pA5
CHARGE-TRANSFERCROSSSECTIONINTHELi-Li+SYSTEM
Fouzia BOUCHELAGHEM 1and Moncef BOULEDROUA2
1RadiationPhysicsLaboratory,UniversityBadjiMokhtar–Annaba,23000Annaba,Algeria,
2PhysicsLaboratory,FacultyofMedicine,UniversityBadjiMokhtar–Annaba,
23000Annaba,Algeria
E-mail:,
ABSTRACT:Thisworkdealstheoreticallywiththechargeexchangecrosssectioncomputedforthesystem Li-Li+ assumingaverylowelectricfield.Thecalculationsareperformedquantummechanicallywithinthe Chapman-Enskogmodel1.Thecalculationstartsbyconstructingtheion-atompotentialand,withthissystem,
thecollisionaldynamicsaredeterminedbythemolecularΣg+ andΣ+
states
2 .Thegeradeandungerade
potential-energycurvesareshowninFig. 1.Thepotentialsarefurtherusedtosolvethe radialwaveequationand
therefore to determine the phase shifts. These phase shifts have been used to compute the elastic and charge-transfercross sections.Forillustration,thecharge-transfercrosssectionforthe scatteringatlow energies inthe Σg+andΣu+states arepresented in fig. 2.
KEYWORDS: charge-transfer cross-section,lithium
1.Introduction
Theinteractionbetweenanatom andionofthesame elementleadstohavegerade and ungeradestatesof the diatomicmolecularion,onlythetwolowest electronicstates of the molecular ionare considered in thisinteraction, in thesesystemsthecollisionaldynamicsaredeterminedby the molecular Σg+and Σu+states.
Thepresentpaperisconcernedwithcollisionofneutral
atom-ionsystemsintheultralowenergy.Thecalculation of potentialsusingabinitiodata,Thepotentialarefurther used tosolvethe radialwaveequationandthereforetodetermine the phase shifts, these phase shifts have been used to compute elasticand charge-transfer cross section
2. Construction ofpotential
Theinteractionpotential whichis pertainedtothis collisionisshowninfigure1; fortheexampleLi-Li+. In theΣg+ andΣu+ states.Thesepotentialscurveshavebeen used ab initio data available in literature, at small inter-nuclear separationR,thepotentialcurveswere approximatedwithshort-range potential of theform
V(R) =aexp(-b/R) (1) Inlong-distances,wehaveintroduceddispersiontermsis
given,inatomicunits by R.Côté andA.Dalgarno3
V(R) ~Vdis(R)±Vexch(R) (2) Thedispersion termis given inatomic units
V(R)=-1/2 [C4/R4+C6/R6+C8/R8] (3)
WhereC4,C6,C8 arethedipole,quadrupleandoctopole polarisabilitiesofneutral atom4,theexchangeterm was performedusingtreatmentofTonyCScottetal5andtakes the form
Vexch(R)= (A2n,s/4) (4/e)1/α(R/2)2γ+1exp(-Rαn,s) (4)
Fig.1.The two lowest potential curvesforLi2+.
3.Elasticandtransfer-chargecrosssections
ThescatteringofLibyLi+ maybedescribedbythe appropriate solution ofdifferential equation
[d2/dR2+k2–2μVg,u–l(l+1)/R2]Ug,uE,l (5)
Vg,u ,arethepotentialsasafunctiononinter-nuclear distanceRforeithertheΣg+ andΣu+ statesofLi2+,μisthe reducedmass,k=(2μE)1/2/ħ.Ug,u E,l isthenuclearwave function behavesasymptotically
Ug,uE,l=sin(kR–lπ /2+ηlg,u) (6) For large values of l, the phase shift ηlg,u can be
approximated by
ηlg,u=μπC4k2/8ħ2L3 (7)
The elasticcross sectiongiven isby6
σel= ½ [σgel+σuel] (8) Thesecrosssectioncanbecalculatedfromthephase
shifts scatteringalongtheΣg+and Σu+
∞
σel=4π/k2∑(2l+1)sin2ηlg,u (9)
l=0
We willobtainthecharge-transfercross section of the form
References
[1]L.E.Reichel:1984AModernCourseinStatisticalPhysics
(UniversityofTexas press,Austin).
[2]J.N.Bardsleyetal.:Phys.Rev.A,11,(1975)1911.
[3] R.Côte, andA.Dalgarno:Phys.Rev.A,62,(2000)012709. [4]S.H.Patil,K.T.Tang:Chem.Phys.Lett.295(1998)152.
[5]TonyCScottetal.J.Phys.B:At.Mol.Opt.Phys.37(2004)
4451-4469.
[6]E.W.McDaniel:CollisionPhenomenainIonizedGases,1st ed.
Wiley,NewYork,1964.
∞
σch=π/k2∑(2l+1) sin2(ηlg- ηlu) (10)
l=0
Fig.2.Charge-transfercrosssectionasafunctionofthe collisionenergy.
Ourresultarefoundis reasonablygoodwiththe theoretical result. In Fig. 2, we have presented the charge-transfercrosssectionresultforLi-Li+ system.The natureofthecurveissimplymonotonically decreasingwith the increaseofenergy.
Acknowledgements
Wewouldliketocordiallyexpressthankstoallcontributorsto
ICRP-7/SPP-28/GEC-63fortheircooperationintheconference.