Fine Structure Calculation of Energy Levels, Oscillator Strengths and Lifetimes in Se-Like Ions

Transcription

1 ISSN: ISO 9:8 Crtfd Intrnatonal Journal of Engnrng and Innovatv Tchnology (IJEIT) Volum, Issu 6, Dcmbr Fn Structur Calculaton of Enrgy Lvls, Oscllator Strngths and Lftms n S-Lk Ions M. Mossad, Abr Mra and Shrouk El- Ashry Abstract Enrgs of fn-structur lvls as wll as wavlngths, oscllator strngths and transton probablts for forbddn transtons (E ) among th fn-structur lvls of th trms blongng to th, and s p f confguratons for Br II, Sb XVIII and T XIX, ar calculatd usng xtnsv confguraton-ntracton wav functons. Th fully rlatvstc Multconfguraton Drac-Fock mthod takng nto account ffcts n ntrmdat couplng ar ncorporatd by mans of th Brt-Paul Hamltonan. Our calculatd nrgy lvls ar compard wth th rsults of HFR and th avalabl masurmnts. Ky words Multconfguraton Drac-Fock mthod; nrgy lvls; wavlngths; transton probablts; collson strngths; lftms I. INTRODUCTION Th xtrm-ultravolt (EUV) Br II, Sb XVIII and T XIX lns ar usful for lctron dnsty dagnostc n th solar atmosphr []. Th studs of th spctra of sulfur, bng on of th most abundant lmnts n th unvrs, yld astrophyscally ntrstng quantts []. Accurat atomc data such as absorpton oscllator strngths and transton probablts n S I ar rqurd for solar and stllar abundanc calculatons []. Masur th lftm for th fn-structur lvls blongng to th, and s p f confguratons. Thy also calculatd th lftms for ths lvls n a suprposton-of-confguratons mthod [] calculatd th oscllator strngths and transton probablts for som P,,, D, S stats for and D, P, D,, 5 P, F,,, F, G and P stats for and P,,, F,,, P, D, D, and G stats for s p f transtons and th lftms of th S I s lctronc squnc, usng th multconfguratonal Hartr-Fock mthod [5]. Th dtrmnaton of th onzaton balanc for a gvn plasma tmpratur s spcally snstv to th valus of th xctaton cross sctons usd to corrlat th ntnsty of a gvn ln to th abundanc of th corrspondng on spcs. Knowng th corrct charg stat dstrbuton s crtcal for undrstandng radaton lvls, nrgy dposton and nrgy balanc of hgh tmpratur plasmas [6]. In ths study, nrgy lvls, radatv rats and lctron mpact xctaton for fn structur lvls of Br II, Sb XVIII and T XIX. ons ar calculatd usng mcdfgm [7] cod (Mult-Confguraton Drac-Fock and Gnral Matrx Elmnts). Th MCDF calculatons wr compltd wth th ncluson of th rlatvstc two body Brt ntracton and th quantum lctrodynamcs corrctons (QED) whch ars du to slf-nrgy and vacuum polarzaton. Atomc collson procsss ar mportant n many fundamntal and appld aras of currnt rsarch [8]. II. METHOD OF CALCULATION Atomc stat wav functons ar rprsntd by th J- dpndnt CI xpansons of th form [9]. K ( JM ) b ( L S JM ), () Whr ach of th K sngl-confguraton functons s constructd from on-lctron functons, and L S th couplng of th orbtal and th spn dfns angular momnta to gv th total angular momntum J. Th b mxng coffcnts ar obtand by dagonalzng th Brt-Paul Hamltonan wth rspct to th bass functon. Th Brt-Paul Hamltonan hr conssts of th nonrlatvstc trm plus th on-body mass corrcton, Darwn trm, and spn-orbt, spn-othr-orbt, and spn-spn oprators. Th ncluson of mass corrcton, Darwn, and spn-spn trms shft th nrgy of a confguraton as a whol, whl th spn-orbt and spn-othr-orbt trms caus th fn-structur splttng. Th radal parts of th onlctron functons ar xprssd n analytc forms as a sum of Slatr-typ orbtals P nl K C ( ) /( p )! p r xp( r), PI Whr n and l, rspctvly, ar th prncpal and C orbtal quantum numbrs. Th paramtrs, p, and n quaton () ar th xpanson coffcnts, xponnts, and powrs of r, rspctvly, and ar dtrmnd varatonally []. Th wav functons gvn by quaton () ar thn usd to calculat th xctaton nrgs of th fn-structur lvls, lngth and vlocty forms of oscllator strngths, and transton probablts among th fn-structur lvls. Th radatv lftm of an xctd stat s calculatd from radatv transton probablts usng th rlaton () 5

2 / A ISSN: ISO 9:8 Crtfd Intrnatonal Journal of Engnrng and Innovatv Tchnology (IJEIT) III. RESULTS AND DISCUSSIONS Extnsv sts of fn structur nrgy lvls and oscllator strngths and transton probablts for th bound-bound transtons ar obtand for som mmbrs of S lk ons: Br II, Sb XVIII and T XIX. Th nrgy lvls and bound-bound transtons ar dscussd sparatly n th followng two sctons. A.FINE STRUCTURE IN ENERGY LEVELS A total of about fn structur nrgy lvls ar obtand for som mmbrs of S-lk ons whr all lvls hav bn dntfd. Th numbr of lvls obtand far xcd th obsrvd or prvously calculatd ons. Th nrgy lvl valus obtand usng th MCDF and HFR mthod for th, and s p f forbddn transtons n S -lk ons ar prsntd n tabls (- ). In ths tabls w prsnt our calculatd nrgs compard wth masurmnts. In gnral th calculatd nrgs of Br II, Sb XVIII and T XIX ons ar agrabl wth th masurd valus. Th tabls contan som sts of lvls of Br II, Sb XVIII and T XIX ons. Tabls - show that th agrmnt btwn MCDF and HFR nrgy lvls n our mmbrs of S-lk ons. Multplrs can b spcally confusng. B. WAVELENGTHS AND TRANSITION PROBABILITIES, OSCILLATOR STRENGTHS Volum, Issu 6, Dcmbr A Whr s th transton probablty? () Th wavlngths, transton probablts for th - and - s p f forbddn transtons wr calculatd usng th fully rlatvstc MCDF mthod ar rportd n tabls (-6). Th calculatd MCDF transton probablts ar prsntd n both lngth and vlocty gaugs, whl th oscllator strngths ar only shown n lngth gaug. Excptons to ths ar som fw transtons; whr th agrmnt. Not only s ths ovrall good agrmnt hghly satsfactory, but t also gvs a clar ndcaton of th accuracy of th rsults. Tabls (-6) prsnt th oscllator strngths (ƒ L ) and th transton probablts (A) for transtons among n = lvls of Br II, Sb XVIII and T XIX ons. W prsnt n tabl (7) a comparson btwn th MCDF, and HFR transton wavlngths (n Å) for th rlvant transtons and oscllator strngths. C. RADIATIVE LIFETIMES Th radatv lftm of an xctd stat s calculatd A from radatv transton probablty usng th rlaton ().In tabls (8-), w prsnt th calculatd MCDF and HFR radatv lftm ( n sc ) of - and - s p f. Tabl (): MCDF and HFR nrgy lvls (n cm - ) of, and s p f confguraton for Br II on Confguraton s p f J LS P P P D S D P G D 5 P F F F F D P MCDF (cm - ) HFR (cm - ) Exp (cm - )

3 7 8 9 ISSN: ISO 9:8 Crtfd Intrnatonal Journal of Engnrng and Innovatv Tchnology (IJEIT) Volum, Issu 6, Dcmbr s p f s p f s p f s p f s p f s p f s p f D D D G P P P Tabl (): MCDF and HFR nrgy lvls (n cm - ) of,s p d and s p f confguraton for Sb XVIII on. Confguraton J LS P MCDF (cm - ) HFR (cm - ) P P D S 9 6 D P G D F P F F F D s p f D s p f D s p f D s p f G s p f P s p f P 5 7 s p f P

4 ISSN: ISO 9:8 Crtfd Intrnatonal Journal of Engnrng and Innovatv Tchnology (IJEIT) Volum, Issu 6, Dcmbr s p f P 8 95 Tabl (): MCDF and HFR nrgy lvls (n cm - ) of, and s p f confguraton for T XIX on. Confguraton J LS P MCDF (cm - ) HFR (cm - ) P P 957 D S D P G 5 9 D F P F F F D s p f D s p f D s p f D s p f G s p f P s p f P s p f P s p f P Tabl () :MCDF Transton wavlngths (n Å ), Transton probablts vlocty (n sc - ) and Oscllator strngth ƒ L for lns of Br II Forbddn transtons (E). Lowr Uppr λ A V ƒ L ( P ) sp d ( D ) sp d ( D ) sp d ( F ) E E+.786E+.E-6.6E E-6 8

5 ISSN: ISO 9:8 Crtfd Intrnatonal Journal of Engnrng and Innovatv Tchnology (IJEIT) ( P ) ( P ) Volum, Issu 6, Dcmbr s p f ( P ) E+ ( D ) E+ ( P ) E+ ( F ) E+ ( D ) E+ ( F ) E+ ( F ) E+ s p f ( D ) E+ s p f ( P ) E+ s p f ( G ) E+ s p f ( D ) E+ ( D ) ( P ) ( F ) ( G ) ( D ) ( F ) ( F ) ( F ) s p f ( D ) s p f ( G ) s p f ( P ) s p f ( D ) E+.9889E+.7589E E E+.57E E+.95E+5.999E+.5589E E+.69E+.E-6.97E-8.8E-7.9E-8.E-6.9E-6 5.E-6.7E-7 5.9E-7.5E E-7 8.E-7 5.E-7.7E-8.9E-7 8.9E-8 6.5E-7.E E-6.76E-8.E-8.6E-7.E-7 ( D ) ( S ) ( D ) ( G ) ( F ) ( P ) s p f ( D ) ( D ) ( D ) E+5.855E+5.657E E+5.986E+.88E+.865E+.8E-6.7E-5.8E-5.5E-6.E-8 6.7E-7.6E-8 Tabl (5): MCDF Transton wavlngths (n Å ), Transton probablts vlocty (n sc - ) and Oscllator strngth ƒ L for lns of Sb XVII Forbddn transtons (E). Lowr Uppr λ A V ƒ L ( P ) ( P ) ( P ) sp d ( D ) sp d ( D ) sp d ( F ) s p f ( P ) ( D ) ( P ) ( F ) ( F ) ( F ) s p f ( D ) s p f ( D ) s p f ( P ) s p f ( G ) ( D ) ( P ) ( F ) ( G ) ( D ) ( F ) ( F ) ( F ) s p f ( D ) s p f ( G ) s p f ( P ) s p f ( D ) E E+.88E E E+6.798E+6.979E E E E E E E E+.657E E E+5.76E E+5.887E E E E+7.569E+7.598E+7.7E-5.E-7 6.9E-5.86E E-6.E-6.E-5 6.5E-6.5E-6.7E-5.58E-5 8.6E-6.7E-6 6.9E-8 9.E-6 8.E-7.E-6 7.8E-7.87E-7.7E-5.8E-5.67E-6.E-5.E-5.67E-5 9

6 ISSN: ISO 9:8 Crtfd Intrnatonal Journal of Engnrng and Innovatv Tchnology (IJEIT) ( D ) ( S ) Volum, Issu 6, Dcmbr ( D ) ( G ) ( F ) ( P ) ( D ) s p f ( D ) ( D ) ( D ) E+7.589E E E+6.6E+.8898E+5.999E+.6686E+.86E-5.9E-5.99E-5.8E-6 6.8E-8.5E-7.E-7.5E-7 Tabl (6) :MCDF Transton wavlngths (n Å ), Transton probablts vlocty (n sc - ) and Oscllator strngth ƒ L for lns of T XIX Forbddn transtons (E). Lowr Uppr λ A V ƒ L ( P ) ( P ) ( P ) ( D ) ( S ) sp d ( D ) sp d ( D ) sp d ( F ) s p f ( P ) ( D ) ( P ) ( F ) ( F ) ( F ) s p f ( D ) s p f ( D ) s p f ( P ) s p f ( G ) ( D ) ( P ) ( F ) ( G ) ( D ) ( F ) ( F ) ( F ) s p f ( D ) s p f ( G ) s p f ( P ) s p f ( D ) ( D ) ( G ) ( F ) ( P ) ( D ) s p f ( D ) ( D ) ( D ) E E+ 9.65E+6.97E E E E E+6 5.9E E+7.95E E E E+5.7E E E+5.65E E+.997E+.6589E E E E E E+7.55E+7.6E E+7.558E E E E+.E-5.8E-7 5.E-5.E-6 7.E-6 7.6E-7.5E-5 7.6E-6.E-5.6E-5.5E-5 9.6E-6.7E-6 9.E-8.6E-7 6.8E-7 9.7E-7 9.E-7 7.5E-8.6E-8.6E-5.87E-6.5E-5.9E-5.57E-5.75E-5.8E-5.76E-5.6E-5.E-8.97E-7.E-5.8E-7 Tabl (7): Comparson btwn MCDF and HFR Transton wavlngths (n Å ) and oscllator strngths for S -lk ons. Z Intal Fnal MCDF HFR λ ƒ L λ ƒ L 5 ( P ) ( D ) 98..9E E-8 ( P ) ( P ) 99..E E-7 ( P ) ( F ) E E-8 ( P ) ( D ) E E-6 ( P ) ( P ) E E-7 ( P ) ( F ) E E-7 ( P ) ( D ) E E-7 ( D ) ( D ) 7..8E E-6 5 ( P ) ( D ) 9.5.8E E-6 ( P ) ( P ) 95..E E-6 ( P ) ( F ) E E-6 ( P ) ( D ) E E-7

7 ISSN: ISO 9:8 Crtfd Intrnatonal Journal of Engnrng and Innovatv Tchnology (IJEIT) Volum, Issu 6, Dcmbr ( P ) ( P ) 8. 9.E-6 8..E-5 ( P ) ( F ) E E-9 ( P ) ( D ) E E-6 ( D ) ( D ) E E-5 ( P ) ( D ) 89..9E E-5 ( P ) ( P ) E E-6 5 ( P ) ( D ) 8. 7.E E-5 ( P ) ( P ) E E-6 ( P ) ( F ) 8.6.5E E-6 ( P ) ( D ) E E-7 ( P ) ( P ) 7.99.E E-7 ( P ) ( F ) E E-8 ( P ) ( D ) E E-6 ( D ) ( D ) 8..7E E-5 Tabl (8): MCDF and HFR radatv lftm (n sc) of, and s p f confguraton for Br II on. Lowr ( P ) ( P ) ( S ) ( P ) ( D ) Uppr ( D ) ( D ) ( F ) s p f ( P ) ( D ) ( P ) ( F ) ( F ) ( F ) ( D ) s p f ( D ) s p f ( P ) s p f ( G ) s p f ( D ) ( D ) ( D ) ( D ) ( P ) ( F ) ( G ) ( D ) ( F ) ( F ) ( F ) s p f ( G ) s p f ( P ) s p f ( P ) s p f ( D ) s p f ( D ) s p f ( D ) ( D ) ( G ) ( F ) ( P ) ( D ) s p f ( D ) Lftm lngth Gaug 9.8E-5.5E-5.5E-5.9E-.E-.E- 9.E-.5E-5.5E-5.E-5.6E-.7E- 6.E-.E-.E- 5.E-.9E-5.8E-5.E-.E-.E-.E-5.E-5 7.E-6.5E- 8.E-5.8E-.7E-.7E-.7E- 6.8E-6.8E-6.7E-6.E-6.5E-.E- Lftm vlocty Gaug.E-.8E-5.8E-5.5E-.E-.5E-.E-.6E-5.5E-5.5E-5.8E-.E- 7.E-.E-.E-.E-.8E-5.E-5 6.7E-.E-.5E-.8E-5.E-5 7.5E-6.8E- 9.9E-5 5.6E-.E-.E-.E- 8.9E-6.5E-6.7E-6 5.8E-6.6E- 9.8E- Lftm (HFR).E-.5E-6.5E-6 6.E-5 7.E-.E- 7.E-5 6.E-6.E-6.E-5 9.5E-5 9.E-5.6E- 6.5E-5.8E-5.E-.E-5 5.5E-5.7E- 7.E-5.8E-5.8E-5 6.6E-6.5E-6 7.7E-.E- 5.7E- 7.7E-.E- 8.E-5.E-6.5E-6.8E-6.E-6 5.8E-6 5.E-

8 ISSN: ISO 9:8 Crtfd Intrnatonal Journal of Engnrng and Innovatv Tchnology (IJEIT) Volum, Issu 6, Dcmbr Tabl (9): MCDF and HFR radatv lftm (n sc) of, and s p f confguraton for Sb XVIII on. Lowr ( P ) ( P ) ( S ) ( P ) ( D ) Uppr ( D ) ( D ) ( F ) s p f ( P ) ( D ) ( P ) ( F ) ( F ) ( F ) s p f ( D ) s p f ( P ) s p f ( G ) s p f ( D ) ( D ) ( D ) ( D ) ( P ) ( F ) ( G ) ( D ) ( F ) ( F ) ( F ) s p f ( G ) s p f ( P ) s p f ( P ) s p f ( D ) s p f ( D ) ( D ) ( G ) ( F ) ( P ) ( D ) s p f ( D ) Lftm lngth Gaug.6E-7.9E-5 8.E-8.E-6.7E-7 5.6E-7.6E-7.E-7.E-6.8E-8.E-7.E-6 5.E-8.E-5 9.E-5.E-5 5.7E-8.E-6.E-6 9.E-7 5.6E-6 9.E-8 6.8E-8 9.E-8.7E-8.9E-8.E-7.6E-8 5.E-8 6.8E-8 6.7E-8.E-7.E-5.E-6 Lftm vlocty Gaug.E-7.8E-5 8.7E-8.E-6.E-7 5.8E-7.E-7.E-7.E-6.E-8.6E-7.E-6 5.5E-8.E-5 7.E-5.5E-5 7.E-8.6E-6.6E-6 9.7E-7 6.7E-6 9.8E-8 7.E-8 9.9E-8.9E-8.E-8.E-7.9E-8 6.E-8 7.E-8 7.9E-8.E-7.E-5.E-6 Lftm (HFR).E-8.E-6.E-8 9.6E-7.E-7 5.5E-7.5E-7 5.E-7 8.9E-7.9E-8 8.E-8 5.E-7.E-8.8E-5 8.E-6.E-6 9.7E-8.7E- 7.E-7.E-6.8E-6 6.E-8.E-8 6.7E-8.9E-8.9E-8.E-7.6E-8 5.5E-8.E-8.5E-8 7.5E-7.E-.9E-6 Tabl (): MCDF and HFR radatv lftm (n sc) of, and s p f confguraton for T XIX on. Lowr ( P ) ( P ) ( S ) Uppr ( D ) ( D ) ( F ) s p f ( P ) ( D ) ( P ) ( F ) ( F ) ( F ) s p f ( D ) s p f ( P ) s p f ( G ) s p f ( D ) ( D ) ( D ) Lftm lngth Gaug.6E-7.9E-5 8.E-8.E-6.7E-7 5.6E-7.6E-7.E-7.E-6.8E-8.E-7.E-6 5.E-8.E-5 9.E-5 Lftm vlocty Gaug.E-7.8E-5 8.7E-8.E-6.E-7 5.8E-7.E-7.E-7.E-6.E-8.6E-7.E-6 5.5E-8.E-5 7.E-5 Lftm (HFR).E-8.E-6.E-8 9.E-7.E-7 5.5E-7.5E-7 5.E-7 8.9E-7.9E-8 8.E-8 5.E-7.E-8.8E-5 8.E-6

9 ISSN: ISO 9:8 Crtfd Intrnatonal Journal of Engnrng and Innovatv Tchnology (IJEIT) ( P ) ( D ) III. CONCLUSION Volum, Issu 6, Dcmbr.E-5 5.7E-8.E-6.E-6 9.E-7 5.6E-6 9.E-8 6.8E-8 9.E-8.7E-8.9E-8.E-7.6E-8 ( D ) ( P ) ( F ) ( G ) ( D ) ( F ) ( F ) ( F ) s p f ( G ) s p f ( P ) s p f ( P ) s p f ( D ) s p f ( D ) ( D ) ( G ) ( F ) ( P ) ( D ) s p f ( D ) Accurat and larg-scal calculatons hav bn carrd out for th st of fn structur nrgy lvls and transton probablts for Br II, Sb XVIII and T XIX ons. Th st of rsults far xcds th currntly avalabl xprmntal and thortcal data. W rport nrgy lvls and radatv rats for forbddn transtons wth th fully rlatvstc mutlconfguraton Drac-Fock mthod. Th rsults ar obtand n ntrmdat couplng ncludng rlatvstc ffcts usng th Brt Paul R-matrx mthod (BPRM) n th clos couplng approxmaton. Both th nrgs and th transton probablts show vry good agrmnt, wthn -%, wth almost all accurat calculatd and masurd valus avalabl. Ths ndcats that for ths hghly chargd ons th hghr ordr rlatvstc and th quantum lctrodynamcs corrctons QED ffcts omttd n th BPRM calculatons may lad to an rror not xcdng th stmatd uncrtanty. Th rsults from th prsnt work should b partcularly usful n th analyss of X-ray and Extrm Ultravolt spctra from astrophyscal and laboratory sourcs whr non-local thrmodynamc qulbrum (NLTE) atomc modls wth many xctd lvls ar ndd. ACKNOWLEDGMENT Th authors wsh to thank Dr. J. P. Dsclaux and Dr. P. Indlcat for allowng us to us th mcdfgm cod. Th frst and scond author would lk to thank Kafrlshkh Unvrsty, rsarch support box. REFERENCES [] A. K. Bhata, G. A. Doschk and U. Fldman, A&A, 86,, 98. [] H. Spnrad and M. S. Vardya, ApJ, 6, 99, 966. & H. L.Hlfr, G.Wallrstn, ApJS, 6,, 968. [] S. R. Pottasch, ApJ, 7, 95, 96. [] C. Fros Fschr, Phys. Scr.,, 8, E-8 6.8E-8 6.7E-8.E-7.E-5.E-6.5E-5 7.E-8.6E-6.6E-6 9.8E-7 6.E-6 9.8E-8 7.E-8 9.9E-8.9E-8.E-8.E-7.9E-8 6.E-8 7.E-8 7.9E-8.E-7.E-5.E-6.E-6 9.7E-8.7E- 7.E-7.E-6 6.8E-6 6.E-8.E-8 6.7E-8.9E-8.9E-8.E-7.5E-8 5.5E-8.E-8.5E-8 7.5E-7.E-.9E-6 [5] A. Farrag, E. Luc-Kong and J. Snzll, At. Data Nucl. Data Tabls, 7, 59, 98. [6] O.Nagy and Fatma El-Sayd, Enr Lvls, Transton Probablts and Elctron Impact Exctatons Of G-Lk Pr, Nd, Pm, Sm and Eu Ions, Atomc data and Nuclar Data Tabls,. [7] J. P. Dsclaux and P. Indlcato, MCDFGME, [8] R. E. H. Clark and D. H. Rtr, "Nuclar Fuson Rsarch, Undrstandng Plasma-Surfac Intractons", (Sprngr-Vrlag Brln, Hdlbrg, 5. [9] R. Glass, and A. Hbbrt, Comput. Phys. Commun., 6, 9, 978. [] A. Hbbrt, Comput. Phys. Commun., 9,, 975. AUTHOR BIOGRAPHY Prof. Dr. Mohsn Mossad, Profssor of Sold Stat Physcs, Physcs Dpartmnt, Faculty of Scnc, Kafrlshkh Unvrsty, Egypt. Dr. Abr Mra, Lctur of Thortcal Physcs, Physc Dpartmnt, Faculty of Scnc, Kafrlshkh Unvrsty, Egypt. Dr. Shrouk El- Ashry, Lcturr of Plasma Physcs, Faculty of Scnc, Tanta Unvrsty, Egypt.