Electron Impact Ionization Cross Sections of Tungsten Atoms and Tungsten Ions )

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1 Electron Impact Ionzaton Cross Sectons o Tungsten Atoms and Tungsten Ions ) Ghanshyam PUROHIT 1,2), Daj KATO 1,3,4) and Izum MURAKAMI 1,3) 1) Natonal Insttute or Fuson Scence, Natonal Insttutes o Natural Scences, Orosh-cho, Tok, Gu , Japan 2) Department o Physcs, Sr Padampat Snghana Unversty, Bhatewar, Udapur , Inda 3) Department o Fuson Scence, SOKENDAI, Orosh-cho, Tok, Gu , Japan 4) Department o Advanced Energy Engneerng Scence, Kyushu Unversty, Kasuga, Fukuoka , Japan (Receved 27 December 2017 / Accepted 7 March 2018) Tungsten (W) and tungsten based materals have been recommended as the plasma acng component n the current uson devces. The electron nduced processes on these materals are o prme mportance or the applcaton purposes. Electron mpact total onzaton cross sectons (TICS) are reported or the W atoms and W + ons. The TICSs have been calculated n the varants o dstorted wave approxmaton (DWA) usng Hartree-Fock wave unctons and dstorted potental wth sem-classcal exchange. Present TICS results have been compared wth the avalable theoretcal and expermental results. Reasonable agreement wth the exstng theoretcal results have been obtaned or the TICS o W atoms by present sem-relatvstc dstorted wave approach, however there are certan dscrepances or the TICS o W + ons. Derental cross sectons (DCSs) have also been calculated at projectle energy 100 ev or the onzaton o W atoms and W + ons and the DCSs have been ound to be senstve on the scatterng angle. c 2018 The Japan Socety o Plasma Scence and Nuclear Fuson Research Keywords: total cross secton, DWA, onzaton, Hartree-Fock potental, uson plasma, derental cross secton, TDCS, TICS DOI: /pr Introducton The onzaton cross sectons are essental n the modelng o plasma n uson research. The electron collson processes on heavy atoms and ther ons are mportant to study snce they employ certan phenomena whch are derent rom lghter targets. The tungsten (W) and tungsten based materals have been recommended as one o the materals to be used as plasma acng components or the Internatonal Thermonuclear Expermental Reactor (ITER) [1] and the Demonstraton Power Staton (DEMO) as these materals have thermophyscal propertes sutable or uson applcaton [2 4]. Tungsten s already n use as plasma acng components n tokamaks such as JET [5] and ASDEX-Upgrade [6]. In the uson devces the tungsten and related materals may exhbt hgh meltng temperature, strong resstance aganst sputterng and shorter penetraton depth etc. Electron nduced processes such as exctaton and onzaton are prevalent n such magnetc uson devces n a wde range o energes wth sgncant varaton o temperature and densty [7]. A relable data base s requred or the electron mpact onzaton and exctaton cross sectons or W to model the electron nduce nteractons and to unauthor s e-mal: ghanshyam.puroht@spsu.ac.n ) Ths artcle s based on the presentaton at the 26th Internatonal Tok Conerence (ITC26). derstand the spectroscopy nvolved. Detaled knowledge o electron tungsten nteractons and W electronc structure s stll scarce, however the W ons have been studed extensvely. In earler eorts, drect onzaton cross sectons o the W atom were calculated usng sem-relatvstc dstorted-wave method [8] and electron mpact sngle onzaton cross sectons were calculated or the W sonuclear sequence [9]. In later eorts electron nduced onzaton cross sectons or W and W + ons have been reported [10]. Very recently electron mpact ntegral cross sectons [11] and electron mpact sngle and double onzaton cross sectons [12] have been calculated or W atoms. Expermental data are avalable or the onzaton o W + [13, 14], however no cross secton measurements have been reported or onzaton o W atoms. We report n ths communcaton the electron mpact onzaton cross sectons or the W atoms and W + ons. The onzaton cross sectons have been calculated n the dstorted wave approxmaton (DWA). We compare the results o present calculatons wth the avalable theoretcal and expermental results. We also report the electron mpact derental cross sectons (DCS) or the onzaton o W atoms and W + ons or whch no earler studes are avalable. The trends o DCS may gve ner detals o electron tungsten nteractons whch may be o help to understand the structure o target or applcaton purposes c 2018 The Japan Socety o Plasma Scence and Nuclear Fuson Research

2 Bre theoretcal ormalsm used to calculate onzaton cross sectons s descrbed n next secton. 2. Theory In the electron mpact sngle onzaton process, an ncdent electron o lnear momentum k and energy E onzes the target (atom / on) and the two emergng electrons are descrbed by the lnear momentum and energy (k, E ) and (k e, E e ), where the scattered (prmary) electron s speced by subscrpt and the ejected (secondary) electron s speced by subscrpt e. The energy conservaton prncple states; E = E + E e + E b, (1) where l, l are electron orbtal angular momentum quantum numbers n ncdent and nal channels respectvely, l e s the ejected electron quantum number and L s the total orbtal angular momentum. Energes obey the conservaton dened n eq. (1) F s the onzaton ampltude, rom eq. (3), t can be wrtten as F 2 = 2 + g 2 Re ( g ). (7) Perormng the ntegrals over the angles n the eq. (4) and (5), the ampltude may be wrtten as F = λ (l b l l e l L) χ b χ V e χe χ λ, (8) λ where E b s the energy o the bound electron. The trple derental cross secton (TDCS) or the electron mpact sngle onzaton, whch s the probablty o sngle onzaton, s expressed n atomc unts as d 3 σ dω dω e de = (2π) 4 k k e k T(k, k e, k ) 2. (2) The expresson n Eq. (2) ncludes a sum over nal and average over ntal magnetc and spn state degeneracy. The T matrx n Eq. (2), whch s the subject o approxmaton, ncludes nteracton between the ncdent and target electrons and the nucleus. TDCS (eq. 2) or the onzaton s wrtten n terms o drect and exchange ampltude as where d 3 σ dω dω e de = (2π) 4 k k e k av l ( 2 + g 2 Re( g) ), m= l (3) = χ ( ) (k, r )χ e ( ) (k e, r e ) V e χ (+) (k, r )χ b (r e ), (4) g = χ ( ) (k, r e )χ e ( ) (k e, r e ) V e χ (+) (k, r )χ b (r e ). (5) Here V e s the nteracton potental between the ncdent and target electrons responsble or the onzaton. The dstorted waveuncton or the ncdent electron s represented by χ (+). χ ( ) and χ e ( ) represent the dstorted waveunctons or the two outgong electrons and each s orthogonalzed wth respect to χ b. χ b s the target wave uncton, whch s the ejected electron wave uncton beore collson. The potentals are obtaned rom the Hartree-Fock unctons o McLean and McLean [15] and localzed verson o potental s employed [16, 17]. Usng partal wave expanson and perormng angular ntegratons on eq. (2) the total onzaton cross secton s gven by σ(e ) = 16 πe E 0 de e l,l e,l (2L + 1) F 2, (6) here λ s the angular actor. The Hartee-Fock target wave unctons [15] have been used or the calculatns o TDCS. The total onzaton cross sectons or W atoms and W + ons have been calculated n two varants o dstorted wave approxmaton (DWA) namely Cowan structure calculaton [18] and HULLAC [19]. The Hartree-Fock target wave uncton and Hartree potental wth sem-classcal exchange [17] and correlaton correcton has been used or the sem relatvstc DWA calculatons wth Cowan ormalsm [18]. Ionzaton cross sectons usng Cowan ormalsm have been calculated n ne-structure and conguraton mode. The ne-structure mode ncludes the relatvstc eects emprcally n the calculatons. The DWA cross secton results usng HULLAC [19] have been obtaned wth ully relatvstc bass unctons or target electrons. The bass uncton s obtaned as a soluton o the snglepartcle Drac equaton wth a central-led parametrc potental whch represents a nuclear eld and a sphercally averaged nter-electronc nteracton. The parametrc potental s optmzed teratvely so that rst-order conguraton average energy o the total Hamltonan or the ground state conguraton wth a gven set o orbtal unctons becomes the mnmum. Contnuum bass unctons are also calculated wth the same parametrc potental. The results and dscusson s presented n next secton. 3. Results and Dscusson The electron mpact total onzaton cross secton (TICS) or W atom s plotted as a uncton o ncdent electron energy n Fg. 1. The present results calculated n the DWA are compared wth other theoretcal TICS results [11, 12] reported recently and no measurements are avalable to compare. The sold lne s present TICS calculated usng HULLAC [19] and the dashed and dotted curves are the present TICS calculated usng semrelatvstc dstorted wave Cowan ormalsm [18]. The dashed-dot curve represents the TICS or W atoms calculated n the sem-relatvstc dstorted wave approxmaton [12] and the dash-dot-dot curve s the TICS result or W atoms calculated through the electron-atom scatterng process usng a complex potental [11].

3 Fg. 1 Total onzaton cross sectons o W atoms plotted as a uncton o ncdent electron energy, sold curve: present DWA results n HULLAC [19], dashed and dotted curves: present DWA results n Cowan ormalsm wth nestructure and conguraton mode; dash-dotted curve: results o [12] and dash-dot-dotted curve: results o [11]. Fg. 3 Total onzaton cross sectons o W + ons plotted as a uncton o ncdent electron energy, dash-dot-dotted curve: results o [10]; dash-dotted curve: results o [8]; sold crcles and hollow trangles: measurements [14] and [13]; other curves are the same as Fg. 1. Fg. 2 Ionzaton cross sectons o W atom subshells calculated n DWA usng HULLAC [19], sold curve: total; dashed curve: 5d subshell; dotted curve: 6s subshell; dash-dotted curve: 4 subshell; dash-dot-dotted curve: 5p subshell. Fg. 4 Ionzaton cross sectons o W + on subshells calculated n DWA usng HULLAC [19], sold curve: total; dashed curve: 5d; dotted curve: 6s; and dash-dotted curve: 5p subshell. Present results wth HULLAC [19], Cowan ormalsm wth ne structure mode [18] and sem-relatvstc dstorted wave results o [12] gve nearly same vales o TICS. Present results calculated n the conguraton mode wth Cowan ormalsm gves slghtly hgher and results o [11] wth complex potental gves slghtly smaller values o TICS or W atoms. Ionzaton cross sectons calculated n the DWA usng HULLAC [19] or the ndvdual subshells 6s, 5d, 4 and 5p o W atoms are plotted n Fg. 2 along wth the TICS. The major contrbuton comes rom the 6s and 5d subshells. The electron mpact TICS results or the W + are presented n the Fg. 3. Present DWA results are compared wth the sem-relatvstc dstorted wave [12] and Coulomb-Born [10] results. The theoretcal TICS results are also compared wth the avalable measurements [13, 14]. Present DWA results wth HULLAC (sold curve) and Cowan ormalsm n conguraton mode (dashed curve) gves hgher values o TICS than the measurements, however the DWA results wth HULLAC are less than the sem-relatvstc dstorted wave results o [12]. The Coulomb-Born results [10] are slghtly hgher than the measurements and the present DWA results calculated wth ne-structure mode are almost 50% smaller rom the measurements. Ionzaton cross sectons calculated n the DWA usng HULLAC [19] or the ndvdual subshells 5d, 6s and 5p o W + on are plotted n Fg. 4 along wth the TICS. The major contrbuton comes rom the 5d and 6s subshells. The TICS results obtaned rom HULLAC [19] (sold lne n Fg. 1) and ne-structure mode n Cowan ormalsm [18] (dashed lne n Fg. 2) matches well or the W atoms. For the onzaton o W +, the HULLAC [19] results (sold lne n Fg. 3) are hgher rom the avalable measuremnets however the Cowan [18] results n ne-structure mode (dashed lne n Fg. 3) are smaller than the measurements. The conguraton mode n Cowan ormalsm (dot-

4 or the W + ons requre urther eorts to understand the complex collson dynamcs o the hgh Z target. Fg. 5 Fg. 6 TDCS or W atoms plotted as a uncton o ejected electron angle or derent scatterng angles, sold curve: 2 0 ; dashed curve: 5 0 ; dotted curve: 10 0 ; dash-dotted curve: TDCS or W atoms plotted as a uncton o ejected electron angle or derent scatterng angles, legends are the same as Fg. 5. ted lne n Fg. 3) gves nearly two tmes hgher values o cross sectons rom the measuements. Further studes or the hgher charged states o W may be requred to decde about the sutablty o better approach. The electron mpact trple derental cross secton (TDCS) results are presented or the onzaton o W (6s) atoms and W + (5d) ons n Fgs The TDCS results have been calculated n the DWBA approach or the projectle energy 100 ev and ejected electron energy 2 ev at varous scatterng angles. The TDCSs or W atoms are plotted or scatterng angles 2 0,5 0,10 0 and 15 0 n Fg. 5. A clear two peak structure,.e bnary and recol peaks, s observed or the onzaton takng place rom 6s orbtal o the W atom. The two peak structure also exst or the onzaton rom 5d orbtal at smaller scatterng angle however the TDCS or hgher scatterng angles show splttng o peaks. The magntude o TDCS decreases wth ncrease n scatterng angle and the poston o the peaks also sht towards hgher values o ejected electron angle. The electron mpact TDCS or the onzaton o W + (5d) and W + (4) are plotted n Fg. 6. The trends o TDCS or the onzaton o tungsten ons are derent rom the trends o TDCS or the tungsten atoms. The TDCS trends or the onzaton o W + does not show the two peak structure, the TDCS observed Conclusons Electron mpact onzaton cross sectons have been calculated or the W atoms and W + ons n the dstorted wave ormalsm. Present dstorted wave TICS results show nearly the same magntude as obtaned by semrelatvstc dstorted wave results obtaned earler or the W atoms. The dstorted wave TICS results or the W + ons overestmate the measurements and Coulomb-Born results, however, the dstorted wave TICS calculated wth ne-structure mode or W + ons show smaller values. The TICSs have been calculated n sem-relatvstc approach n the Cowan ormalsm and n the ully relatvstc approach n HULLAC. As the major contrbuton to cross secton s rom outer shells, present eorts should be capable to produce the reasonable TICS data. However hgher degree o uncertanty s observed n the calculated TICS so urther studes are requred to obtan more accurate results. The derental cross sectons or the W atoms and W + ons are ound to be senstve on the drecton o momentum transer.e. scatterng angle. Further eorts are antcpated or the calculaton o onzaton cross sectons or tungsten atoms and ons whch are mportant or the uture uson devces. Acknowledgments Ths work was perormed durng GP s JSPS Invtatonal Fellowshp stay n Natonal Insttute or Fuson Scence (NIFS), Tok, Japan. GP acknowledges NIFS or provdng hosptalty. GP acknowledges JSPS Long Term Fellowshp AY 2017 (L17538) provded by Japan Socety or Promoton o Scence. GP also acknowledge Sr Padampat Snghana Unversty (SPSU), Udapur, Inda or provdng sabbatcal leave. We acknowledge the NIFS database or provdng the numercal cross secton results or W + ons. [1] G. Federc, Phys. Scr. T124, 1 (2006). [2] S. Wurster et al.,j.nucl.mater.442, S181 (2013). [3] J. de Prado et al., Mater. Des. 112, 117 (2016). [4] J.W. Coenen et al.,phys.scr.t167, (2016). [5] M. Groth et al., Nucl. Fuson 53, (2013). [6] M. Mayer et al.,phys.scr.128, 106 (2007). [7] V. Phlpps, J. Nucl. Mater. 415, S2 (2011). [8] M.S. Pndzola and D.C. Grn, Phys. Rev. A 46, 2486 (1992). [9] S.D. Loch et al., Phys. Rev. A 72, (2005). [10] L. Vanshten et al., J. Phys. B: At. Mol. Opt. Phys. 44, (2011). [11] F. Blanco et al., Plasma Sources Sc. Technol. 26, (2017). [12] M.S. Pndzola et al., J. Phys. B: At. Mol. Opt. Phys. 50, (2017). [13] R.G. Montague et al., J. Phys. B: At. Mol. Opt. Phys. 17, 2707 (1984). [14] M. Stenke et al., J. Phys. B: At. Mol. Opt. Phys. 28, 2711

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