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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. Layout of Talk. Atomic data needed What elements we aim to examine

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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

layout of talk
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
atomic data needed
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)
Los Alamos Atomic Physics Codes



Structure +

Oscillator strengths +

Slater integrals



Structure +

Oscillator strengths +

Slater integrals


Collisional excitation


Collisional ionization/




Populations from

Saha equation

+ UTA’s = spectrum

Populations from

rate equations

+ UTA’s = spectrum


Los Alamos Atomic Physics Codes
  • CATS: Cowan’s semi-relativistic atomic structure code
    • Now available to run through the web:
    • 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
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.
los alamos atomic physics codes strengths weaknesses
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
los alamos atomic physics codes recent highlights
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
los alamos atomic physics codes recent highlights1
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
los alamos atomic physics codes proposed work
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+
background to time dependent approach
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
development of time dependent approach
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
time dependent close coupling method
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
electron scattering temkin poet model no angular momenta in problem
Electron scattering: Temkin-Poet model (no angular momenta in problem)
  • Not antisymmetrized
  • Final state shows
    • elastic scattering
    • exchange scattering
    • ionization
time dependent close coupling method1
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
recent tdcc calculations
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
electron impact ionization of li 2
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

electron impact ionization of be q
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

electron impact excitation of be q
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

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