Диссертация (1149156), страница 14
Текст из файла (страница 14)
Âàæíî, ÷òî âðåìÿ ôîðìèðîâàíèÿ ñâåðõòîíêîé ñòðóêòóðû ∆τhf äëÿ ÌÇÈ ñ Z ∼ 60 ïðèìåðíî ðàâíî âðåìåíè çàõâàòà108∆τcap , îïðåäåëÿåìîìó ñêîðîñòüþ ïåðåõîäà äëÿ èñïóùåííîãî ôîòîíà. Âðåìåííîé èíòåðâàë ∆τhf ìîæåò áûòü ïîëó÷åí èç ñîîòíîøåíèÿ íåîïðåäåëåííîñòèâðåìåíè è ýíåðãèè:∆τhf ∆Ehf ≥ ~ .(4.30)Äëÿ ÌÇÈ ñ Z ∼ 60 õàðàêòåðíîå çíà÷åíèå ∆Ehf îöåíèâàåòñÿ ∼ 1 ýÂ, òîãäàèç ýòîãî ñëåäóåò, ÷òî: ∆τhf ∼ 10−15 ñ.Ñêîðîñòü ïåðåõîäà äëÿ E1 ôîòîíîâ äëÿ Z ∼ 60 ïðèìåðíî òàêîãî æå ïîðÿäêà, ïîýòîìó ∆τhf ≃ ∆τcap è ñâåðõòîíêàÿ ñòðóêòóðà, è âîëíîâàÿ ôóíêöèÿ(4.29) ìîãóò áûòü ñôîðìèðîâàíû âî âðåìÿ ïðîöåññà çàõâàòà.
Ïîñëå ðàäèàöèîííîé ðåêîìáèíàöèè êîíå÷íîå ñîñòîÿíèå ãåëèåïîäîáíîãî ÌÇÈ îïèñûâàåòñÿìàòðèöåé ïëîòíîñòè:ρFf =∑nFff MF ψF∗ f MF ψFf MFf ,Fff(4.31)MFfãäå ψFf MFf âîëíîâûå ôóíêöèè, ïðåäñòàâëåííûå âûðàæåíèåì 4.29. ×èñëàFçàïîëíåíèÿ nFff MF îïðåäåëÿþòñÿ ÷åðåç íîðìèðîâàííûå âåðîÿòíîñòè ïåðåõîfäàFnFff MFf= ∑WFi s→Ff MFfMFfWFi s→Ff MFf,(4.32)ãäåWFi s→Ff MFf =∑nFFii MF nssms WFi MFi sms →Ff MFfi(4.33)MFi msω2(2π)2∑∫WFi MFi sms →Ff MFf =∗(e,k)∗(e,k)dν ⟨Ff MFf (12)|A(1) + A(2) |Fi MFi (1)sms (2)⟩(4.34)eÇäåñü ÷ècëà 1 è 2 îòíîñÿòñÿ ê ïåðåìåííûì äâóõ ýëåêòðîíîâ, ñîîòâåòñòâåííî. Ïîëàãàåì, ÷òî êîíå÷íàÿ âîëíîâàÿ ôóíêöèÿ àíòèñèììåòðèçîâàíà îòíîñèòåëüíî çàìåíû 1 2, ïîýòîìó íåò íåîáõîäèìîñòè àíòèñèììåòðèçîâàòü109ôóíêöèþ íà÷àëüíîãî ñîñòîÿíèÿ.
 ìàòðè÷íîì ýëåìåíòå 4.34 áðà è êåò ôóíêöèè ⟨Fi MFi sms | è |Ff MFf ⟩ ýòî íà÷àëüíàÿ è êîíå÷íàÿ âîëíîâûå ôóíêöèè,êîòîðûå îïðåäåëåíû èç óðàâíåíèé (4.26)-(4.29), A(e,k) ôîòîííàÿ âîëíîâàÿôóíêöèÿ ñ ïîëÿðèçàöèåé e è âîëíîâûì âåêòîðîì k = ων , ãäå ω ÷àñòîòàôîòîíà. Òàê êàê â ýêñïåðèìåíòå, êîòîðûé ìû ðàññìàòðèâàåì íàïðàâëåíèåôîòîíà íå âûäåëåíî, ìû âêëþ÷àåì ñóììèðîâàíèå ïî ïîëÿðèçàöèè ôîòîíà èèíòåãðèðîâàíèå ïî íàïðàâëåíèþ âûëåòà ôîòîíà â âûðàæåíèå 4.34.Ïîäñòàíîâêà âîëíîâûõ ôóíêöèé, îïðåäåëåííûõ óðàâíåíèÿìè (4.26)(4.29), â âûðàæåíèå 4.34 è ó÷åò òîãî, ÷òî îïåðàòîð èçëó÷åíèÿ ôîòîíà íåçàâèñèò îò ÿäåðíûõ ïåðåìåííûõ, äàåò:WFi MFi sms →Ff MFf =∑∫e×dν∑∑∑IiIiCFJiiM(MJi MIi )CFJiiM(MJ′ i MI′i )FFMJi MIi MJ′ MI′∑iMJf MIf MJ′ MI′fiiiJ IJ ICFff Mf F (MJf MIf )CFff Mf F (MJ′ f MI′f )fff∗(e,k)×⟨Jf MJf |A(1)∗(e,k)×⟨Jf MJ′ f |A(1)∗(e,k)|Ji MJi , sms ⟩∗∗(e,k)|Ji MJ′ i , sms ⟩+ A(2)+ A(2)(4.35)×⟨If MI′f |Ii MI′i ⟩∗ ⟨If MIf |Ii MIi ⟩ .Ñóùåñòâóþò äâà ãëàâíûõ êàíàëà ðàññìàòðèâàåìîãî ïðîöåññà.
Ïåðâûé êàíàëñîîòâåòñòâóåò ñëó÷àþ, êîãäà çàõâàòà íå ïðîèñõîäèò, è èîí â êîíå÷íîì ñîñòîÿíèè îñòàåòñÿ îäíîýëåêòðîííûì. Âòîðîé êàíàë ñîîòâåòñòâóåò ñëó÷àþ, êîãäàçàõâàò ïðîèñõîäèò, è èîí â êîíå÷íîì ñîñòîÿíèè ÿâëÿåòñÿ äâóõýëåêòðîííûì.Îòìåòèì, ÷òî Ii = If . Åñëè êîíå÷íîå ñîñòîÿíèå ñîîòâåòñòâóåò äâóõýëåêòðîííîìó ÌÇÈ è ïîëíûé óãëîâîé ìîìåíò ýëåêòðîíà ðàâåí íóëþ.Jf = MJf = MJ′ f = 0,Ff = I,MFf = MIf = MI′f ,110(4.36)(4.37)MIi = MI′i ,MJi = MJ′ i .(4.38)Òîãäà (4.35) ñâîäèòñÿ êWFi s→Ff MFf = WFi s→00,IMI =××∑∫∑∑∑nFFii MF nssmsiMFi ms0IIif(CFJiiM(MJi MIi ))2 (CIf M(0MIf ))2FIifMJi2∗(e,k)∗(e,k)dν ⟨00|A(1) + A(2) |Ji MJi , sms ⟩ .(4.39)eÄëÿ äàëüíåéøåãî óïðîùåíèÿ óðàâíåíèÿ (4.39) ðàññìîòðèì âîïðîñ ïåðåâîðîòà ñïèíà â ïðîöåññå ðàäèàöèîííîé ðåêîìáèíàöèè. Ðàíåå ýòà ïðîáåëìàîáñóæäàëàñü â [17] äëÿ çàõâàòà 100% ïîëÿðèçîâàííîãî ýëåêòðîíà íåïîëÿðèçîâàíûì ãîëûì ÿäðîì.
Ñîãëàñíî ðåçóëüòàòàì, êîòîðûå ïðèâåäåíû â [17],ïðîèñõîäèò èñïóñêàíèå ôîòîíà ñ ïî÷òè íóëåâîé ïðîåêöèåé óãëîâîãî ìîìåíòàíà íàïðàâëåíèå ïó÷êà ýëåêòðîíîâ.  [17] çàõâàò ýëåêòðîíà ãîëûì ÿäðîì ïðîèñõîäèò áåç ïåðåâîðîòà ñïèíà. Âû÷èñëåíèÿ, êîòîðûå áûëè ïðîâåäåíû äëÿçàðÿäîâ ÿäðà Z = 50, 70, 90 â [17], ïîêàçûâàþò, ÷òî âêëàä îò ïåðåâîðîòàñïèíà ñòàíîâèòñÿ ïðèíåáðåæèìî ìàë ïîñëå èíòåãðèðîâàíèÿ ïî óãëàì ìåæäó íàïðàâëåíèåì âûëåòà ôîòîíà è íàïðàâëåíèåì èîííîãî (è ýëåêòðîííîãî)ïó÷êà.
Ìû íå ïðåäïîëàãàåì, ÷òî âûëåòåâøèé ôîòîí áóäåò ðåãèñòðèðîâàòüñÿ,òîãäà ýêñïåðèìåíòàëüíàÿ ñõåìà áóäåò ñîîòâåòñòâîâàòü òàêîìó èíòåãðèðîâàíèþ. Ïîêàæåì, ÷òî ïðîöåññû ñ ïåðåâîðîòîì ñïèíà òàê æå ïðåíåáðåæèìî ìàëû è â ñëó÷àå çàõâàòà ïîëÿðèçîâàííîãî ýëåêòðîíà îäíîýëåêòðîííûì ÌÇÈ.Ðàññìîòðèì ðåçóëüòàòû ðàñ÷åòîâ ñå÷åíèÿ ýòîãî ïðîöåññà:Eu62+ (1s1/2 ) + e → Eu61+ (11 S0 ) + γ .(4.40)Ðåçóëüòàòû ðàñ÷åòîâ äàíû â Òàáëèöå 4.1. Âêëàäîì ìåæýëåêòðîííîãî âçàèìîäåéñòâèÿ â ñå÷åíèå ìû ïðåíåáðåãàåì.
Âû÷èñëåíèÿ áûëè ïðîâåäåíû äëÿ111íåïîëÿðèçîâàííîãî íà÷àëüíîãî îäíîýëåêòðîííîãî èîíà è äëÿ ïîëíîñòüþ ïîëÿðèçîâàííîãî íà÷àëüíîãî ýëåêòðîíà. Ìû ïîëàãàåì, ÷òî â ðåçóëüòàòå èçëó÷àåòñÿ ôîòîí. Åñëè ïðè èçëó÷åíèè ôîòîíà ýëåêòðîí ìåíÿåò ñâîþ ïðîåêöèþñïèíà íà ïðîòèâîïîëîæíóþ (ïðîèñõîäèò ïåðåâîðîò ñïèíà), ôîòîí óíîñèòïðîåêöèþ óãëîâîãî ìîìåíòà mph = 1, åñëè èçìåíåíèÿ ñïèíà ýëåêòðîíà íåïðîèñõîäèò, òî mph = 0. Ðåçóëüòàòû âû÷èñëåíèé ïîêàçûâàþò, ÷òî â ïðîöåññåèçëó÷åíèÿ E1 ôîòîíà, êîòîðûé äàåò ãëàâíûé âêëàä â ïðîöåññ ðàäèàöèîííîéðåêîìáèíàöèè, âêëàä ïåðåâîðîòà ñïèíà îòíîñèòåëüíî ìàë.
Ýòî ìîæíî îáúÿñíèòü òåì ôàêòîì, ÷òî îïåðàòîð èçëó÷åíèÿ E1 ôîòîíà â íåðåëÿòèâèñòñêîìïðåäåëå íå çàâèñèò îò ñïèíà ýëåêòðîíà. Ïðè èçëó÷åíèè ìàãíèòíîãî ôîòîíàìîæåò ïðîèñõîäèòü ïåðåâîðîò ñïèíà è, êàê ñëåäñòâèå, ïîòåðÿ ïîëÿðèçàöèè,íî âêëàä èçëó÷åíèÿ ìàãíèòíîãî ôîòîíà â ïðîöåññ ðàäèàöèîííîé ðåêîìáèíàöèè ìàë.
Ñå÷åíèå σRR áûëî ñîñ÷èòàíî â ðàìêàõ êâàíòîâîé ýëåêòðîäèíàìèêè(ÊÝÄ) ñ ïîìîøüþ ìåòîäà, ðàçâèòîãî â [23]. Ýòîò ìåòîä ó÷èòûâàåò ðåëÿòèâèñòñêèå è ÊÝÄ ýôôåêòû â ìåæýëåêòðîííîì âçàèìîäåéñòâèè ïî òåîðèèâîçìóùåíèé. Ðåçóëüòàò âûðàæàåòñÿ â âèäå ôîðìóëû:mphSFNSF NSFmSFph σRR + mph σRR=totσRRSFNSF1 × σRR+ 0 × σRR=≈ 1.5 × 10−2 ,totσRR(4.41)(4.42)totNSFSFãäå σRR= σRR+ σRR, èíäåêñû SF, NSF îçíà÷àþò âêëàäû ñ ïåðåâîðîòîìñïèíà (spin-ip) è áåç ïåðåâîðîòà ñïèíà, ñîîòâåòñòâåííî. Ýòîò ðåçóëüòàò ïîêàçûâàåò, ÷òî âêëàä mph ìîæåò áûòü îïóùåí. îòñóòñòâèè ïåðåâîðîòà ñïèíà, ïðåíåáðåãàÿ çíà÷åíèåì ïðîåêöèè óãëîâîãî ìîìåíòà ôîòîíà, ìû ìîæåì ïðåäñòàâèòü ìàòðè÷íûé ýëåìåíò â (4.39) ââèäå:∗(e,k)⟨00|A(1)∗(e,k)+ A(2)∗(e,k)|Ji MJi , sms ⟩ = ⟨0||A(1)112∗(e,k)+ A(2)||Ji s⟩δMJi +ms ,0(4.43)Òàáëèöà 4.1: Âêëàäû îò ðàçëè÷íûõ òèïîâ èñïóùåííûõ ôîòîíîâ â ïðîöåññ ðàäèàöèîííîéðåêîìáèíàöèè ñ ïåðåâîðîòîì (SF) è áåç ïåðåâîðîòà (NSF) ñïèíà.
Ïðåäñòàâëåíî ñå÷åíèåäëÿ çàõâàòà ýëåêòðîíà âîäîðîäîïîäîáíûì ìíîãîçàðÿäíûì èîíîì ñ çàðÿäîì Z = 63 â îñíîâíîå ñîñòîÿíèå 1s. Íà÷àëüíàÿ ýíåðãèÿ ýëåêòðîíà â ñèñòåìå ïîêîÿ èîíà ðàâíà 1 ý (ñì.ïðè÷èíó âûáîðà äàííîé ýíåðãèè â ñëåäóþùåì ðàçäåëå). Êîíå÷íîå ñîñòîÿíèå ãåëèåïîäîáíîãî èîíà 11 S0 . Çíà÷åíèÿ ñå÷åíèÿ äàíû â áàðíàõ (b) èëè êèëîáàðíàõ (Kb).PhotonSFσRRSFσRRtotσRRE12.6 kb332 kb335 kbEJ(J > 1)6.4 b172 b178 bMJ21.9 b13.8 b36 bãäå ⟨∥ ∥⟩ îçíà÷àþò 'ðåäóöèðîâàííûé' ìàòðè÷íûé ýëåìåíò, íå çàâèñÿùèé îòïðîåêöèè óãëîâîãî ìîìåíòà.
Òàê êàê ms = ±1/2, òî nsms = δms ,±1/2 (100% ïîëÿðèçîâàííûé ýëåêòðîí). Òîãäà ñèìâîë Êðîíåêåðà â óðàâíåíèè (4.43) ìîæíîçàìåíèòü íà(4.44)δMJi +ms ,0 = δMJi ,∓1/2 ,çíàê '+' ñîîòâåòñòâóåò ñïèíîâîé ïîëÿðèçàöèè íà÷àëüíîãî ýëåêòðîíà âäîëüèîííîãî ïó÷êà, çíàê '−' ñîîòâåòñòâóåò ïîëÿðèçàöèè ñ ïðîòèâîïîëîæíûì íàïðàâëåíèåì. Ìû äîëæíû ïðèíÿòü âî âíèìàíèå òàêæå òîò ôàêò, ÷òî0I(4.45)f(0MIf ))2 = 1 .(CIf MIfÒîãäà â ñîîòâåòñòâèè ñ (4.32) íîðìèðîâàííûå ÷èñëà çàïîëíåíèÿ äëÿ ÿäðàäâóõýëåêòðîííîãî ÌÇÈ â êîíå÷íîì ñîñòîÿíèè îïðåäåëÿþòñÿ êàê:∑InIff MIf= ∑MFiIinFFii MF (CFJiiM(MJi , MIf ))2FMIf MFiiiIinFFii MF (CFJiiM(MJi , MIf ))2Fii.(4.46)Çäåñü ìû èñïîëüçóåì ðàâåíñòâî MIi = MIf , êîòîðîå ñëåäóåò èç (4.35). Ñòåïåíü ÿäåðíîé ïîëÿðèçàöèè â äâóõýëåêòðîííîì ÌÇÈ â êîíå÷íîì ñîñòîÿíèè:λIf1 ∑ Ifn I f M I MI f .=fIfMIf113(4.47)Ïîäñòàíîâêà ÷èñåë çàïîëíåíèÿ â óðàâíåíèÿ (4.47), (4.46) nFFii MF èç âûðàæåiíèÿ (4.20) ïðèâîäèò ê ðåçóëüòàòó:7,157λIf (MJi = ms = +1/2) = − .15λIf (MJi = ms = −1/2) =(4.48)(4.49)Òàêèì îáðàçîì, ïîñëå çàõâàòà ïîëÿðèçîâàííîãî ýëåêòðîíà, ÿäðà â ýòèõ èîíàõñòàíîâÿòñÿ ÷àñòè÷íî ïîëÿðèçîâàííûìè ñî ñòåïåíüþ ïîëÿðèçàöèè ðàâíîé ≈47%.
Ñóùåñòâóþò ðàçëè÷íûå êîíå÷íûå ñîñòîÿíèÿ äâóõýëåêòðîííûõ ÌÇÈ ñïîëíûì óãëîâûì ìîìåíòîì ðàâíûì íóëþ. Âåðîÿòíîñòè (ñå÷åíèÿ) çàõâàòàýëåêòðîíà â ðàçëè÷íûå ñîñòîÿíèÿ äâóõýëåêòðîííîãî èîíà, âû÷èñëåííûå âðàìêàõ ÊÝÄ ìåòîäà, ðàçâèòîãî â [23], äàþòñÿ â Òàáëèöå 4.2.Òàáëèöà 4.2: Ñå÷åíèå çàõâàòà ýëåêòðîíà âîäîðîäîïîäîáíûì èîíîì ñ çàðÿäîì Z = 63 âîñíîâíîì ñîñòîÿíèè 1s â K - è L-îáîëî÷êè ãåëèåïîäîáíîãî èîíà ïðè ýíåðãèè ýëåêòðîíà âñèñòåìå ïîêîÿ ÿäðà 1 ý (1.823 × 10−3 ÌýÂ/íóêëîí).  ýòè âû÷èñëåíèÿ âêëþ÷åíû òîëüêîèñïóùåííûå ôîòîíû ñ ïîëíûì óãëîâûì ìîìåíòîì Jph = 1, 2. Íà÷àëüíûé îäíîýëåêòðîííûé èîí òàê æå, êàê è íà÷àëüíûé ýëåêòðîí ïðåäïîëàãàþòñÿ íåïîëÿðèçîâàííûìè.Electron shell,Cross section (Kb)statePopulationpercentageK , (1s)2 1 S0416243%L, (1s2s) 1 S03103.2%L, (1s2p1/2 ) 3 P04014.1%L, total559757%K + L, total9758100%Ýòè ðåçóëüòàòû ïîêàçûâàþò, ÷òî 50% ãåëèåïîäîáíûõ èîíîâ â êîíå÷íîìñîñòîÿíèè áóäóò â ñîñòîÿíèÿõ ñ íóëåâûì ïîëíûì óãëîâûì ìîìåíòîì.1144.4Îöåíêà ÷èñëà èîíîâ ñ ïîëÿðèçàöèåé ÿäðà è íóëåâûì ïîëíûì ýëåêòðîííûì ìîìåíòîì çà îäèí îáîðîò ýòîì ïàðàãðàôå ìû ïðèâèäåì ïîðÿäîê âåëè÷èíû äëÿ ÷èñëà èîíîâ Nc , êîòðûå çàõâàòÿò ýëåêòðîí çà îäèí îáîðîò.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
