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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 <[email protected]> Recent CCC progress in atomic and molecular collision theory
Introduction
Convergent close-coupling theory
Recent applications of CCC
Igor Bray <[email protected]> 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 <[email protected]> Recent CCC progress in atomic and molecular collision theory
Introduction
Convergent close-coupling theory
Recent applications of CCC
MotivationIntroduction
The primary motivation is to provide accurate atomicand 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 <[email protected]> Recent CCC progress in atomic and molecular collision theory
Introduction
Convergent close-coupling theory
Recent applications of CCC
MotivationIntroduction
The primary motivation is to provide accurate atomicand 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 <[email protected]> Recent CCC progress in atomic and molecular collision theory
Introduction
Convergent close-coupling theory
Recent applications of CCC
ChallengesIntroduction
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 <[email protected]> Recent CCC progress in atomic and molecular collision theory
Introduction
Convergent close-coupling theory
Recent applications of CCC
History: computationalIntroduction
Prior to the 1990s theory and experiment generallydid 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 <[email protected]> Recent CCC progress in atomic and molecular collision theory
Introduction
Convergent close-coupling theory
Recent applications of CCC
History: computationalIntroduction
Prior to the 1990s theory and experiment generallydid 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 <[email protected]> Recent CCC progress in atomic and molecular collision theory
Introduction
Convergent close-coupling theory
Recent applications of CCC
History: formal theoryIntroduction
Prior to 2008, no satisfactory mathematicalformulation 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 validfor 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 <[email protected]> Recent CCC progress in atomic and molecular collision theory
Introduction
Convergent close-coupling theory
Recent applications of CCC
History: formal theoryIntroduction
Prior to 2008, no satisfactory mathematicalformulation 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 validfor 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 <[email protected]> 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 theorytarget 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 <[email protected]> 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 theorytarget 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 <[email protected]> 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 theorytarget 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 <[email protected]> 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 NℓH= 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
-100H(S) Ps(S) H(P) Ps(P) H(D) Ps(D) H(F)
Energy levels (eV)
Igor Bray <[email protected]> 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 |φnk〉〈kφn|T |φik i〉
E + i0 − εn − k2/2. (2)
ill-conditioned, but unitary (no double counting).
Igor Bray <[email protected]> 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 |φnk〉〈kφn|T |φik i〉
E + i0 − εn − k2/2. (2)
ill-conditioned, but unitary (no double counting).
Igor Bray <[email protected]> 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 |φnk〉〈kφn|T |φik i〉
E + i0 − εn − k2/2. (2)
ill-conditioned, but unitary (no double counting).
Igor Bray <[email protected]> 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
GLn(r
′, r ′′) =∑
∫
dkfL(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
∫
d3k〈k fφf |V′|φnk〉〈kφn|T |φik i〉. (4)
Works for kf = 0 for neutral and ionic targets.
Igor Bray <[email protected]> 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
GLn(r
′, r ′′) =∑
∫
dkfL(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
∫
d3k〈k fφf |V′|φnk〉〈kφn|T |φik i〉. (4)
Works for kf = 0 for neutral and ionic targets.
Igor Bray <[email protected]> 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
GLn(r
′, r ′′) =∑
∫
dkfL(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
∫
d3k〈k fφf |V′|φnk〉〈kφn|T |φik i〉. (4)
Works for kf = 0 for neutral and ionic targets.
Igor Bray <[email protected]> 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 <[email protected]> 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
0
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
Wehlitz0.000
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 <[email protected]> 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 spectrum2 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 <[email protected]> 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 spectrum2 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 <[email protected]> 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 spectrum2 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 <[email protected]> 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 spectrum2 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 <[email protected]> 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
one- and two-centre positron-hydrogen calculations
N N N Ps
NNPs
ε=0 ε=0 ε=0
ε=0
Nε=0
ε=0
H
H
H
i i
f f
σfi
(2)σfi
(1) H(1) (2) (2)
(2)
(2)
(1)
Igor Bray <[email protected]> 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
0 20 40 60 80 100
cross section (
π a02)
projectile energy (eV)
totalCCC(309, 0)CCC(202,202)
0.00
0.01
0.02
0.03
0.04
0 20 40 60 80 100
Ps(continuum)
Ps(bound)
electron loss
[Bailey et al. Phys. Rev. A 91, 012712 (2015)]
Igor Bray <[email protected]> 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) + p̄ → H̄ + e−
100
101
102
103
104
105
106
107
108
10-5 10-4 10-3 10-2 10-1 100 101
cros
s se
ctio
n (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 <[email protected]> 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) + p̄ → H̄ + 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 formationPs(n
i = 1)
Ps(ni = 2)
Ps(ni = 3)
Ps(ni = 4)
Ps(ni = 5)
[Kadyrov et al. Nature Communications 8, 1544 (2017)]
Igor Bray <[email protected]> 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)+p̄ →
{
H̄(1s) + e−
Ps(1s) + p̄
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 <[email protected]> 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)+p̄ →
{
H̄(2s) + e−
Ps(2s) + p̄
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 <[email protected]> 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
Cro
ss S
ection (
units o
f a
02)
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 <[email protected]> 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
0
2
4
6
8
10
12
14
16
18
20
10 100 1000
cross
sec
tio
n (
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.
0
2
4
6
8
10
12
10 100 1000cr
oss
sec
tio
n (
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 <[email protected]> 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
0
2
4
6
8
10
10 100
cro
ss s
ecti
on
(in
a.u
.)
incident energy (eV)
Ps-formationCCC(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 <[email protected]> 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
Cro
ss S
ection (
units o
f a
02)
Incident Energy (eV)
CCCFerch et al.van Wingerden et al.Hoffman et al.Deuring et al.JonesSubramanian and KumarNickel et al.Zhou et al.
[Zammit et al. Phys. Rev. Lett. 116, 233201 (2016)]Igor Bray <[email protected]> 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
0
1
2
3
4
50 100 150 200 250 300
Cro
ss S
ection (
units o
f a
02)
Incident Energy (eV)
CCCRMPS Gorfinkiel and TennysonTDCC Pindzola et al.Rapp and Englander-GoldenKrishnakumar and SrivastavaStraub et al.Lindsay and Mangan
[Zammit et al. Phys. Rev. Lett. 116, 233201 (2016)]Igor Bray <[email protected]> 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
cros
s se
ctio
n (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 <[email protected]> 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
cro
ss s
ecti
on
(1
0-1
6 c
m2)
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 <[email protected]> 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
sec
tion (
10
-16 c
m2)
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
sec
tion (
10
-16 c
m2)
projectile energy (keV)
McClure Bayfield Wittkower Hvelplund
0.0
0.5
1.0
1.5
2.0
101
102
103
cross
sec
tion (
10
-16 c
m2)
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
sec
tion (
10
-16 c
m2)
projectile energy (keV)
Shah 81 Shah 87 Kerby 95
[Abdurakhmanov et al. J. Phys. B 49, 115203 (2016)]
Igor Bray <[email protected]> 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
cro
ss s
ecti
on
(1
0-1
6 c
m2)
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
cro
ss s
ecti
on
(1
0-1
6 c
m2)
projectile energy (keV)
Knudsen Hvelplund Andersen
[Abdurakhmanov et al. PRL 111, 173201 (2013)]Igor Bray <[email protected]> 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
cro
ss s
ecti
on
(1
0-1
6 c
m2)
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 <[email protected]> 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 <[email protected]> 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 <[email protected]> Recent CCC progress in atomic and molecular collision theory