Détermination des abondances des éléments chimiques d'étoiles A et F naines membres de deux amas ouverts. Contraintes sur les modèles évolutifs incluant les processus de transport.
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(2) Universit´ e Montpellier II Sciences et techniques du Languedoc. ` THESE pour obtenir le grade de. Docteur de l’Universit´ e Montpellier II Discipline: Physique Formation Doctorale: Astrophysique Ecole Doctorale: Information Structures Syst` emes (I2S) pr´esent´ee et soutenue publiquement le 14 D´ecembre 2007 par. Marwan Gebran. D´ etermination des abondances des ´ el´ ements chimiques d’´ etoiles A et F naines membres de deux amas ouverts. Contraintes sur les mod` eles ´ evolutifs incluant les processus de transport. Composition du jury Pr´esident :. Bertrand Plez. Rapporteurs :. Philippe Stee Georges Alecian. Examinateurs :. G´erard Jasniewicz Alain Hui-Bon-Hoa.
(3) . Richard Monier. Groupe de Recherche en Astronomie et Astrophysique du Languedoc UMR5024, Universit´e Montpellier II, Place E. Bataillon, 34095 Montpellier CEDEX 05.
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(44) < ûÑùþ. >. »4C ýûÑþ. GIHKJMLONQPSR2HTUHKJWVXYJTXYP. FZF[F[FVF[F[TQFH JMFZLOF[NQPSFR2HF[T F[FF[FZF[FF[F[FF[FZFF \ E F ] ^_] ^_] NQ|~}9`baTXYce|~dfL dgcehjVilRlkn}mp oKqMOdfhjJrgTsWXYmg|~ceL hji ^t^u^t^u^^t^u^t^u^t^u^t^^u^t^u^t^u^t^ v E Fxw ] ^y{R2^_z ] NUNQ|~&OhjHKasR0Nh dgVc_mg_ce|hjilz0JW 0WXc_T ace0Mk/ WiMkoKmgaUh dgsWMnFrfktF[dfmfFZkn_F[xoKFc_rfF[kF[^tF^u^tF[^uFZ^tF^ F Fe\ zF[FF[F[FFZF[FF[F[FF[FZF[FF[F[FF[FZFF ] ^^_] ¡qMdfhjrgsWmgcehjilMoKiMd¢ekt+hji0mgc_i2£^t^u^^t^u^t^u^t^u^t^^u^t^u^t^u^t^ ¤ ] ^^ ¡qMdfhjrgsWmgcehjiMoKiMd¥ek+d/roKcek+dknm¥¦nxoKrg§ cedfdknaUkni0mOWk+d¥iWc_¨kQoK©u/ª¦niMknr¬« § cek ^u^t^u^t^t^u^^u^t^u^t^t^u^t^u^^t^u^t^u^t^u^t^^u^t^u^t^u^t^ Q] . #W,K6ch R 4 b ca =gW,#W K24XZ #* Q6 =,MTb+/ 3&, } + /x, A4 b+ K2,t/ #/{Q2 = 23&ced24 +K2 + q /V +4V#*B/V3 2 ? + L/ 4 ch#/V R 4 ' B/04V#k3& 2 2 +ch + L/I)K6 UQ2b 43&K2, /Q$# 2 , + WQ2IH b+4 + L/ *+3&K2* 12 + 0Q2 e,NM¦#/Vca3& !216R 4 [Q2 ,NMObB/V3& , 5S# 2 U*+ * 1$#!6 /V4 `2s j4 #!2!m ,, E, [ 23/ 3& 2 'Q2 a/V4V# 2 Z\ +4/U4 #Q2#/VtZ=!m3&K24[#d]3K6/V 4eg",.# 4b 3,K6/ 3& "Q2 ',MTb ILK$#/ 3& "Q2 [/ 4V# 6 Z\ 4X/-¡\ +*+/V 3& 2 5 +/ 45 3 ¤ 5mpq 2 K6 /V `Q$# 2 f,.#E *B/V 3& 65 16`s (# { /V43_Q6K24 A, + {Q2IH b+4 / q 3K24 *+ xQSMT3&!$#*+ /Vb;# 2 6ILK2 , + {/V43& chb+*k# 2 ca {4 !]3& 6 V#d2, Q2 Y,NMOb+,.#4%& ca /Q6 ;4V# +5. ¯®K. ° <ßú'CoF4±8=<GD9<}ú{@ úYD@±. qp ch YQ2K* / 4 'Q2 [,NMObB/V3& , `6,.#E,K6ch R 4 f(#a K2d64;, + !64 3)* K2 fQSMO#d2 34 !6/ 3& S`$Q MOb+ch 3& B/Q6 Q6JH]K2 3& S5#0* 3& 6 $# V# 6* Q2 }!24 3!24 b+/Vb+ x!21_ ILK2 + Q2Khch , Ke!m 4ch B/}Q2 ;ch K_U* 3&c-^ !24 2Q64 o, + a!612b 23chR+ 2 aQSMT /V +4V#*B/V3 2 - /V4 4 #k&3& 2 6 ca /a +/a%#5}y0 Q2bBª$ 2 /E,NMO /V 6 / b !]b+* ª2I)K6K ²=QSMTK2 h4V#k&3& 6 2 ca /Q2 Z\4b ILK2 + 2* t/VK2b; + gY,MT 2 X/ # / B/A f!64 3&!$#%& k# /Q$# 2 ,#jQ24 *B/V3 ~n *+3&chca ebB/ # /Y, e4V#!2!]34/0 + L/ 4 ν -,#jILK$# /V~rt/VbUQ E B/0, [t!24 3)Q2K2t/ ~n · − 5 → dS dΩdνdt Q E + /f,.#UILK$# / /Vb0Q MOb+ 2 4%& 0/V4 # 2 !]3&4X/Vb+ '!2#4, 04 #¨3& 2 2 +ch + /WQ2 0Z\4b ILK2 6* '* 3&ca!24 0 + L/ 4 ³ Æà ÃO¾ ÁN¸¾ÀNÃT!Á xÀ -¶ »X´Ã #Å µ·¸ I ¸ À\Á¸ µk¶³Næ¶Â X¸{¸X¾ erg · s−1 · cm−2 · rad−2 · Hz−1 ' ν. 1.
(45) ·¸ L ¹Z Y']_P»ºW¼¾½®L¹W¹eP^N4TWY ¸/¿ *k]õZSÀK,-PUT B/ Q$# 2 xK2 h# 2%&, 3&, Q2 / 4V#k(& +4 V# L/K2 ab , b ca /}Q2 ; K24XZ #* ;Q Q t ¡ ª$ν%&+K24dν 5 ¤ 5$#EZ\34 cUK2, X/,.#UdΩ K6 (# /V E. ν. S. !] + 2Q$# /, =/ ca!2 . − → dE = I (~r , ~n , ν, t)~n · dS dΩdνdt = I (~r , ~n , ν, t)dS cos θdΩdνdt. eMO3-. 3 θ + /0,NM¦# 6%&, ' ,K2caR+4 5. ¡ 5 ¤. 43. ¡ 5 ¤ dEν /V4 U,.#h 23&4 ch#, [g,#h K2cos 4Z #θdS *+ U +dΩdtdν /,.#hQ64 +*+/ 3& Q2 U!243&!$#%#/V3 PQ2KJ4 #k&3& Q2 Iν =. d. E E ÆWÇ ÁÃÂ!ÄuÅ F iUÈÉoKcedf+kQoK»/ c_i0mfkniMdgc_mf¦¡dgs¦+ncËÊ0Mk I (~r , ~n , ν, t) mgro+¨knrfdoKi2mWiMk¡dgWr¬ÈÌoj+k¢ÍÏÎMoKiMdWi{oKiW§ ek d hj_ceWk dΩ knmÐÈÌoKcedoKi0m¢WiloKiW§ ek θ o+¨k+uxoZiMhjrga¯oKek ^. !$#4/ 4Q2 =,MT / 2 /Vb} !mb *+ ª$ILK2 `&!2, K2 K24 {ILK$# /Vt/Vb ?!] +K6(& + L/xÐB/V4 =*k#, * K2, b + 5&qMT /V + 2 t/Vb u ch3¨& + 2 2 KÑW X/fQ6 +ª$ 2 Y!$#40. 561 ¤. Z 2π Z π ¡ 1 I (~r , ~n , ν, t) sin θdθdφ IdΩ = 4π Ò$K)"ch3& 63_* 1243&ch#/V I)K6 KÓQ2 Y,.#U4 #Q2#/V 3& F~ (~r0, ν, t)0 /Q2bBª$ 2Q2 Y,.#Uch# 2 R 4 K2t(# /V E Z ¡ ~ F (~r, ν, t) = I~n dΩ 1 J(~r, ~n, ν, t) = 4π. Ô Æmà æ¾ ÁN¸¾À ÃOÁ qÂ=´ Ä+¸X¾·¾·¸ J ¸À Á¸fµ¨¶·³Ã¦Âà ¸{¸X¾ erg.s · cm ÕXÆ)¸&Ö µ µ F ¸À Á¸f¨µ ¶·³ÃO¶ ¸?¸¾ erg · s · cm · Hz ' ν. ν. °. Z. −1. −2. −1. −1. −2. · Hz−1. '. 5O° ¤.
(46) ·¸ L ¹Z Y0]_P{ºW¼¾½®L¹W¹eP^N4TWY ¸/¿ *k]^ZSÀK,ePUT 0!243_Q2K6 / ~ !$#4AK2 2 / b0Q2 /V +ch!6 +/ − → 23&K6 Q63& 2 2 0, ZÒ$K_g-/ 4V#k(& +4 ;,.#[ K24XZ #* Q2 0Z\4b ILK2 6* F 5m(~pqr, "ν,* t)3& 2· dS Q2b+4V# /K2 2 Y K24Z #*+ [K6 2 / b`2 23K2 ;3&d6/V + 23& 2 ' dS ¡ 52 ¤ 0 0 vG3&K24 µ = cos θ `$,.#-ILK$# /Vt/VbY/V3/V#, 0QSMTb 6 4 % YILK2/V4V#k( 4 eK2 6 [ K24Z #*+ [K6 2 /V#4 0!$#4; +* 3& 2Q6 B/;!$#4;K2 2t/Vb0Q2 0Z\4 b+ILK2 2*+ e + /' Z +1 ¡ 65 5 ¤ Iµ dµ F = 2π − → Fν = F~ (~r, ν, t) · dS =. Z. Z. − → I~n · dS dΩ =. I cos θdΩ =. Z. 2π. Z. π. I cos θ sin θd θdφ. ν. eMO#K6/ 4 Y!$#4X/;,.#-!24 3& oQ2 '4V#Q2.#/ 3& Ï×= X/fQ63& 2 2b+ [!$#40 −1. dEν cos θ cdtdS. ¡ 5C ¤. Iν cos θdνdΩ c. ¡ 65 7 ¤. dPν =. pq "4 ca!2,#Ûk# /. Iν. !$#4 V#-(#, +K24Q23& 6 2b 'Q$# 2 ;,NMOb+I)K2#/V 3& 45 3-3 3&d_/V + /Y dPν =. p{/; K64f,NMO + 2 +cUd2, 0Q6 # 2%&, 3&, Q2 0. ¸¢Ø¸pظ. Ù. 4π Pν = c. ¢£<%¨F É#³Â%¨#i°<¨;. Z. Iν cos2 θdΩ. ¡ 65 8 ¤. ~ "Z # * #K, K2ca 2 +K_ILK2/V4 #k(& 4 [K2 2 e*+3&K2* 12 'Q2 '%#'QSMTb !$# K24Q s (#a /V 4 #%& 4;#¨( * f , 0%#0 +,3& o, ;,3& = K6 (# /V + ' vG3&K24;K2 2 '#d2 3&4 !_/V3 ¡ 5 Ú ¤ dIν = Iν κν ρds vG3&K24;K2 2 Yb ca 3& ¡ 5 E ¤ dIν = jν ρds #k(& +* κ et j , =*+3_ B×a* + /V QSMO#d2 3&4 !6/ 3& S Ú +/;QSMTb ca 3 !$#4AK2 2 / bQ2 0ch# 4 + !m *B/V ( B^ ca /k` νρ b+/V#ν /e,#cj# E(&3&, K2caILK2 - %25T* c −3 5lA * x!m 4ch B/[Q MObB(#,K2 +4', Ed2,# QSMT /V + 2 t/Vb Q23 2 2bY!$#4,NMOb+I)K2#/V 3& oQ2 0/V4V# 2 Z\ +4/Y #-!24 3Z\3& 2Q2 +K24;3&!6/V ILK2 . τν. dIν = jν ρ − κν ρIν ds. ¡ 5 3 ¤. dτν = ρκν ds. ¡ 5 1 ¤. + /Q2b+ª2 2 Y!$#4Y. ÛÆ)ÇA¶·³¸ÀÀ æ´B¾W¹¨¸q³Ç+¹¨Ã¢Ç ÁNæ´B¾ ¸ À\Á¸µk¶³Næ¶ X¸{¸X¾ ' ·À Ácm−2 · Hz−1' ɱ Ü Æà µ·¾·ÃOÁ x¹¨µ0»´k¸Ý»XÃO¸¾ Á¹Là ÇBPÝÀ ν´+³N¶·ÁNæ´B¾WÂ=Ç+ÀNÀNâÅ+µ¸ dyn ¸ ±N± Æà µ·¾·ÃOÁ x¹¨µ0»´k¸Ý»XÃO¸¾ Á¹Là ÂAâÀÀ æ´B¾WÂÇBÀÀ ⊵·¸ j κ¸ νÀ\Á ergcm· s2−1· g·−1Hz−1 · rad−2 · g−1 ' ν. 2.
(47) ·¸ L ¹Z Y']_P»ºW¼¾½®L¹W¹eP^N4TWY ¸/¿ *k]õZSÀK,-PUT G#-Z\3& 2*B/V 3& 3&K64 * . Sν. X/Q2b+ª$ 6 Y!$#4Y jν κν. Sν =. xMTb ILK$#/V3 Q2Ko/V4 # 2 XZ\ 4/; + /W#,34 =!24b /Vb+ e 3K2 ;,.#UZ\3&4 ca K2 (# /V E dIν = −Iν + Sν dτν. px oZ\3& 2*B/V 3& oQ2 Y,.#U!m3& t/V3 +/Q2Ko/V ca!2 +`$3& o3&d6/V /Y. ¡ 5 ° ¤ ¡ 5 2 ¤. ¡ 5 5 ¤ 8 * Q t *+ [ILK2 Q s b+/V# /,.#EQ2 / # 2* '!$#4* 3&K24K2 '!$#4,.#E,K2caR+4 0!m 2Q$# L/WK2 / ca!2 Q t `m3& P#aQ sÖ 23&K2 chR+ 2 Yg-,.#UZ\3&4cUK2, W K2t(# L/ E dIν =. ∂Iν ∂Iν ds + dt ∂s ∂t. 1 ∂Iν ∂Iν + = jν ρ − κν ρIν c ∂t ∂s. ¡ 5 C ¤. 1∂ ~ + ~n · ∇)I(~ r , ~n, ν, t) = ρj(~r, ~n, ν, t) − ρκ(~r, ~n, ν, t)I(~r, ~n, ν, t) c ∂t. ¡ 5 7 ¤. G#-Z\3&4ch ,#-!2,K2 %b 2b+4V#, 0Q2 Y,MTb ILK$#/ 3& oQ2 0/V4 # 2 XZ\ 4/ + /' (. {® Þ. 7ÍÌ;F4ß{ ÎD@ ß[C. 8àWáÌtâXÎúYD@ß[C Î D<ßú'CoF4±8=<GD. ¸pØ\¹¶Øå¸ §©¨F¢±°S¨F%u<¨;G«ã墣fä® æåÆß!¢£¨;,°[ãç! ><;!. #!24 b+ 6* Q6 #/V3&ca o B/Q6 "3& 2 oQ$# 2 ,NM¦#/Vca3& !216R 4 Q MOK2 6 bB/V3& , /V4 #Q2K2t/o!$#4 , o4 # + #d2 3&4!6/V 3& ILK20 K2!m 4!]3 /P#K !m *+/ 4 * 3& / LKS5; *k#, * K2,Q MOK2 !m *B/V4 ) /V12bB/VILK2 6b * + /V jK2 2 jdm3& 2 6 j* 3 2 $# V# 2* hQ2 [* 3& 2Q6 /V 3& 2 '!21) ILK2 + UQ2Kca, +K3- Z\3&4 ca /;, + ;4V# 5. A$'vl*%do0&æèr$0 ©&s+ tu eE"¦+"¦${I*> 0$0". * 3&K6* 12 agQ2JH]b 4 /V + -!24 3Z\3& 2Q2 +K24 E%&b+3&chbB/V4ILK2 qMO#/Vca3& !612R 4 /EQ6b * 3K2!]b+ o ¡ x80Úgj,#h K64Z #*+ ¤ 5 e!$# V#% UQ2 WN* 3)3&4 Q23 2 2b + !612b 4ILK2 Y#K_* 3)3&4 Q23 2 2b + !2,# 2 f 23&K2x i Q23& 2 2 j¡\ª2%&K24 5 3 ¤ ds = −. +/. dτν = −. ¡ 5 8 ¤. dx cos θ. ¡ 45 3Ú ¤. ρκν dx cos θ. W,34 ,MTb ILK$#/V3 "Q6 Y/ 4V# 6 Z\ 4X/f#K24V#-,#eZ\3&4 ca 0 K2t(# /V -. 5. ± É Æmà µ¾·ÃTÁ! x¹¨¸qÌ¢Ç}Ë¥´+¾»ÁÃO´+¾WÀN´Bµ³»X¸. Sν. ¸ À\Á. dIν cos θ = Iν − Sν dτν erg.s−1 · cm−2 · rad−2 · Hz−1. '. ¡ 45 3 ¤.
(48) ·¸ L ¹Z Y0]_P{ºW¼¾½®L¹W¹eP^N4TWY ¸/¿ *k]^ZSÀK,ePUT Vers l'observateur. x dx. ds. θ. x-dx. Vers le centre de l'étoile E /Æ é ÁÃÂ!ÄuÅ Few nk sWrf¦+dfkni2moKmgcehjiê/ WiMku§¦+hjaUknmgrgcekusWxoKi«ÌsoKroK_enek ^. qp !m3& V# / µ = cos θ ¡ θ X/0,MO# 2%&, e + L/ 4 U,#j 23&4cj#, Ugh,.#j K24Z #*+ -Q2 U,NMObB/V3& , ' +/0,#j, %& 2 eQ6 () b ¤ 3 "3d6/V /Y ¡ 5 33 ¤ dIν =I −S µ dτν. ν. ν. |_K6* * + (& +ch + / 3 L/* #,*+K2,b+ !m3&K24;* 1$#*+K2 2 'Q2 Y* ;*+3&K2* 12 + e #!243Z\3& 2Q2 +K24Y3&!6/ ILK2 τν g!$#4X/V 40Q2 E,.#cj# -(3&,K2caILK2 3&4 !_/V3 κ Q2K"ca, KJ. ρ. +/'Q2K* 3) +×a*+ /'QSMO#d_^. ν. #U/V +ch!mb 4 #/VK64 3-. dτν = −ρκν. T (τ ). dx µ. I)K6 MTb * 4 / "!24 caR 4 Y#!2!243k6 cj#/V3 Q$# 2 ;, 0*k# ;%&4 4 3 (τ + q(τ )) T 4 (τ ) = Teff 4. q(τ ) = 0.6940 − 0.1167e−1.9720τ + . . .. ¡ 5 3.1 ¤ ¡ 45 3° ¤ ¡ 45 3E2 ¤. + /,.#eZ\3 2*+/ 3& oQ2 'f3!6Z5 * # x%&4 {!] +K6/x +4()4xQ2 !64 caR+4 t/Vb 4 #/V 3& UQ2KE!243ª$,2¬'¡ τ ¤ ch# {*+ , K2t^½* 6 + /}4 +*k#, * K2, b sK6 ILKSMOga*+ 'ILK2 ',MTb ILK2 , d24 f4V#Q2#/VtZ½ § 3&t/; V#/ XZ # / 5 ±\Í ÆL¸&Öµ µ¹à ¾·¸X³ÈBæ¸{³Ç+¹¨Ã¢Ç ÁNæßB¸?¸ÁG»X´B¾kßB¸ »ÁÃOß+¸¾·¸{ß Ç³Ã¦¸?¶ÇBÀ¹à µ·¾·¸q¶·³´Ë¥´+¾¹¨¸µ·³4%=Ì à ǵ¨Á³N¸q¹¨¸{Ìà ÇÁNÂ=´+ÀN¶·¼ë³N¸ '. C.
(49) ·¸ L ¹Z Y']_P»ºW¼¾½®L¹W¹eP^N4TWY ¸/¿ *k]õZSÀK,-PUT #0Z\3 2*+/ 3& U 3&K24* Sν (tν ) ILK2$ X/k`&Q2# 2 x, =* # qQ2 ,NMOb+I)K6, d24 }/V12 +4 ca3_Q__ 2#ch ILK2 =,3)*k#, \Ó ¡Npq¬; ¤ `$,#-Z\3 2*+/ 3& Q2 'vq,.# 2* ¯J. ¡ 45 35 ¤. 2hν 3 1 hν 2 c e kB T (tν ) − 1. Bν (tν ) =. y0 "!m K6/ _ª$ Q6b Q2K2 4 Y,MT / 2 /Vb0Q6K"4 #k&3& 2 6 ca /g-,#E K24Z #* YQ2 Y,MTb+/ 3&, e Iν (τ = 0, µ) =. Z. ∞. tν. Bν (tν )e− µ. 0. ¡ 45 3 C ¤. dtν µ. y0K"d2 o 2*+3&4 ', [Ò2K_o4V#Q2.#/ Zb+ch !$#4,MTb+/ 3&, gE V#- K64Z #*+ ¡ τ = 0 ¤ Fν (0, µ) = 2π. 3&K #¨( *. Fν (0) = 2. Z. Iµ (0, µ)µdµ. ¡ 45 37 ¤. S(tν )E2 (tν )dtν. ¡ 45 38 ¤. Z. ∞. 1 0. 0. ¡ 65 1&Ú ¤ 1 x eMOK6 j!m3& /xQ2 ()K2 ; LK2chb+4 I)K6 `,MT / b %&4 #, Q2KlÒ2K_a X/Q6 *+4 bB/V b ;!m3&K24q!m3&K6(&34{/V + 24q*+3&ca!6/V Q2 Y,.#-* 3& / 4 d6K6/V 3& Q2 0/V3&K_/V ;, ;Q2JH]b 4 /V + ;* 3&K2* 16 WQ6 '!64 3Z\3& 6Q2 K24;3&!_/VILK2 τ En (x) =. Z. ∞. t. −n −xt. e. dt = x. n−1. Z. ∞. t−n e−t dt. i. Iν (τ = 0, µ) =. #¨( *. X. e−τνi B(τνi )∆τν. ¡ 65 1 ¤. τi. ¡ 561>3 ¤ px * 3& 2 b ILK2 + 2* `!]3K24o* 1$#ILK2 *+3&K2* 12 Q2 ,NM¦#/Vca3& !216R 4 Q2 b+/ 3&, ` ,Z #K2Q24 # * #,*+K2, +4", * 3) +×a* /V ;QSMO#d2 3&4 !6/ 3& j +/,#[Z\3& 2*B/V3 3&K24* a¡\I)K6 X/;Q$# 2 , W* # Q2 ,NM¦pq¬;,.#[Z\3& 6*+/V 3& Q2 vx,# 2* ¯ ¤ 5 ∆τ = τνi+1 − τνi. {®ì. ú >@BD+Ì í 8;F F4ß´Î<?>A8;Fîág߯ï [. #Z\3&4 ca `A,MT /V + 2 t/VbJ B/,#«!]3& / 3& ÑQ6 "4V# 3 L/"Q2K6 g,NM¦#d2 3&4!6/V 3& Q2K4V#k&3 2 2 B^ ch + L/f!$#4;, ;!$#4X/V*+K2, + ;I)K6G*+3& 2 X/V / K2 /f,MO#/Vca3& !212R 4 YQ2 [,NMObB/V3& , 52W +K_"/_!m QSMO#d2 3&4 !6/ 3& B_ X/V / `mK6 2 YQ$# 2 ;, 0*+3& /V )K" +/,NM¦#K_/V4 0Q2# 2 ;, + 4V# 05. 7. ± Ü Æ_ÇÁN¸XÂ=¶- X³½Ç Áµ·³N¸{¸ À\ÁG»X´B¾À ÁÇB¾+Á¸?¹Ç¾À»½¼Ç+Å µ·¸q»´Bµ»½¼·¸'.
(50) ·¸ L ¹Z Y0]_P{ºW¼¾½®L¹W¹eP^N4TWY ¸/¿ *k]^ZSÀK,ePUT. ¸¢ØSðظ l³<¨#i° <¨; ;¥«¨;·<®. j*+3_ B×h*+ + L/eQSMO#d2 34 !6/ 3& / 3/ #,}Q2# 2 e, h*+3& /V )K4 b K2, / jQ2 j,MO#d2 34 !6/ 3& Q2 j!6,K2 K64 !243_*+ K2 q!21) ILK2 q*+,.# b ?Q$# 2 Q2 K_U*k#/ b %&34 + 53&4 I)K MOK2 -b+, +*+/V43& U + /x#44V#* 16bAQ2 = 3& U 2¥^ ( k#KQ MOb+ 2 4%& `),#'!2#4/ * K6, Q2 B(_ /= 3& 2 b 5L# 2 * f*k# }3& j!2#4 , Q MOK2 6 f/V4 # 2 /V 3& N Z ¿ñ N Z0MO]_PB5 'Q2 K__ R ca e!212b+ 23&caR 2 [ [Q2b 43&K2, ',34 ILKSMTK2 2 [* 1$#4%& e + /W#* *+b , +4 b+ U,3&4 ;Q2 e 3& P!$# V#%& Ug !243k6 cht/VbQ MOK2 6 [#K6/V4ó ò$*MT X/W,#e/V4V# 2 t/V3¦ N Z0MO]UP ñ N Z0MO]_PB5 ©,}«##K2 =,#JQ2J H]K2 3& !2#4U, + Ub , *B/V4 3 2 -, d24 + ¡ Q6J H]K2 3& ¬123&ca 3 ¤ +/-!2#4-,MT1_Q64 3&%&R+ 2 2 +K6/V4 h¡ Q2IH K2 3& ow#k), %&1 ¤ 5 vG3&K24W, fb+/V3, + f +/zA`],NM¦#d2 3&4!6/V 3& "Q2K2 Ugh,MT1L)Q243&%&R+ 2 U 2 +K6/V4 e X/0Q23&ca 2# /V 'Q$# 2 f, eQ63^ ch# 6 3&!6/ ILK2 0 +/, * 3) +×a*+ / fQSMO#d2 3&4 !_/V3 "*+3&4 4 !]3& 6Q$# /V 3& /,.#eZ\3&4ch 0 K2 (# /V E vG3&K24;, + =/V4V# 2 t/V3 2 =Q2Ko/)!] ', bB^, d24 f + *+c 2 B/f!2#4#/V3&ca QSMT1)Q24 3&%R 2 ' 2 K_/V4 a ¡ 5411 ¤ /A, ;Z #*+/ K24}Q2 '#K6 L/Q23& 6 2bW!$#4,#YZ\3&4cUK2, . αbf (H) = α0 gbf. k# (& +* α = 1.0449 × 10−26 !]3&K64 K2 (# /V0 -. λ. ôe`L +/. gbf. λ3 n5. ¡ 45 1° ¤ #k(& +* R = 1.0968 × 10−3 ô −1 ,#[*+3& 2 /V# /V Q6 0w;)Q2dm 4%U +/ n , LK2cab 4 3eI)K2# /VILK2 W!24 2* !$#,5 =*+3_ B×h*+ + L/{QSM¦#d2 3&4!6/V 3& U + a*+c 2 !2#4{#/ 3&ca AQSMT1_Q64 3&%&R+ 2 ; 2 K_/V4 A!]3&K64{, + ?/V4 # 2 t/V 3& 2 G* 3&c-^ ca 2Û # /;!$#4;, 0 6 (& #K n MTb *+4 /#,3&4 0 0.3456 λR 1 gbf = 1 − − 1 2 (λR) 3 n2. i. ¡ 45 1E2 ¤ n 3 log e = 0.43429 ` θ = 5040 #k( * T ,#[/V +ch!mb 4 #/VK24 0 "Õ0 ,t(_ S` I = hR*0,NMOb+ 2 4%& Q MO 3& 2 #^ / 3& Q2 Y,NMO1)Q24 3%&R 2 Y B/ χ T, 0!m3/V + /V +,SQSMT B_* t/ #/ 3& oQ2 + f 6 (& #K_o K2!mb 4 K24 g n + 2 κ(Hbf ) = α0 λ. 3. i +2 hnX g i. bf n3. · 10. −θχ. i log e −χ3 θ −Iθ (10 − 10 ) + 2θI. 3. i. ¡ 45 15 ¤ vG3&K24A, }/V4V# 2 t/V3 2 Q6K/_!m , d24 B^, d24 `&, W*+3_ B×h*+ + L/=QSM¦#d2 3&4!6/V 3& j!2#4AZ\4V#*+/V 3& jQ MOb+, *B/V43& 2 #k# L/K6 2 q(_t/V + x*+3&ch!64 { / 4 v B/ v+dv K6 (# /K2 2 qQ2 / 4 d6K6/V 3& Q2 }P#·_ , ,t^HA3&, / ch# 2 +MOb+* 4 t/;Q2 Y,.#-ch# 2R+4 K2 (# / a h. χ3 = I 1 −. αff (H) =. 1 (ni + 3)2. i. 2 h2 e2 R 1 2m 1/2 33/2 πm3 v3 πkT. lA YILK2Q23& 6 2 YK2 *+3_ B×a* + /fQ MO3&!2#* t/VbYQ2 Y,.#eZ\3&4ch - 3. κ(Hff ) = α0 λ3 gff. gff. log e · 10−θI 2θI. + /, Z #*B/V +K24;Q2 ['#K6 L/;!m3&K24;,NM¦#d6 3&4!6/V 3& , d24 ^, d24 ' gff = 1 +. 0.3456 log e 1 + (λR)1/3 θχλ 2. ¡ 45 1 C ¤ ¡ 45 17 ¤ ¡ 45 18 ¤. 8.
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