ATBASE User's Guide, Study notes of Physics

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ATBASE UserÅs Guide

P. Wang

December 1993

UWFDM-

ATBASE User’s Guide

Ping Wang

Fusion Technology Institute University of Wisconsin 1500 Engineering Drive Madison WI 53706

December 1993

UWFDM-

• 1. Introduction
• 2. Computer Code ATBASE
  • 2.1. Program Outline
  • 2.2. Primary Input
  • 2.3. Computational Procedure
  • 2.4. Output
• 3. STATE
  • 3.1. Program Outline
  • 3.2. Input
  • 3.3. Output
• 4. ATTABLE
  • 4.1. Program Outline
  • 4.2. Input
  • 4.3. Rate Coefficient Calculations
  • 4.4. Output
• 5. DWBORN
  • 5.1. Program Outline
  • 5.2. Input
  • 5.3. Output
• 6. MICPSSR
  • 6.1. Program Outline
  • 6.2. Input
  • 6.3. Output
• 7. BEAMTAB
  • 7.1. Program Outline
  • 7.2. Input
  • 7.3. Output
• 8. CKFYED
  • 8.1. Program Outline
  • 8.2. Input
  • 8.3. Output
• 9. CKFTAB
  • 9.1. Program Outline
  • 9.2. Input
  • 9.3. Output
• 10. Running Codes in a Chain Manner
  • 10.1. Simple Atomic Model
  • 10.2. Complete Coupling Atomic Model
    • Energy Density Plasmas 10.3. Atomic Model for Analyzing X-ray Line Emission Spectra From High
    • Heated Plasmas 10.4. Atomic Model for Analyzing X-ray Line Emission Spectra of Ion Beam

1. Introduction

ATBASE is a suite of FORTRAN 77 computer codes used for generating large-scale high quality basic atomic data. It includes the following eight codes:

(1) ATBASE: This is the main segment of the package. It is a configuration-interaction code with Hartree-Fock wavefunctions. It computes atomic radial wavefunctions, atomic energy levels, transition oscillator strengths, photoionization cross sections, and autoionization rates.

(2) STATE: This code sets up the input table of configurations for the ATBASE calculation.

(3) DWBORN: This code computes collision strengths for electron-impact excitation by using a distorted wave Born method.

(4) ATTABLE: This code does data organization for the basic data outputted from ATBASE and/or DWBORN, computes all related rate coefficients, and creates an atomic model (i.e., detailed formatted atomic data tables) for applications.

(5) MICPSSR: This code computes ion impact ionization cross sections (for both single and multiple ionization processes).

(6) BEAMTAB: This code generates a formatted data table for ion impact ionization cross sections.

(7) CKFYED: This code does large scale calculations for fluorescence yields.

(8) CKFTAB: This code generates a formatted data table for fluorescence yields.

In order to generate an atomic model for a specific problem, these codes must be run in a chain in one of the following combinations:

(1) STATE/ATBASE/ATTABLE

(2) STATE/ATBASE/DWBORN/ATTABLE

(3) STATE/ATBASE/ATTABLE/CKYED/CKFTAB

This code is based on the modification of three of Cowan’s atomic physics codes (RCN, RCN2, and RCG) [2,3] and Fischer’s multiconfiguration Hartree-Fock program (MCHF) [4]. The fine structure levels (nlLSJ) of a many-electron atomic system are evaluated within the framework of a configuration interaction (CI) treatment, while the term structure levels (nlLS) are calculated by taking a proper averaged summation over the relevant fine structure levels.

As shown in Figure 1, ATBASE consists of four blocks: primary input, self-consistent- field calculation, CI calculation with intermediate-coupling scheme, and primary output. There are 53 data files involved in the whole calculation. These files can be classified into three groups: input files, intermediate data files, and final output files. A detailed classification for these files is given in Table 1.

2.2. Primary Input

To run ATBASE, the user needs to provide the following information:

(1) specify atomic system,

(2) specify physical models,

(3) specify calculation parameters.

The basic input structure for ATBASE is shown in Figure 2. The primary input consists of four input files:

(1) atbase.inp — a namelist input file which contains all computation switches and parameters.

(2) config.inp — a formatted data input file which specifies atomic system to be calculated. This file can be generated by running STATE.

(3) hygen cfg — a formatted data file which contains all the hydrogenic states for the system. This file can also be generated by running STATE.

(4) ev.expdat — a formatted data input file which contains experimental data for atomic energy levels. This is an optional input. This file should be provided only if the user wants to incorporate experimental data in the calculation.

configuration-interaction calculations

radial integrals (^) f(nl Ä n'l')

output

self-consistent- field calculations

photoionization cross sections

primary input; configuration table

E (^) av

E (^) LS E^ LSJ f(J Ä J') (^) f(LS-L'S')

Figure 1. Flow diagram for ATBASE calculations.

Further details of these input files are given in Table 2 through Table 5. It should be noted that only a few parameters in ‘atbase.inp’ are dependent on atomic system. In the following, step by step guidance is given for how to prepare input for ATBASE calculations.

STEP 1: Determine the purpose for running ATBASE. For the current version of ATBASE, make the following choices:

(a) do large scale calculations to obtain atomic energy levels, transition oscillator strengths, and photoionization cross sections for a specific atomic system;

(b) do detailed calculations to obtain atomic physics data for a few specific atomic states of an atom (with the inclusion of a large number of configurations to account for correlation effects).

(c) do detailed calculations to obtain autoionization rates and/or dielectronic recombination rate coefficients for a specific electronic configuration.

STEP 2: In all cases, first determine the nuclear charge Z and the number of bound electrons in the atomic system of interest.

STEP 3: For choice (a), run STATE to generate electronic configurations for the system. Two files, ‘config.inp’ and ‘hygen cfg’ will be generated by running STATE (see Section 3 for running STATE). For choice (b), edit ‘config.inp’ by typing in all relevant electronic configurations in the sequence as indicated in Table 3. For choice (c), figure out all the possible exit channels for the specific autoionizing configuration and edit ‘config.inp’ by typing in all relevant electronic configurations in the sequence as indicated in Table 5.

STEP 4 : Edit namelist input file ‘atbase.inp’. Since most of the parameters in ‘atbase.inp’ have been set as defaults, in most cases the user only needs to change the following nine parameters:

(1) switch parameters (on=1, off=0):

ISWICH(1) = 1, compute energy levels and f-values. This switch should be always on.

ISWICH(2) = 1, compute photoionization cross sections. If there is interest in obtaining photoionization cross section data, turn off this switch by setting the parameter to 0.

SWICH(3) = 0, compute electron impact excitation cross sections. This option has not been completed yet.

ISWICH(4) = 0, compute autoionization rates. If autoionization rates for a specific electronic configuration are to be calculated, turn this switch on by setting the parameter to 1.

ISWICH(5) = 0, compute dielectronic recombination rate coefficients. If dielectronic recombination rate coefficients for a specific electronic configuration are to be calculated, turn this switch on by setting the parameter to 1.

(2) physical model selections:

IHF = 2, choose Hartree-Fock model by setting ‘IHF=2’, choose HX model by setting ‘IHF=1’. It is suggesed that the user choose ‘ihf=2’.

IREL = 1, if ‘IREL=0’ ATBASE does non-relativistic self-consistent-field calculations, if ‘IREL=1’ ATBASE does relativistic self-consistent-field calculations. For elements with Z ≤ 20, IREL should be set equal 0, while for elements with Z > 20, IREL should be set equal to 1.

(3) output criteria:

FVMIN= 1.0e-5, only consider those transitions with oscillator strength values larger than ‘fvmin’. In most cases, 1.0e-5 is appropriate.

(4) incorporating experimental data:

IEXPSW = 0, if the user wants to incorporate experimental data in the calculation, set IEXPSW equal 1, otherwise set IEXPSW equal 0. If ‘IEXPSW=1’, a formatted data table, ‘ev.expdat’, which contains experimental energy data must be provided by the user.

STEP 5: Check the following files to see whether they are consistent with the problem:

(1) config.inp:

Are all electronic configurations of your interest in the table? If this is for a large scale calculation, there must be at least one Rydberg state type configuration in the table.

(a) the trivial (unit-matrix) coefficient of Eav, the center-of-gravity energy of each configuration;

(b) the coefficients fk , gk, and d of the single-configuration direct and exchange Coulomb- interaction (F k^ and Gk^ ) and spin-orbit-interaction (ζ) radial integrals, and the coefficients rdk and rke of the direct and exchange configuration-interaction Coulomb radial integrals Rk^ , which are involved in the calculation of the Hamiltonian (energy-level) matrix elements;

(c) the magnetic-dipole matrix elements, and the angular coefficients of the electric-dipole and electric-quadrupole reduced matrix elements

P (^) l,l(t)′ = 〈l‖rt‖l′〉. (2.1)

Combining these angular coefficients with the radial integrals in the data file CILSJ INP, energy levels and intermediate-coupling eigenvectors are computed. And finally the energy levels and eigenvectors are used for computation of spectrum-line wavelengths and the associated oscillator strengths and radiative transition probabilities.

2.3.B. Calculating Photoionization Cross Sections

The calculations of photoionization cross sections are performed in subroutine BFDATA. BFDATA first calls subroutine INPUT3 to read in all bound configuration structure data from data file WFUNT DAT and to determine the electronic configurations of a residual ion after ionization. Then BFDATA calls subroutine EKMESH to construct a universal kinetic energy mesh for an ejected electron in threshold unit. Photoionization cross sections for each subshell are calculated in 50 kinetic energy points ranging from threshold to 500 times the threshold. In order to obtain a detailed shape of the cross sections (e.g., Cooper minimums, etc.), the whole kinetic energy region is divided into 5 sub-regions as shown in Table 6. The mesh points are distributed over each sub-region in a logarithm manner. In the calculation of photoionization cross sections, continuum wavefunctions are calculated by using a frozen core approximation, i.e., all bound wavefunctions are assumed to be unchanged before and after ionization. Configuration-interaction and autoionization resonance structure are not included.

2.3.C. Calculating Autoionization Rates and Dielectronic Recombination Rate Coefficients

First of all, it should be mentioned that the calculation of autoionization rates and dielectronic recombination rate coefficients in ATBASE is not done in an automatic manner, the user must do some hand calculations to set up the input properly. The following information must be supplied by the user as input for ATBASE to calculate autoionization rates and dielectronic recombination rate coefficients:

(1) Doubly excited (autoionizing) configuration.

(2) All possible stable configurations of residual ion after autoionization.

(3) All possible stable configurations of the ion after radiative decay from the autoionizing configuration.

(4) Threshold correction for doubly excited configuration. In some cases, not all the levels of the doubly excited configuration are autoionizing levels, only a few levels lie above the ionization limit of the ion. For this kind of configuration, the configuration- average energy Eav may be below the ionization limit. In such cases, the user must first calculate atomic energy levels for configurations in both (1) and (2) to determine the kinetic energies of a free electron via autoionization. These actual kinetic energies are assigned to the array element GODEPS (i) relative to the ith configuration of the residual ion.

(5) EIONRY, the ionization energy (in Ry) from the ground level of the recombined ion to the center of gravity energy of the ground configuration of the recombining ion. If EIONRY=0, the reference point is taken as the center of the gravity energy of the ground configuration of the recombined ion instead of the ground level.

(6) AEDGE, this is an edge value for excluding the non-physical autoionization. Only those levels with energy Ej > AEDGE can autoionize. AEDGE is in units of 1000 cm−^1 referenced to the same Emin as Ej does.

3. STATE

3.1. Program Outline

This is a code for generating input configuration tables for ATBASE calculations. Strictly speaking, STATE only functions as a convertor. It first takes the specifications for the atomic level structure from the user, and then goes into two pre-supplied electronic configuration tables, CONFIG.TAB and AUTOST.TAB, to dig out the proper configurations and outputs them to the files CONFIG.INP and HYGEN CFG in the format accepted by ATBASE. There are 4 files involved in running STATE. These files are listed in Table 7, along with the default logical unit numbers, names, types, and a brief description of their contents.

3.2. Input

STATE takes the input parameters in an interactive manner. In running STATE, the user must be able to answer the following questions about the level structure of an atomic system:

(1) what is the atomic number of the atomic system (atom/ion)? — input atomic nuclear charge Z.

(2) how many bound electrons are there in the atomic system? — input the number of bound electrons, the difference of (1) and (2) is the charge state of the atomic system.

(3) what kind of spectrum do you want to calculate? x-ray spectrum or thermal spectrum?

— x-ray spectrum and thermal spectrum are associated with two completely different energy level structures, x-ray spectrum is associated with inner-shell transitions, while the thermal spectrum is not. If the user is interested in the x-ray spectrum, those configurations with inner-shell holes must be included in the table.

(4) what is the maximum principal quantum number (nmax)? — to set up an atomic data table, the user must set a cutoff boundary for the bound states. This parameter limits the configuration table by only including the configurations with principal quantum number

not larger than nmax. For carbon atom, for example, if the input parameter is 4, only the following configurations will be included in CONFIG.INP:

1 s^22 s^22 p^2 ,

1 s^22 s^12 p^3 ,

1 s^22 s^22 p^13 s^1 ,

1 s^22 s^22 p^13 p^1 ,

1 s^22 s^22 p^13 d^1 ,

1 s^22 s^22 p^14 s^1 ,

1 s^22 s^22 p^14 p^1 ,

1 s^22 s^22 p^14 d^1 ,

1 s^22 s^22 p^14 f^1.

In most cases, nmax = 10 is a proper selection.

(5) what is the boundary for hydrogenic approximation (nhy)? — most users are usually only interested in spectra being associated with low excited levels. However, in order to take account of the influence of highly excited states on ionization balance and low excited state occupation numbers, it is necessary to include highly excited states in the calculation. Since no detailed spectrum information is required for these highly excited states, a hydrogenic approximation can be used to describe their average properties. It should be noted that nhy must be bounded by nmax, i.e., nhy ≤ nmax. A general guideline for setting this parameter is that if the outer shell principal quantum number of the ground configuration is ng, then nhy ≥ ng + 2.

(6) do you want to consider LS term structure? — if no, input 1, if yes, input 2.

(7) do you want to consider fine structure splitting? Specify the outer shell principal quantum number (nf ) and orbital quantum number (lf ) for the configurations you would like to consider fine structure. — Fine structure splitting will be considered for those

Atomic raw data files are arranged in the sequence of ionic state. There are four different raw data files for each ion. Each file is designated by the number of bound electrons in the ion and an extension specifying data property. #.LEV is a data file which contains atomic structure data such as energy levels, number of shells, binding energy of each shell and the radius of each shell, etc., where # represents the ion with # bound electrons, #.FDA is a data file contains all the oscillator strengths, #.PDA is a data file containing photoionization cross sections, and #.STRENG is a data file containing collision strengths of electron impact excitations. Data files #.LEV, #.FDA, and #.PDA are generated from ATBASE calculations, while #.STRENG is generated from DWBORN calculations. If #.STRENG is not supplied, the collisional coupling between levels will not be complete; only electric-dipole-allowed couplings are considered.

4.3. Rate Coefficient Calculations

Rate coefficients for the following atomic physics processes are calculated in ATTABLE. A Maxwellian distribution is assumed for free electrons in all cases.

(1) Spontaneous decay. Spontaneous decay rates are deduced from the corresponding transition energies and oscillator strengths.

(2) Electron impact excitation. For electric dipole allowed transitions, electron impact excitation rate coefficients are calculated by using a semiclassical impact parameter method [5], while for forbidden transitions, collision strengths must be supplied from data file #.STRENG which is generated from DWBORN calculations.

(3) Electron collisional deexcitation. Deexcitation rate coefficients are obtained from the detailed balance relationship with excitations.

(4) Electron impact ionization. Rate coefficients are calculated by using Burgess’ semiempirical formula [6].

(5) Electron collisional recombination (three body recombination). Rate coefficients are obtained from the detailed balance relationship with ionizations.

(6) Radiative recombination. Rate coefficients are obtained by integrating Hartree-Fock photoionization cross sections weighted by a Maxwellian distribution.

(7) Dielectronic recombination. Rate coefficients are calculated by using Burgess-Mert semiempirical formula [7].

4.4. Output

Two output files, ATOMIC.DAT and PIXFIT.DAT, are generated from running ATTABLE.

ATOMIC.DAT contains the following information for a specific atom:

(1) atomic nuclear charge Z;

(2) total number of atomic energy levels included in the model;

(3) energy level structure for each ion;

(4) oscillator strengths and spontaneous decay rates for all transitions;

(5) rate coefficients for b-b transitions at a specially designed plasma temperature grid;

(6) rate coefficients for b-f transitions at a specially designed plasma temperature and density grid.

PIXFIT.DAT contains subshell photoionization cross sections for all states in the model. Photoionization cross sections are fit to

σ(ν) = σ(ν 1 ){β(ν ν^1 )φ^ + (1 − β)(ν ν^1 )φ+1} (4.2)

where ν 1 is the ionization threshold value. Four fitting parameters, σ(ν 1 ), ν 1 , β and φ are listed in PIXFIT.DAT for each subshell of all atomic states.

5. DWBORN

5.1. Program Outline

DWBORN is a code for computing electron impact excitation cross sections by using a distorted wave Born method [8]. The calculations of this code may serve two purposes:

(1) as a benchmark for the calculated results of semiclassical impact parameter method;