Energy loss and mean excitation energy within the shellwise local plasma approximation

1. Energy loss and mean excitation energy within the shellwise local plasma approximation Claudia Montanari, Darío Mitnik, Claudio Archubi and Jorge Miraglia

2. IAFEInstituto de Astronomía y Física del EspacioBuenos Aires, Argentina

3. Shellwise Local Plasma Approximation • General considerations • Atomic densities • Bethe limit • Validity range • Results

4. Inelastic processes Shellwise Local Plasma Approximation • General considerations • Atomic densities • Bethe limit • Validity range • Results

5. e ZT e Zp Inelastic processes Target ionization Projetile, bare ion or with bound electrons Frozen (screening) or active (inelastic transitions, antiscreening)

6. Inelastic processes Colective description Free electron gas Dielectric formalism Input: densities and binding energies Shellwise Local Plasma Approximation • General considerations • Atomic densities • Bethe limit • Validity range • Results Lindhard et al (1953, 67), Brandt-Lundqvist (1966, 1967, 1970), Bonderup (1967), Chu et al (1970, 1972)

7. Shellwise Local Plasma Approximation Independent shell approximation j=0  Cross sections 1 Stopping 2 Straggling

8. Dielectric function Lindhard (1954) e-e correlation to all orders ZP to first order Levine & Louie (1982), energy gap Enl , shell to shell response, satisfies f-sum rule

9. Hartree Fock for neutral atoms Atoms Miraglia et al Phys Rev A 81 042709 (2010) Dirac equation, Z>54 Grasp or Hullac codes W, Au 4f shell with 14 electrons Z 54 Complex systems Molecules Insulator surfaces Montanari et al, Phys Rev A 79 032903 (2009) In process García et al Phys Rev A 75 042904 (2007) Shellwise Local Plasma Approximation • General considerations • Atomic densities • Bethe limit • Validity range • Results

10. Atomic densities in solids Al 14 Moruzzi et al, Calculated electronic properties of metals (1978) 12 Hartree-Fock, Bunge et al, Atomic Data and Nuclear Data Tables (1993) 10 8 4p r2d(r) 6 4 2 0.5 1 1.5 2 2.5 3 r

11. Shellwise Local Plasma Approximation • General considerations • Atomic densities • Bethe limit • Validity range • Results

12. Perturbative ZP < ZT intermediate to high energies impact velocity v > ve Shellwise Local Plasma Approximation • General considerations • Atomic densities • Bethe limit • Validity range • Results

13. Stopping power • Energy loss straggling • Ionization cross sections Shellwise Local Plasma Approximation • General considerations • Bethe limit • Validity range • Atomic densities • Results

14. Stopping SLPA Mermin-Lindhard

15. Stopping

16. Stopping

17. Stopping Z=83 Z=82

18. Lindhard Scaling Lindhard and Scharff(1952) Bethe limit and mean excitation energy Stopping number L(v) High but not relativistic limit Mean excitation energies (in eV) for W, Au, Pb, and Bi Element Z I (SLPA) ICRU Report 49 W 74 710 727 +/-30 Au 79 814 790 +/-30 Pb 82 810 823 +/-30 Bi 83 840 823 +/-30 Bethe-Bloch I=k ZT k=10eV Montanari et al, Phys Rev A 80 012901 (2009)

19. Bethe limit and mean excitation energy Sigmund, NIMB 230,1 (2005)

20. Bethe limit and mean excitation energy

21. 2 MeV Bethe limit and mean excitation energy

22. Histop, no perturbative FEG Nestor Arista (CAB, Bariloche, Argentina) Moni Behar (Porto Alegre, UFRGS) and collaborators qi CASP code, Grande and Schiwietz Antiscreening (e-e interaction) Recent work CDW-EIS Zn0+C+i, less than 1% Ionization of both, projectile and target SLPA He in Zn, less than 1% Miraglia, 2010 Phys. Rev. A 73, 024901 2006 Stopping Heavier ions? • Perturbative limit • Charge states in solids • Projectile excitation/ionizarion

23. Stopping

24. Stopping Antiscreening 1% Excitation and ionization due to e-e interaction

25. Stopping

26. Stopping

27. Stopping

28. Stopping

29. Straggling

30. Straggling

31. ¥ é ù kv - 2 2 Z dk 1 r ò ò ò = w nl P CS d d r Im ê ú ( ( ) ) p e w d 2 v k k , , r , E ë û nl nl nl 0 0 e ZT e Zp Inelastic processes Ionization probabilities of the nl-shell

32. Ionization cross sections ECPSSR, Basbas, Brandt y Laubert (1973)

33. Ionization cross sections ECPSSR, Basbas, Brandt y Laubert (1973)

34. Ionization cross sections Miraglia et al Phys Rev A 78 052705 (2008); Phys Rev A 81 042709 (2010)

35. Ionization cross sections Miraglia et al Phys Rev A 78 052705 (2008); Phys Rev A 81 042709 (2010)

36. Ionization cross sections

37. Concluding remarks SLPA • Ab-initio calculation (bound electrons) • Dielectric formalism, includes electronic correlation • Perturbative first order in ZP • Input  just densities n(r) and binding energies • Fast calculation (PC), the same for 4f, 3d o 2p • Good results for stopping, straggling and ionization cross sections Future • Complex elements, molecules, clusters • Non perturbative calculation • Semilocal approximation  P(b) multiple ionization • Screening among different FEG

38. Buenos Aires, Argentina Thank you!

39. Montanari et al, Phys Rev A 79, 032903 (2009)