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Calculation of atomic collision data for heavy elements using perturbative and non-perturbative techniques

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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
- 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

- 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

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

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

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.

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/WeaknessesLos 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 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

- 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

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

- 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

- 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)

- Not antisymmetrized
- Final state shows
- elastic scattering
- exchange scattering
- ionization

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

- 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 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 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 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

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