James Colgan, Honglin Zhang, Christopher Fontes, and Joe Abdallah,

1. Calculation of atomic collision data for heavy elements using perturbative and non-perturbative techniques James Colgan, Honglin Zhang, Christopher Fontes, and Joe Abdallah, Los Alamos National Laboratory, NM, USA

2. Layout of Talk • Atomic data needed • What elements we aim to examine • Los Alamos suite of codes for collisional data production • Plane-Wave-Born Approximation • Distorted-Wave Method • Time-dependent close-coupling approach to excitation/ionization • Recent examples of TDCC calculations and comparisons with other work • Conclusions

3. Atomic data Needed • Collisional excitation • Collisional ionization • Recombination • Photo-induced processes • These processes all produce cross sections and/or rate coefficients • These data must be constructed in such a way that plasma modeling codes can easily use the data (e.g. IPCRESS, random-access binary file format)

4. Los Alamos Atomic Physics Codes LTE Non-LTE Structure + Oscillator strengths + Slater integrals CATS/ RATS Structure + Oscillator strengths + Slater integrals CATS/RATS/ACE Collisional excitation Photoionization/ Collisional ionization/ Auto-ionization Photoionization GIPPER Populations from Saha equation + UTA’s = spectrum Populations from rate equations + UTA’s = spectrum ATOMIC

5. Los Alamos Atomic Physics Codes • CATS: Cowan’s semi-relativistic atomic structure code • Now available to run through the web: http://aphysics2.lanl.gov/tempweb/ • Hartree-Fock method developed by Bob Cowan used for the atomic structure calculations • Plane-Wave-Born excitation data • Various semi-relativistic corrections included • RATS: Relativistic version of the atomic structure code • Uses a Dirac-Fock-Slater (DFS) potential for atomic orbitals (cf Doug Sampson) • Calculates energy levels and configuration average energies • Oscillator strengths • Plane-Wave-Born excitation collision strengths • New “fractional occupation number” capability to significantly speed up large calculations • GIPPER: Ionization cross sections • Semi-relativistic and fully relativistic • Photo-ionization cross sections • Electron-impact ionization cross sections • Auto-ionization rates

6. Los Alamos Atomic Physics Codes • ACE: Electron impact excitation cross sections/collision strengths • Electron-impact excitation cross sections calculated using either First-order many-body theory (FOMBT) or using the distorted-wave approximation (DWA) • TAPS: Display code • Displaying data from IPCRESS files and calculating rates • Designed to take input from any/all of the above codes • ATOMIC: plasma modeling code (LTE and non-LTE) • Reads in data from all of the atomic collision codes above • Can replace PWB collisional data with distorted-wave data from ACE, if required • Produces populations and plasma quantities for a given temperature/density. Also produces spectra for comparison with other codes/experiment • Ongoing participation in NLTE-4 workshop to compare various plasma modeling codes with each other and with experiment • Recently parallelized and modularized to significantly improve speed up.

7. Consistent treatment of all states and ion stages; accurate and fast calculations for highly ionized species Storage of atomic data in a compact binary format (IPCRESS files) which allows very large amounts of data to be stored in a manageable form Codes are now in a mature state, are portable, and well tested on a variety of platforms PWB/DW approximations may produce inaccurate collisional data, especially for neutral or near-neutral systems (less of a problem for hot plasmas where ions are likely to be more stripped) No current ability to insert (more accurate) data from other calculations instead of PWB/DW, if required Complications can arise due to problems with consistent treatment of resonance contribution from autoionizing states when combining different types of calculations Los Alamos Atomic Physics Codes:Strengths/Weaknesses

8. Los Alamos Atomic Physics Codes:Recent Highlights Blue lines are ATOMIC Red lines are experiment • Comparisons have been made with a recent experiment measuring a germanium X-ray spectrum from laser pulse experiments performed in Italy • LANL plasma kinetic code ATOMIC used to simulate spectra • Good agreement found • A configuration-average model used to calculate populations • Detailed fine-structure spectrum obtained by statistically distributing the populations over the corresponding level structure for each configuration

9. Los Alamos Atomic Physics Codes:Recent Highlights • Comparison with a recent Xe emissivity experiment (shown) and with a calculation from an independent plasma kinetic code • Agreement only fair in this case • More recent hybrid fine-structure (level to level) calculations are in better agreement

10. Los Alamos Atomic Physics Codes:Proposed Work • We now propose using these LANL atomic physics codes to generate a comprehensive collisional data set for silicon • Only sporadic calculations available for this element: • Ionization cross sections measured for Si+, Si2+, Si3+, Si6+, Si7+ • DW calculations for Si+, Si2+, Si3+, also some non-perturbative calculations (TDCC/CCC/R-matrix) available for Si3+ • Very little excitation cross section data seems to be available • No collisional data available for excitation or ionization from excited states of these ions • No calculations available for the neutral Si atom • Our proposal is to benchmark these DW calculations with selected TDCC calculations for Si, Si+, Si2+

11. Background to time-dependent approach Why is a time-dependent approach useful? • We ‘know’ the solution at t=- and t=+: just product of an electron wave packet and target atom/ion • We then time evolve this t=- solution by direct numerical solution of the Schrödinger equation • Allows (in principle) a numerically exact description of 3-body Coulomb problem of two electrons moving in field of atomic ion • Allows accurate calculations of • Total integral cross sections • fully differential cross sections • Electron-impact ionization • Straightforward extraction of excitation cross sections • Data necessary for modeling of plasma fusion devices as well as astrophysical modeling

12. Development of time-dependent approach • Bottcher (1982) studied e-H system near threshold by following time evolution of a wave packet • Was one of the earliest time-dependent approaches to ionization using a wave packet approach • Ihra et al (1995) performed similar calculations in the s-wave model. Also Odero et al (2001) performed time-dependent e-H scattering calculations • Pindzola and Robicheaux, Pindzola and Schultz (1996) formulated the time-dependent close-coupling method to study e-H at the peak of the ionization cross section • This was followed by Temkin-Poet studies of the threshold law for e-H (Robicheaux et al, 1997), and differential cross sections (Pindzola and Robicheaux, 1997) • Electron scattering cross sections for many atomic species have now been calculated including H, He, Li, C, Ne, Li+, Li2+, Mg+, Al2+, Si3+; more currently underway

13. Time-Dependent Close-Coupling Method • Angular reduction of the Schrödinger equation for a 2-electron wavefunction results in • A set of radial, coupled differential equations • Initial state is a product of a one-electron bound orbital and a wavepacket representing the incoming electron • We propagate on a uniform radial mesh for suitable time interval

14. Electron scattering: Temkin-Poet model (no angular momenta in problem) • Not antisymmetrized • Final state shows • elastic scattering • exchange scattering • ionization

15. Time-Dependent Close-Coupling Method • Obtain bound and continuum radial orbitals by diagonalization of one-dimensional Hamiltonian: • (eg, e-Li scattering) use pseudopotential to generate 2s orbital • Frozen-core orbital so that only two active electrons in system • Obtain probabilities by projecting propagated wavefunction on to one-electron bound orbitals

16. Recent TDCC calculations • Detailed study of excitation and ionization cross sections and rate coefficients for Li and Be isonuclear sequences • Initial studies made of heavier ions, such as Mo+ • New calculations of electron-impact double ionization (and including ionization-excitation) of He • New calculations of electron-impact ionization of H2+, the first electron-impact molecular time-dependent calculation

17. Electron-impact ionization of Li2+ Computed ionization cross sections for first 4 ns states of Li2+ We compare TDCC (squares) with RMPS calculations (solid red line), and with 2 DW calculations (dashed lines) DW calculations are well above close-coupling calculations for the excited states Demonstrates that inter-channel coupling effects on ionization from excited states are important

18. Electron-impact ionization of Beq+ Computed ionization cross sections for ground and first excited state of all ions of Be For neutral stage; DW cross sections higher than non-perturbative methods This disagreement gets worse for excited states Non-perturbative methods TDCC, RMPS, and CCC are all in good agreement

19. Electron-impact excitation of Beq+ Completing our comprehensive study of Be isonuclear sequence collisional processes Computed excitation cross sections for ground and first excited state of all ions of Be Non-perturbative methods are again in good agreement

20. Conclusions/Future Work • Los Alamos suite of codes are well suited for producing large amounts of collisional atomic data for heavy elements • We will use this capability to generate an extensive database of excitation and ionization cross sections for several elements of interest to fusion, beginning with Si • Time-dependent non-perturbative calculations will be used to benchmark these perturbative methods, especially for near-neutral systems • This approach can also compute differential cross sections if necessary. • This approach will result in a comprehensive database of excitation and ionization cross sections (and rate coefficients), with some indication of the accuracy of the data produced • Future years will extend these calculations to other heavier systems of interest to fusion