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Stopping, straggling and inner-shell ionization within the shellwise local plasma approximation

CAARI 2010-Fort Worth. 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

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Stopping, straggling and inner-shell ionization within the shellwise local plasma approximation

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  1. CAARI 2010-Fort Worth 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.

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

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

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

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

  6. Shellwise local plasma approximation (SLPA) r v 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 ZP < ZT intermediate to high impact energies,

  7. Shellwise local plasma approximation Dielectric response 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

  8. Calculation • Bound nl-shells j=0, ionization cross section j=1, stopping cross section (SCS); j=2, square straggling(W2) • total

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

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

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

  12. 0 EF 4f 7/2 -3.11 4f 5/2 -3.25 -4.13 5s 4d 5/2 -11.8 -12.5 4d 3/2 Au

  13. 0 EF 4f 7/2 -3.11 4f 5/2 -3.25 -4.13 5s 4d 5/2 -11.8 -12.5 4d 3/2 Au

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

  15. Au 0 EF -3.17 4f -4.13 5s 4d -12.1

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

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

  18. 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 ZP • Independent shells vs screening among shells • Locality Future • Complex elements, molecules, clusters • Non perturbative calculation • Semilocal approximation • Screening among different FEG

  19. 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

  20. Buenos Aires, Argentina Thank you!

  21. CAARI 2010-Fort Worth 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.

  22. screening

  23. -1.15 4f 7/2 -1.23 4f 5/2 0 W 5p 3/2 -1.35 -1.66 5p 1/2 5s -2.77

  24. Straggling

  25. Stopping

  26. X-section

  27. 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

  28. 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

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