Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom

1 IAEA–Vienna,AustriaFebruary18-20,2019

Asymptoticbasissetsemiclassicalcoupledchannelcalculations

forion-atomcollisions:backgroundandtestcasesatintermediateimpactenergy

AlainDuboisandNicolasSisourat

LaboratoryofPhysicalChemistry– MatterandRadiationUMR7614SorbonneUniversité-CNRS

2ndResearchCoordinationMeetingoftheCRPonDataforAtomicProcessesofNeutralBeamsinFusionPlasma

2 IAEA–Vienna,AustriaFebruary18-20,2019

ü  theunderstandingandmodelingof

• theultra-fastelectronicdynamicsinatomicandmolecularsystems

• theinterplayofthemanyopenchannels=>nonperturbativeapproaches…

• …includingtheatomic/molecularelectronicspectrum(+somehowthecontinuum)…

• …andthestaticanddynamicalelectroniccorrelations

MOTIVATIONS

ü  Fundamentalaspectsofdynamicalfew-bodyquantumsystemsand

computationsofcrosssectionsforapplications

3 IAEA–Vienna,AustriaFebruary18-20,2019

eV/u keV/u MeV/u

APPROXIMATEREGIONSOFVALIDITYOFVARIOUSTHEORETICALAPPROACHES

quantal

semiclassical

close-coupling

perturbative

asymptoticA/MOrbitals

transientMolecularOrbitals

semiclassical

close-coupling

excitationelectroncapture/electrontransfer

ionisation

P + T ! P� + T+P ⇤ + T ⇤

P + T+ + e�{

asymptoticAtomicOrbitals

4 IAEA–Vienna,AustriaFebruary18-20,2019

THEORETICALTREATMENT:

THEORETICALAPPROACH

•  semi-classicalapproach

impactparameterapproximation

•  suddenapproximation(formoleculartargets)

Eikonalequation

with

)

Hel(t) =X

i

"�1

2�i �

Zt

ri� Zp

|~ri � ~R(t)|

#+X

i<j

1

rij

R(t)

Semi-classicalapproach

SuddenapproximationHel(t)� i

@

@t

� ({~ri}, t) = 0

~R(t) = ~b+ ~v t

5 IAEA–Vienna,AustriaFebruary18-20,2019

THEORETICALTREATMENT:

andexpansiononasetofasymptotictargetandETF-augmentedprojectilestates

eigenfunctions(eigenvalues)

oftheT/PHamiltonians

Y

j0

ei~v.~rj0 e�i 12 v

2t

�T/P (✏T/P )�Tk ({~ri0}, t) = �T

k ({~ri0}) e�i✏Tk t

�Pk ({~rj0}, t) = �P

k ({~rj0}) e�i✏Pk t

ETF ({~ri})#

#

({~ri}, t) =X

k

ak(t) �Tk ({~ri0}, t) �P

k ({~rj0 6=i0}, t)

THEORETICALAPPROACH

6 IAEA–Vienna,AustriaFebruary18-20,2019

THEORETICALTREATMENT:

THEORETICALAPPROACH

•  solve

withevaluationofallmatrixelements,e.g.

•  tocomputeprobabilityandcrosssections

andalsodifferentialcrosssections…

Hel(t)� i

@

@t

� ({~ri}, t) = 0 ) i ˙a = ¯S�1 ¯M a

< iP jP | 1

r12e�i~v.(~r1+~r2)| kT lT >

Pij(v, b) = limt!+1

|aj(b, v, t)|2

�ij(v) = 2⇡

Z 1

0Pij(v, b) b db

7 IAEA–Vienna,AustriaFebruary18-20,2019

THEORETICALTREATMENT:

andexpansiononasetofasymptotictargetandETF-augmentedprojectilestates

eigenfunctions(eigenvalues)

oftheT/PHamiltonians

Y

j0

ei~v.~rj0 e�i 12 v

2t

�T/P (✏T/P )�Tk ({~ri0}, t) = �T

k ({~ri0}) e�i✏Tk t

�Pk ({~rj0}, t) = �P

k ({~rj0}) e�i✏Pk t

ETF ({~ri})#

#

({~ri}, t) =X

k

ak(t) �Tk ({~ri0}, t) �P

k ({~rj0 6=i0}, t)

•  Descriptionofthemultielectronic

-  developedonproductsofGaussianTypeOrbitals with=

-  whichshouldbespin-adapted(inourspin-freeapproach)implementedstraightforwardlyfor2electronsbutalsofornotseparableNe>2electronssystems

�({~ri}) =X

i,j,k

Ci,j,k Gi(~r1) Gj(~r2) ...|� >=X

ijk

Cijk|ijk >|� >=X

ijk

Cijk|ijk >

Descriptionofthemulti-electronicstates

THEORETICALAPPROACH

8 IAEA–Vienna,AustriaFebruary18-20,2019

))

•  exampleforH+-Licollisionsystemwhichshoulddescribe

(whentakingintoaccountthe3e-):

ü  elastic/excitation

ü  singletransfer

ü  doubletransfer

•  thetotalsystemisdoublet(andstaysdoublet)butbothpartnerschangespinmultiplicityduringthecollision complexityandCPU

•  GrouptheoryandYoungdiagrams…tominimize

H+ + Li ! H

+ + Li⇤

H+ + Li ! H

⇤ + Li+

�Li+

(1s2 1S)�H(2s 2S), ...,�Li+

(1s2s 1S)�H(2s 2S),�Li+

(1s2p 3P )�H(2p 2P ), ... �TTP

�Li2+

(1s 2S)�H�(1s2 1S), ... �TPP

H+ + Li ! H

� + Li2+

|� >=X

ijk

Cijk|ijk >

�Li(1s22s1 2S),�Li(1s22p1 2P ), ...,�Li(1s12s2 2S), ... �TTT

THEORETICALAPPROACH

9 IAEA–Vienna,AustriaFebruary18-20,2019

•  alltogether

withstatesofpositiveenergies…

forNT=NP=14(5"s"+3*3"p"GTO)…and≈400states(cut-offinenergy)

ourphilosophy:keepthesamebasisset(GTO,states)forallconsideredenergies

matrixsizesinnonadaptedbasisfor: (NT+NP)6~5108

matrixsizesinadaptedbasis:(NT(NT2-1)/3+NT2NP+NTNP(NP+1)/2)2~3107

({~ri}, t) =X

k

cTTTk (t) �TTT

k ({~ri}) e�i✏TTTk t ETFTTT ({~ri})

+X

k

cTTPk (t) �TTP

k ({~ri}) e�i✏TTPk t ETFTTP ({~ri})

+X

k

cTPPk (t) �TPP

k ({~ri}) e�i✏TPPk t ETFTPP ({~ri})

Li⇤ +H

+

Li+⇤ +H

⇤

Li2+⇤ +H

�⇤

ETFTTT ({~ri})

ETFTTP ({~ri})

ETFTPP ({~ri})

THEORETICALAPPROACH

10 IAEA–Vienna,AustriaFebruary18-20,2019

H+Li+(1s2) H++Li(1s22s1) H+Li+(1s12s1)Why?

•  studied,experimentallyandtheoretically

butnevercompletelynorovera

wideenergydomain

•  agenuine3-electronsystemwith

lowTandPcharges

•  goodcandidatetocheck:

-processesfromvalenceorinner-shells

-electroniccorrelationeffects

-frozencore/modelpotentialapproximations

����������

F. Aumayr and H.P. Winter (1985) S. L. Varghese, W. Waggoner, and C.L.Cocke (1984) M. B. Shah, D.S. Elliott, and H.B. Gilbody (1985) R. D. DuBois (1985) R. D. DuBois and L. H. Toburen (1985)

¢✕

★

n☐

A. M. Ermolaev (1984)

_

Theory :

Experiments :

L

K

TESTCASE3:H++LiCOLLISIONS

11 IAEA–Vienna,AustriaFebruary18-20,2019

TESTCASE3:H++LiCOLLISIONS

RESULTS1:GLOBALPROCESSES

Comparisonwithexperiments

ü  Verygoodagreement!

ü  1sttimeprocessesfrominner-shell(IS)andvalence-shell(VS)

12 IAEA–Vienna,AustriaFebruary18-20,2019

TESTCASE3:H++LiCOLLISIONS

RESULTS2:GLOBALPROCESSES(VSVS.IS)

Comparisonwith1-electronsimulations(modelpotential)

ü  weakcorrelationeffects

ü  modelpotentialvalidatedbut

�2independant1ecalc.+

IndependentElectronApprox

�1ecalc.failtoreproducepeakat

≈4keVforcaptureandexcitation

Crosssections(cm-2)

13 IAEA–Vienna,AustriaFebruary18-20,2019

TESTCASE2:H++H-COLLISIONS

H++H-(1s2)à H(n)+H SEC(neutralization) àH(n)+H* Transfer-Excitation àH-(1s2)+H+ DEC àH++H++e ionisation

Why?•  relative(physical)stiffnessoftheequations•  importanceofcorrelation…•  convergenceofthebasisintwodirections…

14 IAEA–Vienna,AustriaFebruary18-20,2019

TESTCASE2:H++H-COLLISIONS

JunwenGaoetal,PRLaccepted(2019)

DECcrosssectio

ns

15 IAEA–Vienna,AustriaFebruary18-20,2019

TESTCASE2:H++H-COLLISIONS

Convergence:•  GTObasis1:11«s»+8*3«p»+2*5«d»•  butalso9«s»+6*3«p»+1*5«d»•  and11«s»,8*3«p»+4*5«d»•  forGTObasis1:1977states,with1446aboveionisationthreshold(1425,3725)forDEC10%at0.2keVand30%forloweronesandforionization

ionizatio

ncrosssectio

ns

16 IAEA–Vienna,AustriaFebruary18-20,2019

Convergenceandoscillations

in-and-outRosenthal’smodel

whenplottedas1/vP

TESTCASE2:H++H-COLLISIONS

T =⇡

R ReRi �EdR Molecularenergycurvesof

importanceforDECprocess

17 IAEA–Vienna,AustriaFebruary18-20,2019

TESTCASE2:H+HCOLLISIONS

H+HàH*+H* excitationanddi-excitation

samemethodbut20yearsagoweused•  exactboundH-states•  withfullcalculationofallcoupling(includingcorrelation)•  H(n=1,2,3)onbothcenters,•  i.e.includingsingleexcitationanddi-excitationH(n=2)+H(n=2)andH(n=2)+H(n=3)

HansenandDubois,JPB31L861(1998)

PaleolithicCC!

18 IAEA–Vienna,AustriaFebruary18-20,2019

TESTCASE2:H+HCOLLISIONS

HansenandDubois,JPB31L861(1998)

H(2s)+H(1s)orH(Σ) H(2p)+H(1s)orH(Σ)

19 IAEA–Vienna,AustriaFebruary18-20,2019

H+HàH*+H* excitationanddi-excitation àH++H- transfer àH+ +H++e ionisation

B1oneachcenter:9GTO«s»and6*3GTO«p»B2 ""12"""7""B1includes135statesH*HandH-(includingpseudo-states)

B2"189 "" ""

TESTCASE2:H+HCOLLISIONS

NicolasSisouratPhDthesis(2008)

BronzeageCC!

20 IAEA–Vienna,AustriaFebruary18-20,2019

NicolasSisouratPhDthesis(2008)

B2B1

JPHAD

21 IAEA–Vienna,AustriaFebruary18-20,2019

NicolasSisouratPhDthesis(2008)

JPHADB2B1

3s,3p,4sand4pexcitation

22 IAEA–Vienna,AustriaFebruary18-20,2019

NicolasSisouratPhDthesis(2008)

23 IAEA–Vienna,AustriaFebruary18-20,2019

TESTCASE1:H++H(n)COLLISIONS

H++H(nlm)à H(n’l’m’)+H+ SEC

•  veryrarestudiessofar…•  quantitiesofcomputations(10foronlyn=1ton=3)•  manyopenchannels•  sothatconvergenceissues

ü  thebasisshouldincludelargen’andsolargel’ü  thereforeverylargenumberofGTOü  timepropagationsareverylong

24 IAEA–Vienna,AustriaFebruary18-20,2019

TESTCASE1:H++H(n)COLLISIONS

Convergence:•  s,p,d,f,gGTOoneachcenter•  Actualbasisset: 160statesoneachcenter(OKupton=7)•  Testbasisset: 191statesoneachcenter•  forH(n=1,2)initialstates:<3%forshellcaptureandforallenergies

2.5ev/u-100keV/u•  forH(n=3)initialstates: 4%forhighestandlowestenergies

10%forintermediateenergiesweperformedalsomicrocanonicalCTMCcalculations

25 IAEA–Vienna,AustriaFebruary18-20,2019

TESTCASE1:H++H(n)COLLISIONS

A.Taoutioui,JPB51,235202(2018)

H++H(n=1)à H+H+

26 IAEA–Vienna,AustriaFebruary18-20,2019

TESTCASE1:H++H(n)COLLISIONS

A.Taoutioui,JPB51,235202(2018)

Scalinglaws•  impactvelocity:vsc=v/ve(n)≈vn

•  n4scalingofSECTCSathighenergies(geometrical,asCTMC)

27 IAEA–Vienna,AustriaFebruary18-20,2019

TESTCASE1:H++H(n)COLLISIONS

A.Taoutioui,JPB51,235202(2018)

Scalinglaws•  impactvelocity:vsc=v/ve(n)≈vn

•  n4scalingofSECTCSathighenergies(geometrical)

•  n3scalingofSECTCSatlowenergies

28 IAEA–Vienna,AustriaFebruary18-20,2019

TESTCASE1:H++H(n)COLLISIONS

A.Taoutioui,JPB51,235202(2018)

Scalinglaws•  impactvelocity:vsc=v/ve(n)≈vn

•  combinedscaling

29 IAEA–Vienna,AustriaFebruary18-20,2019

CONCLUSIONSANDPERSPECTIVES

Thefieldisoldbutjuststartingforapplications:Renaissance

thereexistfewfantasticcodes/groupsworldwidewhichtrytodothe

same,withdifferentindependentclose-couplingapproaches(QM,SC

MO,SCAO)•  buttheyface

ü  differentnumerics

ü  differentconvergenceissues(alsoincludingovercompletness)

ü  differentrangeofvalidity•  For(quasi)one-electronsystemswecangototheendofit

butmulti-activeelectronsystemsarestillverychallenging…

WP:…C6+-H(JPB2000),Li3+-H(JPB2016,Nicolas),C4+-He(PRA2017)

30 IAEA–Vienna,AustriaFebruary18-20,2019

ISIAC26PARISFRANCE20-22/07/2019

JanPetter Jérémie Nicolas Gabriel JunwenHansen Caillat Sisourat Labaigt Gao