Recent CCC progress in atomic and molecular collision theory I. - PowerPoint PPT Presentation

Introduction Convergent close-coupling theory Recent applications of CCC 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 Igor Bray <I.Bray@curtin.edu.au> Recent CCC progress in atomic and molecular collision theory

Introduction Convergent close-coupling theory Recent applications of CCC Igor Bray <I.Bray@curtin.edu.au> Recent CCC progress in atomic and molecular collision theory

Introduction Convergent close-coupling theory Recent applications of CCC Outline Introduction 1 Convergent close-coupling theory 2 target structure and scattering new approach to solving CCC equations internal consistency Recent applications of CCC 3 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles Igor Bray <I.Bray@curtin.edu.au> Recent CCC progress in atomic and molecular collision theory

Introduction Convergent close-coupling theory Recent applications of CCC Motivation Introduction 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. Igor Bray <I.Bray@curtin.edu.au> Recent CCC progress in atomic and molecular collision theory

Introduction Convergent close-coupling theory Recent applications of CCC Motivation Introduction 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. Igor Bray <I.Bray@curtin.edu.au> Recent CCC progress in atomic and molecular collision theory

Introduction Convergent close-coupling theory Recent applications of CCC Challenges Introduction 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) Igor Bray <I.Bray@curtin.edu.au> Recent CCC progress in atomic and molecular collision theory

Introduction Convergent close-coupling theory Recent applications of CCC History: computational Introduction 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. Igor Bray <I.Bray@curtin.edu.au> Recent CCC progress in atomic and molecular collision theory

Introduction Convergent close-coupling theory Recent applications of CCC History: computational Introduction 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. Igor Bray <I.Bray@curtin.edu.au> Recent CCC progress in atomic and molecular collision theory

Introduction Convergent close-coupling theory Recent applications of CCC History: formal theory Introduction 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 , 230405 (2008), Kadyrov et al. Annals of Physics, 324 , 1516 (2009), Bray et al. Physics Reports, 520 , 135 (2012). Igor Bray <I.Bray@curtin.edu.au> Recent CCC progress in atomic and molecular collision theory

Introduction Convergent close-coupling theory Recent applications of CCC History: formal theory Introduction 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 , 230405 (2008), Kadyrov et al. Annals of Physics, 324 , 1516 (2009), Bray et al. Physics Reports, 520 , 135 (2012). Igor Bray <I.Bray@curtin.edu.au> Recent CCC progress in atomic and molecular collision theory

Introduction target structure and scattering Convergent close-coupling theory new approach to solving CCC equations Recent applications of CCC internal consistency Convergent close-coupling theory target structure For complete Laguerre basis ξ ( λ ) nl ( r ) , target states: “one-electron” (H, Ps, Li,. . . ,Cs, H + 2 ) N l φ ( λ ) � C n ′ nl ξ ( λ ) nl ( r ) = n ′ l ( r ) , n ′ = 1 “two-electron” (He, Be,. . . ,Hg, Ne, . . . Xe, H 2 , H 2 O) φ ( λ ) � C n ′ n ′′ nls ξ ( λ ) n ′ l ′ ( r 1 ) ξ ( λ ) nls ( r 1 , r 2 ) = n ′′ l ′′ ( r 2 ) , n ′ , n ′′ Diagonalise the target (FCHF) Hamiltonian � φ ( λ ) | H T | φ ( λ ) � = ε ( λ ) δ fi . f i f Igor Bray <I.Bray@curtin.edu.au> Recent CCC progress in atomic and molecular collision theory

Introduction target structure and scattering Convergent close-coupling theory new approach to solving CCC equations Recent applications of CCC internal consistency Convergent close-coupling theory target structure For complete Laguerre basis ξ ( λ ) nl ( r ) , target states: “one-electron” (H, Ps, Li,. . . ,Cs, H + 2 ) N l φ ( λ ) � C n ′ nl ξ ( λ ) nl ( r ) = n ′ l ( r ) , n ′ = 1 “two-electron” (He, Be,. . . ,Hg, Ne, . . . Xe, H 2 , H 2 O) φ ( λ ) � C n ′ n ′′ nls ξ ( λ ) n ′ l ′ ( r 1 ) ξ ( λ ) nls ( r 1 , r 2 ) = n ′′ l ′′ ( r 2 ) , n ′ , n ′′ Diagonalise the target (FCHF) Hamiltonian � φ ( λ ) | H T | φ ( λ ) � = ε ( λ ) δ fi . f i f Igor Bray <I.Bray@curtin.edu.au> Recent CCC progress in atomic and molecular collision theory

Introduction target structure and scattering Convergent close-coupling theory new approach to solving CCC equations Recent applications of CCC internal consistency Convergent close-coupling theory target structure For complete Laguerre basis ξ ( λ ) nl ( r ) , target states: “one-electron” (H, Ps, Li,. . . ,Cs, H + 2 ) N l φ ( λ ) � C n ′ nl ξ ( λ ) nl ( r ) = n ′ l ( r ) , n ′ = 1 “two-electron” (He, Be,. . . ,Hg, Ne, . . . Xe, H 2 , H 2 O) φ ( λ ) � C n ′ n ′′ nls ξ ( λ ) n ′ l ′ ( r 1 ) ξ ( λ ) nls ( r 1 , r 2 ) = n ′′ l ′′ ( r 2 ) , n ′ , n ′′ Diagonalise the target (FCHF) Hamiltonian � φ ( λ ) | H T | φ ( λ ) � = ε ( λ ) δ fi . f i f Igor Bray <I.Bray@curtin.edu.au> Recent CCC progress in atomic and molecular collision theory

Introduction target structure and scattering Convergent close-coupling theory new approach to solving CCC equations Recent applications of CCC internal consistency e + -H energies for N ℓ H = N ℓ Ps = 12 − ℓ , for ℓ ≤ 3 1000 100 10 Energy levels (eV) 1 0.1 H(S) Ps(S) H(P) Ps(P) H(D) Ps(D) H(F) -0.01 -0.1 -1 -10 -100 H(S) Ps(S) H(P) Ps(P) H(D) Ps(D) H(F) Igor Bray <I.Bray@curtin.edu.au> Recent CCC progress in atomic and molecular collision theory

Introduction target structure and scattering Convergent close-coupling theory new approach to solving CCC equations Recent applications of CCC internal consistency two-center positron scattering Positron-target wavefunction is expanded as N T N Ps | Ψ (+) � � | φ T n F T | φ Ps n F Ps � ≈ ni � + ni � . (1) i n = 1 n = 1 Solve for T fi ≡ � k f φ f | V | Ψ (+) � at E = ε i + ǫ k i , i � 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 �� k φ n | T | φ i k i � � + . (2) E + i 0 − ε n − k 2 / 2 n = 1 ill-conditioned, but unitary (no double counting). Igor Bray <I.Bray@curtin.edu.au> Recent CCC progress in atomic and molecular collision theory