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1 IAEA–Vienna,AustriaFebruary18-20,2019
Asymptoticbasissetsemiclassicalcoupledchannelcalculations
forion-atomcollisions:backgroundandtestcasesatintermediateimpactenergy
AlainDuboisandNicolasSisourat
LaboratoryofPhysicalChemistry– MatterandRadiationUMR7614SorbonneUniversité-CNRS
2ndResearchCoordinationMeetingoftheCRPonDataforAtomicProcessesofNeutralBeamsinFusionPlasma
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2 IAEA–Vienna,AustriaFebruary18-20,2019
ü theunderstandingandmodelingof
• theultra-fastelectronicdynamicsinatomicandmolecularsystems
• theinterplayofthemanyopenchannels=>nonperturbativeapproaches…
• …includingtheatomic/molecularelectronicspectrum(+somehowthecontinuum)…
• …andthestaticanddynamicalelectroniccorrelations
MOTIVATIONS
ü Fundamentalaspectsofdynamicalfew-bodyquantumsystemsand
computationsofcrosssectionsforapplications
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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
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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
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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
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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
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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
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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
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• 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
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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
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11 IAEA–Vienna,AustriaFebruary18-20,2019
TESTCASE3:H++LiCOLLISIONS
RESULTS1:GLOBALPROCESSES
Comparisonwithexperiments
ü Verygoodagreement!
ü 1sttimeprocessesfrominner-shell(IS)andvalence-shell(VS)
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TESTCASE3:H++LiCOLLISIONS
RESULTS2:GLOBALPROCESSES(VSVS.IS)
Comparisonwith1-electronsimulations(modelpotential)
ü weakcorrelationeffects
ü modelpotentialvalidatedbut
�2independant1ecalc.+
IndependentElectronApprox
�1ecalc.failtoreproducepeakat
≈4keVforcaptureandexcitation
Crosssections(cm-2)
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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…
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TESTCASE2:H++H-COLLISIONS
JunwenGaoetal,PRLaccepted(2019)
DECcrosssectio
ns
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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
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16 IAEA–Vienna,AustriaFebruary18-20,2019
Convergenceandoscillations
in-and-outRosenthal’smodel
whenplottedas1/vP
TESTCASE2:H++H-COLLISIONS
T =⇡
R ReRi �EdR Molecularenergycurvesof
importanceforDECprocess
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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!
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TESTCASE2:H+HCOLLISIONS
HansenandDubois,JPB31L861(1998)
H(2s)+H(1s)orH(Σ) H(2p)+H(1s)orH(Σ)
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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!
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20 IAEA–Vienna,AustriaFebruary18-20,2019
NicolasSisouratPhDthesis(2008)
B2B1
JPHAD
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NicolasSisouratPhDthesis(2008)
JPHADB2B1
3s,3p,4sand4pexcitation
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NicolasSisouratPhDthesis(2008)
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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
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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
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TESTCASE1:H++H(n)COLLISIONS
A.Taoutioui,JPB51,235202(2018)
H++H(n=1)à H+H+
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TESTCASE1:H++H(n)COLLISIONS
A.Taoutioui,JPB51,235202(2018)
Scalinglaws• impactvelocity:vsc=v/ve(n)≈vn
• n4scalingofSECTCSathighenergies(geometrical,asCTMC)
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TESTCASE1:H++H(n)COLLISIONS
A.Taoutioui,JPB51,235202(2018)
Scalinglaws• impactvelocity:vsc=v/ve(n)≈vn
• n4scalingofSECTCSathighenergies(geometrical)
• n3scalingofSECTCSatlowenergies
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TESTCASE1:H++H(n)COLLISIONS
A.Taoutioui,JPB51,235202(2018)
Scalinglaws• impactvelocity:vsc=v/ve(n)≈vn
• combinedscaling
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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)
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ISIAC26PARISFRANCE20-22/07/2019
JanPetter Jérémie Nicolas Gabriel JunwenHansen Caillat Sisourat Labaigt Gao