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Nuclear Excitation in Plasmas

Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France. Nuclear Excitation Processes in Plasmas. ElectronInelasticScattering. NEEC. NEET. PhotonAbsorption. NeutronInelasticScattering. . . . . G. GosselinNow. P. MorelNext Talk. . G. GosselinNow. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France.

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Nuclear Excitation in Plasmas

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    1. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Nuclear Excitation in Plasmas G. Gosselin, P. Morel, V. Mot, N. Pillet (CEA, France)

    2. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Nuclear Excitation Processes in Plasmas

    3. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Multi-Scale Modeling Microscopic model : quantum tools Fermi Golden rule Perturbation methods Partial wave scattering (PWBA, DWBA, ) Macroscopic model Relativistic average atom Statistical Thermodynamics Plasma Physics

    4. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Thermodynamic Equilibrium Ions, electrons and photons are at thermodynamic equilibrium Nuclear populations are not Boltzmann law does not apply

    5. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Thermodynamic Equilibrium Equilibration time (under stationary conditions) Populations at equilibrium

    6. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    7. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Internal Conversion / Electronic Capture

    8. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Internal conversion (IC) Fermi Golden rule Final state density Internal conversion rate for one electron

    9. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Internal conversion coefficient Ratio : electron emission / photon emission

    10. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Electronic capture (NEEC) Electron capture cross section Fermi Golden rule Final state density

    11. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France NEEC cross section Laboratory conditions Non excited atom Natural level widths Conversion coefficient a

    12. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Relativistic Average Atom Thomas-Fermi-Dirac model The atom lies in a spherical box whose radius is dictated by density Average atom : mean value of binding energies and occupation numbers Relativistic : necessary for heavy nuclei internal conversion calculations

    13. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Electronic Transition Average atom deficiency Unique binding energy for each atomic shell Numerous electronic configurations Distribution of the binding energy over a statistical width e

    14. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Macroscopic transition rates Energy constraint : Excitation rate De-excitation rate

    15. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Plasma transition rate NEEC excitation rate Internal conversion de-excitation rate Principle of detailed balance fulfilled (Boltzmann)

    16. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    17. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    18. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    19. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    20. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Enhanced nuclear decay in plasmas Decay of isomeric level through excitation of a level lying above the isomeric level Intuition : should become important when DE ~ kT Isomeric lifetime changes in astrophysical plasmas

    21. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    22. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Electron Inelastic Scattering Free electrons in plasma Very low energy (~keV) Very huge numbers (> 1024 e/cm3) Inelastic scattering Coulomb excitation process Low cross section Attractive potential

    23. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Coulomb Excitation Semi-classical approach Classical trajectory (hyperbole) Excitation probability deduced from time dependant perturbation method Diverges for attractive potentials Quantum mechanics approach Perturbation theory [Alder] Multipole development Cross section How to choose a good wave function ?

    24. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Quantum Coulomb Excitation PWBA Approximation Plane wave Works well at high energy DWBA Approximation Distorted wave function Works well over the whole energy domain Radial equation can be solved by two methods Exact solution (only with an unscreened potential) WKB method

    25. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Radial Equation Exact solution Hypergeometric functions Numerical evaluation very difficult for low energies WKB Method Approximate radial equation resolution Solution by Langer Asymptotic solutions ? Bessel functions

    26. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France WKB Method Radial equation

    27. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France WKB theory by Langer Radial equation Variable and function change Oscillating region Exponential region

    28. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    29. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    30. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Threshold artifact Non Zero cross section at threshold Systematic effect for any nuclear transition Same artifact in atom excitation in atomic physics Classical image Electron acceleration in Coulomb field In plasma, no global acceleration as the total charge inside the ion sphere is zero For isolated ion, a pseudo-continuity could be reached with NEEC cross section ?

    31. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    32. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    33. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Present and Future Self consistent excitation and de-excitation model Photon Absorption/Emission NEEC/Internal Conversion NEET/BIC Electron inelastic scattering Principle of detailed balance at thermodynamic equilibrium Prospective Screened ions for electron inelastic scattering Multi-configuration effects in NEET

    34. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    35. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    36. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Photonic excitation and de-excitation

    37. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Breit and Wigner cross section If Doppler effect can be neglected If photons are at thermodynamic equilibrium Photon absorption

    38. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Photon emission Mode occupation number Induced emission rate Spontaneous emission Total emission

    39. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    40. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    41. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    42. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    43. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Electronic configurations G < D : no overlap Global treatment for NEEC Detailed treatment for NEET G > D : heavy overlap Global treatment for NEEC and NEET

    44. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France GANIL : NEEC experiment

    45. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Blackbody photon distribution Thermodynamic equilibrium Photon distribution Radiative intensity Maximum : E=1.594 kBT

    46. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Photon absorption Breit and Wigner cross section Number of excited nuclei per unit of time ?' : photon frequency in ion local frame

    47. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    48. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    49. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    50. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    51. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    52. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    53. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    54. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Excitation phenomena description Radiative processes Photon absorption Photon emission Bound/free electron processes Internal conversion Electron capture (NEEC) Enhanced de-excitation process

    55. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Photon Absorption With a smooth photon spectrum Example : 181Ta

    56. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France Asymptotic Enhancement Factor

    57. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    58. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

    59. Gilbert GOSSELIN, Vincent MEOT, Pascal MOREL, Nathalie PILLET, CEA/DAM/DIF, France

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