannoe na sferich. chasticah izluchenie lineino polyarizovano vdol' napravleniya, perpendikulyarnogo ploskosti, prohodyashei cherez napravlenie raprostraneniya padayushei i rasseyannoi voln. Stepen' polyarizacii p dlya nepolyarizovannogo padayushego izlucheniya ravna
$p={\sin^2\theta\over{1+\cos^2\theta}}$ . (7)
Pri R.r. na nesferich. chasticah stepen' polyarizacii zavisit takzhe ot ih orientacii.

R.r. na mezhzvezdnyh pylinkah chastichno obuslovlivaet yavlenie mezhzvezdnogo pokrasneniya izlucheniya zvezd (sm. takzhe Mezhzvezdnoe pogloshenie). Potok rasprostranyayushegosya v dannom napravlenii izlucheniya vsledstvie R.r. vbok. Oslablenie uvelichivaetsya s umen'sheniem dliny volny, poetomu proshedshee skvoz' mezhzvezdnuyu sredu izluchenie okazyvaetsya pokrasnevshim otnositel'no ishodnogo.

(I.G. Mitrofanov)

I. G. Mitrofanov, "Fizika Kosmosa", 1986
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