The convergent close-coupling method. CCC method for electron-atom scattering

Transcription

1 Introducton Nonrelatvstc CCC theory The convergent close-couplng method or electron-atom scatterng I. Bray, D. V. Fursa, A. S. Kadyrov, A. T. Stelbovcs ARC Centre or Antmatter-Matter Studes, Curtn Unversty o Technology, Perth, Western Australa IAEA, Venna, November, 2009 Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

2 Introducton Nonrelatvstc CCC theory Igor Bray CCC method or electron-atom scatterng

3 Outlne Introducton Nonrelatvstc CCC theory 1 Introducton Motvaton Dstant hstory Recent hstory 2 Nonrelatvstc CCC theory atomc target structure electron-atom scatterng convergence studes 3 electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

4 Introducton Motvaton Introducton Nonrelatvstc CCC theory Motvaton Dstant hstory Recent hstory The prmary motvaton s to provde accurate atomc collson data or scence and ndustry: Astrophyscs Fuson research Lghtng ndustry Medcal and materals applcatons Provde a rgorous oundaton or collson theory wth long-ranged (Coulomb) potentals. Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

5 Introducton Motvaton Introducton Nonrelatvstc CCC theory Motvaton Dstant hstory Recent hstory The prmary motvaton s to provde accurate atomc collson data or scence and ndustry: Astrophyscs Fuson research Lghtng ndustry Medcal and materals applcatons Provde a rgorous oundaton or collson theory wth long-ranged (Coulomb) potentals. Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

6 Introducton Dstant hstory Introducton Nonrelatvstc CCC theory Motvaton Dstant hstory Recent hstory Pror to the 1990s theory and experment generally dd not agree or: electron-hydrogen exctaton or onsaton, electron-helum exctaton or onsaton, sngle or double photoonsaton o helum. Consequently, we have been developng the convergent close-couplng (CCC) theory or electron/postron/photon/(ant)proton collsons wth atoms/ons/molecules that s applcable at all energes or the major exctaton and onsaton processes. Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

7 Introducton Dstant hstory Introducton Nonrelatvstc CCC theory Motvaton Dstant hstory Recent hstory Pror to the 1990s theory and experment generally dd not agree or: electron-hydrogen exctaton or onsaton, electron-helum exctaton or onsaton, sngle or double photoonsaton o helum. Consequently, we have been developng the convergent close-couplng (CCC) theory or electron/postron/photon/(ant)proton collsons wth atoms/ons/molecules that s applcable at all energes or the major exctaton and onsaton processes. Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

8 Introducton Recent hstory Introducton Nonrelatvstc CCC theory Motvaton Dstant hstory Recent hstory Pror to 2008, no satsactory mathematcal ormulaton n the case o long-range (Coulomb) potentals or postve-energy scatterng n Two-body problems Three-body problems Consequently, have developed a surace ntegral approach to scatterng theory that s vald or shortand long-range potentals, see Kadyrov et al. PRL, 101, (2008) and Annals o Physcs (2009). Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

9 Introducton Recent hstory Introducton Nonrelatvstc CCC theory Motvaton Dstant hstory Recent hstory Pror to 2008, no satsactory mathematcal ormulaton n the case o long-range (Coulomb) potentals or postve-energy scatterng n Two-body problems Three-body problems Consequently, have developed a surace ntegral approach to scatterng theory that s vald or shortand long-range potentals, see Kadyrov et al. PRL, 101, (2008) and Annals o Physcs (2009). Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

10 Introducton Nonrelatvstc CCC theory Nonrelatvstc CCC theory target structure and scatterng atomc target structure electron-atom scatterng convergence studes Structure: usng the Laguerre bass ξ (λ) nl (r) wrte: one-electron (H, L,..., Cs) states: φ (λ) nl (r) = Cnl n ξ(λ) n l (r) n two-electron (He, Be,..., Hg) states: φ (λ) nls (r 1, r 2 ) = n n nls ξ(λ) n l (r 1 )ξ (λ) n l (r 2 ). n,n C Coecents C are obtaned by dagonalsng the target (FCHF) Hamltonan φ (λ) H T φ (λ) = ε (λ) δ. (1) Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

11 Introducton Nonrelatvstc CCC theory atomc target structure electron-atom scatterng convergence studes Hydrogen l = 0 energes or λ = 1 Laguerre bases energy (ev) Laguerre bass sze N Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

12 Introducton Nonrelatvstc CCC theory atomc target structure electron-atom scatterng convergence studes φ (λ) ε (r) or N = 70, λ = 2 and φ (R 0) ε (r) or R 0 = l=0 ε=1ev CCC-B CCC-L 0.5 φ ε (r) radus (a.u.) Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

13 Introducton Nonrelatvstc CCC theory atomc target structure electron-atom scatterng convergence studes Scatterng: Electron-atom waveuncton s expanded as Ψ (+) A N n=1 φ (λ) n φ (λ) n ψ (+) AI N ψ (+). (2) Solve or T k φ (λ) V Ψ (+) at E = ε (λ) + ǫ k, k φ (λ) + N n=1 T φ (λ) k = k φ (λ) V φ (λ) k d 3 k k φ (λ) V φ (λ) n Have step-uncton behavour: k φ (λ) k kφ (λ) n T φ (λ) k E + 0 ε (λ) n ǫ k. (3) T φ (λ) k 0 or ε (λ) > ǫ k. Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

14 Introducton Nonrelatvstc CCC theory atomc target structure electron-atom scatterng convergence studes Scatterng: Electron-atom waveuncton s expanded as Ψ (+) A N n=1 φ (λ) n φ (λ) n ψ (+) AI N ψ (+). (2) Solve or T k φ (λ) V Ψ (+) at E = ε (λ) + ǫ k, k φ (λ) + N n=1 T φ (λ) k = k φ (λ) V φ (λ) k d 3 k k φ (λ) V φ (λ) n Have step-uncton behavour: k φ (λ) k kφ (λ) n T φ (λ) k E + 0 ε (λ) n ǫ k. (3) T φ (λ) k 0 or ε (λ) > ǫ k. Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

15 Introducton Nonrelatvstc CCC theory atomc target structure electron-atom scatterng convergence studes Scatterng: Electron-atom waveuncton s expanded as Ψ (+) A N n=1 φ (λ) n φ (λ) n ψ (+) AI N ψ (+). (2) Solve or T k φ (λ) V Ψ (+) at E = ε (λ) + ǫ k, k φ (λ) + N n=1 T φ (λ) k = k φ (λ) V φ (λ) k d 3 k k φ (λ) V φ (λ) n Have step-uncton behavour: k φ (λ) k kφ (λ) n T φ (λ) k E + 0 ε (λ) n ǫ k. (3) T φ (λ) k 0 or ε (λ) > ǫ k. Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

16 Introducton Nonrelatvstc CCC theory atomc target structure electron-atom scatterng convergence studes Dene scatterng ampltude va Φ ( ) H E Ψ (+) k φ ( ) I N ( H E)AI N ψ (+) where ε = ε (λ) = φ ( ) ensured φ ( ) [ Dscrete exctaton Ionsaton (N) (N) [ ε = q 2 φ (λ) ε < 0, φ ( ) k φ (λ) I N = φ ( ) φ (λ) = 1 (k ) = k φ (λ) T φ (λ) k, (q, k ) = q ( ) T φ (λ) k, φ (λ) φ (λ) ] : ] /2, wth φ( ) q ( ) : φ (λ) k φ (λ) T φ (λ) k,. Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

17 Introducton Nonrelatvstc CCC theory atomc target structure electron-atom scatterng convergence studes Dene scatterng ampltude va Φ ( ) H E Ψ (+) k φ ( ) I N ( H E)AI N ψ (+) where ε = ε (λ) = φ ( ) ensured φ ( ) [ Dscrete exctaton Ionsaton (N) (N) [ ε = q 2 φ (λ) ε < 0, φ ( ) k φ (λ) I N = φ ( ) φ (λ) = 1 (k ) = k φ (λ) T φ (λ) k, (q, k ) = q ( ) T φ (λ) k, φ (λ) φ (λ) ] : ] /2, wth φ( ) q ( ) : φ (λ) k φ (λ) T φ (λ) k,. Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

18 Introducton Nonrelatvstc CCC theory atomc target structure electron-atom scatterng convergence studes Dene scatterng ampltude va Φ ( ) H E Ψ (+) k φ ( ) I N ( H E)AI N ψ (+) where ε = ε (λ) = φ ( ) ensured φ ( ) [ Dscrete exctaton Ionsaton (N) (N) [ ε = q 2 φ (λ) ε < 0, φ ( ) k φ (λ) I N = φ ( ) φ (λ) = 1 (k ) = k φ (λ) T φ (λ) k, (q, k ) = q ( ) T φ (λ) k, φ (λ) φ (λ) ] : ] /2, wth φ( ) q ( ) : φ (λ) k φ (λ) T φ (λ) k,. Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

19 Introducton Nonrelatvstc CCC theory Nonrelatvstc CCC theory convergence studes atomc target structure electron-atom scatterng convergence studes e -H exctaton and total onsaton (S-wave model) s Poet 1978 CCC(30) CCC(10) CCC(5) s cross secton (πa 0 2 ) s 0.04 onzaton projectle energy (ev) Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

20 Introducton Nonrelatvstc CCC theory Nonrelatvstc CCC theory convergence studes atomc target structure electron-atom scatterng convergence studes electron-mpact exctaton at 3 Ry cross secton (a 0 2 ) trplet CCC(10) CCC(20) CCC(30) energy (Ry) -0.1 snglet CCC(10) CCC(20) CCC(30) Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

21 Introducton Nonrelatvstc CCC theory Nonrelatvstc CCC theory convergence studes atomc target structure electron-atom scatterng convergence studes cross secton (a 0 2 /Ry) electron-mpact onsaton dσ (e) at 3 Ry de trplet CCC(10) CCC(20) CCC(30) energy (Ry) snglet CCC(10) CCC(20) CCC(30) CCC( ) Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

22 Introducton Nonrelatvstc CCC theory Nonrelatvstc CCC theory convergence studes atomc target structure electron-atom scatterng convergence studes Can estmate true SDCS rom σ on cross secton (πa 0 2 /Ry) snglet FDM CCC estmate and dσ de (E/2) ε < k 2 /2 ε > k 2 / secondary energy ε (Ry) Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

23 Introducton Nonrelatvstc CCC theory electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen electron-mpact exctaton 54.4 ev e-h 2p angular correlaton parameters photon - e p + e - e - Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

24 Introducton Nonrelatvstc CCC theory electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen electron-mpact exctaton 54.4 ev e-h 2p angular correlaton parameters P scatterng angle (deg) P 2 Wegold, 1979 Wllams, 1980 Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

25 Introducton Nonrelatvstc CCC theory electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen electron-mpact exctaton 54.4 ev e-h 2p angular correlaton parameters P scatterng angle (deg) P 2 Wegold, 1979 Wllams, 1980 CCC, 1992 Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

26 Introducton Nonrelatvstc CCC theory electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen electron-mpact exctaton 54.4 ev e-h 2p angular correlaton parameters P scatterng angle (deg) P 2 Wegold, 1979 Wllams, 1980 CCC, 1992 Crowe, 1996 Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

27 Introducton Nonrelatvstc CCC theory electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen 21.8 ev e-l 2p angular correlaton parameters superelastc electrons 21.8 ev laser beam lthum beam ncdent electrons 20 ev laser polarzaton Igor Bray CCC method or electron-atom scatterng

28 Introducton Nonrelatvstc CCC theory electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen 21.8 ev e-l 2p angular correlaton parameters P scatterng angle (deg) P 2 Teubner, 1996 CCC, 1996 Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

29 Introducton Nonrelatvstc CCC theory electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen 20 ev e-na spn asymmetres and spn-resolved L A ex (3S) A ex (3P) NIST CCC CC L L scatterng angle (deg) Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

30 Introducton Nonrelatvstc CCC theory electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen electron-mpact onsaton e-h total onsaton cross secton σ = E 0 dεdσ de (ε). cross secton (10-17 cm 2 ) exp, JPB (1987) CCC, PRL (1993) CCC(S=0) CCC(S=1) exp, PRA(1985) total energy E (ev) Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

31 Introducton Nonrelatvstc CCC theory electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen 25 ev e-h sngly derental cross secton dσ de (ε) Shyn (1992) cross secton (10-17 cm 2 ev -1 ) CCC(93) CCC( ) secondary energy ε (ev) E Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

32 Introducton Nonrelatvstc CCC theory electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen 25 ev e-h doubly derental cross sectons d2 σ dedω (θ) E s =2eV E s =4eV cross secton (10-19 cm 2 sr -1 ev -1 ) E s =3eV scatterng angle (deg) E s =5.7eV Shyn (1992) Chlders (2004) ECS CCC Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

33 Introducton Nonrelatvstc CCC theory electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen 25 ev e-h E A = E B = 5.7 ev coplanar FDCS cross secton (10-19 cm 2 /sr 2 /ev) θ AB =80 o Roeder 1.4 CCC 1.2 ECS θ AB =100 o θ AB =120 o θ AB =150 o scatterng angle θ B Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

34 Introducton Nonrelatvstc CCC theory electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen ully derental cross secton (a.u.) e-na E A = E B ev coplanar ully derental Xsecs E A =E B =3eV Murray CCC E A =E B =5eV E A =E B =15eV 3 2 E A =E B =20eV E A =E B =10eV E A =E B =30eV scatterng angle θ A =-θ B (deg) Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

35 Introducton Nonrelatvstc CCC theory electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen e-h total onsaton cross secton σ = E 0 dεdσ de (ε) cross secton (10-17 cm 2 ) S Shah et al, JPB (1987) CCC, PRL (1993) total energy (ev) 2S Derance et al, JPB (1981) CCC, JPB (1997) total energy (ev) Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

36 Introducton Nonrelatvstc CCC theory electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen cross secton (10-17 cm 2 ) e-he total onsaton cross sectons S 10 exp, JPB(1984) CCC, PRA(1995) total energy (ev) S exp, JPB(1976) CCC, JPB(2003) CCC(S=0) CCC(S=1) exp, PRA(1989) total energy (ev) Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

37 Introducton Nonrelatvstc CCC theory electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen electron-mpact onsaton e-l + total onsaton cross sectons S Borovk et al, JPB (2008) CCC, JPB (2008) cross secton (10-18 cm 2 ) projectle energy (ev) S S Borovk et al, JPB (2008) CCC, JPB (2008) projectle energy (ev) Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

38 Introducton Nonrelatvstc CCC theory electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen proton-mpact on hydrogen Electron-transer cross secton, CC(1,1) model 10 2 Total Cross Secton (10-16 cm 2 ) Newman [26] Fte [27] Fte [28] Gealy [29] McClure [30] Bayeld [31] Wttkower [32] Hvelpland [33] Schwab [34] present CDW2S [12] Incdent Energy (ev/amu) Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

39 Introducton Nonrelatvstc CCC theory Concludng remarks electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen A general surace-ntegral approach to scatterng theory has been ormulated. There are (almost) no substantal dscrepances between CCC and experment or: electron-mpact exctaton or onsaton o quas oneand two-electron targets photon-mpact sngle and double onsaton o He Presently we are extendng CCC to postron collsons wth quas one- and two-electron targets mult-channel proton collsons more complcated targets, such as nert gases and molecules. Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

40 Introducton Nonrelatvstc CCC theory Concludng remarks electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen A general surace-ntegral approach to scatterng theory has been ormulated. There are (almost) no substantal dscrepances between CCC and experment or: electron-mpact exctaton or onsaton o quas oneand two-electron targets photon-mpact sngle and double onsaton o He Presently we are extendng CCC to postron collsons wth quas one- and two-electron targets mult-channel proton collsons more complcated targets, such as nert gases and molecules. Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng

41 Introducton Nonrelatvstc CCC theory Concludng remarks electron-mpact exctaton electron-mpact onsaton proton-mpact on hydrogen A general surace-ntegral approach to scatterng theory has been ormulated. There are (almost) no substantal dscrepances between CCC and experment or: electron-mpact exctaton or onsaton o quas oneand two-electron targets photon-mpact sngle and double onsaton o He Presently we are extendng CCC to postron collsons wth quas one- and two-electron targets mult-channel proton collsons more complcated targets, such as nert gases and molecules. Igor Bray <I.Bray@curtn.edu.au> CCC method or electron-atom scatterng