Electron Impact Excitation Cross Sections of Xenon for Optical Plasma Diagnostic

Transcription

1 FINAL REPORT (Project Reerence: AOARD ) Electron Impact Exctaton Cross Sectons o Xenon or Optcal Plasma Dagnostc Submtted to: THE ASIAN OFFICE OF AREOSPACE RESEARCH & DEVELOPMENT Submtted by: Dr. Rajesh Srvastava, Proessor Department o Physcs Indan nsttute o Technology (I.I.T.) Roorkee INDIA

2 Report Documentaton Page Form Approved OMB No Publc reportng burden or the collecton o normaton s estmated to average 1 hour per response, ncludng the tme or revewng nstructons, searchng exstng data sources, gatherng and mantanng the data needed, and completng and revewng the collecton o normaton. Send comments regardng ths burden estmate or any other aspect o ths collecton o normaton, ncludng suggestons or reducng ths burden, to Washngton Headquarters Servces, Drectorate or Inormaton Operatons and Reports, 1215 Jeerson Davs Hghway, Sute 1204, Arlngton VA Respondents should be aware that notwthstandng any other provson o law, no person shall be subject to a penalty or alng to comply wth a collecton o normaton t does not dsplay a currently vald OMB control number. 1. REPORT DATE 20 NOV REPORT TYPE Fnal 3. DATES COVERED to TITLE AND SUBTITLE Electron Impact Exctaton Cross Sectons o Xenon or Optcal Plasma Dagnostcs 5a. CONTRACT NUMBER FA b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Rajesh Srvastava 5d. PROJECT NUMBER 5e. TASK NUMBER 5. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Indan Insttute o Technology, Roorkee,IIT Roorkee,Roorkee,Inda,IN, SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) AOARD, UNIT 45002, APO, AP, PERFORMING ORGANIZATION REPORT NUMBER N/A 10. SPONSOR/MONITOR S ACRONYM(S) AOARD SPONSOR/MONITOR S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved or publc release; dstrbuton unlmted 13. SUPPLEMENTARY NOTES 14. ABSTRACT In ths project the researcher had taken up the calculaton o xenon apparent emsson-exctaton cross sectons or emsson lnes that have dagnostc value n the analyss o Xe-propelled electrc thruster plasmas. Followng conclusons were made rom the study ï ½ The RDW method has been shown to be applcable to transtons between excted states. ï ½ Snce the exctaton energy o these transtons s relatvely small, rst-order theores are vald at lower energes than or exctatons rom the ground states. ï ½ The accuracy o the cross secton depends crucally on the accuracy o the oscllator strengths obtaned rom the target wave unctons. ï ½ The use o a relatvstc ormalsm (j-j couplng) clearly explans the huge varaton n the magntudes o these cross sectons. ï ½ The objectves o the project have been acheved and the amed metastable exctaton cross secton results o xenon were obtaned that are requred or the CRM model o Dressler and co workers and these are beng tested and new plasma modelng results are under calculaton. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT a. REPORT unclassed b. ABSTRACT unclassed c. THIS PAGE unclassed Same as Report (SAR) 18. NUMBER OF PAGES 20 19a. NAME OF RESPONSIBLE PERSON Standard Form 298 (Rev. 8-98) Prescrbed by ANSI Std Z39-18

3 Outlne o the Report 1. Introducton and Background o the Project 2. Outlne o the Work Done 3. Detaled Descrpton o the Work 3.1 Energy levels o xenon 3.2 Descrpton o the states n relatvstc j-j couplng scheme 4. Calculaton o Exctaton Cross Sectons o Xenon 4.1 Salent eatures o RDW method 4.2 Bre Descrpton o RDW Theory 4.3 Calculaton o Atomc Waveunctons 5. Xenon Cross Sectons: Results, Dscusson and Concluson 6. Applcaton o Cross sectons to CRM Model o Dressler and co workers 7. Future Work 8. Reerences 9. Lst o Publcatons

4 1. Introducton and Background o the Project In ths project we had proposed to take up the calculaton o xenon apparent emsson-exctaton cross sectons or emsson lnes that have dagnostc value n the analyss o Xe-propelled electrc thruster plasmas. In act, these cross sectons are vtal or models that are necessary or proper ntegraton and letme predctons o Hall eect thrusters. The expermental measurement o cross secton and plasma related analyss n ths connecton have been n progress and are beng carred out by Dr. R. A. Dressler and hs group at the Ar Force Research Laboratory, Hanscom AFB [1]. To supplement ths work we had planned to perorm at I.I.T. Roorkee n Inda relable calculatons or electron mpact exctaton cross secton to provde relevant cross secton data needed or the study o xenon propelled electrc thrusters. Below we brely ntroduce the xenon propelled electrc thrusters. An on engne reles on electrcally charged atoms, or ons, to generate thrust. Xenon, an nert, noncombustble gas, s electrcally charged and the ons are accelerated to a speed o about 62,900 mles per hour (30 klometers per second). The ons are then emtted as exhaust rom the thruster (see gure below o an on engne or llustraton), creatng a orce, whch propels the spacecrat n the opposte drecton. The prmary advantage o electrc propulson s ecency. An on engne s 10 tmes more ecent than ts alternatve, a chemcal propulson system. Wth xenon, t s possble to reduce propellant mass onboard a spacecrat by up to 90 percent. The advantages o havng less onboard propellant nclude a lghter spacecrat, and, snce launch costs are set based on spacecrat weght, reduced launch cost.

5 The use o these electrostatc thrusters, however, poses new challenges regardng ther proper engneerng and ntegraton on satelltes. Precse modelng o the satellte plasma envronment s requred. A sutable approach s requred or analyzng xenon-propelled Hall thruster optcal radaton based on apparent electron and on mpact emsson cross sectons assocated wth lnes n vsble and near-nrared regon o the spectrum. The current proposal addresses as a rst step to get accurate theoretcal electron mpact cross sectons or the processes where ntally excted metastable states vz. 1s 3 and 1s 5 o xenon are excted by electrons to the 2p n states wth n =1,10 n Paschen s notaton. For these exctatons no other theoretcal calculatons are avalable and also scarce expermental data have been reported [2,3]. We address here n ths project the Hall eect thrusters (HET), whch are a hgh-specc mpulse alternatve to chemcal propulson systems o spacecrat [1,4]. In HETs, a gas, typcally xenon or krypton, s ecently onzed n a dscharge, and postve ons are electrostatcally accelerated to generate thrust. The perormance, plasma characterstcs, and durablty o HETs are extensvely evaluated both n ground-based test acltes and n space. Basc characterstcs o HET plasmas, such as charge speces denstes and temperatures have been tradtonally measured by varous plasma probes. However, at HET condtons, tradtonal plasma-probe dagnostcs are aected by problems such as the perturbaton o the local envronment by the probe, the complexty assocated wth nterpretng the probe characterstcs, and detrmental eects n regons o hgh temperatures (e.g., n the HET dscharge). Consequently, HET plasma parameters reported rom probe experments exhbt sgncant dspartes. Optcal plasma dagnostcs crcumvent these problems and are thus an attractve alternatve to probe measurements. A key component o collsonal radatve model (CRM) s a set o emsson cross sectons assocated wth the energy transer processes that lead to populaton o states that radatvely relax through emsson n the spectral regon o nterest [1,4]. Proper mplementaton o a CRM has been prmarly hampered by the lack o a comprehensve cross secton set. In act, these cross sectons are vtal or models that are necessary or proper ntegraton and letme predctons o Hall eect thrusters (HET). I we ocus on emsson exctaton cross sectons or Xe propelled HETs, the optcal radaton arses rom electron xenon atom collsons, o whch

6 the most mportant contrbuton can be assumed to be comng rom ollowng exctaton processes: e + Xe Xe* + e (1) e + Xe m Xe* + e (2) The astersks n processes (1) and (2) sgny excted speces that lead to optcal emssons. Superscrpt m ndcates metastable states. The process (1), whch deals wth the exctaton o xenon rom the ground state to upper excted states have been studed theoretcally and expermentally [1-4]. The process (2) whch deals wth exctaton o the metastable state has not been explored. Metastable states o the noble gases are mportant consttuents o plasmas. In addton to ther long letme, these states have large nelastc cross sectons as compared to the exctaton rom the ground state [3]. Thus t s mportant to nclude these processes n the modelng o plasma whch s prme objectve o the present project. 2. Outlne o the work done Electron mpact exctaton o xenon atoms rom metastable states to upper 2p n (n = 1-10) excted states have been consdered. Exctaton cross sectons are calculated usng the Relatvstc dstorted-wave (RDW) theory. Fne-structure atomc states are represented by mult- conguraton Drac-Fock wave unctons. Contnuum projectle electron dstorted waves are obtaned through Drac equatons. Calculatons are compared wth expermental results [2]. The cross sectons are ncorporated n the CRM model.e. n the analyss o Xe-propelled electrc thruster plasmas, beng carred out by Dr. R. Dressler at AFB, Hanscom [1,4].

7 3. Detaled Descrpton o the Work done 3.1 Energy levels o Xenon The ground state o xenon has 5p 6 conguraton. The rst excted state has a 5p 5 6s conguraton wth our ne-structure levels wth J = 0, 1, 1, 2. The states wth J = 0 and 2 are long-lved metastable states.e. 1s 3 and 1s 5 states. We consder the electron exctaton o these two metastable states to the hgher lyng 5p 5 6p conguraton havng ten ne-structure levels.e. 2p n (n = 1-10) excted states. The gure below shows the energy levels o the xenon

8 3.2 Descrpton o the states n relatvstc j-j couplng scheme The ground states o the noble gases have an np 6 outer shell n the nonrelatvstc representaton where n = 5 or xenon. In the relatvstc j-j couplng scheme, ths shell s broken nto two subshells and represented as n p 2 np 4 where p represents a p electron wth total angular momentum (orbtal angular momentum plus spn) j = 1/2 whle p has j = 3/2. Thus the metastable states have conguratons p 5 p 6s 4 5 p5 p 6 s wth J=2 1s 5 wth J=0 1s 3 Paschen notaton Upper states have conguratons p 5 p 6 p p 5 p 6 p 4 5 p5 p p5p 6 p p wth J = 0, 1, 2, 3 wth J = 1, 2 wth J = 1, 2 wth J = 0, 1 These upper ten states are represented n the Paschen notaton by 2p 1-2p 10 n order o decreasng energy but order o J values may change wth atom. The ollowng gure shows dagrammatcally the exctaton transtons consdered n the present work.

9 4. Calculaton o Exctaton Cross Sectons n Xenon For cross secton calculaton we use relatvstc dstorted wave (RDW) method. The salent eatures o the RDW are as ollows: 4.1 Salent eatures o RDW method As relatvstc eects should be ncluded n the study o electron mpact exctaton o heavy atoms where spn-orbt eects are mportant, our method ncorporates ull relatvstc eects. Our method consders drectly the ne-structure target states wthout any approxmaton. Our method ncludes spn-polarzed electrons n a natural way.

10 Our Relatvstc Dstorted Wave (RDW) method nvolves solvng the Drac equatons to descrbe both the bound and contnuum electrons. The relatvstc eects are thus ncorporated to all orders n a natural way. 4.2 Bre Descrpton o RDW Theory The dstorted-wave T-matrx or the electron mpact exctaton o an atom havng N electrons and nuclear charge Z rom an ntal state to nal state can be wrtten as (atomc unts are used throughout) T DW = + χ ( 1, 2,..., N + 1) V U ( N + 1) Aχ (1, 2,..., N + 1) where V s the target-projectle nteracton gven by Z V = r here + N 1 N+ 1 j= 1 r j r N + 1 r j (j = 1,, N) poston co-ordnates o the target electrons r N+1 U A The wave unctons poston co-ordnate o the projectle electron wth respect to the nucleus o the atom dstorton potental antsymmetrzaton operator ( ) χ + ch, where ch reers to the two channels,.e. ntal and nal, are represented as a product o the N-electron target wave unctons φ ch and a projectle-electron dstorted-wave uncton DW+ ( ) F ( ),.e. χ + ( ) ch DW+ ( ) (,,..., N + ) = φ (,,..., N) F ( k, N + ). ch Here + reers to an outgong wave whle - denotes an ncomng wave. The projectle electron contnuum waveunctons are gven by ch ( ) ( ˆ ˆ ) F (, ) 1 η e a µ r χ r ± ± κ ( k) 1 κ κm µ k r = (2 ) 3/2 π κm κ m r gκ ( r) χ κm ( rˆ ) ch where 1/2 a µ ( ˆ) 4 l E c2 ( 1 ) * ( ˆ κm k π = + l m µ j m Y k) 2E m l 2 l m l l

11 The spn-orbt unctons are gven by χ 1 κm( rˆ, σ) = ( µ ν j my) (ˆ) r ψ ( σ) µν 2 µ 1ν 2 and 1 m ( rˆ, ) = ( µ ) ˆ ( ) 2 j my (r) σ 1 2 where J m ψ ( σ) (1/2) υ total angular momentum o the orbtal the z-component o j normalzed two-component spn wave unctons and = 2 j The spn-angular state s characterzed by quantum number κ, whch s dened as κ = j= -1/2 or > j = + 1/2 The radal parts κ (r) and g κ (r) are obtaned rom the Drac equatons d ( ) 1( 2 ) ( ) 1 r r c c U E g r cr W ( ; r) 0 dr κ + κ + κ ch κ = Q d ( ) 1( 2 ) ( ) 1 r g r c c U E r cr W ( ; r) 0 dr κ κ + + κ ch κ + = P Here U s dstorton potental and W s exchange terms Drac equatons are solved usng the boundary condtons 1 l (r) sn(k chr + ) r k 2 c l g (r) cos(k r r 2 ch c + E 2 + ch )

12 Wave uncton a(b) o the target atom s soluton o Drac equaton wth Hamltonan The sngle electron central eld Drac orbtals are gven by where Z 1 H atom c c r r nm N N 2 = α j + β + j= 1 rj < j j 1P ˆ n (r) m ( r,) ( r,)= Q ˆ r n (r) -m ( r,) α, β Drac matrces j momentum operator o the jth target electron P nκ larger component o the radal part o the waveuncton Q nκ smaller component o the radal part o the waveuncton The bound state orbtals satsy the ollowng orthogonalty condtons, 0 χ [ Pn (r)pn (r) + Qn (r)qn(r)] = n n dr κ m( r ˆ, σ ) χκ m ( rˆ, σ ) = δκ κ δ m m Ater obtanng the waveunctons or target atom bound states and the projectle electron contnuum states, We evaluate the scatterng ampltude or the exctaton o a noble gas atom n a metastable state wth total angular momentum J and magnetc quantum number M to a nal 5p 5 6p state wth angular momentum J, M as ( J k 2 DW,M, µ ; J,M, µ ) = ( 2 π ) T ( J,M, µ ; J,M, µ k ) where and are the spn projectons n the ntal and nal channels. Then wth our normalzaton the derental cross secton (DCS) s gven by 1 DCS = 2( 2J + 1) M, µ, M, µ ( J,M, µ ; J,M, µ ) 2 and the ICS s obtaned by ntegratng the DCS over all scatterng angles. dσ σ = Tot d Ω dω

13 4.3 Calculaton o the Atomc wave unctons The metastable states are sngle conguraton wave unctons. Φ = p 5 p 6s J = 2 Φ = 4 5 p5 p 6s J = 0 The excted 2p n states are lnear combnatons o the 5p 5 6p conguratons wth the same J value. Φ = c 5 p 5p 6 p c 5p 5 p 6 p c 5 p5p 6 p c 5p5p 6 p J The mxng coecents c s o the varous conguratons to the ne-structure levels o the nal states are gven n tables 1. These wave unctons are Drac-Fock wave unctons calculated rom the GRASP92. To optmze the waveunctons obtaned, we have compared n table 2, our calculated values o energy derences wth the correspondng expermental values lsted n NIST Database [5]. We have also presented n table 3 the comparson o our calculated optcal oscllator strengths wth the avalable theoretcal [6] and expermental [2] results or the optcally allowed transtons. Table 1. Contrbutons o the varous conguratons to the 5p 5 6p states o Xe Conguratons 5 p 2 5p 3 6 p 5 p 2 5p 3 6p 5 p 5p 4 6 p 5 p 5p 4 6p J = 0 levels 2p p J = 1 levels 2p p p p J = 2 levels 2p p p

14 Table 2. Energy derences (ev) or the transtons consdered: NIST - expermental values rom the NIST database [5]; GRASP - calculated values usng the GRASP92 program Table 3: Dpole oscllator strengths or transtons n Xe: GRASP92, present calculatons; Theory, theoretcal calculatons [6]; Expt., values derved rom hgh energy cross secton measurements [2]. Transton NIST GRASP 1s5-2p s5-2p s5-2p s5-2p s5-2p s5-2p s5-2p s5-2p s5-2p s5-2p s5-1s Intal state 1s 5 1s 3 Fnal state GRASP Theory Expt GRASP Theory 2p p p ±0.19 2p p ±0.10 2p p p Xenon Cross Sectons: Results, Dscusson and Concluson We observe that the transtons we consdered are o the ollowng type Transtons rom the 1s 5 J = 2 state are allowed to the 2p n states wth J = 1, 2, 3. Transtons rom the 1s 3 J = 0 state are allowed only to the 2p n states wth J = 1.

15 All other transtons are orbdden but the transton rom 1s 3 J = 0 state to the 2p n states wth J = 3 s dentcally zero n a rst-order theory. The gure below shows dagrammatcally the all optcally allowed transtons states to 2p n states o Xe rom metastable Fttng o the calculated allowed transton cross sectons: For allowed transtons we nd the cross secton takes on the Bethe-Born orm at larger energes σ = 2 4π a0 E [ln ( E) + b] E E where E energy o the ncdent electron n Rydbergs E exctaton energy o the transton optcal oscllator strength o the transton b ttng constant

16 We have tted our exctaton cross secton results to the above Bethe-Born ormula and the ttng constant b or the allowed transtons s gven n table-4. Table 4: Values o constant b or allowed transtons Atom Intal State Fnal State Xenon 1s 3 1s 5 2p p p p p p p p p p These tted cross sectons, thus, allow us to predct the cross secton at any desred energy and can be easly used n plasma modelng as such. At larger energes we nd that the cross sectons or orbdden transtons behave as E -3 where E s the energy o the ncdent electron. Comparson o our cross sectons wth avalable expermental results Jung et al [2] have recently publshed measurements o cross sectons or the exctaton rom the metastable 1s 5 state o Xe to the {2p 5-2p 10 } manold. Only two o these transtons (2p 6 and 2p 8 ) were measured at hgher energes. For exctaton to the J = 1 states, whch are allowed transtons rom ether o the metastable ntal states, those that nvolve a change o core conguratons are several orders o magntude smaller than those that don t. We note that the cross secton or the 1s 5-2p 7 transton s much smaller than or the others wthout a change n core whch s n conormty wth the magntudes o the oscllator strengths. We compare our results wth the measured cross sectons o Jung et al [2] n Fgures 1 and 2. Our cross sectons agree reasonably well wth the measured cross sectons at larger energes or the exctaton o the 2p 6 and 2p 8 states but there s a systematc devaton as the ncdent electron energy decreases beng roughly a actor o two larger around 8 ev. The agreement wth those transtons whch were not measured at hgher energes s comparable to

17 these two cases. Our cross sectons are always above the measured values at 8 ev wth the excepton o that or the 2p 5 state whch may mply that cascade contrbutons rom more hghly excted states are larger n ths case as suggested by Jung et al [2]. 100 (a) Cross secton (10-20 m 2 ) (b) Electron energy (ev) Fgure 1: Integrated cross sectons or electron exctaton o xenon rom the 1s 5 state to the: (a) 2p 6 state; (b) 2p 8 state. Sold curve, presents RDW calculatons; expermental ponts wth error bars, Jung et al [2]. Cross secton (10-20 m 2 ) (a) (c) Electron energy (ev) (b) (d) Fgure 2: Integrated cross sectons or electron exctaton o xenon rom the 1s 5 state to the: (a) 2p 5 state; (b) 2p 7 state; (c) 2p 9 state; (d) 2p 10 state. Sold curve, presents RDW calculatons; expermental ponts wth error bars, Jung et al [2].

18 The ollowng conclusons can be drawn rom the above presentaton o our results The RDW method has been shown to be applcable to transtons between excted states. Snce the exctaton energy o these transtons s relatvely small, rst-order theores are vald at lower energes than or exctatons rom the ground states. The accuracy o the cross secton depends crucally on the accuracy o the oscllator strengths obtaned rom the target wave unctons. The use o a relatvstc ormalsm (j-j couplng) clearly explans the huge varaton n the magntudes o these cross sectons. We have presented here our selected results and these are now publshed [7] and presented at varous conerences (see the secton o lst o publcatons). Our entre results publshed and unpublshed wll be utlzed n the uture modelng calculatons. We have acheved our target and obtaned the amed metastable exctaton cross secton results o xenon requred or the CRM model o Dressler and co workers [1,4] and these are beng tested and new plasma modelng results are under calculaton. 6. Applcaton o Cross sectons to CRM Model o Dressler and co workers We have been normed that our calculatons o electron-exctaton rom the 5p 5 6s J=2 metastable level (1s 5 state n Paschen notaton) to the lowest sx 5p 5 6p (2p) levels have allowed Dressler and co workers at AFB Hanscom to develop a collsonal radatve model (CRM) or Xe near-nrared (NIR) emssons based on populaton and depopulaton o the metastable level through 1s 5 2p transtons. Applcaton o the model to spectral ntenstes observed n the plume o a Hall thruster, however, demonstrates that the model overestmates the populaton o the 1s 5 state. The observed spectrum can be reproduced wth hgh delty addtonal metastable de-exctaton mechansms are eectve. On the demand o the Hanscom Group, we have urther carred out calculatons or the exctaton o xenon rom ts 1s 5 level to 1s 2, 1s 3 and 1s 4 levels. Thereater, the group has demonstrated that the electron-nduced depopulaton through the exctaton to 5p 5 6s J=1 (1s 4 ) and other 5p 5 6s levels, or whch newly calculated cross sectons are presented, can account or the addtonal de-

19 exctaton mechansms and gve relable results. Ths work we are plannng to present n the GEC-2007 meetng to be held at Arlngton VA, durng October 2-5, 2007 (see lst o publcatons). 7. Future Work In the lght o recent expermental results o Jung et al [8] we have carred out relatvstc dstorted wave calculatons or electron mpact exctaton o the ten hgher-lyng ne-structure levels o the 3p 5 5p conguraton o argon rom the lowest metastable states (the J = 0, 2 levels o the 3p 5 4s conguraton). We compare our theoretcal results wth ther expermental results and dscuss the derences rom the smlar exctaton to the 3p 5 4p levels rom the same metastable states [9]. In the lght o ths work on argon, we eel that n xenon also the electron mpact exctaton o the ten hgher-lyng ne-structure levels o the 5p 5 7p conguraton rom the lowest metastable states (the J = 0, 2 levels o the 5p 5 6s conguraton) possbly can contrbute. Ths has to be tested and we are currently workng on ths aspect as well. In addton, as ponted out by the Hanscom group that the electron exctaton o Xe + on can nluence the results o CRM model, we would thereore, lke to test ths as well. Currently, we are also plannng to extend our RDW calculatons to the exctaton o Xe + ons whch wll be our uture work.

20 8. Reerences 1 G. F. Karabadzhak, Y. Chu and R. A. Dressler, J. Appl. Phys., 99 (2006) R. O. Jung, J. B. Board, L. W. Anderson and C. C. Ln, Phys. Rev. A, 72 (2005) J. B. Board, C. C. Ln and C. A. Dejoseph Jr, J. Phys. D: Appl. Phys., 37 (2004) R Y. Chu, B. L. Austn, S. Wllams, R. A. Dressler and G. F. Karabadzhak, J. Appl. Phys., 99 (2006) C.M. Maloney, J.L. Peacher, K. Bartschat and D.H. Madson, Phys. Rev. A, 61 (2000) R. Srvastava, A. D. Stauer and Lalta Sharma, Phys. Rev. A, 74 (2006) R. O. Jung J. B. Board, L; W; Anderson and C. C. Ln., Phys. Rev. A 75, (2007) Lalta Sharma, R. Srvastava and A. D. Stauer, Phys. Rev. A (n Press).

21 9. Lst o Publcatons 1. Exctaton o the metastable states o the noble gases, (R. Srvastava, A. D. Stauer and Lalta Sharma), Phys. Rev. A 74 (2006) Exctaton o the 3p 5 5p levels o Argon rom the 3p 5 4s metastable levels, (Lalta Sharma, R. Srvastava and A. D. Stauer), Phys. Rev. A (n Press). 3. Exctaton o the metastable states o argon, (Lalta Sharma, Rajesh Srvastava and A. D. Stauer), Journal o Physcs Conerence Seres (n Press). 4. Exctaton o the metastable states o the noble gases, (Lalta Sharma, Rajesh Srvastava and A. D. Stauer), 7 th Asan Internatonal Semnar on Atomc and Molecular Physcs, 4 th -7 th December, 2006, IIT Madras, Chenna. 5. Electron mpact exctaton o the ntally excted atoms: A ully relatvstc approach, (Rajesh Srvastava, Lalta Sharma and A.D. Stauer), 9 th European Conerence on Atoms, Molecules & Photons, 6 th 11 th May 2007, Heraklon, Greece. 6. Exctaton rom the metastable states o nert gases, (Rajesh Srvastava, Lalta Sharma and A.D. Stauer), 25th Internatonal Conerence on Photonc, Electronc and Atomc Collsons (ICPEAC-XXV), Freburg (Germany), July 25-31, 2007 (Accepted) 7. Exctaton rom the ground states o nert gases, (Lalta Sharma, Rajesh Srvastava and A. D. Stauer), 25th Internatonal Conerence on Photonc, Electronc and Atomc Collsons (ICPEAC-XXV), Freburg (Germany), July 25-31, 2007 (Accepted) 8. Exctaton o the 3p 5 5p levels o Argon rom the 3p 5 4s metastable levels, (Rajesh Srvastava, Lalta Sharma and A.D. Stauer), Gaseous Electronc Conerence-2007, Arlngton VA, October 2-5, 2007, (Submtted) 9. Passve optcal dagnostc o electrc propulson Xe plasma: the role o metastable atoms, (R. A. Dressler, Y. Chu, Lalta Sharma, R. Srvastava and G. Karabadzhak), Gaseous Electronc Conerence-2007, Arlngton VA, October 2-5, 2007, (Submtted)