Recent CCC progress in atomic and molecular collision theory

Transcription

1 Recent CCC progress in atomic and molecular collision theory I. Abdurakhmanov, J. Bailey, A. Bray, I. Bray, D. Fursa, A. Kadyrov, C. Rawlins, J. Savage, and M. Zammit Curtin University, Perth, Western Australia Research School of Physics and Engineering, ANU Theoretical Division, Los Alamos National Laboratory, USA Vapour Shielding CRP, IAEA, Vienna, Mar., 2019

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3 Outline 1 2 target structure and scattering new approach to solving CCC equations 3 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles

4 Motivation The primary motivation is to provide accurate atomic and molecular collision data for science and industry Astrophysics Fusion research Lighting industry Neutral antimatter formation Medical: cancer imaging and therapy Provide a rigorous foundation for collision theory with long-ranged (Coulomb) potentials.

5 Motivation The primary motivation is to provide accurate atomic and molecular collision data for science and industry Astrophysics Fusion research Lighting industry Neutral antimatter formation Medical: cancer imaging and therapy Provide a rigorous foundation for collision theory with long-ranged (Coulomb) potentials.

6 Challenges Collisions between particles on the atomc scale are difficult to calculate: Governed by the Laws of Quantum Mechanics Charged particles interact at large distances Countably infinite discrete spectrum Uncountably infinite target continuum Can be multicentred (charge exchange, Ps-formation)

7 History: computational Prior to the 1990s theory and experiment generally did not agree for: electron-hydrogen excitation or ionization, electron-helium excitation or (single) ionization, single or double photoionization of helium. The convergent close-coupling (CCC) theory for electron, positron, photon, (anti)proton collisions with atoms or molecules is applicable at all energies for the major excitation and ionization processes.

8 History: computational Prior to the 1990s theory and experiment generally did not agree for: electron-hydrogen excitation or ionization, electron-helium excitation or (single) ionization, single or double photoionization of helium. The convergent close-coupling (CCC) theory for electron, positron, photon, (anti)proton collisions with atoms or molecules is applicable at all energies for the major excitation and ionization processes.

9 History: formal theory Prior to 2008, no satisfactory mathematical formulation in the case of long-ranged (Coulomb) potentials for positive-energy scattering in Two-body problems, Three-body problems. Surface integral approach to scattering theory is valid for short- and long-ranged potentials: Kadyrov et al. Phys. Rev. Lett., 101, (2008), Kadyrov et al. Annals of Physics, 324, 1516 (2009), Bray et al. Physics Reports, 520, 135 (2012).

10 History: formal theory Prior to 2008, no satisfactory mathematical formulation in the case of long-ranged (Coulomb) potentials for positive-energy scattering in Two-body problems, Three-body problems. Surface integral approach to scattering theory is valid for short- and long-ranged potentials: Kadyrov et al. Phys. Rev. Lett., 101, (2008), Kadyrov et al. Annals of Physics, 324, 1516 (2009), Bray et al. Physics Reports, 520, 135 (2012).

11 target structure and scattering new approach to solving CCC equations target structure For complete Laguerre basis ξ (λ) nl (r), target states: one-electron (H, Ps, Li,...,Cs, H + 2 ) φ (λ) nl (r) = N l n =1 C n nlξ (λ) n l (r), two-electron (He, Be,...,Hg, Ne,... Xe, H 2, H 2 O) φ (λ) nls (r 1, r 2 ) = C n n nls ξ (λ) n l (r 1 )ξ (λ) n l (r 2 ), n,n Diagonalise the target (FCHF) Hamiltonian φ (λ) f H T φ (λ) i = ε (λ) f δ fi.

12 target structure and scattering new approach to solving CCC equations target structure For complete Laguerre basis ξ (λ) nl (r), target states: one-electron (H, Ps, Li,...,Cs, H + 2 ) φ (λ) nl (r) = N l n =1 C n nlξ (λ) n l (r), two-electron (He, Be,...,Hg, Ne,... Xe, H 2, H 2 O) φ (λ) nls (r 1, r 2 ) = C n n nls ξ (λ) n l (r 1 )ξ (λ) n l (r 2 ), n,n Diagonalise the target (FCHF) Hamiltonian φ (λ) f H T φ (λ) i = ε (λ) f δ fi.

13 target structure and scattering new approach to solving CCC equations target structure For complete Laguerre basis ξ (λ) nl (r), target states: one-electron (H, Ps, Li,...,Cs, H + 2 ) φ (λ) nl (r) = N l n =1 C n nlξ (λ) n l (r), two-electron (He, Be,...,Hg, Ne,... Xe, H 2, H 2 O) φ (λ) nls (r 1, r 2 ) = C n n nls ξ (λ) n l (r 1 )ξ (λ) n l (r 2 ), n,n Diagonalise the target (FCHF) Hamiltonian φ (λ) f H T φ (λ) i = ε (λ) f δ fi.

14 target structure and scattering new approach to solving CCC equations e + -H energies for N l H = N l Ps = 12 l, for l Energy levels (ev) H(S) Ps(S) H(P) Ps(P) H(D) Ps(D) H(F) H(S)Ps(S)H(P)Ps(P)H(D)Ps(D)H(F)

15 two-center positron scattering target structure and scattering new approach to solving CCC equations Positron-target wavefunction is expanded as Ψ (+) i N T n=1 N Ps φ T nfni + T n=1 Solve for T fi k f φ f V Ψ (+) i at E = ε i +ǫ ki, φ Ps n F Ps ni. (1) k f φ f T φ i k i = k f φ f V φ i k i N T +N Ps + d 3 k k fφ f V φ n k kφ n T φ i k i. (2) E + i0 ε n k 2 /2 n=1 ill-conditioned, but unitary (no double counting).

16 two-center positron scattering target structure and scattering new approach to solving CCC equations Positron-target wavefunction is expanded as Ψ (+) i N T n=1 N Ps φ T nfni + T n=1 Solve for T fi k f φ f V Ψ (+) i at E = ε i +ǫ ki, φ Ps n F Ps ni. (1) k f φ f T φ i k i = k f φ f V φ i k i N T +N Ps + d 3 k k fφ f V φ n k kφ n T φ i k i. (2) E + i0 ε n k 2 /2 n=1 ill-conditioned, but unitary (no double counting).

17 two-center positron scattering target structure and scattering new approach to solving CCC equations Positron-target wavefunction is expanded as Ψ (+) i N T n=1 N Ps φ T nfni + T n=1 Solve for T fi k f φ f V Ψ (+) i at E = ε i +ǫ ki, φ Ps n F Ps ni. (1) k f φ f T φ i k i = k f φ f V φ i k i N T +N Ps + d 3 k k fφ f V φ n k kφ n T φ i k i. (2) E + i0 ε n k 2 /2 n=1 ill-conditioned, but unitary (no double counting).

18 target structure and scattering new approach to solving CCC equations new approach to solving CCC equations Use complete sets of states to isolate G L n(r, r ) = dk f L (kr )f L (kr ) E + i0 ǫ n ε k = π k n f L (k n r < )(g L (k n r > )+i f L (k n r > )). (3) Eq. (2) becomes [A. Bray et al. CPC (2017)] k f φ f T φ i k i = k f φ f V φ i k i N T +N Ps + d 3 k k f φ f V φ n k kφ n T φ i k i. (4) n=1 Works for k f = 0 for neutral and ionic targets.

19 target structure and scattering new approach to solving CCC equations new approach to solving CCC equations Use complete sets of states to isolate G L n(r, r ) = dk f L (kr )f L (kr ) E + i0 ǫ n ε k = π k n f L (k n r < )(g L (k n r > )+i f L (k n r > )). (3) Eq. (2) becomes [A. Bray et al. CPC (2017)] k f φ f T φ i k i = k f φ f V φ i k i N T +N Ps + d 3 k k f φ f V φ n k kφ n T φ i k i. (4) n=1 Works for k f = 0 for neutral and ionic targets.

20 target structure and scattering new approach to solving CCC equations new approach to solving CCC equations Use complete sets of states to isolate G L n(r, r ) = dk f L (kr )f L (kr ) E + i0 ǫ n ε k = π k n f L (k n r < )(g L (k n r > )+i f L (k n r > )). (3) Eq. (2) becomes [A. Bray et al. CPC (2017)] k f φ f T φ i k i = k f φ f V φ i k i N T +N Ps + d 3 k k f φ f V φ n k kφ n T φ i k i. (4) n=1 Works for k f = 0 for neutral and ionic targets.

21 e-he + 2s and 2p excitation target structure and scattering new approach to solving CCC equations cross section (a.u.) cross section (a.u.) s ngf agf singlet s ngf agf triplet p 2p ngf ngf agf agf electron energy above threshold (ev)

22 target structure and scattering new approach to solving CCC equations Helium single and double photoionisation cross section (Mb) σ σ 2 2 Samson ngf 1 ngf 0.03 agf agf Wehlitz σ ngf agf Doerner σ 3 ngf agf Wehlitz photoelectron energy above threshold (ev) [A. Bray, A. Kheifets, I. Bray, PRA 95, (2017)] [A. Kheifets, A. Bray, I. Bray, PRL 117, (2016)]

23 target structure and scattering new approach to solving CCC equations In positron scattering there are two centres: 1 target: discrete and continuous spectrum 2 positronium: discrete and continuous spectrum One-centre complete expansion: Ps-formation is within ionization σ (1) ion : e-loss boundary condition problem in the extended Ore gap Two-centre complete expansion: explicit Ps-formation σ (2) Ps and breakup σ (2) brk : e-loss ill-conditioned, but no double counting Internal consistency: above ionization threshold: σ (1) ion = σ(2) Ps +σ (2) brk below Ps-formation threshold: σ (1) ii = σ (2) ii

24 target structure and scattering new approach to solving CCC equations In positron scattering there are two centres: 1 target: discrete and continuous spectrum 2 positronium: discrete and continuous spectrum One-centre complete expansion: Ps-formation is within ionization σ (1) ion : e-loss boundary condition problem in the extended Ore gap Two-centre complete expansion: explicit Ps-formation σ (2) Ps and breakup σ (2) brk : e-loss ill-conditioned, but no double counting Internal consistency: above ionization threshold: σ (1) ion = σ(2) Ps +σ (2) brk below Ps-formation threshold: σ (1) ii = σ (2) ii

25 target structure and scattering new approach to solving CCC equations In positron scattering there are two centres: 1 target: discrete and continuous spectrum 2 positronium: discrete and continuous spectrum One-centre complete expansion: Ps-formation is within ionization σ (1) ion : e-loss boundary condition problem in the extended Ore gap Two-centre complete expansion: explicit Ps-formation σ (2) Ps and breakup σ (2) brk : e-loss ill-conditioned, but no double counting Internal consistency: above ionization threshold: σ (1) ion = σ(2) Ps +σ (2) brk below Ps-formation threshold: σ (1) ii = σ (2) ii

26 target structure and scattering new approach to solving CCC equations In positron scattering there are two centres: 1 target: discrete and continuous spectrum 2 positronium: discrete and continuous spectrum One-centre complete expansion: Ps-formation is within ionization σ (1) ion : e-loss boundary condition problem in the extended Ore gap Two-centre complete expansion: explicit Ps-formation σ (2) Ps and breakup σ (2) brk : e-loss ill-conditioned, but no double counting Internal consistency: above ionization threshold: σ (1) ion = σ(2) Ps +σ (2) brk below Ps-formation threshold: σ (1) ii = σ (2) ii

27 target structure and scattering new approach to solving CCC equations one- and two-centre positron-hydrogen calculations (1) (2) (2) (1) NH (2) NH N σ Ps fi i ε=0 σ fi i ε=0 ε=0 f f N ε=0 (2) H N ε=0 (1) H ε=0 (2) N Ps

28 target structure and scattering new approach to solving CCC equations cross section (π a 0 2 ) e + -H(1s) calculated with CCC(N H l max, N Ps l max ) for L = total CCC(30 9, 0) CCC(20 2,20 2 ) Ps(continuum) 0.2 Ps(bound) projectile energy (ev) electron loss [Bailey et al. Phys. Rev. A 91, (2015)]

29 antihydrogen formation antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles Ps(n 3)+ p H+e cross section (a.u.) (anti)hydrogen formation CCC Ps(1s) CCC Ps(2s) CCC Ps(2p) CCC Ps(3s) CCC Ps(3p) CCC Ps(3d) UBA Ps(2s) UBA Ps(2p) UBA Ps(1s) Variational Ps(1s) Merrison Ps energy ε (ev) [Kadyrov et al. Phys. Rev. Lett. 114, (2015)]

30 antihydrogen formation antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles Ps(n 5)+ p H+e cross section (a.u.) Ps(n) energy(ev) antih formation Ps(n i = 1) Ps(n i = 2) Ps(n i = 3) Ps(n i = 4) Ps(n i = 5) [Kadyrov et al. Nature Communications 8, 1544 (2017)]

31 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles antihydrogen formation and elastic scattering { H(1s)+e Ps(1s)+ p Ps(1s)+ p 10 4 cross section (a.u.) Ps(1s)+p 10-1 TT Ps(1s) L=0 H(1s) Ps(1s) energy (ev) [Fabrikant et al. Phys. Rev. A 94, (2016)]

32 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles antihydrogen formation and elastic scattering Ps(2s)+ p cross section (a.u.) L=0 { H(2s)+e Ps(2s)+ p Ps(2s) energy (ev) Ps(2s)+p TT Ps(2s) H(2s) [Fabrikant et al. Phys. Rev. A 94, (2016)]

33 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles positron scattering on molecular hydrogen e + -H 2 collisions: total cross section Cross Section (units of a 0 2 ) GTCS X 1 Σ g CCC l max =8 N=556 Hoffman et al. Machacek et al. ang. corrected Machacek et al. Charlton et al. Karwasz et al. Zecca et al Incident Energy (units of ev) [Zammit et al. Phys. Rev. A 87, (2013)]

34 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles positron scattering on molecular hydrogen e + -H 2 collisions: cross section (a.u.) GTCS CCC(14 2,2 1 ) CCC(10 8,0) Machacek et al. Hoffman et al. Charlton et al. Karwasz et al. Zecca et al. cross section (a.u.) electron-loss CCC(14 2,2 1 ) CCC(10 8,0) Moxom et al. Fromme et al incident energy (ev) incident energy (ev) [Utamuratov et al. Phys. Rev. A 92, (2015)]

35 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles positron scattering on molecular hydrogen e + -H 2 collisions: Ps-formation cross section (in a.u.) Ps-formation CCC(14 1,1) CCC(14 1,3) CCC(14 2,3) Biswas et al. Zhou et al. Fromme et al. Machacek et al incident energy (ev) [Utamuratov et al. Phys. Rev. A 92, (2015)]

36 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles electron scattering on molecular hydrogen e -H 2 collisions: total cross section 100 Cross Section (units of a 0 2 ) 10 CCC Ferch et al. van Wingerden et al. Hoffman et al. Deuring et al. Jones Subramanian and Kumar Nickel et al. Zhou et al Incident Energy (ev) [Zammit et al. Phys. Rev. Lett. 116, (2016)]

37 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles electron scattering on molecular hydrogen e -H 2 collisions: total ionization 4 Cross Section (units of a 0 2 ) CCC RMPS Gorfinkiel and Tennyson TDCC Pindzola et al. Rapp and Englander-Golden Krishnakumar and Srivastava Straub et al. Lindsay and Mangan Incident Energy (ev) [Zammit et al. Phys. Rev. Lett. 116, (2016)]

38 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles electron scattering on molecular hydrogen e -H 2 collisions: b 3 Σ + u excitation b 3 Σ u + Nishimura and Danjo (1986) Khakoo and Segura (1994) MCCC (2017) experiment (2018) cross section (a.u.) incident energy (ev) [Zawadski et al. PRA 98, R (2018)]

39 proton scattering on hydrogen p + -H collisions: cross section (10-16 cm 2 ) antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles experiment: e-loss QM-CCC(50 8, 0): e-loss QM-CCC: e-loss QM-CCC: ionization QM-CCC: e-capture projectile energy (kev) [Abdurakhmanov et al. J. Phys. B 49, (2016)]

40 proton scattering on hydrogen antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles p + -H collisions: capture and ionization cross section (10-16 cm 2 ) McClure 10-4 Bayfield Wittkower Hvelplund projectile energy (kev) electron capture Winter Kolakowska QM-CCC cross section (10-16 cm 2 ) Shah 81 Shah 87 Kerby projectile energy (kev) ionization Toshima Winter Sidky Ovchinnikov Kolakowska QM-CCC [Abdurakhmanov et al. J. Phys. B 49, (2016)]

41 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles antiproton scattering on molecular hydrogen p -H 2 collisions: total ionization cross section (10-16 cm 2 ) Knudsen Hvelplund Andersen Lu.. hr I Lu.. hr II Lee I Lee II Ermolaev CCC projectile energy (kev) [Abdurakhmanov et al. PRL 111, (2013)]

42 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles antiproton scattering on molecular hydrogen p -H 2 collisions: comparison with H and He cross section (10-16 cm 2 ) Knudsen: H Hvelplund: He Knudsen: He Hvelplund: H 2 Knudsen: H 2 H He H projectile velocity (a.u.) [Abdurakhmanov et al. PRL 111, (2013)]

43 Concluding remarks antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles CCC method has been implemented for scattering of electrons, positrons, photons, protons and antiprotons on quasi one- and two-electron targets, as well as inert gases. Two-center problems have self-consistency checks To-do list Ps-H, Ps-He +, Ps-H + 2 Ps-Ne +, and other inert gas ions H-He +, H-H + 2, H-Ne+, and other inert gas ions X 2, H 2 O and other molecular targets

44 Concluding remarks antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles CCC method has been implemented for scattering of electrons, positrons, photons, protons and antiprotons on quasi one- and two-electron targets, as well as inert gases. Two-center problems have self-consistency checks To-do list Ps-H, Ps-He +, Ps-H + 2 Ps-Ne +, and other inert gas ions H-He +, H-H + 2, H-Ne+, and other inert gas ions X 2, H 2 O and other molecular targets