Диссертация (1145426), страница 21

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Óð. (4.71) ). Ðåçóëüòàòû ðàñ÷¼òà ïðèâåäåíû íà íà Ðèñ. 4.27 Ðàñ÷¼òûïîêàçûâàþò, ÷òî âûëåò ôîòîíîâ ïîä óãëîì 90◦ ïðåîáëàäàåò ïî ñðàâíåíèþ ñâûëåòîì ïîä óãëîì 0◦ îñîáåííî â îáëàñòè ðåçîíàíñîâ. Âäàëè îò ðåçîíàíñîâôîòîíû âûëåòàþò ãëàâíûì îáðàçîì ïîä 90◦ , ÷òî ïðèâîäèò ê ñîîòâåòñòâóþùåìó ðîñòó ïàðàìåòðà A.  ðàìêàõ íåðåëÿòèâèñòñêîãî ïðèáëèæåíèÿ ýòîÿâëåíèå åñòåñòâåííî îáúÿñíÿåòñÿ êàê çàïðåò íà èçëó÷åíèå ôîòîíîâ ïîä óãëàìè 0◦ è 180◦ ïðè ðåêîìáèíàöèè ñ ãîëûìè ÿäðàìè [78, 91, 92].158Òàáëèöà 4.3: Ñðàâíåíèå ýíåðãèé (E − 3mc2 = ∆E − i Γ2 , â keV) òð¼õýëåêòðîííûõ ñîñòîÿíèéè ñîîòâåòñòâóþùèõ ðåçîíàíñíûõ ýíåðãèé () íàëåòàþùåãî ýëåêòðîíà (íà âòîðîé ëèíèè).Âòîðàÿ è òðåòüÿ êîëîíêè ñîäåðæàò äèàãîíàëüíûå ýëåìåíòû ìàòðèöû V .

Êîëîíêè 4-6ïîêàçûâàþò ñîáñòâåííûå çíà÷åíèÿ ìàòðèöû V , ïîñ÷èòàííîé â ðàçëè÷íûõ ïðèáëè÷åíèÿõ.VVCoulombCoulomb+BreitCoulomb(with retardation)Three electronstate(1s(2s 2s)0 )1/2∆EΓ-198.350-198.282-198.2990.0000.0310.03263.416(1s(2s 2p1/2 )1 )1/2-198.1740.03263.541(1s(2p1/2 2p1/2 )0 )1/2-198.0580.06363.658(1s(2s 2p3/2 )1 )3/2-193.8320.02767.883(1s(2s 2p3/2 )1 )1/2-193.8560.02667.859(1s(2p1/2 2p3/2 )2 )5/2-193.7450.05867.970(1s(2p1/2 2p3/2 )1 )3/2-193.7880.05867.928(1s(2p1/2 2p3/2 )1 )1/2-193.7320.05767.983(1s(2s 2p3/2 )2 )3/2-193.8600.02667.855(1s(2p1/2 2p3/2 )2 )3/2-193.7230.05867.993(1s(2p3/2 2p3/2 )2 )5/2-189.4260.05372.289(1s(2p3/2 2p3/2 )2 )3/2-189.3690.05272.346(1s(2p3/2 2p3/2 )0 )1/2-189.334∆E63.433(1s(2s 2p1/2 )0 )1/2Γ63.366(1s(2s 2p1/2 )1 )3/2∆E0.05372.381-198.3040.000-198.3770.021-198.2910.0160.006-198.3570.032-198.1310.003-198.0480.034-193.7690.022-193.8570.016-193.7500.056-193.8010.032-193.7360.041-193.9270.010-193.7170.052-189.4260.0270.0580.05372.291-189.36972.058-189.2880.02667.99971.968-189.3240.05767.79067.772-189.4150.05867.98067.594-193.6100.05867.91567.692-193.7880.02667.96767.665-193.6900.02767.86067.635-193.7170.05967.94867.561-193.7470.03263.66967.588-193.8210.03263.58563.421-193.7950.03163.36063.373-197.9620.00463.42663.151-198.009(without retardation)(with retardation)∆EΓ0.05272.348-189.33272.0940.05372.385159∆EΓ63.34063.102-198.231Coulomb+Breit63.078-198.281ΓCoulomb+Breit-198.3270.00463.058-198.2810.03163.105-198.2450.03263.140-198.0000.03263.385-197.9440.06063.441-193.6790.02767.706-193.8240.02667.561-193.7300.05867.655-193.7180.05867.667-193.6980.05767.687-193.8970.02667.488-193.5940.05867.791-189.3850.05372.001-189.3250.05272.060-189.2690.05372.117-198.3320.00263.054-198.2890.02163.097-198.2560.01163.129-198.0020.01263.384-197.9540.03163.431-193.9010.02667.485-193.8220.03467.563-193.7520.02267.634-193.7320.02967.654-193.6950.05667.691-193.6860.00967.700-193.6060.02967.780-189.4140.01071.971-189.3240.05272.061-189.2860.02772.100(1s (2s 2s)15151212996633063.033cross section (kbarn))0 1/263.0463.0563.06431 - (1s (2s 2p1/22 - (1s (2s 2p21/23 - (1s (2s 2p4 - (1s (2p1/21/22p063.3263.07213) )1 3/263.3363.342163.3563.361 - (1s (2s 2p0 1/2) )1 1/21/2)0 1/243) )22 - (1s (2s 2p14 - (1s (2p0 1/201/2) )1/20 1/2) )1/23 - (1s (2s 2p) )11 3/2) )1/22p1 1/21/2) )0 1/2063.163.22163.35 63 472.063.41 - (1s (2s 2p3/22 - (1s (2s 2p3 - (1s (2p1.54 - (1s (2p5 - (1s (2p1.01/21/21/23/22p2p2p6 - (1s (2s 2p0.57 - (1s (2p1/23/22p0.067.51.0(1s (2s 2s)67.667.767.8211 - (1s (2p2 - (1s (2p3 - (1s (2p0.53/23/23/22p2p2p3/23/23/267.963.4) )1) )13/23/23/2) )1) )13/25/2263.6341/263.75 671 - (1s (2s 2p3 - (1s (2p1.55 - (1s (2p1.00.50.068.031.0) )1/27 - (1s (2p67.867.912 5/21/21/21/21 - (1s (2p2 3/22 - (1s (2p3 - (1s (2p0.53/22p2p2p2) )13/2113/23/21/2) )) )3/23/23/23/2) )2) )1) )25/21/23/23) )0.02p) )68.02) )0 1/23/24 - (1s (2s 2p6 - (1s (2p3/23/22 - (1s (2s 2p3/23/2) )22.01/22) )23/2) )63.513/23/23/22p2p2p3/23/23/2) )2 5/2) )2 3/2) )0 1/20.072.072.172.372.4K, kinetic energy (keV)Ðèñ.

4.19: Ïîëíîå ñå÷åíèå äèýëåêòðîííîé ðåêîìáèíàöèè ñ äâóõýëåêòðîííûì óðàíîì êàêôóíêöèÿ êèíåòè÷åñêîé ýíåðãèè ýëåêòðîíà, K . Ëåâàÿ êîëîíêà îòâå÷àåò òî÷íîìó ÊÝÄ ðàñ÷¼òó (Coulomb + Breit ñ çàïàçäûâàíèåì), ïðàâàÿ êîëîíêà ïðåäñòàâëÿåò ðåçóëüòàòû ðàñ÷¼òà áåç áðåéòîâñêîãî âçàèìîäåéñòâèÿ. Êðàñíûå ïóíêòèðíûå ëèíèè îáîçíà÷àþò ïîçèöèèðåçîíàíñîâ, îòâå÷àþùèå äâàæäûâîçáóæä¼ííûì ñîñòîÿíèÿ.160(1s (2s 2s)15(1s (2p12Full)0 1/22p1/20 1/29663363.05363.06(1s (2s 2p2(1s (2p11/2(1s (2s 2p63.0663.07FullDRREC0 1/22)1/263.0531 3/20 1/22p63.04) )1/2(1s (2s 2s)063.0363.07) )1/2(1s (2s 2pREC12963.04DR15) )DR063.03cross section (kbarn)1/21/2) )0 1/21) )1 1/2DR0063.163.263.363.4(1s (2s 2p(1s (2s 2p(1s (2p3(1s (2p(1s (2p21/21/21/2(1s (2s 2p1(1s (2p1/263.1) )3/21) )3/22p2p2p13/23/23/22p23/267.567.61.067.767.82) )1) )15/2(1s (2p(1s (2p0.53/23/23/22p2p2pDR2REC3/21/213/2) )23/2067.9(1s (2p63.4FullDR063.31/2) )) )3/263.23/23/23/23/268.0) )2 5/2) )67.567.667.767.867.968.0Full1.0DR2 3/2REC) )0 1/2DR0.50.00.072.072.172.072.1K, kinetic energy (keV)Ðèñ.

4.20: Ëåâûé ãðàôèê îòâå÷àåò èíòåðôåðåíöèè âêëàäîâ ðàçëè÷íûõ äâàæäûâîçáóæä¼ííûõ ñîñòîÿíèé äðóã ñ äðóãîì. Ïóíêòèðíûå ëèíèè ïðåäñòàâëÿþò îòäåëüíûå âêëàäûäâàæäûâîçáóæä¼ííûõ ñîñòîÿíèé áåç ó÷¼òà íåðåçîíàíñíîãî ïðÿìîãî êàíàëà ðàäèàöèîííîãî çàõâàòà. Êðàñíàÿ ëèíèÿ ïðåäñòàâëÿåò ïîëíîå ñå÷åíèå äèýëåêòðîííîé ðåêîìáèíàöèèáåç ó÷¼òà íåðåçîíàíñíîãî ïðÿìîãî êàíàëà ðàäèàöèîííîãî çàõâàòà. Âåðòèêàëüíûå ëèíèèîáîçíà÷àþò ïîçèöèè ðåçîíàíñîâ, îòâå÷àþùèå äâàæäûâîçáóæä¼ííûì ñîñòîÿíèÿì. Ïðàâàÿêîëîíêà îòâå÷àåò èíòåðôåðåíöèè äèýëåêòðîííîé ðåêîìáèíàöèè (êðàñíàÿ ëèíèÿ) è ïðÿìîãî ðàäèàöèîííîãî çàõâàòà ýëåêòðîíà (ãîëóáàÿ ïðåðûâèñòàÿ ëèíèÿ).

×¼ðíàÿ ñïëîøíàÿëèíèÿ ïîêàçûâàåò ðåçóëüòàòû ïîëíîãî ðàñ÷¼òà.161polar emission angle (degree)180180150150120120909060603030063.03063.3263.0463.0563.0663.071801801501501201209090606030300063.163.263.363.41801501501201209090606030300067.667.767.867.968.01801501501201209090606030300072.1732488244063.3363.3463.3563.362502001501005063.563.663.70220176132884467.818072.097663.418067.5122067.9068.0907254361872.372.40K, kinetic energy (keV)Ðèñ. 4.21: Äèôôåðåíöèàëüíîå ñå÷åíèå (dσ/dΩ, in barn/sr) äèýëåêòðîííîé ðåêîìáèíàöèèêàê ôóíêöèÿ êèíåòè÷åñêîé ýíåðãèè íàëåòàþùåãî ýëåêòðîíà (K ). Ãðàôèêè â ëåâîé ÷àñòèîòâå÷àþò òî÷íîìó ÊÝÄ ðàñ÷¼òó (Coulomb + Breit ñ çàïàçäûâàíèåì) äèôôåðåíöèàëüíîãî ñå÷åíèÿ, ãðàôèêè â ïðàâîé ÷àñòè ïðåäñòàâëÿþò ðåçóëüòàòû ðàñ÷¼òà áåç áðåéòîâñêîãîâçàèìîäåéñòâèÿ.162cross section (kbarn)polar emission angle (degree)321018063.163.263.363.40.350.251500.150.05120-0.0590-0.16-0.2660-0.36-0.4630-0.560-0.6663.163.263.363.4K, kinetic energy (keV)Ðèñ.

4.22: Âêëàäû âûñøèõ ìóëüòèïîëåé â ïîëíîå è äèôôåðåíöèàëüíîå ñå÷åíèå. Âåðõíèéãðàôèê îòâå÷àåò ïîëíîìó ñå÷åíèþ (in kbarn). Êðàñíàÿ ïóíêòèðíàÿ ëèíèÿ ïðåäñòàâëÿåòðåçóëüòàòû ðàñ÷¼òà, ãäå ó÷ò¼í òîëüêî ÷ëåí j0 = 1 (ñì. Óð. (4.21)). ×¼ðíàÿ ëèíèÿ îáîçíà÷àåò ðàñ÷¼ò ñ 0 < j0 < 10. Íèæíèé ãðàôèê ïîêàçûâàåò îòíîñèòåëüíûé âêëàä âûñøèõìóëüòèïîëåé δσ .163180113510221509081207959056868145460341227301140polar emission angle (degree)063.0363.0463.0563.0663.071802502251502001751201509012510060755030250063.163.263.363.418075.868.215060.653.112045.59037.930.36022.715.2307.60.0067.567.667.767.867.918068.045.240.715036.231.612027.19022.618.16013.69.0304.50.0072.072.1K, kinetic energy (keV)Ðèñ. 4.23: Äèôôåðåíöèàëüíîå ñå÷åíèå (dσ/dΩ, â barn/sr) äèýëåêòðîííîé ðåêîìáèíàöèèñ äâóõýëåêòðîííûì óðàíîì äëÿ ïîëÿðèçîâàííûõ íàëåòàþùèõ ýëåêòðîíîâ (µ = −1/2) èâûëåòåâøèõ ôîòîíîâ ñ öèðêóëÿðíîé ïîëÿðèçàöèåé e+ (ñì. Óð.

(4.59)).164180180150150120120909060603030000.420.290.160.03polar emission angle (degree)-0.1063.063.163.263.363.4-0.23-0.36-0.49-0.62-0.75-0.8863.30 63.35 63.40 63.45 63.50 63.55 63.60 63.65 63.70180180150150120120-0.2749090-0.470606030300067.567.667.767.867.968.00.020-0.078-0.176-0.372-0.568-0.666-0.764-0.862-0.96067.867.968.0180180150150120120-0.2419090-0.415606030300071.9572.0072.0572.1072.1572.250.020-0.067-0.154-0.328-0.502-0.589-0.676-0.763-0.85072.3072.3572.40K, kinetic energy (keV)Ðèñ. 4.24: Ïàðàìåòð Ñòîêñà P1 (ñì. Óð. (4.68)) êàê ôóíêöèÿ êèíåòè÷åñêîé ýíåðãèè íàëåòàþùåãî ýëåêòðîíà K .

Ãðàôèêè â ëåâîé êîëîíêå îòâå÷àþò òî÷íîìó ÊÝÄ ðàñ÷¼òó (Coulomb+ Breit ñ çàïàçäûâàíèåì) äèôôåðåíöèàëüíîãî ñå÷åíèÿ, ãðàôèêè â ïðàâîé êîëîíêå ïðåäñòàâëÿþò ðàñ÷¼ò áåç áðåéòîâñêîãî âçàèìîäåéñòâèÿ.165180180150150120120909060603030000.1100.0870.0640.041polar emission angle (degree)0.01863.063.163.263.363.463.318018015015012012090906060303000-0.005-0.028-0.051-0.074-0.097-0.12063.463.563.663.70.1300.0970.0640.031-0.00267.567.667.767.867.968.0-0.035-0.068-0.101-0.134-0.167-0.20067.81801801501501201209090606030300067.968.00.0400.0220.004-0.014-0.03271.9572.0072.0572.1072.1572.25-0.050-0.068-0.086-0.104-0.122-0.14072.3072.3572.40K, kinetic energy (keV)Ðèñ.

4.25: Ïàðàìåòð Ñòîêñà P2 (ñì. Óð. (4.69)) êàê ôóíêöèÿ êèíåòè÷åñêîé ýíåðãèè íàëåòàþùåãî ýëåêòðîíà K . Ãðàôèêè â ëåâîé êîëîíêå îòâå÷àþò òî÷íîìó ÊÝÄ ðàñ÷¼òó (Coulomb+ Breit ñ çàïàçäûâàíèåì) äèôôåðåíöèàëüíîãî ñå÷åíèÿ, ãðàôèêè â ïðàâîé êîëîíêå ïðåäñòàâëÿþò ðàñ÷¼ò áåç áðåéòîâñêîãî âçàèìîäåéñòâèÿ.166polar emission angle (degree)1801801501501201200.490900.0606030300063.063.163.263.363.463.31.00.80.60.2-0.2-0.4-0.6-0.8-1.063.463.563.663.71801801501501201200.490900.06060303001.00.80.60.2-0.2-0.4-0.6-0.8-1.0067.567.667.767.867.968.067.867.968.01801801501501201200.490900.0606030300071.9572.0072.0572.1072.151.00.80.60.2-0.2-0.4-0.6-0.8-1.072.2872.3272.3672.40K, kinetic energy (keV)Ðèñ.

4.26: Ïàðàìåòð Ñòîêñà P3 (ñì. Óð. (4.70)) êàê ôóíêöèÿ êèíåòè÷åñêîé ýíåðãèè íàëåòàþùåãî ýëåêòðîíà K . Ãðàôèêè â ëåâîé êîëîíêå îòâå÷àþò òî÷íîìó ÊÝÄ ðàñ÷¼òó (Coulomb+ Breit ñ çàïàçäûâàíèåì) äèôôåðåíöèàëüíîãî ñå÷åíèÿ, ãðàôèêè â ïðàâîé êîëîíêå ïðåäñòàâëÿþò ðàñ÷¼ò áåç áðåéòîâñêîãî âçàèìîäåéñòâèÿ.1670differential cross section (barn/sr)12000900015001209080009060400300063.063.163.263.363.463.363.463.563.663.716030120208010400067.567.667.767.867.968.067.867.968.01280608404200072.072.172.372.4K, kinetic energy (keV)Ðèñ.

4.27: ( Ñðàâíåíèå äèôôåðåíöèàëüíûõ ñå÷åíèé âûëåòà ôîòîíà ïî óãëîì 0◦ (σ 0 (θ = 0◦ ),÷¼ðíàÿ (ñïëîøíàÿ) ëèíèÿ, â barn/sr) è äèôôåðåíöèàëüíîãî ñå÷åíèÿ âûëåòà ôîòîíà ïîäóãëîì 90◦ (σ 0 (θ = 90◦ ), êðàñíàÿ (ïóíêòèðíàÿ) ëèíèÿ, â barn/sr). Ãðàôèêè â ëåâîé êîëîíêåîòâå÷àþò òî÷íîìó ÊÝÄ ðàñ÷¼òó (Coulomb + Breit ñ çàïàçäûâàíèåì) äèôôåðåíöèàëüíîãîñå÷åíèÿ, ãðàôèêè â ïðàâîé êîëîíêå ïðåäñòàâëÿþò ðàñ÷¼ò áåç áðåéòîâñêîãî âçàèìîäåéñòâèÿ.168128864420063.063.163.263.363.463.3863.463.563.663.712A684420067.567.667.767.867.968.0867.867.968.0766544322072.072.172.372.4K, kinetic energy (keV)Ðèñ.

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