asymptotic basis set semiclassical coupled channel ......iaea – vienna, austria 1 february 18-20,...

1 IAEA–Vienna,AustriaFebruary18-20,2019

Asymptoticbasissetsemiclassicalcoupledchannelcalculations

forion-atomcollisions:backgroundandtestcasesatintermediateimpactenergy

AlainDuboisandNicolasSisourat

LaboratoryofPhysicalChemistry– MatterandRadiationUMR7614SorbonneUniversité-CNRS

2ndResearchCoordinationMeetingoftheCRPonDataforAtomicProcessesofNeutralBeamsinFusionPlasma


ü  theunderstandingandmodelingof

• theultra-fastelectronicdynamicsinatomicandmolecularsystems

• theinterplayofthemanyopenchannels=>nonperturbativeapproaches…

• …includingtheatomic/molecularelectronicspectrum(+somehowthecontinuum)…

• …andthestaticanddynamicalelectroniccorrelations

MOTIVATIONS

ü  Fundamentalaspectsofdynamicalfew-bodyquantumsystemsand

computationsofcrosssectionsforapplications


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


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



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



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



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


))

•  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


•  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


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



RESULTS1:GLOBALPROCESSES

Comparisonwithexperiments

ü  Verygoodagreement!

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



RESULTS2:GLOBALPROCESSES(VSVS.IS)

Comparisonwith1-electronsimulations(modelpotential)

ü  weakcorrelationeffects

ü  modelpotentialvalidatedbut

�2independant1ecalc.+

IndependentElectronApprox

�1ecalc.failtoreproducepeakat

≈4keVforcaptureandexcitation

Crosssections(cm-2)


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…



JunwenGaoetal,PRLaccepted(2019)

DECcrosssectio

ns



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


Convergenceandoscillations

in-and-outRosenthal’smodel

whenplottedas1/vP


T =⇡

R ReRi �EdR Molecularenergycurvesof

importanceforDECprocess


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!



HansenandDubois,JPB31L861(1998)

H(2s)+H(1s)orH(Σ) H(2p)+H(1s)orH(Σ)


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 "" ""


NicolasSisouratPhDthesis(2008)

BronzeageCC!



B2B1

JPHAD



JPHADB2B1

3s,3p,4sand4pexcitation


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



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



A.Taoutioui,JPB51,235202(2018)

H++H(n=1)à H+H+




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

•  n4scalingofSECTCSathighenergies(geometrical,asCTMC)





•  n4scalingofSECTCSathighenergies(geometrical)

•  n3scalingofSECTCSatlowenergies





•  combinedscaling


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)


ISIAC26PARISFRANCE20-22/07/2019

JanPetter Jérémie Nicolas Gabriel JunwenHansen Caillat Sisourat Labaigt Gao

asymptotic basis set semiclassical coupled channel ......iaea – vienna, austria 1 february 18-20,...

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