Biemont, E.

Palmeri, P.

Quinet, P.

Trabert, E.

UNT Digital Library

UCRL-JRNL-223518Relativistic atomic data for EUV andX-ray Spectra of highly charged Cu-, Zn-,Ga-, and Ge-like ions (70 (less than orequal to) Z (less than or equal to) 92)P. Quinet, E. Biémont, P. Palmeri, E. TräbertAugust 8, 2006Journal of PhysicsDisclaimer   This document was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the University of California nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or the University of California, and shall not be used for advertising or product endorsement purposes.  Relativistic atomic data for EUV and X-ray spectraof highly charged Cu-, Zn-, Ga- and Ge-like ions(70 ≤ Z ≤ 92)P Quinet†‡, E Bie´mont†‡, P Palmeri† and E Tra¨bert#† Astrophysique et Spectroscopie, Universite´ de Mons-Hainaut, B-7000 Mons, Belgium‡ IPNAS, Sart Tilman B15, Universite´ de Lie`ge, B-4000 Lie`ge, Belgium# Physics and Advance Technologies, Lawrence Livermore National Laboratory, Livermore,CA 94550-9234, USAE-mail: quinet@umh.ac.beAbstract. Wavelengths and transition probabilities have been calculated for the n=4, ∆n=0allowed transitions in the heavy Cu-, Zn-, Ga- and Ge-like ions with Z=70-92. Fully relativisticmulticonﬁguration Dirac-Fock (MCDF) computations were carried out. The present results arecompared to and agree well with recent electron-beam ion-trap (EBIT) measurements in Yb,W, Os, Au, Pb, Bi, Th and U ions.1. IntroductionRecently, accurate experimental wavelengths for high Z (Z ≥ 70) elements were measured at theLivermore electron beam ion trap (EBIT) for some transitions in the EUV and X-ray spectra ofhighly charged ytterbium (Z = 70), tungsten (Z = 74), osmium (Z = 76), gold (Z = 79), lead (Z= 82), bismuth (Z = 83), thorium (Z = 90) and uranium (Z = 92) along the copper, zinc, galliumand germanium isoelectronic sequences [1-8]. In these latter works, it was pointed out thatavailable calculations for these ions, carried out with diﬀerent theoretical approaches, featureddiﬀerent isoelectronic trends (relative to the experimental trend). These new measurementsjustify a detailed theoretical analysis of radiative parameters for heavy ions (Z ≥ 70) alongthe isoelectronic sequences. The new theoretical results will be useful as a test of experimentalobservations, and their predictive power will be valuable where experimental data are missing.2. Theoretical methodIn the present work, energy levels, wavelengths and transition rates for the n = 4, ∆n = 0transitions in highly charged Cu-, Zn-, Ga- and Ge-like ions were obtained using the fullyrelativistic multiconﬁguration Dirac-Fock (MCDF) approach with the latest version of GRASP,the General-purpose Relativistic Atomic Structure Package, developed by Norrington [9] fromthe original MCDF code of Grant and coworkers [10-11] and improved by Dyall et al [12].The computations were done with the extended average level (EAL) option, optimizing aweighted trace of the Hamiltonian using level weights proportional to 2J+1. The orthogonalityof the wavefunctions was consistently included in the diﬀerential equations by using oﬀ-diagonalLagrange multipliers. Most of the conﬁgurations belonging to the n=4 complex were included inthe calculations. These conﬁgurations are listed in the following subsections. They are expectedto take the most important conﬁguration interaction eﬀects into account for the high ionizationstages considered in the present work. The calculations were then completed with the inclusionof the relativistic two-body Breit interaction and of the the quantum electrodynamic corrections(QED) due to self-energy and vacuum polarization using the routines developed by McKenzieet al [11]. In these routines, the leading correction to the Coulomb repulsion between electronsin quantum electrodynamics is considered as a ﬁrst perturbation using the transverse Breitoperator given by Grant and McKenzie [13], the second order vacuum polarization corrections areevaluated using the prescription of Fullerton and Rinker [14], and the self-energy contributionsare estimated by interpolating the hydrogenic n=1,2 results of Mohr [15-16] and by scaling tohigher n states according to 1/n3. For each ion, the nuclear eﬀects were estimated by consideringa uniform charge distribution in the nucleus with the usual atomic weight.2.1. Cu-like ions from Yb41+ to U63+The wavelengths and transition rates for the 4s-4p, 4p-4d and 4d-4f transitions were obtainedusing the following non-relativistic conﬁgurations in the calculations: 3d104s, 3d104d, 3d94s2,3d94s4d, 3d94p2, 3d94p4f, 3d94d2, 3d94f2, 3d84s24d, 3p53d104s4p, 3p53d104s4f, 3p53d104p4d,3p53d104d4f, 3s3p63d104s2, 3s3p63d104s4d, 3s3p63d104p2, 3s3p63d104p4f, 3s3p63d104d2,3s3p63d104f2 (even parity) and 3d104p, 3d104f, 3d94s4p, 3d94s4f, 3d94p4d, 3d94d4f,3d84s24p, 3d84s24f, 3p53d104s2, 3p53d104s4d, 3p53d104p2, 3p53d104p4f, 3p53d104d2, 3p53d104f2,3s3p63d104s4p, 3s3p63d104s4f, 3s3p63d104p4d, 3s3p63d104d4f (odd parity). This corresponds to1494 relativistic conﬁguration state functions.2.2. Zn-like ions from Yb40+ to U62+For these ions, results were obtained for the 4s2–4s4p, 4s4p–4p2 and 4s4p–4s4d transitions. All ofthe even and odd conﬁgurations belonging to the n=4 complex were included in the calculations.These conﬁgurations were 4s2, 4p2, 4d2, 4f2, 4s4d, 4p4f and 4s4p, 4s4f, 4p4d, 4d4f for each parity,respectively, and were expected to take the most important conﬁguration interaction eﬀects intoaccount for the high ionization stages considered.2.3. Ga-like ions from Yb39+ to U61+The wavelengths and transition probabilities for the 4s24p–4s24d and 4s24p–4s4p2 transitionswere obtained using, in the MCDF calculations, all of the odd conﬁgurations except 4p4f2 and4f3 and all of the even conﬁgurations except 4s4f2 and 4d4f2 within the n=4 complex. Theseconﬁgurations are 4s24p, 4s24f, 4s4p4d, 4s4d4f, 4p3, 4p24f, 4p4d2, 4d24f and 4s24d, 4s4p2, 4s4p4f,4s4d2, 4p24d, 4p4d4f, 4d3 for the odd and even parities, respectively, and generate a total of 437relativistic conﬁguration state functions (CSFs).2.4. Ge-like ions from Yb38+ to U60+The following non-relativistic conﬁgurations were considered in the calculations: 4s24p2, 4s24p4f,4s24d2, 4s24f2, 4s4p24d, 4s4p4d4f, 4p4, 4p24d2, 4p24f2 (even parity) and 4s24p4d, 4s24d4f, 4s4p3,4s4p24f, 4s4p4d2, 4s4p4f2, 4s4d24f, 4p34d, 4p24d4f, 4p4d3 (odd parity). This corresponds to 1526relativistic conﬁguration state functions.3. ResultsA large amount of radiative parameters (wavelengths and transition rates) were obtained alongthe copper, zinc, gallium and germanium isoelectronic sequences. The complete sets of data willbe published elsewhere [17-20]. In Table 1, we report a sample of results showing a comparisonbetween the MCDF wavelengths and those measured in EBIT devices [1-8] and in laser-producedplasmas [21-24] for the 4s J=1/2 – 4p J ′=3/2 and the 4s2 J=0 – 4s4p J ′=1 resonance transitionsin Cu-like and Zn-like ions, respectively.Table 1. Comparison between MCDF wavelengths obtained in the present work and thosemeasured experimentally for resonance transitions in Cu- and Zn-like ions.Seq. Transition Z Ion MCDF ExperimentThis work EBIT OtherCu 4s J=1/2 – 4p J ′=3/2 70 Yb XLII 76.014 75.8595(47)3 75.842(15)2374 W XLVI 62.444 62.3355(45)362.3355(19)2 62.304(15)2276 Os XLVIII 56.652 56.5630(20)5,779 Au LI 49.006 48.9280(26)3 48.928(15)2148.92(1)182 Pb LIV 42.441 42.3740(58)3 42.349(15)2183 Bi LV 40.463 40.4066(20)5,7 40.394(15)2190 Th LXII 29.054 29.0227(10)5,7 28.990(15)2129.0224(30)392 U LXIV 26.452 26.4233(15)5,7 26.400(15)2126.4325(19)3 26.406(15)23Zn 4s2 J=0 – 4s4p J ′=1 70 Yb XLI 73.464 73.8070(66)4 73.792(20)2474 W XLV 60.676 60.9300(54)4 60.900(20)2460.9310(17)276 Os XLVII 55.178 55.3840(50)879 Au L 47.883 48.0583(49)4 48.063(20)2448.05(1)182 Pb LIII 41.584 41.7185(45)4 41.689(20)2483 Bi LIV 39.680 39.8151(20)8 39.792(20)2490 Th LXI 28.639 28.7227(67)4 28.702(20)2428.7303(11)892 U LXIII 26.106 26.1868(36)4 26.157(20)2426.1861(10)8In Figures 1 and 2, we show the wavelength diﬀerences between our MCDF calculationsand the experimental measurements for some resonance transitions in the diﬀerent sequences.It can be observed that the diﬀerences between EBIT measurements and MCDF calculationsshow a smooth behaviour along the sequences, ∆λ decreasing monotically with increasing Zwhile striking discontinuities can be noticed when comparing calculated wavelengths with thosemeasured in laser-produced plasmas for Cu-like and Zn-like ions. This can be explained by thefact that, contrary to laser-produced plasma experiments, EBIT devices are able to select chargestates and therefore to avoid blends between lines of diﬀerent charge states that can deterioratethe accuracy of the wavelength measurements. Another explanation, as suggested by Kim etal. [25], would be the alteration of the line proﬁles by self-absorption in high density plasmasproduced by laser.4. AcknowledgementsPQ, PP and EB are respectively Research Associates and Research Director of the BelgianFNRS. ET thanks the German Research Association (DFG) and the US Department of EnergyZ70 72 74 76 78 80 82 84 86 88 90 92∆λ = λEXPT - λ MCDF (A)-0.2-0.10.00.10.20.30.4Zn-like ions(4s2 J=0 - 4s4p J'=1)Cu-like ions(4s J=1/2 - 4p J'=3/2)Figure 1. Comparison between experimentaland MCDF wavelengths for transitions inCu- and Zn-like ions. Full and opensymbols correspond to EBIT and laser-produced plasma experiments, respectively.Z70 72 74 76 78 80 82 84 86 88 90 92∆λ = λEXPT - λ MCDF (A)0.00.10.20.30.40.5Ga-like ions(4s24p- J=1/2 - 4s4p-4p J'=1/2)Ga-like ions(4s24p- J=1/2 - 4s24d- J'=3/2)Ga-like ions(4s24p- J=1/2 - 4s4p-4p J'=3/2)Ge-like ions(4p-2 J=0 - 4s24p-4d- J'=1)Ge-like ions(4p-2 J=0 - 4s4p-24p J'=1)Figure 2. Comparison between experimentaland MCDF wavelengths for transitions alongthe Ga (circles) and Ge (squares) isolectronicsequences.by University of California Lawrence Livermore National Laboratory (Contract W-7405-Eng-48).5. References[1] Tra¨bert E, Beiersdorfer P, Fournier K B, Utter S B and Wong K L 2001 Can. J. Phys. 79 153[2] Utter S B, Beiersdorfer P and Tra¨bert E 2002 Can. J. Phys. 80 1503[3] Utter S B, Beiersdorfer P, Tra¨bert E and Clothiaux E J 2003 Phys. Rev. A 67 032502[4] Utter S B, Beiersdorfer P and Tra¨bert E 2003 Can. J. Phys. 81 911[5] Tra¨bert E, Beiersdorfer P and Chen H 2004 Phys. Rev. A 70 032506[6] Tra¨bert E, Beiersdorfer P, Fournier K B and Chen M H 2004 Can. J. Phys. 82 1[7] Tra¨bert E, Beiersdorfer P, Fournier K B and Chen M H 2005 Can. J. Phys. 83 829[8] Tra¨bert E, Beiersdorfer P, Fournier K B and Chen M H 2005 Can. J. Phys. 83 1[9] Norrington P H 2002 http://www.am.qub.ac.uk/DARC/[10] Grant I P, McKenzie B J, Norrington P H, Mayers D F and Pyper N C 1980 Comput. Phys. Commun. 21207[11] McKenzie B J, Grant I P and Norrington P H 1980 Comput. Phys. Commun. 21 233[12] Dyall K G, Grant I P, Johnson C T, Parpia F A and Plummer E P 1989 Comput. Phys. Commun. 55 425[13] Grant I P and McKenzie B J 1980 J. Phys. B 13 2671[14] Fullerton L W and Rinker G A 1976 Phys. Rev. A 13 1283[15] Mohr P J 1974 Ann. Phys. 88 52[16] Mohr P J 1975 Phys. Rev. Lett. 34 1050[17] Quinet P, Bie´mont E, Palmeri P and Tra¨bert E 2006a At. Data Nucl. Data Tables (to be published)[18] Quinet P, Bie´mont E, Palmeri P and Tra¨bert E 2006b At. Data Nucl. Data Tables (to be published)[19] Palmeri P, Quinet P, Bie´mont E and Tra¨bert E 2006a At. Data Nucl. Data Tables (to be published)[20] Palmeri P, Quinet P, Bie´mont E and Tra¨bert E 2006b At. Data Nucl. Data Tables (to be published)[21] Seely J F, Ekberg J O, Brown C M, Feldman U, Behring W E, Reader J and Richardson M C 1986 Phys.Rev. Lett. 57 2924[22] Seely J F, Brown C M and Behring W E 1989 J. Opt. Soc. Am. B 6 3[23] Kania D R, MacGowan B J, Keane C J, Brown C M, Ekberg J O, Seely J F, Feldman U and Reader J 1990J. Opt. Soc. Am. B 7 1993[24] Brown C M, Seely J F, Kania D R, Hammel B A, Back C A, Lee R W and Bar-Shalom A 1994 At. DataNucl. Data Tables 58 203[25] Kim Y K, Baik D H, Indelicato P and Desclaux J P 1991 Phys. Rev. A 44 148

Relativistic atomic data for EUV and X-ray Spectra of highly charged Cu-, Zn-, Ga-, and Ge-like ions (70 (less than or equal to) Z (less than or equal to) 92)

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Relativistic atomic data for EUV and X-ray Spectra of highly charged Cu-, Zn-, Ga-, and Ge-like ions (70 (less than or equal to) Z (less than or equal to) 92)

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