Ni26+離子態(tài)分辨光復(fù)合過(guò)程的R矩陣?yán)碚撗芯?/h1>
2015-02-02 03:03:00頡錄有董晨鐘張登紅
頡錄有，馬 馳，馬 堃，董晨鐘，張登紅
(甘肅省原子分子物理與功能材料重點(diǎn)實(shí)驗(yàn)室，
西北師范大學(xué)物理與電子工程學(xué)院，甘肅蘭州 730070)
Ni26+離子態(tài)分辨光復(fù)合過(guò)程的R矩陣?yán)碚撗芯?/p>
頡錄有，馬馳，馬堃，董晨鐘，張登紅
(甘肅省原子分子物理與功能材料重點(diǎn)實(shí)驗(yàn)室，
西北師范大學(xué)物理與電子工程學(xué)院，甘肅蘭州730070)
摘要：利用基于相對(duì)論R矩陣?yán)碚摰腄ARC程序系統(tǒng)計(jì)算了Ni25+離子基態(tài)1s22s(2S1/2)和激發(fā)態(tài)1s22p(2P1/2,2P3/2)的光電離截面，并通過(guò)細(xì)致平衡原理獲得了統(tǒng)一的光復(fù)合過(guò)程(即輻射復(fù)合和雙電子復(fù)合)態(tài)分辨的截面，計(jì)算結(jié)果給出了輻射復(fù)合與雙電子復(fù)合過(guò)程間的干涉效應(yīng).為了標(biāo)識(shí)和分析KLL共振能區(qū)所有的共振峰，基于相對(duì)論組態(tài)相互作用理論(RCI)的FAC程序被用來(lái)計(jì)算共振峰的能量、強(qiáng)度及其相關(guān)的雙激發(fā)態(tài)的輻射、俄歇躍遷幾率以及共振寬度等.利用統(tǒng)一的光復(fù)合截面進(jìn)一步得到了KLL雙電子復(fù)合過(guò)程的伴線強(qiáng)度，并與孤立共振近似下FAC的計(jì)算結(jié)果以及以前的理論和實(shí)驗(yàn)結(jié)果進(jìn)行了比較，對(duì)存在的一致性和偏差進(jìn)行了分析和討論.
關(guān)鍵詞：光復(fù)合截面;相對(duì)論R矩陣?yán)碚?共振能量;共振強(qiáng)度
在高溫、低密等離子體(如太陽(yáng)、磁約束聚變裝置等產(chǎn)生的等離子體等[1])中，高電荷態(tài)離子的光復(fù)合過(guò)程強(qiáng)烈影響著等離子體的電離平衡及輻射X光譜[2-4].高電荷態(tài)離子的光復(fù)合(PR)主要包括非共振的輻射復(fù)合(RR)過(guò)程和共振的雙電子復(fù)合(DR)過(guò)程[5].輻射復(fù)合指靶離子直接俘獲自由電子到其束縛態(tài)，同時(shí)放出一個(gè)光子的過(guò)程；雙電子復(fù)合是一個(gè)間接過(guò)程，靶離子首先俘獲自由電子，同時(shí)內(nèi)部一個(gè)束縛電子被激發(fā)，形成共振雙激發(fā)態(tài)，共振態(tài)不穩(wěn)定將進(jìn)一步通過(guò)輻射光子躍遷到低能態(tài).RR與DR過(guò)程有著相同的初、末態(tài)，兩種過(guò)程之間存在干涉[4].以往的理論研究對(duì)光復(fù)合過(guò)程的處理多采用獨(dú)立過(guò)程和孤立共振近似，忽略了RR與DR過(guò)程間的干涉以及重疊態(tài)間的干涉[8].近年來(lái)，在統(tǒng)一的理論框架下處理DR和RR過(guò)程的理論，如投影算符近似[6]、密耦合近似下的扭曲波理論[4,7]以及R-矩陣?yán)碚揫8-11]等已被建立，其顯著的特點(diǎn)是DR與RR之間的干涉和重疊態(tài)間的干涉能夠被予以很好地考慮，利用這些理論人們已開展了一系列研究，并取得了很好的結(jié)果[12-18].實(shí)驗(yàn)方面，隨著重離子儲(chǔ)存環(huán)、電子束離子阱(EBIT)等實(shí)驗(yàn)裝置及相關(guān)測(cè)量技術(shù)的不斷提高，人們已開展了許多高電荷態(tài)離子，如U90+,Hg75+…78+和Bi79+光復(fù)合過(guò)程的研究[19-21]，并觀測(cè)到了顯著的DR與RR間的干涉[19-22].
類He離子是高溫天體、實(shí)驗(yàn)室等離子體中重要的電荷態(tài)離子，其光復(fù)合過(guò)程產(chǎn)生的X射線譜，特別是DR過(guò)程的雙電子伴線對(duì)等離子體中電子溫度及非麥克斯韋的電子分布十分敏感，是等離子體診斷的重要工具[1-3]；同時(shí)，由于類He離子簡(jiǎn)單的結(jié)構(gòu)，常被人們選作細(xì)致揭示相對(duì)論效應(yīng)、電子關(guān)聯(lián)效應(yīng)及其檢驗(yàn)理論和實(shí)驗(yàn)的重要體系[23].
Ni是天體中重要的高豐度元素，本文將重點(diǎn)以類He的Ni26+離子為例，利用基于全相對(duì)論R-矩陣?yán)碚摰挠?jì)算程序DARC(the Dirac Atomic R-matrix Codes)[24]并結(jié)合基于相對(duì)論組態(tài)相互作用的FAC(the Flexible Atomic Code )程序[25]開展其光復(fù)合過(guò)程的研究.相對(duì)論R-矩陣?yán)碚撚捎谄湎到y(tǒng)考慮了相對(duì)論效應(yīng)，并能給出精細(xì)的共振結(jié)構(gòu)，目前已被廣泛用于高電荷態(tài)離子光電離、電子碰撞激發(fā)等過(guò)程的研究中[26]，但對(duì)于光復(fù)合過(guò)程，由于計(jì)算的復(fù)雜性，相關(guān)的研究工作十分匱乏.本文一個(gè)重要目的即為檢驗(yàn)該理論在處理高電荷態(tài)離子光復(fù)合過(guò)程中的有效性和精確性.
1理論方法
1.1光復(fù)合截面
在KLL共振能區(qū)，即靶離子俘獲自由電子到L殼層，同時(shí)激發(fā)其K殼層束縛電子到L殼層的能量區(qū)間，Ni26+離子態(tài)分辨的光復(fù)合過(guò)程可以表示如下
(1)
其中,(a),(b)和(c)表示可能的雙電子復(fù)合過(guò)程的通道及其形成的中間雙激發(fā)態(tài);(d)和(e)表示輻射復(fù)合(或雙電子復(fù)合)過(guò)程的末態(tài).
在全相對(duì)論R-矩陣?yán)碚撝校哂蠳電子的靶離子與自由電子復(fù)合形成(N+1)電子體系的Dirac-Coulomb 哈密頓量可以表示為[6]
(2)
其中，第一項(xiàng)描述了單電子的動(dòng)能和勢(shì)能；第二項(xiàng)表示電子-電子間的庫(kù)倫相互作用;i和j分別表示第i和j個(gè)電子;Z為核電荷數(shù);α和β為狄拉克矩陣.
在密耦合近似下，(N+1)電子體系的波函數(shù)可以表示為[6]
(3)
根據(jù)細(xì)致平衡原理，在電偶極近似下，處于初態(tài)精細(xì)能級(jí)j的靶離子俘獲自由電子形成(N+1)電子體系的光復(fù)合末態(tài)i的PR截面可以表示為[27]
(4)
(5)
其中，gi為光電離初態(tài)的統(tǒng)計(jì)權(quán)重;c為光速;ω為光子能量;Mi→j為光電離矩陣元
(6)
其中，Ψi和Ψj分別為光電離初、末態(tài)的波函數(shù);D為電偶極輻射場(chǎng)算符.
目前研究中，為了獲得高精度的光電離截面，基于相對(duì)論多組態(tài)Dirac-Fock(MCDF)理論[28]的GRASP2K程序包[29]被用來(lái)計(jì)算Ni26+離子的靶態(tài)波函數(shù)，計(jì)算中包括了1snl(n=1~5,l=0,1,…,n-1)共15個(gè)組態(tài)，49個(gè)精細(xì)能級(jí).不同角動(dòng)量的連續(xù)電子的波函數(shù)由30個(gè)基函數(shù)線性組合而成.為保證能夠分辨所有精細(xì)的共振峰，在光電離截面的計(jì)算中，選取了10-3Ry的光電子能量步長(zhǎng).表1給出了目前利用相對(duì)論R矩陣和MCDF理論并考慮相同電子關(guān)聯(lián)的情況下計(jì)算所得49個(gè)靶態(tài)的精細(xì)結(jié)構(gòu)能級(jí)，作為比較，表中也給出了NIST數(shù)據(jù)[30].從表中可以看出，MCDF理論結(jié)果與NIST數(shù)據(jù)符合的非常好，R矩陣?yán)碚摰慕Y(jié)果與NIST數(shù)據(jù)有大約0.1%的偏差，經(jīng)分析其主要來(lái)自Breit相互作用的影響，該效應(yīng)在目前的R矩陣程序中沒有被考慮[24].圖1給出了目前計(jì)算所得Ni25+離子基態(tài)1s22s(2S1/2)和激發(fā)態(tài)1s22p(2P1/2,2P3/2)的光電離截面，從圖中可以看出，目前計(jì)算在長(zhǎng)度(L)和速度(V)兩種規(guī)范下的結(jié)果符合的非常好，反應(yīng)了目前計(jì)算對(duì)電子關(guān)聯(lián)效應(yīng)的考慮是比較完善的.
1.2光復(fù)合共振線的強(qiáng)度
光復(fù)合截面的共振峰包含了DR過(guò)程雙電子伴線的信息，共振峰的中心位置對(duì)應(yīng)共振能量.由于DR與RR間的干涉，共振峰通常呈現(xiàn)非對(duì)稱分布，即Fano線型[31].通過(guò)對(duì)光復(fù)合截面在共振能量εs附近區(qū)域積分，可以獲得DR過(guò)程雙電子伴線的強(qiáng)度
(7)
在獨(dú)立過(guò)程和孤立共振近似下，DR過(guò)程的伴線強(qiáng)度也可以通過(guò)下式獲得[32]
表1 Ni26+離子能級(jí)(eV)的比較
(8)
其中,i,d,f分別為DR過(guò)程的初態(tài)、中間雙激發(fā)態(tài)和末態(tài);σDR(ε)為雙電子復(fù)合截面;Edi為共振能量;gi和gd分別為初態(tài)i和中間雙激發(fā)態(tài)d的統(tǒng)計(jì)權(quán)重;Aa和Ar分別為Auger幾率和輻射躍遷幾率;求和下標(biāo)i′和f′表示遍及中間態(tài)d到所有可能的Auger末態(tài)i′和輻射末態(tài)f′.對(duì)所有可能末態(tài)f對(duì)應(yīng)的Sidf進(jìn)行求和進(jìn)一步可以獲得給出初態(tài)下某一共振態(tài)的DR伴線強(qiáng)度.
圖1 Ni25+離子基態(tài)1s22s(2S1/2)及激發(fā)態(tài)
2結(jié)果與討論
圖2給出了利用DARC程序計(jì)算所得[Ni26+(1s21S0)+e-]J→Ni27+(1s22s2SJ′=1/2)+hν光復(fù)合過(guò)程分通道的截面及總截面(分通道截面的求和).根據(jù)對(duì)稱性，在電偶極近似下，光復(fù)合初、末態(tài)的總角動(dòng)量需滿足ΔJ=J-J′=0,±1，其中J和J′分別對(duì)應(yīng)光復(fù)合初態(tài)(靶離子+自由電子)及末態(tài)(N+1電子體系的束縛態(tài))的總角動(dòng)量量子數(shù).從圖中可以看出，目前計(jì)算所得長(zhǎng)度規(guī)范(L)和速度規(guī)范(V)下光復(fù)合的截面一致性非常好.在KLL共振能區(qū)，對(duì)應(yīng)通道J=1/2和J=3/2，分別有3條共振線，經(jīng)分析它們分別來(lái)自中間雙激發(fā)態(tài)[1s2s2p]J=1/2和[1s2s2p]J=3/2.作為對(duì)計(jì)算結(jié)果的檢驗(yàn)，圖2也給出了獨(dú)立過(guò)程近似下利用基于MCDF理論的RATIP程序[28]計(jì)算所得RR過(guò)程的截面.不難看出目前MCDF理論的結(jié)果與R矩陣?yán)碚摰墓鈴?fù)合結(jié)果的背景截面吻合的很好.圖3和圖4分別給出了目前R矩陣?yán)碚撚?jì)算的Ni26+(1s2)→Ni25+(1s22p2P1/2,2P3/2)光復(fù)合過(guò)程態(tài)分辨的分通道的截面和總截面，作為比較，圖中同時(shí)給出了目前利用MCDF理論所得RR過(guò)程的截面.結(jié)果表明，在KLL能區(qū)，上述兩個(gè)過(guò)程分別包含了6條和9條共振線，MCDF理論和R矩陣?yán)碚撍肦R過(guò)程的截面普遍符合的很好，在5380~5460 eV能區(qū)的共振線附近出現(xiàn)的偏差，一定程度上反應(yīng)了DR與RR過(guò)程間的干涉和重疊共振效應(yīng)的影響.
圖2 Ni26+離子1s21S0→1s22s 2S1/2光復(fù)合
圖3 Ni26+離子1s21S0→1s22p 2P1/2
為了對(duì)圖1中KLL共振能區(qū)的共振峰(對(duì)應(yīng)雙電子伴線)進(jìn)行標(biāo)識(shí)和分析，本文利用基于相對(duì)論組態(tài)相互作用的FAC程序[25]對(duì)Ni25+離子涉及1s2s2,1s2s2p,1s2p2雙激發(fā)組態(tài)的精細(xì)能級(jí)、輻射和Auger幾率以及共振寬度等進(jìn)行了計(jì)算，并在孤立共振近似下(見(8)式)得到了22條雙電子伴線的強(qiáng)度，所得結(jié)果與R矩陣?yán)碚?、Nahar等[27]
圖4 Ni26+離子1s21S0→1s22p 2P3/2
表2Ni26+離子KLL共振能區(qū)雙電子伴線的標(biāo)記、對(duì)應(yīng)的躍遷、共振能(eV)、
Auger和輻射幾率(s-1)、共振態(tài)寬度(eV)以及伴線強(qiáng)度(×10-20cm2ev)
Tab 2The KLL resonances in electron-ion recombination of Ni26+correspond to the 22 dielectronic satellite lines.
The columns represent the key notation for a satellite line,the resonant transition,resonant energy in the present DARC and FAC calculations,and from BPRM[27]and NIST[30]results,the Auger decay probabilitiesAjfand radiative transition probabilitiesAji(s-1),resonant widthΓd(eV) and the satellite strength in 10-20cm2eV in the present work from the DARC and FAC calculations,and from BPRM results[27].
KeyTransitionEdi/eVAadfArdiDARCFACBPRM[27]NIST[30](×1013s-1)Γd/eVRS/(×10-20cm2eV)DARCFACBPRM[27]o1s2s2(2S1/2)→1s22p(2P3/2)5302.05293.85296.05294.115.351.220.11810.260.170.891.18*p1s2s2(2S1/2)→1s22p(2P1/2)5302.25293.85296.05294.115.351.350.11810.570.370.881.32*v1s2p(3p)2s(4P1/2)→1s22s(2S1/2)5314.05306.35312.35307.90.010.920.00620.040.00390.060.98*u1s2p(3p)2s(4P3/2)→1s22s(2S1/2)5320.65311.25321.35312.70.123.060.02097.390.070.163.21*r1s2p(1p)2s(2P1/2)→1s22s(2S1/2)5358.95352.05357.25351.24.7240.510.29808.341.353.8040.10*40.00?q1s2p(1p)2s(2P3/2)→1s22s(2S1/2)5373.45365.35372.25364.30.0566.130.43601.680.030.0864.60*i1s2p2(4P1/2)→1s22p(2P1/2)5379.65371.25397.45372.60.044.290.02860.070.010.084.62*
續(xù)表2
h1s2p2(4P1/2)→1s22p(2P3/2)5379.65371.25379.45372.60.040.010.02860.000420.000026.0(-3)0.01*f1s2p2(4P3/2)→1s22p(2P3/2)5391.55383.35393.35384.30.111.790.01260.190.030.311.91*t1s2p(3p)2s(2P1/2)→1s22s(2S1/2)5387.55380.95385.85379.98.3127.780.027813.892.045.5226.80*27.00?g1s2p2(4P3/2)→1s22p(2P1/2)5391.75383.35394.35384.30.110.010.01260.010.00030.010.01*s1s2p(3p)2s(2P3/2)→1s22s(2S1/2)5392.15385.05394.35383.411.600.0030.07640.110.00211.290.005*e1s2p2(4P5/2)→1s22p(2P3/2)5400.85390.85402.15391.53.196.330.06284.511.014.856.51*k1s2p2(2D3/2)→1s22p(2P1/2)5418.35411.55414.45410.613.0945.280.430339.765.7718.4043.70*44.00?d1s2p2(2P1/2)→1s22p(2P1/2)5419.95411.45424.15410.60.1374.530.63354.480.030.0872.50*73.00?l1s2p2(2D3/2)→1s22p(2P3/2)5418.65411.55414.45410.613.096.950.43032.510.441.447.52*c1s2p2(2P1/2)→1s22p(2P3/2)5419.95411.45424.15410.60.1321.470.63350.630.00450.1721.40*21.00?j1s2p2(2D5/2)→1s22p(2P3/2)5430.05420.95427.65420.113.6727.880.273818.424.3727.2226.80*27.00?b1s2p2(2P3/2)→1s22p(2P1/2)5444.95436.95447.75435.64.000.800.58491.070.020.210.68*a1s2p2(2P3/2)→1s22p(2P3/2)5445.25436.95447.75435.64.0083.960.584937.861.206.1280.90*81.00?m1s2p2(2S1/2)→1s22p(2P3/2)5464.75457.75468.15455.62.6635.460.25787.790.382.7434.30*34.00?n1s2p2(2S1/2)→1s22p(2P3/2)5464.95457.75468.15455.62.661.000.25780.330.010.141.02*
Note:*Ref[33],?Ref[30].
圖5(a)為KLL共振能區(qū)附近Ni26+(1s2)離子光復(fù)合過(guò)程的總截面，圖5(b)為利用FAC計(jì)算所得22條雙電子伴線的位置和強(qiáng)度.為了與Kannp等[34]EBIT實(shí)驗(yàn)測(cè)量的KLL雙電子復(fù)合過(guò)程的實(shí)驗(yàn)結(jié)果進(jìn)行比較，我們分別對(duì)DRAC和FAC計(jì)算的雙電子伴線強(qiáng)度進(jìn)行了Gauss卷積(FWHM=54 eV)，所得結(jié)果與實(shí)驗(yàn)結(jié)果[34]見圖5(c)，其中，為了消除由于Breit相互作用引起的共振能的偏差，DARC的結(jié)果均向左平移了12 eV.從圖中可以看出，目前理論KLL伴線的位置和線型與實(shí)驗(yàn)結(jié)果整體符合較好，在5 230~5 460 eV能區(qū)，DARC結(jié)果略高于實(shí)驗(yàn)結(jié)果.在5 460~5 550 eV能區(qū)實(shí)驗(yàn)結(jié)果普遍高于理論結(jié)果，其主要原因是實(shí)驗(yàn)測(cè)量中還觀測(cè)到了其他電荷態(tài)Ni離子的貢獻(xiàn)[34]由于實(shí)驗(yàn)的分辨率(54 eV)仍然比較低，不能對(duì)單個(gè)的共振峰進(jìn)行分辨，所以目前理論中所展現(xiàn)的DR和RR之間的干涉效應(yīng)不能在實(shí)驗(yàn)結(jié)果中被觀測(cè)到.
3結(jié)論
利用基于相對(duì)論R矩陣的理論方法，系統(tǒng)研究了Ni26+離子在 KLL能區(qū)附近的光復(fù)合截面，并對(duì)其中的共振峰進(jìn)行了標(biāo)識(shí)和分析，所得雙電子復(fù)合過(guò)程的伴線強(qiáng)度與FAC程序計(jì)算的結(jié)果以及其他理論和實(shí)驗(yàn)結(jié)果進(jìn)行了比較.結(jié)果表明,① 目前基于相對(duì)論R矩陣的DARC程序可以被用來(lái)獲得高電荷態(tài)離子精細(xì)的態(tài)分辨光復(fù)合截面，其中輻射復(fù)合和雙電子復(fù)合過(guò)程之間的干涉和重要的重疊共振的貢獻(xiàn)能被自動(dòng)考慮；② Breit相互作用對(duì)高電荷態(tài)離子靶態(tài)及共振態(tài)的能級(jí)有重要影響，輻射阻尼效應(yīng)通常會(huì)降低雙電子伴線的強(qiáng)度，在以后的研究中需要對(duì)這兩種效應(yīng)系統(tǒng)考慮；③ 目前相對(duì)論R矩陣?yán)碚摵凸铝⒐舱窠葡掠?jì)算所得雙電子復(fù)合過(guò)程的結(jié)果與EBIT的實(shí)驗(yàn)測(cè)量結(jié)果整體符合比較好，但對(duì)于其中的干涉效應(yīng)需要更精細(xì)的實(shí)驗(yàn)來(lái)觀測(cè).
圖5(a)Ni26+離子KLL共振能區(qū)附近總光復(fù)合截面；(b)FAC計(jì)算的雙電子伴線的位置和強(qiáng)度；(c)理論卷積(FWHM=54 eV)所得雙電子伴線相對(duì)強(qiáng)度與實(shí)驗(yàn)結(jié)果的比較.虛線：DARC的結(jié)果;實(shí)線： FAC的結(jié)果;黑色圓點(diǎn)：Kannp等EBIT實(shí)驗(yàn)結(jié)果[34]
Fig 5(a)The total photorecombination cross section of Ni26+ion nearby KLL energy;(b)Resonant position and strength from FAC calculations;(c)The relative strength of the resonance lines convoluted by use a Gaussian profile of FWHM=50 eV compare to the EBIT results from Kannp et al.[34]The red dotted line shows the rsults of DARC;the black line shows the results of FAC;the black circle with errors show the EBIT results[34].
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(責(zé)任編輯孫對(duì)兄)
The relativistic R-matrix study for level-specific
photorecombination cross sections of Ni26+ion
XIE Lu-you,MA Chi,MA Kun,DONG Chen-zhong,ZHANG Deng-hong
(Key Laboratory of Atomic and Molecular Physics & Functional Materials of Gansu Province,
College of Physics and Electronic Engineering,Northwest Normal University,Lanzhou 730070,Gansu,China)
Abstract:In this study,photoionization cross sections are calculated for the ground level 1s22s(2S1/2)and the excited levels 1s22p(2P1/2,2P3/2) of Ni25+ion using the Dirac atomic R-matrix codes(DARC) based on the relativistic R-matrix method.The unified level-specific photorecombination(i.e.radiative recombination and dielectronic recombination) cross sections of the ground state Ni26+(1s2) iron are obtained through the detailed balance principle.Detailed calculations exhibit interference effects in resonance profiles.To identify and analyze the locations and strengths for all resonant peaks,detailed calculations are performed for all known KLL resonant states by use the Flexible atomic code(FAC) based on the relativity configuration interaction(RCI) method,the resonant energies and strengths together with radiative and Auger transition rates,and the resonant width are listed.The obtained dielectronic satellite energies and strengths from DARC and FAC calculations are compared with earlier theoretic and experimental works and significant differences and similarities are discussed.
Key words:photorecombination cross sections;relativistic R-matrix method;resonant energy;resonant strength
中圖分類號(hào)：O 562.6
文獻(xiàn)標(biāo)志碼：A
文章編號(hào)：1001-988Ⅹ(2015)02-0024-08
作者簡(jiǎn)介：頡錄有(1975—)，男，甘肅武山人，副教授，博士，碩士研究生導(dǎo)師.主要研究方向?yàn)樵咏Y(jié)構(gòu)與原子碰撞.E-mail:xiely@nwnu.edu.cn
基金項(xiàng)目:國(guó)家自然科學(xué)基金資助項(xiàng)目(U1331122,U1332206,11274254，11464042)
收稿日期：2014-10-18;修改稿收到日期:2015-01-04
頡錄有，馬 馳，馬 堃，董晨鐘，張登紅
(甘肅省原子分子物理與功能材料重點(diǎn)實(shí)驗(yàn)室，
西北師范大學(xué)物理與電子工程學(xué)院，甘肅蘭州 730070)
Ni26+離子態(tài)分辨光復(fù)合過(guò)程的R矩陣?yán)碚撗芯?/p>
頡錄有，馬馳，馬堃，董晨鐘，張登紅
(甘肅省原子分子物理與功能材料重點(diǎn)實(shí)驗(yàn)室，
西北師范大學(xué)物理與電子工程學(xué)院，甘肅蘭州730070)
摘要：利用基于相對(duì)論R矩陣?yán)碚摰腄ARC程序系統(tǒng)計(jì)算了Ni25+離子基態(tài)1s22s(2S1/2)和激發(fā)態(tài)1s22p(2P1/2,2P3/2)的光電離截面，并通過(guò)細(xì)致平衡原理獲得了統(tǒng)一的光復(fù)合過(guò)程(即輻射復(fù)合和雙電子復(fù)合)態(tài)分辨的截面，計(jì)算結(jié)果給出了輻射復(fù)合與雙電子復(fù)合過(guò)程間的干涉效應(yīng).為了標(biāo)識(shí)和分析KLL共振能區(qū)所有的共振峰，基于相對(duì)論組態(tài)相互作用理論(RCI)的FAC程序被用來(lái)計(jì)算共振峰的能量、強(qiáng)度及其相關(guān)的雙激發(fā)態(tài)的輻射、俄歇躍遷幾率以及共振寬度等.利用統(tǒng)一的光復(fù)合截面進(jìn)一步得到了KLL雙電子復(fù)合過(guò)程的伴線強(qiáng)度，并與孤立共振近似下FAC的計(jì)算結(jié)果以及以前的理論和實(shí)驗(yàn)結(jié)果進(jìn)行了比較，對(duì)存在的一致性和偏差進(jìn)行了分析和討論.
關(guān)鍵詞：光復(fù)合截面;相對(duì)論R矩陣?yán)碚?共振能量;共振強(qiáng)度
在高溫、低密等離子體(如太陽(yáng)、磁約束聚變裝置等產(chǎn)生的等離子體等[1])中，高電荷態(tài)離子的光復(fù)合過(guò)程強(qiáng)烈影響著等離子體的電離平衡及輻射X光譜[2-4].高電荷態(tài)離子的光復(fù)合(PR)主要包括非共振的輻射復(fù)合(RR)過(guò)程和共振的雙電子復(fù)合(DR)過(guò)程[5].輻射復(fù)合指靶離子直接俘獲自由電子到其束縛態(tài)，同時(shí)放出一個(gè)光子的過(guò)程；雙電子復(fù)合是一個(gè)間接過(guò)程，靶離子首先俘獲自由電子，同時(shí)內(nèi)部一個(gè)束縛電子被激發(fā)，形成共振雙激發(fā)態(tài)，共振態(tài)不穩(wěn)定將進(jìn)一步通過(guò)輻射光子躍遷到低能態(tài).RR與DR過(guò)程有著相同的初、末態(tài)，兩種過(guò)程之間存在干涉[4].以往的理論研究對(duì)光復(fù)合過(guò)程的處理多采用獨(dú)立過(guò)程和孤立共振近似，忽略了RR與DR過(guò)程間的干涉以及重疊態(tài)間的干涉[8].近年來(lái)，在統(tǒng)一的理論框架下處理DR和RR過(guò)程的理論，如投影算符近似[6]、密耦合近似下的扭曲波理論[4,7]以及R-矩陣?yán)碚揫8-11]等已被建立，其顯著的特點(diǎn)是DR與RR之間的干涉和重疊態(tài)間的干涉能夠被予以很好地考慮，利用這些理論人們已開展了一系列研究，并取得了很好的結(jié)果[12-18].實(shí)驗(yàn)方面，隨著重離子儲(chǔ)存環(huán)、電子束離子阱(EBIT)等實(shí)驗(yàn)裝置及相關(guān)測(cè)量技術(shù)的不斷提高，人們已開展了許多高電荷態(tài)離子，如U90+,Hg75+…78+和Bi79+光復(fù)合過(guò)程的研究[19-21]，并觀測(cè)到了顯著的DR與RR間的干涉[19-22].
類He離子是高溫天體、實(shí)驗(yàn)室等離子體中重要的電荷態(tài)離子，其光復(fù)合過(guò)程產(chǎn)生的X射線譜，特別是DR過(guò)程的雙電子伴線對(duì)等離子體中電子溫度及非麥克斯韋的電子分布十分敏感，是等離子體診斷的重要工具[1-3]；同時(shí)，由于類He離子簡(jiǎn)單的結(jié)構(gòu)，常被人們選作細(xì)致揭示相對(duì)論效應(yīng)、電子關(guān)聯(lián)效應(yīng)及其檢驗(yàn)理論和實(shí)驗(yàn)的重要體系[23].
Ni是天體中重要的高豐度元素，本文將重點(diǎn)以類He的Ni26+離子為例，利用基于全相對(duì)論R-矩陣?yán)碚摰挠?jì)算程序DARC(the Dirac Atomic R-matrix Codes)[24]并結(jié)合基于相對(duì)論組態(tài)相互作用的FAC(the Flexible Atomic Code )程序[25]開展其光復(fù)合過(guò)程的研究.相對(duì)論R-矩陣?yán)碚撚捎谄湎到y(tǒng)考慮了相對(duì)論效應(yīng)，并能給出精細(xì)的共振結(jié)構(gòu)，目前已被廣泛用于高電荷態(tài)離子光電離、電子碰撞激發(fā)等過(guò)程的研究中[26]，但對(duì)于光復(fù)合過(guò)程，由于計(jì)算的復(fù)雜性，相關(guān)的研究工作十分匱乏.本文一個(gè)重要目的即為檢驗(yàn)該理論在處理高電荷態(tài)離子光復(fù)合過(guò)程中的有效性和精確性.
1理論方法
1.1光復(fù)合截面
在KLL共振能區(qū)，即靶離子俘獲自由電子到L殼層，同時(shí)激發(fā)其K殼層束縛電子到L殼層的能量區(qū)間，Ni26+離子態(tài)分辨的光復(fù)合過(guò)程可以表示如下
(1)
其中,(a),(b)和(c)表示可能的雙電子復(fù)合過(guò)程的通道及其形成的中間雙激發(fā)態(tài);(d)和(e)表示輻射復(fù)合(或雙電子復(fù)合)過(guò)程的末態(tài).
在全相對(duì)論R-矩陣?yán)碚撝校哂蠳電子的靶離子與自由電子復(fù)合形成(N+1)電子體系的Dirac-Coulomb 哈密頓量可以表示為[6]
(2)
其中，第一項(xiàng)描述了單電子的動(dòng)能和勢(shì)能；第二項(xiàng)表示電子-電子間的庫(kù)倫相互作用;i和j分別表示第i和j個(gè)電子;Z為核電荷數(shù);α和β為狄拉克矩陣.
在密耦合近似下，(N+1)電子體系的波函數(shù)可以表示為[6]
(3)
根據(jù)細(xì)致平衡原理，在電偶極近似下，處于初態(tài)精細(xì)能級(jí)j的靶離子俘獲自由電子形成(N+1)電子體系的光復(fù)合末態(tài)i的PR截面可以表示為[27]
(4)
(5)
其中，gi為光電離初態(tài)的統(tǒng)計(jì)權(quán)重;c為光速;ω為光子能量;Mi→j為光電離矩陣元
(6)
其中，Ψi和Ψj分別為光電離初、末態(tài)的波函數(shù);D為電偶極輻射場(chǎng)算符.
目前研究中，為了獲得高精度的光電離截面，基于相對(duì)論多組態(tài)Dirac-Fock(MCDF)理論[28]的GRASP2K程序包[29]被用來(lái)計(jì)算Ni26+離子的靶態(tài)波函數(shù)，計(jì)算中包括了1snl(n=1~5,l=0,1,…,n-1)共15個(gè)組態(tài)，49個(gè)精細(xì)能級(jí).不同角動(dòng)量的連續(xù)電子的波函數(shù)由30個(gè)基函數(shù)線性組合而成.為保證能夠分辨所有精細(xì)的共振峰，在光電離截面的計(jì)算中，選取了10-3Ry的光電子能量步長(zhǎng).表1給出了目前利用相對(duì)論R矩陣和MCDF理論并考慮相同電子關(guān)聯(lián)的情況下計(jì)算所得49個(gè)靶態(tài)的精細(xì)結(jié)構(gòu)能級(jí)，作為比較，表中也給出了NIST數(shù)據(jù)[30].從表中可以看出，MCDF理論結(jié)果與NIST數(shù)據(jù)符合的非常好，R矩陣?yán)碚摰慕Y(jié)果與NIST數(shù)據(jù)有大約0.1%的偏差，經(jīng)分析其主要來(lái)自Breit相互作用的影響，該效應(yīng)在目前的R矩陣程序中沒有被考慮[24].圖1給出了目前計(jì)算所得Ni25+離子基態(tài)1s22s(2S1/2)和激發(fā)態(tài)1s22p(2P1/2,2P3/2)的光電離截面，從圖中可以看出，目前計(jì)算在長(zhǎng)度(L)和速度(V)兩種規(guī)范下的結(jié)果符合的非常好，反應(yīng)了目前計(jì)算對(duì)電子關(guān)聯(lián)效應(yīng)的考慮是比較完善的.
1.2光復(fù)合共振線的強(qiáng)度
光復(fù)合截面的共振峰包含了DR過(guò)程雙電子伴線的信息，共振峰的中心位置對(duì)應(yīng)共振能量.由于DR與RR間的干涉，共振峰通常呈現(xiàn)非對(duì)稱分布，即Fano線型[31].通過(guò)對(duì)光復(fù)合截面在共振能量εs附近區(qū)域積分，可以獲得DR過(guò)程雙電子伴線的強(qiáng)度
(7)
在獨(dú)立過(guò)程和孤立共振近似下，DR過(guò)程的伴線強(qiáng)度也可以通過(guò)下式獲得[32]
表1 Ni26+離子能級(jí)(eV)的比較
(8)
其中,i,d,f分別為DR過(guò)程的初態(tài)、中間雙激發(fā)態(tài)和末態(tài);σDR(ε)為雙電子復(fù)合截面;Edi為共振能量;gi和gd分別為初態(tài)i和中間雙激發(fā)態(tài)d的統(tǒng)計(jì)權(quán)重;Aa和Ar分別為Auger幾率和輻射躍遷幾率;求和下標(biāo)i′和f′表示遍及中間態(tài)d到所有可能的Auger末態(tài)i′和輻射末態(tài)f′.對(duì)所有可能末態(tài)f對(duì)應(yīng)的Sidf進(jìn)行求和進(jìn)一步可以獲得給出初態(tài)下某一共振態(tài)的DR伴線強(qiáng)度.
圖1 Ni25+離子基態(tài)1s22s(2S1/2)及激發(fā)態(tài)
2結(jié)果與討論
圖2給出了利用DARC程序計(jì)算所得[Ni26+(1s21S0)+e-]J→Ni27+(1s22s2SJ′=1/2)+hν光復(fù)合過(guò)程分通道的截面及總截面(分通道截面的求和).根據(jù)對(duì)稱性，在電偶極近似下，光復(fù)合初、末態(tài)的總角動(dòng)量需滿足ΔJ=J-J′=0,±1，其中J和J′分別對(duì)應(yīng)光復(fù)合初態(tài)(靶離子+自由電子)及末態(tài)(N+1電子體系的束縛態(tài))的總角動(dòng)量量子數(shù).從圖中可以看出，目前計(jì)算所得長(zhǎng)度規(guī)范(L)和速度規(guī)范(V)下光復(fù)合的截面一致性非常好.在KLL共振能區(qū)，對(duì)應(yīng)通道J=1/2和J=3/2，分別有3條共振線，經(jīng)分析它們分別來(lái)自中間雙激發(fā)態(tài)[1s2s2p]J=1/2和[1s2s2p]J=3/2.作為對(duì)計(jì)算結(jié)果的檢驗(yàn)，圖2也給出了獨(dú)立過(guò)程近似下利用基于MCDF理論的RATIP程序[28]計(jì)算所得RR過(guò)程的截面.不難看出目前MCDF理論的結(jié)果與R矩陣?yán)碚摰墓鈴?fù)合結(jié)果的背景截面吻合的很好.圖3和圖4分別給出了目前R矩陣?yán)碚撚?jì)算的Ni26+(1s2)→Ni25+(1s22p2P1/2,2P3/2)光復(fù)合過(guò)程態(tài)分辨的分通道的截面和總截面，作為比較，圖中同時(shí)給出了目前利用MCDF理論所得RR過(guò)程的截面.結(jié)果表明，在KLL能區(qū)，上述兩個(gè)過(guò)程分別包含了6條和9條共振線，MCDF理論和R矩陣?yán)碚撍肦R過(guò)程的截面普遍符合的很好，在5380~5460 eV能區(qū)的共振線附近出現(xiàn)的偏差，一定程度上反應(yīng)了DR與RR過(guò)程間的干涉和重疊共振效應(yīng)的影響.
圖2 Ni26+離子1s21S0→1s22s 2S1/2光復(fù)合
圖3 Ni26+離子1s21S0→1s22p 2P1/2
為了對(duì)圖1中KLL共振能區(qū)的共振峰(對(duì)應(yīng)雙電子伴線)進(jìn)行標(biāo)識(shí)和分析，本文利用基于相對(duì)論組態(tài)相互作用的FAC程序[25]對(duì)Ni25+離子涉及1s2s2,1s2s2p,1s2p2雙激發(fā)組態(tài)的精細(xì)能級(jí)、輻射和Auger幾率以及共振寬度等進(jìn)行了計(jì)算，并在孤立共振近似下(見(8)式)得到了22條雙電子伴線的強(qiáng)度，所得結(jié)果與R矩陣?yán)碚?、Nahar等[27]
圖4 Ni26+離子1s21S0→1s22p 2P3/2
表2Ni26+離子KLL共振能區(qū)雙電子伴線的標(biāo)記、對(duì)應(yīng)的躍遷、共振能(eV)、
Auger和輻射幾率(s-1)、共振態(tài)寬度(eV)以及伴線強(qiáng)度(×10-20cm2ev)
Tab 2The KLL resonances in electron-ion recombination of Ni26+correspond to the 22 dielectronic satellite lines.
The columns represent the key notation for a satellite line,the resonant transition,resonant energy in the present DARC and FAC calculations,and from BPRM[27]and NIST[30]results,the Auger decay probabilitiesAjfand radiative transition probabilitiesAji(s-1),resonant widthΓd(eV) and the satellite strength in 10-20cm2eV in the present work from the DARC and FAC calculations,and from BPRM results[27].
KeyTransitionEdi/eVAadfArdiDARCFACBPRM[27]NIST[30](×1013s-1)Γd/eVRS/(×10-20cm2eV)DARCFACBPRM[27]o1s2s2(2S1/2)→1s22p(2P3/2)5302.05293.85296.05294.115.351.220.11810.260.170.891.18*p1s2s2(2S1/2)→1s22p(2P1/2)5302.25293.85296.05294.115.351.350.11810.570.370.881.32*v1s2p(3p)2s(4P1/2)→1s22s(2S1/2)5314.05306.35312.35307.90.010.920.00620.040.00390.060.98*u1s2p(3p)2s(4P3/2)→1s22s(2S1/2)5320.65311.25321.35312.70.123.060.02097.390.070.163.21*r1s2p(1p)2s(2P1/2)→1s22s(2S1/2)5358.95352.05357.25351.24.7240.510.29808.341.353.8040.10*40.00?q1s2p(1p)2s(2P3/2)→1s22s(2S1/2)5373.45365.35372.25364.30.0566.130.43601.680.030.0864.60*i1s2p2(4P1/2)→1s22p(2P1/2)5379.65371.25397.45372.60.044.290.02860.070.010.084.62*
續(xù)表2
h1s2p2(4P1/2)→1s22p(2P3/2)5379.65371.25379.45372.60.040.010.02860.000420.000026.0(-3)0.01*f1s2p2(4P3/2)→1s22p(2P3/2)5391.55383.35393.35384.30.111.790.01260.190.030.311.91*t1s2p(3p)2s(2P1/2)→1s22s(2S1/2)5387.55380.95385.85379.98.3127.780.027813.892.045.5226.80*27.00?g1s2p2(4P3/2)→1s22p(2P1/2)5391.75383.35394.35384.30.110.010.01260.010.00030.010.01*s1s2p(3p)2s(2P3/2)→1s22s(2S1/2)5392.15385.05394.35383.411.600.0030.07640.110.00211.290.005*e1s2p2(4P5/2)→1s22p(2P3/2)5400.85390.85402.15391.53.196.330.06284.511.014.856.51*k1s2p2(2D3/2)→1s22p(2P1/2)5418.35411.55414.45410.613.0945.280.430339.765.7718.4043.70*44.00?d1s2p2(2P1/2)→1s22p(2P1/2)5419.95411.45424.15410.60.1374.530.63354.480.030.0872.50*73.00?l1s2p2(2D3/2)→1s22p(2P3/2)5418.65411.55414.45410.613.096.950.43032.510.441.447.52*c1s2p2(2P1/2)→1s22p(2P3/2)5419.95411.45424.15410.60.1321.470.63350.630.00450.1721.40*21.00?j1s2p2(2D5/2)→1s22p(2P3/2)5430.05420.95427.65420.113.6727.880.273818.424.3727.2226.80*27.00?b1s2p2(2P3/2)→1s22p(2P1/2)5444.95436.95447.75435.64.000.800.58491.070.020.210.68*a1s2p2(2P3/2)→1s22p(2P3/2)5445.25436.95447.75435.64.0083.960.584937.861.206.1280.90*81.00?m1s2p2(2S1/2)→1s22p(2P3/2)5464.75457.75468.15455.62.6635.460.25787.790.382.7434.30*34.00?n1s2p2(2S1/2)→1s22p(2P3/2)5464.95457.75468.15455.62.661.000.25780.330.010.141.02*
Note:*Ref[33],?Ref[30].
圖5(a)為KLL共振能區(qū)附近Ni26+(1s2)離子光復(fù)合過(guò)程的總截面，圖5(b)為利用FAC計(jì)算所得22條雙電子伴線的位置和強(qiáng)度.為了與Kannp等[34]EBIT實(shí)驗(yàn)測(cè)量的KLL雙電子復(fù)合過(guò)程的實(shí)驗(yàn)結(jié)果進(jìn)行比較，我們分別對(duì)DRAC和FAC計(jì)算的雙電子伴線強(qiáng)度進(jìn)行了Gauss卷積(FWHM=54 eV)，所得結(jié)果與實(shí)驗(yàn)結(jié)果[34]見圖5(c)，其中，為了消除由于Breit相互作用引起的共振能的偏差，DARC的結(jié)果均向左平移了12 eV.從圖中可以看出，目前理論KLL伴線的位置和線型與實(shí)驗(yàn)結(jié)果整體符合較好，在5 230~5 460 eV能區(qū)，DARC結(jié)果略高于實(shí)驗(yàn)結(jié)果.在5 460~5 550 eV能區(qū)實(shí)驗(yàn)結(jié)果普遍高于理論結(jié)果，其主要原因是實(shí)驗(yàn)測(cè)量中還觀測(cè)到了其他電荷態(tài)Ni離子的貢獻(xiàn)[34]由于實(shí)驗(yàn)的分辨率(54 eV)仍然比較低，不能對(duì)單個(gè)的共振峰進(jìn)行分辨，所以目前理論中所展現(xiàn)的DR和RR之間的干涉效應(yīng)不能在實(shí)驗(yàn)結(jié)果中被觀測(cè)到.
3結(jié)論
利用基于相對(duì)論R矩陣的理論方法，系統(tǒng)研究了Ni26+離子在 KLL能區(qū)附近的光復(fù)合截面，并對(duì)其中的共振峰進(jìn)行了標(biāo)識(shí)和分析，所得雙電子復(fù)合過(guò)程的伴線強(qiáng)度與FAC程序計(jì)算的結(jié)果以及其他理論和實(shí)驗(yàn)結(jié)果進(jìn)行了比較.結(jié)果表明,① 目前基于相對(duì)論R矩陣的DARC程序可以被用來(lái)獲得高電荷態(tài)離子精細(xì)的態(tài)分辨光復(fù)合截面，其中輻射復(fù)合和雙電子復(fù)合過(guò)程之間的干涉和重要的重疊共振的貢獻(xiàn)能被自動(dòng)考慮；② Breit相互作用對(duì)高電荷態(tài)離子靶態(tài)及共振態(tài)的能級(jí)有重要影響，輻射阻尼效應(yīng)通常會(huì)降低雙電子伴線的強(qiáng)度，在以后的研究中需要對(duì)這兩種效應(yīng)系統(tǒng)考慮；③ 目前相對(duì)論R矩陣?yán)碚摵凸铝⒐舱窠葡掠?jì)算所得雙電子復(fù)合過(guò)程的結(jié)果與EBIT的實(shí)驗(yàn)測(cè)量結(jié)果整體符合比較好，但對(duì)于其中的干涉效應(yīng)需要更精細(xì)的實(shí)驗(yàn)來(lái)觀測(cè).
圖5(a)Ni26+離子KLL共振能區(qū)附近總光復(fù)合截面；(b)FAC計(jì)算的雙電子伴線的位置和強(qiáng)度；(c)理論卷積(FWHM=54 eV)所得雙電子伴線相對(duì)強(qiáng)度與實(shí)驗(yàn)結(jié)果的比較.虛線：DARC的結(jié)果;實(shí)線： FAC的結(jié)果;黑色圓點(diǎn)：Kannp等EBIT實(shí)驗(yàn)結(jié)果[34]
Fig 5(a)The total photorecombination cross section of Ni26+ion nearby KLL energy;(b)Resonant position and strength from FAC calculations;(c)The relative strength of the resonance lines convoluted by use a Gaussian profile of FWHM=50 eV compare to the EBIT results from Kannp et al.[34]The red dotted line shows the rsults of DARC;the black line shows the results of FAC;the black circle with errors show the EBIT results[34].
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(責(zé)任編輯孫對(duì)兄)
The relativistic R-matrix study for level-specific
photorecombination cross sections of Ni26+ion
XIE Lu-you,MA Chi,MA Kun,DONG Chen-zhong,ZHANG Deng-hong
(Key Laboratory of Atomic and Molecular Physics & Functional Materials of Gansu Province,
College of Physics and Electronic Engineering,Northwest Normal University,Lanzhou 730070,Gansu,China)
Abstract:In this study,photoionization cross sections are calculated for the ground level 1s22s(2S1/2)and the excited levels 1s22p(2P1/2,2P3/2) of Ni25+ion using the Dirac atomic R-matrix codes(DARC) based on the relativistic R-matrix method.The unified level-specific photorecombination(i.e.radiative recombination and dielectronic recombination) cross sections of the ground state Ni26+(1s2) iron are obtained through the detailed balance principle.Detailed calculations exhibit interference effects in resonance profiles.To identify and analyze the locations and strengths for all resonant peaks,detailed calculations are performed for all known KLL resonant states by use the Flexible atomic code(FAC) based on the relativity configuration interaction(RCI) method,the resonant energies and strengths together with radiative and Auger transition rates,and the resonant width are listed.The obtained dielectronic satellite energies and strengths from DARC and FAC calculations are compared with earlier theoretic and experimental works and significant differences and similarities are discussed.
Key words:photorecombination cross sections;relativistic R-matrix method;resonant energy;resonant strength
中圖分類號(hào)：O 562.6
文獻(xiàn)標(biāo)志碼：A
文章編號(hào)：1001-988Ⅹ(2015)02-0024-08
作者簡(jiǎn)介：頡錄有(1975—)，男，甘肅武山人，副教授，博士，碩士研究生導(dǎo)師.主要研究方向?yàn)樵咏Y(jié)構(gòu)與原子碰撞.E-mail:xiely@nwnu.edu.cn
基金項(xiàng)目:國(guó)家自然科學(xué)基金資助項(xiàng)目(U1331122,U1332206,11274254，11464042)
收稿日期：2014-10-18;修改稿收到日期:2015-01-04
