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

1

Introduction

2

Convergent close-coupling theory target structure and scattering new approach to solving CCC equations internal consistency

3

Recent applications of CCC 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 Convergent close-coupling theory Recent applications of CCC target structure and scattering new approach to solving CCC equations 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 )

φ(λ)

nl (r) = Nl

• n′=1

Cn′

nl ξ(λ) n′l (r),

“two-electron” (He, Be,. . . ,Hg, Ne, . . . Xe, H2, H2O) φ(λ)

nls (r1, r2) =

• n′,n′′

Cn′n′′

nls ξ(λ) n′l′(r1)ξ(λ) n′′l′′(r2),

Diagonalise the target (FCHF) Hamiltonian φ(λ)

f

|HT|φ(λ)

i

= ε(λ)

f

δfi.

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 target structure and scattering new approach to solving CCC equations 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 )

φ(λ)

nl (r) = Nl

• n′=1

Cn′

nl ξ(λ) n′l (r),

“two-electron” (He, Be,. . . ,Hg, Ne, . . . Xe, H2, H2O) φ(λ)

nls (r1, r2) =

• n′,n′′

Cn′n′′

nls ξ(λ) n′l′(r1)ξ(λ) n′′l′′(r2),

Diagonalise the target (FCHF) Hamiltonian φ(λ)

f

|HT|φ(λ)

i

= ε(λ)

f

δfi.

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 target structure and scattering new approach to solving CCC equations 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 )

φ(λ)

nl (r) = Nl

• n′=1

Cn′

nl ξ(λ) n′l (r),

“two-electron” (He, Be,. . . ,Hg, Ne, . . . Xe, H2, H2O) φ(λ)

nls (r1, r2) =

• n′,n′′

Cn′n′′

nls ξ(λ) n′l′(r1)ξ(λ) n′′l′′(r2),

Diagonalise the target (FCHF) Hamiltonian φ(λ)

f

|HT|φ(λ)

i

= ε(λ)

f

δfi.

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 target structure and scattering new approach to solving CCC equations internal consistency

e+-H energies for Nℓ

H = Nℓ Ps = 12 − ℓ, for ℓ ≤ 3

0.1 1 10 100 1000 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) Energy levels (eV) 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 target structure and scattering new approach to solving CCC equations internal consistency

two-center positron scattering

Positron-target wavefunction is expanded as |Ψ(+)

i

≈

NT

• n=1

|φT

nF T ni + NPs

• n=1

|φPs

n F Ps ni .

(1) Solve for Tfi ≡ k fφf|V|Ψ(+)

i

at E = εi + ǫki, k fφf|T|φik i = k fφf|V|φik i +

NT+NPs

• n=1
• d3k k fφf|V|φnkkφn|T|φik i

E + i0 − εn − k2/2 . (2) ill-conditioned, but unitary (no double counting).

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 target structure and scattering new approach to solving CCC equations internal consistency

two-center positron scattering

Positron-target wavefunction is expanded as |Ψ(+)

i

≈

NT

• n=1

|φT

nF T ni + NPs

• n=1

|φPs

n F Ps ni .

(1) Solve for Tfi ≡ k fφf|V|Ψ(+)

i

at E = εi + ǫki, k fφf|T|φik i = k fφf|V|φik i +

NT+NPs

• n=1
• d3k k fφf|V|φnkkφn|T|φik i

E + i0 − εn − k2/2 . (2) ill-conditioned, but unitary (no double counting).

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 target structure and scattering new approach to solving CCC equations internal consistency

two-center positron scattering

Positron-target wavefunction is expanded as |Ψ(+)

i

≈

NT

• n=1

|φT

nF T ni + NPs

• n=1

|φPs

n F Ps ni .

(1) Solve for Tfi ≡ k fφf|V|Ψ(+)

i

at E = εi + ǫki, k fφf|T|φik i = k fφf|V|φik i +

NT+NPs

• n=1
• d3k k fφf|V|φnkkφn|T|φik i

E + i0 − εn − k2/2 . (2) ill-conditioned, but unitary (no double counting).

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 target structure and scattering new approach to solving CCC equations internal consistency

new approach to solving CCC equations

Use complete sets of states to isolate GL

n(r ′, r ′′) =

• dk

fL(kr ′)fL(kr ′′) E + i0 − ǫn − εk = − π kn fL(knr<) (gL(knr>) + i fL(knr>)) . (3)

• Eq. (2) becomes [A. Bray et al. CPC 212 55 (2017)]

k fφf|T|φik i = k fφf|V|φik i +

NT+NPs

• n=1
• d3kk fφf|V ′|φnkkφn|T|φik i.

(4) Works for kf = 0 for neutral and ionic targets.

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 target structure and scattering new approach to solving CCC equations internal consistency

new approach to solving CCC equations

Use complete sets of states to isolate GL

n(r ′, r ′′) =

• dk

fL(kr ′)fL(kr ′′) E + i0 − ǫn − εk = − π kn fL(knr<) (gL(knr>) + i fL(knr>)) . (3)

• Eq. (2) becomes [A. Bray et al. CPC 212 55 (2017)]

k fφf|T|φik i = k fφf|V|φik i +

NT+NPs

• n=1
• d3kk fφf|V ′|φnkkφn|T|φik i.

(4) Works for kf = 0 for neutral and ionic targets.

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 target structure and scattering new approach to solving CCC equations internal consistency

new approach to solving CCC equations

Use complete sets of states to isolate GL

n(r ′, r ′′) =

• dk

fL(kr ′)fL(kr ′′) E + i0 − ǫn − εk = − π kn fL(knr<) (gL(knr>) + i fL(knr>)) . (3)

• Eq. (2) becomes [A. Bray et al. CPC 212 55 (2017)]

k fφf|T|φik i = k fφf|V|φik i +

NT+NPs

• n=1
• d3kk fφf|V ′|φnkkφn|T|φik i.

(4) Works for kf = 0 for neutral and ionic targets.

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 target structure and scattering new approach to solving CCC equations internal consistency

e-He+ 2s and 2p excitation

0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300 0.0350 0.0400 10-4 10-3 10-2 10-1 10+0 10+1 10+2 cross section (a.u.) → singlet 2s nGF aGF 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 0.0010 10-4 10-3 10-2 10-1 10+0 10+1 10+2 → triplet 2s nGF aGF 0.0000 0.0100 0.0200 0.0300 0.0400 0.0500 0.0600 10-4 10-3 10-2 10-1 10+0 10+1 10+2 cross section (a.u.) electron energy above threshold (eV) → 2p nGF aGF 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 10-4 10-3 10-2 10-1 10+0 10+1 10+2 → 2p nGF aGF

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 target structure and scattering new approach to solving CCC equations internal consistency

Helium single and double photoionisation

1 2 3 4 5 6 7 8 10-4 10-3 10-2 10-1 10+0 10+1 10+2 10+3 → σ1 Samson nGF aGF 0.00 0.03 0.06 0.09 0.12 0.15 0.18 10-4 10-3 10-2 10-1 10+0 10+1 10+2 10+3 → σ2 nGF aGF Wehlitz 0.00 0.01 0.02 0.03 10-4 10-3 10-2 10-1 10+0 10+1 10+2 10+3 cross section (Mb) photoelectron energy above threshold (eV) → σ3 nGF aGF Wehlitz 0.000 0.002 0.004 0.006 0.008 0.010 10+0 10+1 10+2 10+3 σ2+ nGF aGF Doerner

[A. Bray, A. Kheifets, I. Bray, PRA 95, 053405 (2017)] [A. Kheifets, A. Bray, I. Bray, PRL 117, 143202 (2016)]

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 target structure and scattering new approach to solving CCC equations internal consistency

internal consistency

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

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 target structure and scattering new approach to solving CCC equations internal consistency

internal consistency

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

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 target structure and scattering new approach to solving CCC equations internal consistency

internal consistency

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

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 target structure and scattering new approach to solving CCC equations internal consistency

internal consistency

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

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 target structure and scattering new approach to solving CCC equations internal consistency

• ne- and two-centre positron-hydrogen calculations

N N N Ps N NPs

ε=0 ε=0 ε=0 ε=0

N

ε=0 ε=0

H H H

i i f f σfi

(2)

σfi

(1) H

(1) (2) (2) (2) (2) (1)

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 target structure and scattering new approach to solving CCC equations internal consistency

e+-H(1s) calculated with CCC(NH

lmax, NPs lmax) for L = 0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 20 40 60 80 100 cross section (π a0

2)

projectile energy (eV) total CCC(309, 0) CCC(202,202) 0.00 0.01 0.02 0.03 0.04 20 40 60 80 100 Ps(continuum) Ps(bound) electron loss

[Bailey et al. Phys. Rev. A 91, 012712 (2015)]

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 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles

antihydrogen formation

Ps(n ≤ 3) + ¯ p → ¯ H + e−

100 101 102 103 104 105 106 107 108 10-5 10-4 10-3 10-2 10-1 100 101 cross section (a.u.) Ps energy ε (eV) (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 1997

[Kadyrov et al. Phys. Rev. Lett. 114, 183201 (2015)]

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 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles

antihydrogen formation

Ps(n ≤ 5) + ¯ p → ¯ H + e−

100 101 102 103 104 105 106 107 108 109 10-5 10-4 10-3 10-2 10-1 10+0 cross section (a.u.) Ps(n) energy(eV) antiH formation Ps(ni = 1) Ps(ni = 2) Ps(ni = 3) Ps(ni = 4) Ps(ni = 5)

[Kadyrov et al. Nature Communications 8, 1544 (2017)]

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 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles

antihydrogen formation and elastic scattering

Ps(1s)+¯ p →

• ¯

H(1s) + e− Ps(1s) + ¯ p

10-2 10-1 100 101 102 103 104 10-5 10-4 10-3 10-2 10-1 10+0 cross section (a.u.) Ps(1s) energy (eV) L=0 Ps(1s)+p TT Ps(1s) H(1s)

[Fabrikant et al. Phys. Rev. A 94, 012701 (2016)]

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 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles

antihydrogen formation and elastic scattering

Ps(2s)+¯ p →

• ¯

H(2s) + e− Ps(2s) + ¯ p

100 101 102 103 104 105 106 107 10-5 10-4 10-3 10-2 10-1 10+0 cross section (a.u.) Ps(2s) energy (eV) L=0 Ps(2s)+p TT Ps(2s) H(2s)

[Fabrikant et al. Phys. Rev. A 94, 012701 (2016)]

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 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles

positron scattering on molecular hydrogen

e+-H2 collisions: total cross section

1 10 100 0.1 1 10 100 1000 Cross Section (units of a0

2)

Incident Energy (units of eV) GTCS X1 Σg CCC lmax=8 N=556 Hoffman et al. Machacek et al. ang. corrected Machacek et al. Charlton et al. Karwasz et al. Zecca et al.

[Zammit et al. Phys. Rev. A 87, 020701 (2013)]

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 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles

positron scattering on molecular hydrogen

e+-H2 collisions: internal consistency

2 4 6 8 10 12 14 16 18 20 10 100 1000 cross section (a.u.) incident energy (eV) GTCS CCC(142,21) CCC(108,0) Machacek et al. Hoffman et al. Charlton et al. Karwasz et al. Zecca et al. 2 4 6 8 10 12 10 100 1000 cross section (a.u.) incident energy (eV) electron-loss CCC(142,21) CCC(108,0) Moxom et al. Fromme et al.

[Utamuratov et al. Phys. Rev. A 92, 032707 (2015)]

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 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles

positron scattering on molecular hydrogen

e+-H2 collisions: Ps-formation

2 4 6 8 10 10 100 cross section (in a.u.) incident energy (eV) Ps-formation CCC(141,1) CCC(141,3) CCC(142,3) Biswas et al. Zhou et al. Fromme et al. Machacek et al.

[Utamuratov et al. Phys. Rev. A 92, 032707 (2015)]

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 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles

electron scattering on molecular hydrogen

e−-H2 collisions: total cross section

1 10 100 0.1 1 10 100 Cross Section (units of a0

2)

Incident Energy (eV) CCC Ferch et al. van Wingerden et al. Hoffman et al. Deuring et al. Jones Subramanian and Kumar Nickel et al. Zhou et al.

[Zammit et al. Phys. Rev. Lett. 116, 233201 (2016)]

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 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles

electron scattering on molecular hydrogen

e−-H2 collisions: total ionization

1 2 3 4 50 100 150 200 250 300 Cross Section (units of a0

2)

Incident Energy (eV) CCC RMPS Gorfinkiel and Tennyson TDCC Pindzola et al. Rapp and Englander-Golden Krishnakumar and Srivastava Straub et al. Lindsay and Mangan

[Zammit et al. Phys. Rev. Lett. 116, 233201 (2016)]

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 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles

electron scattering on molecular hydrogen

e−-H2 collisions: b3Σ+

u excitation

0.0 0.5 1.0 1.5 2.0 2.5 3.0 10 15 20 25 cross section (a.u.) incident energy (eV) b 3Σu

+

Nishimura and Danjo (1986) Khakoo and Segura (1994) MCCC (2017) experiment (2018)

[Zawadski et al. PRA 98, 050702R (2018)]

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 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles

proton scattering on hydrogen

p+-H collisions: internal consistency

0.0 2.0 4.0 6.0 8.0 10.0 101 102 103 cross section (10-16 cm2) projectile energy (keV) experiment: e-loss QM-CCC(508, 0): e-loss QM-CCC: e-loss QM-CCC: ionization QM-CCC: e-capture

[Abdurakhmanov et al. J. Phys. B 49, 115203 (2016)]

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 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles

proton scattering on hydrogen

p+-H collisions: capture and ionization

10-5 10-4 10-3 10-2 10-1 100 101 101 102 103 cross section (10-16 cm2) projectile energy (keV) electron capture Winter Kolakowska QM-CCC 10-5 10-4 10-3 10-2 10-1 100 101 101 102 103 cross section (10-16 cm2) projectile energy (keV) McClure Bayfield Wittkower Hvelplund 0.0 0.5 1.0 1.5 2.0 101 102 103 cross section (10-16 cm2) projectile energy (keV) ionization Toshima Winter Sidky Ovchinnikov Kolakowska QM-CCC 0.0 0.5 1.0 1.5 2.0 101 102 103 cross section (10-16 cm2) projectile energy (keV) Shah 81 Shah 87 Kerby 95

[Abdurakhmanov et al. J. Phys. B 49, 115203 (2016)]

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 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles

antiproton scattering on molecular hydrogen

p−-H2 collisions: total ionization

0.0 0.5 1.0 1.5 2.0 2.5 1 10 100 1000 cross section (10-16 cm2) projectile energy (keV) Lu ..hr I Lu ..hr II Lee I Lee II Ermolaev CCC 0.0 0.5 1.0 1.5 2.0 2.5 1 10 100 1000 cross section (10-16 cm2) projectile energy (keV) Knudsen Hvelplund Andersen

[Abdurakhmanov et al. PRL 111, 173201 (2013)]

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 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles

antiproton scattering on molecular hydrogen

p−-H2 collisions: comparison with H and He

0.0 0.5 1.0 1.5 2.0 0.2 0.4 0.6 0.8 1 cross section (10-16 cm2) projectile velocity (a.u.) Knudsen: H Hvelplund: He Knudsen: He Hvelplund: H2 Knudsen: H2 H H2 He

[Abdurakhmanov et al. PRL 111, 173201 (2013)]

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 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles

Concluding remarks

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

X2, H2O and other molecular targets

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 antihydrogen formation positron and electron scattering on molecular hydrogen heavy projectiles

Concluding remarks

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

X2, H2O and other molecular targets

Igor Bray <I.Bray@curtin.edu.au> Recent CCC progress in atomic and molecular collision theory