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)

CATS/RATS

CATS/RATS/ACE

GIPPER

ATOMIC

LTE Non-LTE

Structure +Oscillator strengths +Slater integrals

Structure +Oscillator strengths +Slater integrals

Collisional excitation

PhotoionizationPhotoionization/Collisional ionization/Auto-ionization

Populations fromSaha equation+ UTA’s = spectrum

Populations fromrate equations+ UTA’s = spectrum

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.

Los Alamos Atomic Physics Codes

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:Recent Highlights

• 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

Blue lines are ATOMICRed lines are experiment

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

• 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

Conclusions/Future Work