Positron annihilation on atomic core electrons + positive ions

Transcription

1 ositro aihilatio o atomic core electros positive ios Dermot Gree ad Gleb Gribaki Departmet of Applied Mathematics ad Theoretical hysics, Quee s Uiversity Belfast, Norther Irelad, UK

2 Motivatio ositro aihilatio o core electros is a key process i established experimetal techiques: e.g. ositro-iduced Auger-Electro Spectroscopy (AES) [1] Real eed for accurate core aihilatio gamma-rayspectra ad probabilities - Correlatios??! Discrepacies betwee theory [2] ad measured [3] γ- spectra of oble gases: due to core aihilatio? ositive ios: limited theory, o experimets! [1] Weiss et al., hys. Rev. Lett. 61, 2245 (1988). [2] Dulop ad Gribaki, J. hys. B (2005). [3] Iwata et al., hys. Rev. Lett (1997).

3 Fudametal questios 1) What effect do correlatios have o γ-spectra? Noble gas atoms: Ar, Kr, Xe H-like positive ios: He, Li 2, B 4, F 8 (ioizatio eergies spa those typical of core electros) 2) May-electro atoms: importace of core cotributio to γ-spectra?

4 Outlie 1. May-body theory of aihilatio γ-spectra 2.Results: γ-spectra of obles positive ios i) Effect of correlatios ii) cotributio compariso with experimet

5 Low-eergy positros e.g., thermal: k 0.04au COM frame: =0 Lab: 0 γ γ e e- γ Eγ e e- γ mc2 = 511 kev Eγ = mc2 ϵ Doppler shift: ϵ several kev. γ-spectra: w ( ) shape characteristic of electro state ositro aihilatio gamma-spectra

6 May-body theory of γ-spectra γ-spectrum : w " ( ) = 1 c A. amplitude: A " () =h Ô a () / Z Z 1 2 /c A " () 2 d 4 d N 1 Ôa() N1 " i d 3 re i r ˆ(r)ˆ'(r) NR aihilatio: occurs at sigle-poit! Dyso expasio i: H it = ˆV e e ˆV e e Û HF usig Hatree-Fock as startig approximatio...

7 May-body theory: aihilatio amplitude γ-spectrum : Geeral diagram: w " ( ) = 1 c A " () = e Z 1 2 /c Differet approximatios to: 1) Vertex " Vertex A " () 2 d 4 d 2 γ-rays 2) ositro wavefuctio hole

8 May-body theory: aihilatio amplitude γ-spectrum : Geeral diagram: w " ( ) = 1 c A " () = e Z 1 2 /c Differet approximatios to: 1) Vertex " Vertex A " () 2 d 4 d 2 γ-rays 2) ositro wavefuctio hole

9 Aihilatio amplitude: VERTEX " A " () = Z Z = " " e i r e i r 0th-order (IM) hole "(r)' (r) dr e 1st-order µ µ 2 µ " 1 ``Γ- block µ µ µ µ µ µ "(r 1 ) (r 1, r 2, r)' (r 2 ) dr 1 dr 2 dr o-local vertex correctios: describe short-rage electro-positro iteractios µ 1 2 µ 2

10 Aihilatio amplitude: OSITRON WAVEFUNCTION Geeral diagram: A " () = e " Vertex 2 γ-rays hole Differet approximatios to: 1) Vertex 2) ositro wavefuctio

11 Aihilatio amplitude: OSITRON WAVEFUNCTION = Two approximatios: (1) Hatree-Fock; (2) Dyso Dyso-equatio: Hartree-Fock " " 0 µ " " 0 (H 0 " ) (r) =" (r) " " 0 " " 0 ˆ " " (r) " " 0 " " 0 Z e " " " 0 " (r, r 0 ) " (r 0 )dr 0

12 Aihilatio amplitude: OSITRON WAVEFUNCTION = (H 0 " ) (r) =" (r) e.g., polarizatio of atom: " " 0 µ = X µ,...attractive for small positro eergy. lim r!1 (2) ' d 2r 4 (r r0 ), where d h" 0 V µ, ih, µ V "i (" " " µ " ) local! is the static dipolarizability of the atom. e "

13 Outlie 1. May-body theory of aihilatio γ-spectra 2.Results: γ-spectra of obles positive ios i) Effect of correlatios ii) cotributio compariso with experimet

14 Effect of correlatios: (1) VERTEX γ-spectra (kev -1 ) p static core Krypto Vertex order: Eergy shift (kev) a. / 4p static valece Z w(")d" VERTEX ENHANCEMENT

15 Effect of correlatios: (1) VERTEX γ-spectra (kev -1 ) p static core 4p static Krypto Vertex order: Eergy shift (kev) a. / valece Z w(")d" VERTEX ENHANCEMENT Valece: : " µ (01) (0) electro-positro attractio => icreased aihilatio probability

16 Effect of correlatios: (1) VERTEX: atoms γ-spectra (kev -1 ) p static core 4p static valece Krypto Vertex order: Γ Eergy shift (kev) Γ- block correctio: sigificat for valece, small for core VERTEX ENHANCEMENT : " µ (01) (0) " 1 Valece: µ µ 2 (01 Γ) (0)

17 Effect of correlatios: (1) VERTEX: ositive ios γ-spectra (kev -1 ) Vertex order: 0 Li 2 k=2.00 a.u Eergy shift (kev) VERTEX ENHANCEMENT

18 Effect of correlatios: (1) VERTEX: ositive ios γ-spectra (kev -1 ) Vertex order: Li 2 k=2.00 a.u Eergy shift (kev) VERTEX ENHANCEMENT 1s: " µ (01) (0) 1.66

19 Effect of correlatios: (1) VERTEX: ositive ios γ-spectra (kev -1 ) Vertex order: Γ Li 2 k=2.00 a.u Eergy shift (kev) VERTEX ENHANCEMENT " µ (01) (0) " 1 (01 Γ) (0) 1s: H-like ios: similar behaviour to core electros µ 1 2 µ 2

20 Vertex ehacemet factors Ehacemet factor: " w " ( ) " w IM " ( ) If 1st order domiates: H-like ios: " " 1 / V it E 1 / 1 µ Z 1 " 1 2 µ 1 2 µ 2 2

21 Vertex ehacemet factors H-like ios: F 8 B 4 Li 2 =0.5 a.u. He /(Z-1) 1 / 1 Z 1 d p s 1 ' X (Z 1) 1 s 1.60 p d X MBT CI-Koh [4] [4] Novikov et al. hys. Rev. A, 69, (2004) ; Ioizatio eergy: I / Z 2 ; 1 / p 1 I

22 Vertex ehacemet factors γ Argo Krypto Xeo 4d Valece s 3s 4s s 1/I E (ev -1 ) 3p 4p Valece p 5p l 1 r A C I l I l Valece A 44 ev (1.6 a.u.) C 20 ev (0.75 a.u.) 2.2

23 Vertex ehacemet factors γ H Valece He Li 2 B I E (ev) F 8 l 1 r A C I l I l Valece A 44 ev (1.6 a.u.) C 20 ev (0.75 a.u.) 2.2 w " ( ) " w IM " ( ) Use i IM calculatios to calculate core electro spectra for: (1) atoms across the periodic table (2) codesed matter systems

24 Effect of correlatios: (2) e WAVEFN. γ-spectra (kev -1 ) p static 4p static Krypto Vertex order: Γ Eergy shift (kev) e "

25 Effect of correlatios: γ-spectra (kev -1 ) p Dyso 3p static 4p Dyso 4p static Krypto Vertex order: Γ Eergy shift (kev) (2) e WAVEFN. e OSITRON Wavef. repulsive HF potetial -> attractive potetial [5] Goldaski ad Sayasov, hys. Lett., 13, 300 (1968) [6] Dzuba et al., hys. Scripta T46 (1993) " virtual s-states: low-eergy resoace behaviour of aihilatio probability [5,6]

26 Effect of correlatios: (2) e WAVEFN. γ-spectra (kev -1 ) Li 2 k=2.00 a.u Eergy shift (kev) e OSITRON Wavef. "

27 Effect of correlatios: (2) e WAVEFN. γ-spectra (kev -1 ) Li 2 k=2.00 a.u Eergy shift (kev) e OSITRON Wavef. Nuclear repulsio domiates!...oly vertex ehacemet importat "

28 Outlie 1. May-body theory of aihilatio γ-spectra 2.Results: γ-spectra of obles positive ios i) Effect of correlatios ii) cotributio compariso with experimet

29 Compariso with Expt. -spectra (arb. uits) Valece Argo Exp. (Ref. [3]) Valece Eergy shift (kev) Aihilatio o valece shells isufficiet! Argo [3] Iwata et al., hys. Rev. Lett (1997)

30 Compariso with Expt. -spectra (arb. uits) Valece Nuc. repulsio => Argo Exp. (Ref. [3]) Valece Eergy shift (kev) Val. A. predomiatly occurs o valece shells Argo % of tot a. rate 99.4% 0.6% [3] Iwata et al., hys. Rev. Lett (1997)

31 Compariso with Expt. -spectra (arb. uits) Valece Argo Exp. (Ref. [3]) Valece Total Total Eergy shift (kev) cotributio is vital to obtai agreemet with experimet! Val. Argo % of tot a. rate 99.4% 0.6% [3] Iwata et al., hys. Rev. Lett (1997)

32 Compariso with Expt. -spectra (arb. uits) Exp. (Ref. [3]) Valece Valece Krypto Eergy shift (kev) Valece shells: severely uderestimate high-eergy `wig Krypto [3] Iwata et al., hys. Rev. Lett (1997)

33 Compariso with Expt. -spectra (arb. uits) Exp. (Ref. [3]) Valece Valece Krypto Eergy shift (kev) Krypto Val. cotributio DOMINATES above 5keV % of tot a. rate 98.5% 1.5% [3] Iwata et al., hys. Rev. Lett (1997)

34 Compariso with Expt. -spectra (arb. uits) Exp. (Ref. [3]) Valece Total Valece Krypto Total Eergy shift (kev) Addig core cotributio results i good agreemet! (discrepacy above 6 kev...?) Krypto Val. % of tot a. rate 98.5% 1.5% [3] Iwata et al., hys. Rev. Lett (1997)

35 Compariso with Expt. -spectra (arb. uits) Valece Xeo Exp. (Ref. [3]) Valece Eergy shift (kev) Xeo [3] Iwata et al., hys. Rev. Lett (1997)

36 Compariso with Expt. -spectra (arb. uits) Valece Xeo Exp. (Ref. [3]) Valece Eergy shift (kev) Xeo Val. % of tot a. rate 97.8% 2.2% [3] Iwata et al., hys. Rev. Lett (1997)

37 Compariso with Expt. -spectra (arb. uits) Valece Xeo Exp. (Ref. [3]) Valece Total Total Eergy shift (kev) Ar->Kr->Xe Xeo Val. % of tot a. rate 97.8% 2.2% core aihilatio progressively more importat! [3] Iwata et al., hys. Rev. Lett (1997)

38 Coclusios Ab iitio MBT calculatios of γ-spectra for core ad valece shells of may-electro atoms positive ios. ositro-atom ad (short-rage) electro-positro correlatios are stroger for the valece electros, but are still sigificat for the core! (ad for H-like ios of Z<10). `True vertex ehacemet factors have bee calculated ad follow a simple scalig with the electro ioizatio eergy. Despite the small aihilatio rates (owig to uclear repulsio), the core cotributes sigificatly to the spectrum at large Doppler shifts.

39 Thaks for your attetio. Special thaks to: hd studetship from DEL NI Istitute of Theoretical Atomic ad Molecular hysics (ITAM), Harvard Uiversity, USA. Cliff Surko the Sa Diego experimetal group.

40 Refereces [1] A. Weiss et al., hys. Rev. Lett., 61, 2245 (1988). [2] L. J. M. Dulop ad G. F. Gribaki, J. hys. B., 39, 1647 (2005). [3] K. Iwata, G. F. Gribaki, R. G. Greaves, C. M. Surko, hys. Rev. Lett., 79, 39 (1997). [4] S. A. Novikov, M. W. J. Bromley ad J. Mitroy, hys. Rev. A, 69, (2004). [5] Goldaski ad Sayasov, hys. Lett., 13, 300 (1968). [6] Dzuba et al., hys. Scripta,T46 (1993). This work [7] D. G. Gree ad G. F. Gribaki, ositro aihilatio o hydroge-like ios, To be submitted hys. Rev. A (2012). [8] D. G. Gree ad G. F. Gribaki Ehacemet ad spectra of positro aihilatio o may-electro atoms, To be submitted to hys. Rev. A (2012). dgree09@qub.ac.uk