1. Stopping, straggling and inner-shell ionization within the shellwise local plasma approximation C. C. Montanari and J. E. Miraglia Instituto de Astronomía y Física del Espacio (IAFE) and Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires (UBA), Buenos Aires, Argentina. CAARI 2010-Fort Worth

2. r Shellwise local plasma approximation (SLPA) v r

3. r Free electron gas of local density Shellwise local plasma approximation (SLPA) v r

4. r Free electron gas of local density Inputs: densities and binding energies, shell to shell Shellwise local plasma approximation (SLPA) v r

5. r Free electron gas of local density Inputs: densities and binding energies, shell to shell Dielectric response for each nl-shell, independent shell approx. Shellwise local plasma approximation (SLPA) v r

6. r Free electron gas of local density Inputs: densities and binding energies, shell to shell Dielectric response for each nl-shell, independent shell approx. Perturbative limit Validity limits Z P < Z T intermediate to high impact energies, Shellwise local plasma approximation (SLPA) v r

7. Dielectric response function Shellwise local plasma approximation Lindhard (1954), e-e correlation to all orders Z P to first order Levine & Louie (1982), energy gap E nl, shell to shell response, satisfies f-sum rule

8. j=0, ionization cross section j=1, stopping cross section (SCS); j=2, square straggling (  2 ) Bound nl-shells total Calculation

9.  Stopping  Energy loss Straggling  Ionization of inner shells SLPA Results

13. Relativistic atoms Wave functions and binding energies Dirac equation GRASP, HULLAC

15. Stopping Power of protons in very heavy atoms ( 73< Z <84 )

16. Au -3.25 -4.13 -12.5 0 4f 5/2 5s 4d 3/2 EFEF 4f 7/2 4d 5/2 -11.8 -3.11

17. Au -3.25 -4.13 -12.5 0 4f 5/2 5s 4d 3/2 EFEF 4f 7/2 4d 5/2 -11.8 -3.11

18.  Independent shell approximation  Screening among electrons-correlation  Same shell? Binding energy?  Incertainty in energy SLPA

19. Au -4.13 -12.1 0 5s EFEF 4f 4d -3.17

22. Energy loss straggling of protons in very heavy atoms ( 73< Z <84 )

23. Inner-shell ionization of in Relativistic atoms GRASP, HULLAC

24. Concluding remarks SLPA: Ab-initio calculation (bound electrons) Independent shell approximation includes electronic correlation Input  just densities n(r) and binding energies good for DFT and QCh Fast calculation (PC), the same for 4f, 3d o 2p Limits Perturbative  first order in Z P Independent shells vs screening among shells Locality Future Complex elements, molecules, clusters Non perturbative calculation Semilocal approximation Screening among different FEG

25. Acknowledgements  Darío Mitnik  Claudio Archubi  Nestor Arista  Juan Eckardt  Moni Behar  Lokesh Tribed  Helmut Paul Instituto de Astronomía y Física del Espacio, Buenos Aires, Argentina Insttuto Balseiro and Centro Atómico Bariloche, Argentina Universidad Federal de Rio Grande do Sul, Porto Alegre, Brazil Tata Institute of Fundamental Research, Mumbai, India

26. Thank you! Buenos Aires, Argentina

27. Stopping, straggling and inner-shell ionization within the shellwise local plasma approximation C. C. Montanari and J. E. Miraglia Instituto de Astronomía y Física del Espacio (IAFE) and Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires (UBA), Buenos Aires, Argentina. CAARI 2010-Fort Worth

33. screening

35. W -2.77 -1.35 0 5s 5p 3/2 5p 1/2 -1.66 4f 7/2 -1.15 -1.23 4f 5/2

36. Straggling

37. Stopping

38. X-section

39. Resumé Advantages of the SLPA: 1- e-e correlation to all order 2- Just the electron densities & binding energies. Do not need the continuum. Good for DFT used in QCh. 3- Cartessian coordinates. Not needed central potential 4- Projectile classical trajectory selfconsistent (e impact) Disadvantages 1- First order in the projectile charge 2- It is local 3- It is a model. No perturbative series to follow

40. Future Developmens 1- Heavy atoms f-shell, molecules & clusters 2- Atom-atom antiscreening (= collision of two FEG) 3- Improve the Local hypothesis by extending to momentum space. Intense activity in QCh