Chapter 4. Interaction of Many-Electron Atoms with Electromagnetic Radiation

Transcription

1 Cpte 4. Intecton o ny-ecton Atos wt ectognetc Rdton Redng: Bnsden & ocn Cpte 9

2 ny-ecton Atos n n Fed Htonn V t A e p t A e p V t ea p H H Te-ndependent Htonn nt t H Intecton o te to wt te dton ed Te dependent cödnge equton t X t A e V t X t Ψ Ψ q q q X K ~ wek ed t R e e I c W 4 4 ε πε π Tnston te n te dpoe ppoton sopton Ω d c W s 4 ε πε π spontneous esson

3 eecton Rues o ectc poe Tnstons [ ] H negy egensttes poe t eeent * pec coponents ε ε q q ± q ± : eectonc conguton e.g. He s ± y Wgne-ckt teoe q : vecto opeto q Cesc-Godon coecent c q q vnses uness eecton ues o tnstons ± ± pote s ue: toc sttes ust ve opposte pty P e R

4 - coupng: enegy egensttes poe opeto s ndependent o spn. δ q eecton ues o tnstons ± ± ± ± c One eecton tnston ost usu cse : ± ± Hypene stuctue B Cpte 5. H I wee I s te nuce spn ngu oentu. F I Tot ngu oentu o te to nuceus eectons eecton ues o tnstons F ± F F F ±

5 Oscto nd ne tengts k k k k k Oscto stengt < > sopton esson Tos-Rece-Kun su ue k k Tnstons etween two toc sttes nd s c W α α: ne stuctue constnt c W s α wee not syetc

6 ne stengt: syeted c c α α 4 4 I c W c W s π Tnston tes o spontneous esson sopton nd stuted esson ne ntensty o ny tos s W nue o tos n nt sttes e.g. / 5% 5%

7 gnetc poe nd ectc Qudupoe Tnstons poe ppoton t ~ Å π λ 5 Å k k << λ k e k k! k e ˆ ε k ˆ ε W ~ ˆ ε k ˆ ε Tke ~ k eˆ ˆ ε eˆ k ˆ ε k c

8 y p p Fst te [ ] [ ] H H H H p p [ ] [ ] H dt d p H dt d Usng econd te y c c c ~ ~ ~

9 gnetc dpoe tnstons ~ y c Ot gnetc dpoe oent: e e µ µ B µ B : Bo gneton e e e µ IA π π v -e τ π / v Tot gnetc dpoe oentu: e e µ B µ µ µ ~ Repceent o : ~ c c y y dˆ dˆ k ˆ ε µ B c t eeents o tnston y y e k eˆ ˆ ε eˆ

10 eecton ues o tnstons ± ± d ˆ // eˆ : dˆ eˆ : ± Z c Te toc sttes nd ust ve te se pty. Z ~ : even pty tnston seecton ues o - coupng s Z tos coutes wt s ndependent o c n tnstons e owed ony wtn se ne stuctue utpet: cowve o do-equency egon ~. - GH s s tnston / / Two poton esson nd ode petuton tnston o ge Z tos

11 ectc qudupoe tnstons ~ c ~ depends on k // eˆ nd ˆ ε // eˆ. eecton ues o tnstons eectc qudupoe oent ± ± ± ± c Te toc sttes nd ust ve te se pty ~ : even pty tnston seecton ues o - coupng s Z tos ± ± c ± ± One eecton tnston : ± ± ±

12 Oygen to: gound stte conguton s s p 4 P even pty s s p 4 : tnston.4 ev n geen K Buj nd C Zeppen. o Pys. B P H c H c H eecton ue o tnstons etween coponents o ypene stuctue F ± ± F F

13 pect o te Aks Ak ets: K R Cs F cosed se n s Gound stte conguton : s s : s s p 6 s K : s s p 6 s p 6 4s Z- eecton sceenng e V 4πε coe: specy syetc pc ou o enegy eves: n n µ n. u. wee µ n e quntu deects µ n α n* n α

14 sp sees ns n p duse sees nd n p esonnce nes np n s undent sees n n d sodu -nes yeow ceenng: ge Hge n Asopton spect n s np ν R * * n n s n np sson spect Fne stuctue np P λn H j / 5 λn 4 4 P j / P j / j j 4 j λn /

15 pect o Heu nd te Akne ts Heu nd Ak ets: He Be g C B Zn Cd Hg cosed se n s He Gound stte conguton He : s Be : s s g : s s p 6 s One eecton tnston: n s n s n coe: specy syetc C

16 Two eectons ectton s ss p s He s p P p s e He s dpoe dton e utoonton s s p s Rpd pocess: od nd wek spect nes

17 Fne stuctue H ξ pn-ot ntecton: pn-ote ot ntecton: V B µ π µ vnses o snget sttes pn-spn ntecton: pe Tpet sttes o s n wt s Ze n Z V

18 V V X n V n α X X X pn-spn ntecton: wee Z α pn-ot ntecton: α pn-ote ot ntecton: [ ] 4 Z α [ ] 4 Z X α Fo

19 Atos wt eve Optcy Actve ectons Ads to nye epeent spect eecton ues: nue o spect nes o tnstons etween two tes ndè ntev ue - coupng A A [ ] Tot spttng o te te - coupng A A < v Te etve ntenstes o te utpet nes depend ony on ngu oentu ctos. e.g. stongest nes

20 X-Ry pect Z σ n n. u. σ n << n K-se Z X-y Potoesson XP ~. KeV e K α K β cosed se vence eectons -se Auge tnstons -se

21 tk ect -eecton to n sttc uno eectc ed e ˆ e H Intecton enegy : eve stng ng sttes Te-ndependent petuton teoy pty st ode second ode Wgne-ckt teoe: q q B A

22 pttng o sodu -nes A B onnt contuton s o te neest eve o opposte pty to te eve. Gound stte <

23 Zeen ect -eecton to n sttc uno gnetc ed Intecton enegy : B µ B µ BB H µ B B stong ed cse no Zeen eect: B H >> H eˆ spn-ot coupng µ B B Inteedte cse Pscen-Bck eect: H A petuton µ BB A wek ed cse noous Zeen eect: petuton µ B B gµ BB ndè g cto g H << H