![Page 1: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/1.jpg)
1 IAEA–Vienna,AustriaFebruary18-20,2019
Asymptoticbasissetsemiclassicalcoupledchannelcalculations
forion-atomcollisions:backgroundandtestcasesatintermediateimpactenergy
AlainDuboisandNicolasSisourat
LaboratoryofPhysicalChemistry– MatterandRadiationUMR7614SorbonneUniversité-CNRS
2ndResearchCoordinationMeetingoftheCRPonDataforAtomicProcessesofNeutralBeamsinFusionPlasma
![Page 2: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/2.jpg)
2 IAEA–Vienna,AustriaFebruary18-20,2019
ü theunderstandingandmodelingof
• theultra-fastelectronicdynamicsinatomicandmolecularsystems
• theinterplayofthemanyopenchannels=>nonperturbativeapproaches…
• …includingtheatomic/molecularelectronicspectrum(+somehowthecontinuum)…
• …andthestaticanddynamicalelectroniccorrelations
MOTIVATIONS
ü Fundamentalaspectsofdynamicalfew-bodyquantumsystemsand
computationsofcrosssectionsforapplications
![Page 3: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/3.jpg)
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
![Page 4: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/4.jpg)
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
![Page 5: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/5.jpg)
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
![Page 6: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/6.jpg)
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
![Page 7: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/7.jpg)
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
![Page 8: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/8.jpg)
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
![Page 9: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/9.jpg)
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
![Page 10: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/10.jpg)
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
![Page 11: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/11.jpg)
11 IAEA–Vienna,AustriaFebruary18-20,2019
TESTCASE3:H++LiCOLLISIONS
RESULTS1:GLOBALPROCESSES
Comparisonwithexperiments
ü Verygoodagreement!
ü 1sttimeprocessesfrominner-shell(IS)andvalence-shell(VS)
![Page 12: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/12.jpg)
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)
![Page 13: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/13.jpg)
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…
![Page 14: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/14.jpg)
14 IAEA–Vienna,AustriaFebruary18-20,2019
TESTCASE2:H++H-COLLISIONS
JunwenGaoetal,PRLaccepted(2019)
DECcrosssectio
ns
![Page 15: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/15.jpg)
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
![Page 16: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/16.jpg)
16 IAEA–Vienna,AustriaFebruary18-20,2019
Convergenceandoscillations
in-and-outRosenthal’smodel
whenplottedas1/vP
TESTCASE2:H++H-COLLISIONS
T =⇡
R ReRi �EdR Molecularenergycurvesof
importanceforDECprocess
![Page 17: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/17.jpg)
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!
![Page 18: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/18.jpg)
18 IAEA–Vienna,AustriaFebruary18-20,2019
TESTCASE2:H+HCOLLISIONS
HansenandDubois,JPB31L861(1998)
H(2s)+H(1s)orH(Σ) H(2p)+H(1s)orH(Σ)
![Page 19: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/19.jpg)
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!
![Page 20: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/20.jpg)
20 IAEA–Vienna,AustriaFebruary18-20,2019
NicolasSisouratPhDthesis(2008)
B2B1
JPHAD
![Page 21: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/21.jpg)
21 IAEA–Vienna,AustriaFebruary18-20,2019
NicolasSisouratPhDthesis(2008)
JPHADB2B1
3s,3p,4sand4pexcitation
![Page 22: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/22.jpg)
22 IAEA–Vienna,AustriaFebruary18-20,2019
NicolasSisouratPhDthesis(2008)
![Page 23: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/23.jpg)
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
![Page 24: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/24.jpg)
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
![Page 25: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/25.jpg)
25 IAEA–Vienna,AustriaFebruary18-20,2019
TESTCASE1:H++H(n)COLLISIONS
A.Taoutioui,JPB51,235202(2018)
H++H(n=1)à H+H+
![Page 26: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/26.jpg)
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)
![Page 27: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/27.jpg)
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
![Page 28: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/28.jpg)
28 IAEA–Vienna,AustriaFebruary18-20,2019
TESTCASE1:H++H(n)COLLISIONS
A.Taoutioui,JPB51,235202(2018)
Scalinglaws• impactvelocity:vsc=v/ve(n)≈vn
• combinedscaling
![Page 29: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/29.jpg)
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)
![Page 30: Asymptotic basis set semiclassical coupled channel ......IAEA – Vienna, Austria 1 February 18-20, 2019 Asymptotic basis set semiclassical coupled channel calculations for ion-atom](https://reader033.vdocuments.us/reader033/viewer/2022051812/6029a521f82128637a546cf8/html5/thumbnails/30.jpg)
30 IAEA–Vienna,AustriaFebruary18-20,2019
ISIAC26PARISFRANCE20-22/07/2019
JanPetter Jérémie Nicolas Gabriel JunwenHansen Caillat Sisourat Labaigt Gao