Convergent Close-Coupling approach to atomic and molecular ... · Convergent Close-Coupling theory...

IntroductionConvergent Close-Coupling theory

Comparison with experimentConcluding remarks

Convergent Close-Coupling approachto atomic and molecular collisions

Igor BrayDmitry Fursa, Alisher Kadyrov, Andris Stelbovics

and many students

Head, Physics, Astronomy and Medical Imaging Science,Curtin University, Perth, Western Australia

Tokyo Metropolitan University, September, 2014

Igor Bray <[email protected]> CCC Approach to collisions






Outline1 Introduction

MotivationApplicationsDistant historyRecent history

2 Convergent Close-Coupling theoryTarget structureScattering

3 Comparison with experimente−-H ionisatione−-He-like atom/ion ionisatione+-H2

Photoionisation4 Concluding remarks





Motivation

The primary motivation is to provide accurate atomicand molecular collision data for science and industryCollisions on the atomic scale are difficult tocalculate:

Governed by the Laws of Quantum MechanicsCharged particles interact at infinite distancesCountably infinite discrete spectrumUncountably infinite target continuumCan be multicentred (e.g. charge exchange)

Solved by the Convergent Close-Coupling (CCC)method


http://atom.curtin.edu.au/igor/atomlab/index.html




Motivation









Motivation









Applications

Astrophysics

Fusion research

NeutralAntimattercreation

Lighting industry

Medical andmaterialsapplications





Applications

Astrophysics

Fusion research


Lighting industry






Applications

Astrophysics

Fusion research


Lighting industry






Applications

Astrophysics

Fusion research


Lighting industry






Applications

Astrophysics

Fusion research


Lighting industry






Distant history

Prior to the 1990s theory and experiment generallydid not agree for:

electron-hydrogen excitation or ionisation,electron-helium excitation or ionisation,single or double photoionisation of helium.

The convergent close-coupling (CCC) theory forelectron/positron/photon/(anti)proton collisions withatoms/ions/molecules

based on a complete L2 expansion of the totalwavefunction in the Schrödinger or Dirac equationapplicable at all energies for elastic, excitation,ionisation and charge exchange processes





Distant history

Prior to the 1990s theory and experiment generallydid not agree for:

electron-hydrogen excitation or ionisation,electron-helium excitation or ionisation,single or double photoionisation of helium.

The convergent close-coupling (CCC) theory forelectron/positron/photon/(anti)proton collisions withatoms/ions/molecules

based on a complete L2 expansion of the totalwavefunction in the Schrödinger or Dirac equationapplicable at all energies for elastic, excitation,ionisation and charge exchange processes





Recent history: formal theory

Prior to 2008, no satisfactory mathematicalformulation in the case of long-range (Coulomb)potentials for positive-energy scattering in

Two-body problemsThree-body problems

Developed a surface integral approach to scatteringtheory that is valid for short- and long-rangepotentials

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)





Recent history: formal theory

Prior to 2008, no satisfactory mathematicalformulation in the case of long-range (Coulomb)potentials for positive-energy scattering in

Two-body problemsThree-body problems

Developed a surface integral approach to scatteringtheory that is valid for short- and long-rangepotentials

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)





Recent history: computational

Extended the CCC method to

fully relativistic formalism

multi-centre problems such as positron or protonscattering

heavy projectiles such as (anti)protons and barenuclei

molecular targets: H2 and H+2 thus far. Working on

Ne-like treatment of H2O.





































Target structureScattering

Convergent Close-Coupling theoryTarget structure

Using the complete Laguerre basis ξ(λ)nl (r) write:

“one-electron” (H, Ps, He+, Li, Na, H+2 , . . . ) states:

φ(λ)nl (r) =

∑n′

Cn′

nl ξ(λ)n′l (r)

“two-electron” (He, N5+, Be, Hg, H2, . . . ) states:φ

(λ)nls (r1, r2) =

∑n′,n′′

Cn′n′′

nls ξ(λ)n′l ′(r1)ξ

(λ)n′′l ′′(r2).

Coefficients C are obtained by diagonalising thetarget (FCHF) Hamiltonian

〈φ(λ)f |HT|φ

(λ)i 〉 = ε

(λ)f δfi ; lim

N→∞

N∑n=1

|φ(λ)n 〉〈φ

(λ)n | = IT.





Convergent Close-Coupling theoryTarget structure

Using the complete Laguerre basis ξ(λ)nl (r) write:

“one-electron” (H, Ps, He+, Li, Na, H+2 , . . . ) states:

φ(λ)nl (r) =

∑n′

Cn′

nl ξ(λ)n′l (r)

“two-electron” (He, N5+, Be, Hg, H2, . . . ) states:φ

(λ)nls (r1, r2) =

∑n′,n′′

Cn′n′′

nls ξ(λ)n′l ′(r1)ξ

(λ)n′′l ′′(r2).

Coefficients C are obtained by diagonalising thetarget (FCHF) Hamiltonian

〈φ(λ)f |HT|φ

(λ)i 〉 = ε

(λ)f δfi ; lim

N→∞

N∑n=1

|φ(λ)n 〉〈φ

(λ)n | = IT.





Hydrogen ℓ = 0 energies for λ = 1 Laguerre bases

0.01

0.1

1

10

100

1000energy (eV)

-0.1

-1

-10

-100∞25201510

Laguerre basis size N





Convergent Close-Coupling theoryScattering

Projectile-target wavefunction is expanded as

|Ψ(+)i 〉 ≈ I(N)

T |Ψ(+)i 〉 =

N∑n=1

|φnFni〉 + . . . (1)

Solve for Tfi ≡ 〈k f φf |V |Ψ(+)i 〉 at E = εi + ǫki ,

〈k f φf |T |φik i〉 = 〈k fφf |V |φik i〉

+

N∑n=1

∑∫d3k

〈k f φf |V |φnk〉〈kφn|T |φik i〉

E + i0 − εn − ǫk. (2)

Cross section: σfi ∝ |〈k f φf |T |φik i〉|2.







|Ψ(+)i 〉 ≈ I(N)

T |Ψ(+)i 〉 =

N∑n=1

|φnFni〉 + . . . (1)



+

N∑n=1

∑∫d3k


E + i0 − εn − ǫk. (2)








|Ψ(+)i 〉 ≈ I(N)

T |Ψ(+)i 〉 =

N∑n=1

|φnFni〉 + . . . (1)



+

N∑n=1

∑∫d3k


E + i0 − εn − ǫk. (2)





e−-H ionisatione−-He-like atom/ion ionisatione+-H2Photoionisation

Comparison with experimente−-H ionisation

e−-H total ionisation: σion =∑

f σfi for εf > 0

0

1

2

3

4

5

6

7

1 10 100 1000

cros

s se

ctio

n (1

0-17 cm

2 )

total energy E (eV)

exp, JPB (1987)

CCC, PRL (1993)






e−-He(11S) ionisation

e−-He total ionisation: σion =∑

f σfi for εf > 0

0

5

10

15

20

25

30

35

40

100 1000

cross section (10-18cm2)

projectile energy (eV)

Rejoub et al Sorokin et al CCC

[Bray and Fursa, JPB 44, 061001 (2011)]Igor Bray <[email protected]> CCC Approach to collisions





e−-N5+(23S) ionisation

e−-N5+ total ionisation: σion =∑

f σfi for εf > 0

200 400 600 800 1000

0

2

4

6

8

Cross section ( 10-19

cm2

)

Electron-ion collision energy (eV)

e + N5+(1s2s

3S) → N

6+(1s

2S) + 2e

130 140 150

0

1

2

1s2s 3S1

1s2s 1S0

[Müller et al. Phys. Rev. A 90 010701 (2014)]Igor Bray <[email protected]> CCC Approach to collisions





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]> CCC Approach to collisions




Photoionisation

total single and double photoionisation of He

10-4

10-3

10-2

10-1

10+0

σ1 CCC

Samson

10-5

10-4

10-3

10-2

10-1

1 10 100 1000

cross section (Mb)

total energy E (eV)

σ2 CCC

Wehlitz

10-6

10-5

10-4

10-3

10-2

σ3 CCC

Wehlitz

10-5

10-4

10-3

10-2

1 10 100 1000

σ2+

CCC

Doerner





Concluding remarks

Close-coupling methods “solve” quantum collisionsystems for one- and two-electron atomic targets:

R-matrix with pseudostates (Bartschat, Badnell, )Time-dependent close-coupling (Pindzola, Colgan, )Convergent Close-Coupling (Fursa, Kadyrov, Bray, )

Considerable recent progress with light molecules

Complex atoms and molecules is a work in progress




Concluding remarks








Concluding remarks






Date post:	17-Jun-2020
Category:	Documents
Upload:	others
View:	4 times
Download:	0 times

Convergent Close-Coupling approach to atomic and molecular ... · Convergent Close-Coupling theory...

Documents