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Fizicheskie osnovy stroeniya i evolyucii zvezd

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6.5 Gorenie geliya: 3 alpha-reakciya

Gorenie geliya zatrudneno tem obstoyatel'stvom, chto otsutstvuyut ustoichivye yadra s atomnym vesom i (esli by oni sushestvovali, to byli by vozmozhny reakcii ${}^{4}{\mathrm{He}}+{}^{1}{\mathrm{H}}$ i ${}^{4}{\mathrm{He}}+{}^{4}{\mathrm{He}}$ ). Odnako sliyanie treh yader geliya daet ustoichivoe yadro s atomnym vesom 12: $3\,{}^{4}{\mathrm{He}}\to {}^{12}{\mathrm{C}}$ . Poetomu dal'neishaya evolyuciya zvezdy opredelyaetsya etoi tak nazyvaemoi 3 $\alpha$ -reakciei. Yadra ${}^{8}{\mathrm{Li}}$ i ${}^{8}{\mathrm{Be}}$ neustoichivy i bystro raspadayutsya. Naprimer,

$\displaystyle {}^{8}{\mathrm{Li}}\to {}^{8}{\mathrm{Be}}+e^-+\nu,$

$\displaystyle {}^{8}{\mathrm{Be}}\to 2\,{}^{4}{\mathrm{He}}\qquad (\tau\sim 10^{-16}$ s $\displaystyle ).$

Tem ne menee tot fakt, chto yadro ${}^{8}{\mathrm{Be}}$ hotya i neustoichivo, no vse zhe sushestvuet v techenie vremeni poryadka $10^{-16}$ s, okazyvaetsya sushestvennym. Veroyatnost' reakcii pri troinom stolknovenii $\alpha$ -chastic s proizvol'nymi energiyami namnogo men'she veroyatnosti togo, chto dve $\alpha$ -chasticy imeyut energiyu kak raz takuyu, chto oni (hotya i nenadolgo) obrazuyut sistemu ${}^{8}{\mathrm{Be}}$ . Takaya sistema -- yadro ${}^{8}{\mathrm{Be}}$ v podavlyayushem bol'shinstve sluchaev raspadaetsya obratno na dve $\alpha$ -chasticy, no vse zhe izredka proishodit stolknovenie ${}^{8}{\mathrm{Be}}$ s tretei $\alpha$ -chasticei, privodyashee k obrazovaniyu ${}^{12}{\mathrm{C}}$ . Pri bol'shih temperaturah v termodinamicheskom ravnovesii imeetsya nekotoraya koncentraciya yader ${}^{8}{\mathrm{Be}}$ , opredelyaemaya formuloi Saha:

$\displaystyle [{}^{8}{\mathrm{Be}}]\sim [{}^{4}{\mathrm{He}}]^2e^{-0,3\,\mbox{Mev}/kT}.$

Stolknovenie yader ${}^{4}{\mathrm{He}}$ s ${}^{8}{\mathrm{Be}}$ privodit k obrazovaniyu yadra ${}^{12}{\mathrm{C}}$ . Tak kak veroyatnost' processa proporcional'na proizvedeniyu koncentracii ${}^{4}{\mathrm{He}}$ i ${}^{8}{\mathrm{Be}}$

$\displaystyle [{}^{4}{\mathrm{He}}]\;[{}^{8}{\mathrm{Be}}]\sim [{}^{4}{\mathrm{He}}]^3e^{-0,3\,\mbox{MeV}/kT},$

to skorost' reakcii $\sim \rho ^3$ , esli rasschityvat' ee na edinicu ob'ema, ili $\rho ^2$ -- na edinicu massy. Odnako ni stolknovenie $3\alpha$ , ni stolknovenie ${}^{8}{\mathrm{Be}}$ s $\alpha$ samo po sebe ne privodit k obrazovaniyu stabil'nogo yadra ${}^{12}{\mathrm{C}}$ , poka sistema ne izbavit'sya ot lishnei energii. Izbytok energii treh pokoyashihsya $\alpha$ -chastic nad energiei ${}^{12}{\mathrm{C}}$ raven 7,28 MeV, dlya goryachih $\alpha$ -chastic on eshe bol'she. Pri etom energiyu ne mozhet unesti neitron ili proton -- na eto energii ne hvataet, da i poluchilsya by ${}^{11}{\mathrm{B}}$ ili ${}^{11}{\mathrm{C}}$ , a ne ${}^{12}{\mathrm{C}}$ . Znachit energiyu unosyat fotony ili pary

(sm. nizhe). Snova veroyatnost' processa uvelichivaetsya, esli sistema dolgo zhivet v dannom sostoyanii , t. e. esli my imeem delo s opredelennym vozbuzhdennym sostoyaniem yadra ${}^{12}{\mathrm{C}}$ , a ne sistemoi, sostoyashei iz 6 protonov i 6 neitronov (ili 3 $\alpha$ -chastic) s proizvol'noi energiei, ne ravnoi energii kakogo-libo vozbuzhdennogo sostoyaniya ${}^{12}{\mathrm{C}}$ .


Ris. 36.	Ris. 37.

Yadro ${}^{12}{\mathrm{C}}$ obladaet bol'shim kolichestvom urovnei (ris. 36). Odin iz urovnei s energiei MeV nahoditsya v rezonanse s tremya yadrami geliya -- $3\,{}^{4}{\mathrm{He}}\,$ , obladayushimi izbytkom kineticheskoi energii (7,66-6,28=0,38) MeV. Eto vozbuzhdennoe sostoyanie, tak zhe kak i osnovnoe, imeet spin .Poetomu perehod s urovnya 7,66 MeV v osnovnoe sostoyanie ${}^{12}{\mathrm{C}}$ ne mozhet idti s ispuskaniem odnogo $\gamma$ -kvanta (spin kotorogo raven 1). Naibolee veroyatnym yavlyaetsya perehod s ispuskaniem elektronno-pozitronnoi pary

$\displaystyle {}^{12}{\mathrm{C}}^*\to{}^{12}{\mathrm{C}}+e^++e^-.$

Snyatie vozbuzhdeniya mozhet proishodit' takzhe s ispuskaniem kvantov cherez promezhutochnyi uroven'

MeV. Polnaya veroyatnost' reakcii na edinicu massy proporcional'na $\rho^2 e^{-\Delta E /kT}\simeq \rho^2 e^{-4,4/T_9}$ . Sravnim kaloriinost' $3\alpha$ -reakcii s

-ciklom:

$\displaystyle 4p\to {}^{4}{\mathrm{He}}+26\;$ MeV $\displaystyle ,$

$\displaystyle {}^{4}{\mathrm{He}}\to{1\over 3}\;{}^{12}{\mathrm{C}}+2,4 \;$ MeV $\displaystyle ,$

t.e. vydelenie energii na gramm v $3\alpha$ -reakcii na poryadok men'she.

Postepenno gelii v centre tozhe vygoraet -- voznikaet gelievyi sloevoi istochnik, a vodorod pri etom prodolzhaet goret' vo vneshnem sloevom istochnike (ris. 37). Na stadii gelievogo sloevogo istochnika sil'no vozrastaet svetimost' zvezdy, uvelichivaetsya ee radius, i na diagramme GR zvezda popadaet v oblast' krasnyh sverhgigantov (ris. 35). V dal'neishem (v dostatochno massivnyh zvezdah) zagoraetsya uglerod. Dolzhno idti obrazovanie bolee tyazhelyh elementov O, Mg, Ne i t. d. vo vse ubystryayushemsya tempe. I nakonec, takaya zvezda dolzhna dostich' sostoyaniya, pri kotorom teryaetsya ee ustoichivost'. Odnako poka ne sushestvuet horoshih raschetov, dovedennyh do konca. Polozhenie del uslozhnyaetsya nalichiem bol'shogo chisla sloevyh istochnikov i yadernyh reakcii, skorosti kotoryh ploho izucheny. Krome togo, voznikayut teplovye neustoichivosti, vspyshki i t.p. Vse eto zatrudnyat provedenie detal'nyh raschetov.

Nizhe my obsudim ryad harakternyh momentov, kotorye voznikayut pri raschetov evolyucii zvezd i imeyut dostatochno prostoe fizicheskoe istolkovanie.

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