說明成果第二章

Theenergiesofthesedifferent maydiffer,sowerequireadetaileddesignationofthe statesof

r

2s(2)

d1d 11

庫侖排斥Coulomb

交換相互作用ExchangeGiveeachGiveeachstateaproper2.52.5Many-Electron???RepresentationofExcited?TermsandElectronic?Sub-TermsandSpin-Orbital?DerivationofTermsandSub-RepresentationofExcitedTermsandElectronicSub-TermsandSpin-OrbitalDesignationoftheelectronicstatesofH單電子

多電子nlm軌道與軌道與自旋運(yùn)動(dòng)間

電子間ConfigurationConfiguration組態(tài)OrbitalSolvingnindependentHydrogen-likeEnergySolvingnindependentHydrogen-likeEnergyElectronsfillingtheorbitals(Pauli組態(tài)忽略電子排斥勢(shì)所得到的電子填充方式Electron

1庫侖排斥1庫侖排斥Coulomb交換相互作用ExchangeNo

n NM43 NM43 L2 WithShieldingenergyisrelatedtonandK1GroundState

(1Pauli2(3HundWavefunctionforMany-ElectronSpinandorbitalSpinandorbitalseparation(1,2)11s(2)21s11s212212Ground“WavefunctionforMany-ElectronSpinandorbital

ExcitedExcitedExamplesofExcitedGroundGround Excited

2s1

2p1;Ground Excitedstate2…ExcitedAtomicspectrumrevealingthestate

E=E=E1+E2+J12-

r

2s(2)

d1d

11s(2)2s(1)d

1d 庫侖排斥 交換相互作用11H單電子

多電子量子數(shù)n,l,m,ms Electron

電子間軌道與自旋運(yùn)動(dòng)間組態(tài)狀態(tài)原子光譜項(xiàng)TwoTwoquantumNotationforExcitedStates-Totalorbitalangular Totalspinangular NotationNotationforexcitedL0122S+1 56 量量子數(shù),對(duì)于具體的譜項(xiàng)是一個(gè)具體值(注意:兩處S的不同含義---光譜支項(xiàng)中心若為S,那是L=0的量量子數(shù),對(duì)于具體的譜項(xiàng)是一個(gè)具體值ExcitedNotationforExcitedstates(Singleelectron (Theonlyoneelectronon2pL=l=Twoquantum

S=s=Term 2S+1L InquantumInquantumL=|l?l|,|l?l|+1,…,|l+l|?1,|l ExcitedLNotationforExcitedLLmaxLmax=l1+l2Lmin=l1l2S=|s1s2|,|s1s2|+1,…,|s1+s2|1,|s1+L=|l1l2|,|l1l2|+1,…,|l1+l2|1,|l1+InquantumExcitedL=L=|l1l2|,|l1l2|+1,…,|l1+l2|1,|l1+l1=0,l2=|l1l2|=|l1+l2|=S=0,L=0,S=1=>L=0,S=0=>S=|s1s2|,|s1s2|+1,…,S=0,L=0,S=1=>L=0,S=0=>|s1s2|=0,|s1+s2|=WavefunctionforMany-ElectronSpinandorbitalseparation(1,2)12211s12s22s11s2122TobeStateStateWavefunctionforMany-ElectronContinuedSpinandorbitalseparationState

Spin-OrbitalSpin-Orbital

TobeWavefunctionforMany-ElectronContinuedSpinandorbitalseparation12(State3+state(1,2)12(State3+state(1,2) Tobe22(State3-state(1,2)11s(1)2s(2)2s(1)1s(2)1(1)(2)12StateStateWavefunctionforMany-ElectronContinuedSpinandorbitalseparation(1S12S1)Summary:fourmicrostatesintwotermsMs=M=-sL=S=(1,2)11s(1)2s(2)2s(1)1s(2)1(1)(2)22M=sS=Ms=(2) 2121(1,2)Computationofstate E(1S)= E(3S)= J12

1s(1)1s(1)22s(2) **r1s(2)2s(1)d

d1dPleasegiveprooftotheseequationsPleasePleasegiveprooftotheseequationsExcitedNotationforExcitedSLli J.C.Willmott,原子物理學(xué)，1985,Chapter原子光譜項(xiàng)光譜支項(xiàng)單電子

多電子量子數(shù)n,l,m,ms Electron

電子間

軌道與自旋運(yùn)動(dòng)間光譜支項(xiàng)Twokindsofspin-orbitalcouplingSSL00iiiStrong?00iiiStrong

H lLight Heavy s1s2

LS l1l2WeakcouplingS Lli J|LS|,|LS|1,,|LSMJ=-J,…,NotationforSub-Term:

J=3/2, 2D3/2,TobeContinuedWeakcouplingS=

J=2,1, 3P2,3P1,2s12p1,S= J= S J=

3F4,3F3,Core,S=0,No

S J=S J=S J=S J=S J=

3D4,3D3,3P2,3P1,等價(jià)電子形成的組態(tài)叫做非等價(jià)組態(tài)等價(jià)電子形成的組態(tài)叫做非等價(jià)組態(tài)光譜支項(xiàng)記作例l1=1,l2=2,L=3,2,1s1=1/2,s2=1/2,S=1,0 譜項(xiàng) 3F,3D, 1F,1D,

支項(xiàng)支項(xiàng):以3FL=3S=1所以3F有三個(gè)支項(xiàng):3F43F3法(否則將會(huì)出現(xiàn)一些Pauli原理的情況最基本的作法是“行列式.下面以等價(jià)組態(tài)p2為例來說明“行列式波函數(shù)法”DerivationoftheTermsandSub-ConstrainofPaulirepulsion- No

p-

L=2,1, S=1,

TobeDerivationoftheTermsandSub-MicrostatesinNumberofNumberofNumberofmicrostatesNumberofspin-orbital(1,2)22M10-M2M10-M2(11(111(10)(01(10)(01)(10)(01(10)(010(11)(00(11(11)(00)(11(11)(00)(11(11)(00(11(10)(01(10)(01)(10)(01(10)(01(11(11)(11(11DerivationoftheTermsandSub-ContinuedConstrainofPaulirepulsionC6C6With Howmanyschemesofputtingthesetwoelectronsintothesixspin-orbitals?TobeDerivationoftheTermsandSub-ContinuedConstrainofPaulirepulsion- 21outofthe36termsshouldbewipedoutL=2,1,S=1,

Tobe兩個(gè)同科p電子可能的狀態(tài)組M102(111(10(10)(10(10M0(11(11)(11)(00(11(01(01)(01(01(11DerivationoftheTermsandSub-ContinuedConstrainofPaulirepulsion- ysisof1P,ML=

isnotML=Ms=

Ms= m1=m2=ms1=ms2=

p-

Twoelectronswiththesamespinstateinone withtwoelectronsbelongingtoequivalent Method1:AntisymmetricDerivationoftheTermsandSub-(ML=2)p0(ML=2)p0p p11-pp1pp1pp1Symmetrical

M=- M=-Anti-Symmetrical 12 1(p-1p1+p1p-1),p0p02 p+pp (pp-pp 2 (pp-pp TobeWavefunctionWavefunctionforMany-ElectronSpinandorbital

DerivationoftheTermsandSub-ContinuedDerivationofTermswithPauliprinciple- 12 1(p-1p1+p1p-1),p0p02M=- (p0p-1+p-22 Tobe

DerivationoftheTermsandSub-ContinuedDerivationofTermswithPauliprinciple

Symmetrical==1p-ppMs1(1)(2)2MsM=-s (pp-pp212M=- 1(p-1p1-p1p- 2TobeDerivationoftheTermsandSub-Sub-Termsof3P23P2,3P1,Sub-Tobe withtwoelectronsbelongingtoequivalent MethodMethod首先畫出所有 Pauli原理的微狀態(tài)然后按下列步驟計(jì)算、分類來確定譜項(xiàng)1010211MS=0101/2+（-依此1001000000對(duì)每一個(gè)微狀10100101000將各電子的ms求和得110(2)從ML最大ML1211100001項(xiàng)的L1211100001

并從ML列挑00ML=L，L-1，L-00L的（2L+1）個(gè)分量.這些分量的L 110 MS= 1(3)從MS應(yīng)的最大MS,作為所求譜項(xiàng)的S值001111201 01 (當(dāng)然,這些分量要100000 從M列挑出M= 0L分量的S值相同 0L分量的S值相同 010102111000010

MS=010010001000

(4)(2)、(3)兩步一一組合，，其L

21110

MS=01001

1D 上 1D 0010

1 1D 0 1D MS=行重復(fù)MS=行重復(fù)對(duì)剩余11011001得到新00010001項(xiàng)例就是010MS= 1再 掉1 0 以上00這00些1 行0 !0 00MS=1依此類推00譜項(xiàng)00 請(qǐng)把全過程從頭看一L=2L=1(P)L=0

2111000010

MS=010010001000

withtwoelectronsbelongingtoequivalent Method3:Thesimplestmatrix按右圖所示,分別寫出兩個(gè)等價(jià)電按右圖所示,分別寫出兩個(gè)等價(jià)電子的和ml值折線形框 ml - - --

ml21 --DerivationDerivationoftheTermsandSub-EnergyLevelsof10 101 m-1 mJSpin-InMagnetic組態(tài) 不考慮電電

譜項(xiàng)

支譜項(xiàng)

微能態(tài) 1S0 m 00

10--10-- -

Howtofindtheground1.Thelowestenergy1.ThelowestenergytermshouldhaveHund’sHund’sHund’sThelowestenergytermshouldhavethe spinmultiplicity(2S+1).Forterms