RECENT RADIATIVE AND COLLISIONAL ATOMIC DATA OF ASTROPHYSICAL INTEREST

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RECENT RADIATIVE AND COLLISIONAL ATOMIC DATA OF ASTROPHYSICAL INTEREST

K. Baluja, K. Butler, J. Le Bourlot, C. Zeippen

To cite this version:

K. Baluja, K. Butler, J. Le Bourlot, C. Zeippen. RECENT RADIATIVE AND COLLISIONAL

ATOMIC DATA OF ASTROPHYSICAL INTEREST. Journal de Physique Colloques, 1988, 49 (C1),

pp.C1-129-C1-132. �10.1051/jphyscol:1988128�. �jpa-00227448�

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JOURNAL DE PHYSIQUE

Colloque C1, Suppl6ment au n03, Tome

49,

Mars 1988

RECENT RADIATIVE AND COLLISIONAL ATOMIC DATA OF ASTROPHYSICAL INTEREST

K.L. BALUJA, K. BUTLER', J. LE BOURLOT"' and

C.J.

**Z E I P P E N * ~ Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India**

'~nstitut fur Astronomie und Astrophysik der Universitdt Miinchen, 0-8000 Miinchen, F.R.G.

"~berservatoire d e Paris, Section dlAstrophysique, F-92190 Meudon, France

RESUME. A l'aide de programmes d'ordinateur sophistiquks et de modiles physiques bla- borks, des donnkes atomiques radiatives et collisionnelles prkcises d1int6r@t astrophysique ont 6th ou sont en train d'gtre calculbes. Les cas traitks com- prennent les transitions radiatives entre dtats liks dans les configurations zp4 et 2s2p5 de nombreux ions de la sequence isoblectronique de l'oxygkne, la photoionisation de l'ktat fondamental du fer neutre, l'excitation par impact klectronique des transitions interdites de structure fine dans la configuration fondamentale 3p3 de CE 111, Ar IV et K V, et la production en masse de donnbes radiatives pour les ions des sgquences iso6lectroniques de l'oxygkne et du fluor, en tant que contribution au projet international Opacity.

SUMMAJ$Y.. Using sophis.ticated computer programs and elaborate physical models, accurate radiative and collisional atomic data of astrophysical interest have been or are being calculated. The cases treated include radiative transitions between bound states in the 2p4 and 2 ~ 2 ~ 5 configurations of many ions in the oxygen isoelectronic sequence, the photoionisation of the ground state of neutral iron, the electron impact excitation of the fine-structure forbidden transitions within the 3p3 ground configuration of CL 111, Ar IV and K V, and the mass-production of radiative data for ions in the oxygen and fluorine isoe-

lectronic sequences, as part of the international Opacity Project.

1. INTRODUCTION.

Accurate radiative and collisional atomic data are required for a meaningful interpretation of astronomical observations for a variety of objects including stellar atmospheres, nebulae, quasars, comets, the solar corona, etc. The advent of powerful computing facilities, like the CRAY machines, and the constant improvement of theoretical and numerical methods allow atomic physicists to meet more and more of these needs with numerous and reliable results. The present work is part of a vast international effort involving workers based in a number of laboratories in several countries.

2. METHODS.

To solve the structure problem, either the CIV3 (1) or the SUPERSTRUCTURE (2) co- des are used. The former implements Racah algebra techniques and a formalism combining Hartree-Fock and correlation orbitals, while the latter is based on a Slater-state formalism and a Thomas-Fermi statistical model potential. Both programs allow for configuration-interaction calculations and Breit-Pauli relativistic corrections are treated as perturbations.

The collisional method used in the present work is known as the "close coupling"

approximation (3). The atomic system is represented as a target plus an external electron. The wavefunction for a state SLII (spin, orbital angular momentum, parity) of the total system is given by

where Xi is a target wavefunction, Oi is a free-electron function and A is an antisym- metrisor. The bound states $j are included to describe more accurately electronic cor- relations.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988128

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C1-130 JOURNAL

DE

PHYSIQUE

The present target wavefunctions are obtained with the help of SUPERSTRUCTURE or CIV3 (see above) and the reactance matrices required to evaluate collision strengths (electron impact excitation), photoionisation cross sections (bound-free radiative transitions) or oscillator strengths (bound-bound radiative transitions) are computed using one of the following numerical methods : R-matrix of the code RMATRX (4), inte- gro-differential of the code IMPACT (5) and distorted-wave of the code DSTWAV (6). Al- so, new programs developed in the course of the Opacity Project (7) are employed, in particular in the asymptotic region.

3. RESULTS.

a. Radiative transitions between bound states in the 2p4 and 2 ~ 2 ~ 5 configurations.

Two of us (Baluja and Zeippen 1987a, submitted and 1987b, to be submitted) have built accurate wavefunctions to represent 17 species (from 0 I to Kr XXIX) in the 0 I isoelectronic sequence, using the code CIV3. Spectroscopic orbitals Is, 2s and 2p cor- responding to the ground state zp4 3~ of each ion were taken from (8) and kept fixed at thcir Lartr~e-Fock values. This set of functions was augmented by correlating orbitals 3s, 3p, 3d, obtained by minimising the energy of the 2p4 state. The configurations included in the calculation are 2p4, Z p 3 5 , 2p222, zp2G2, zP2a2, 2 ~ 2 ~ 4 a , 2p2g%, 2 ~ 2 ~ 3 5 5 and 2p6.

The present excitation energies, when including the first-order relativistic corrections, agree well with experiment and with the most accurate and extensive studies available in the literature (9, 10, 11). To assess further the quality of our wavefunctions, we calculated LS-coupling oscillator strengths for the allowed transitions 2p4 3~

-

2s2p5 3 ~ 0 , 2p4 I D , ~ s

-

2 ~ 2 ~ 5 IP0. Finally, we computed M1 and E2 transition probabilities for fine-structure forbidden lines within the 2p4 configuration. Our results compare well with other theoretical data (9, 11). We conclude that our wavefunctions could be used for collisional work involving targets in the 2p4 isoelectronic sequence and that our transition probabilities could be used in astrophysical models or for comparison with other work. Table 1 contains a sample of present excitation energies, compared with experiment.

Table 1. Excitation energies (in a.u.).

transition 2p4 3~

-

2 ~ 2 ~ 5

PO

Zp4 ID

-

2 ~ 2 ~ 5 IPO 2p4 1s

-

2 . ~ 2 ~ 5 1 ~ 0

ion exP pres exP pres exP pres

0 I 0.5752 0.5777 0.7927 0.7814 0.7111 0.7026

F I1 0.7509 0.7547 0.9967 1.0038 0.8871 0.8980

Ne I11 0.9308 0.9324 1.2013 1.2246 1.0650 1.0925 Na IV 1.1102 1.1106 1.4256 1.4445 1.2631 1.2864

Mg V 1.2902 1.2904 1.6475 1.6650 1.4591 1.4812

A t VI 1.4714 1.4711 1.8692 1.8857 1.6548 1.6762

Si VII 1.6542 1.6535 2.0918 2.1074 1.8514 1.8721

S IX 2.0261 2.0245 2.5410 2.5554 2.2477 2.2676

Ar XI 2.4106 2.4066 3.0008 3.0122 2.6517 2.6690 K XI1 2.6088 2.6032 3.2346 3.2448 2.8556 2.8719 Ca XI11 2.8119 2.8040 3.4724 3.4806 3.0613 3.0757 Ti XV 3.2361 3.2216 3.9612 3.9644 3.4741 3.4858 Cr XVII 3.6914 3.6643 4.4698 4.4672 3.8886 3.8937 Mn XVIII 3.9298 3.8968 4.7348 4.7278 4.0923 4.0957 Fe XIX 4.1790 4.1559 5.0058 5.0109 4.2938 4.3092 Ni XXI 4.7136 4.7088 5.5777 5.6094 4.6915 4.7336

Kr XXIX

-

^7.0599

-

^8.2513

-

^6.0095

b. Photoionisation of the ground state of neutral iron.

Neutral iron is of great importance in astrophysics. Unfortunately, it is also a very difficult case to treat due to its large number of electrons. Two of us (Baluja and Zeippen 1987c, in preparation) have attempted to perform a calculation of the photoionisation of the ground state of iron, using the RMATRX code and the Fe I1 target wavefunctions in (12). This representation of the residual ion includes the four even-parity states 3d64s 6 ~ , 3d7 4 ~ , 3d64s 4~ and 3d7 4 ~ . We consider the radiative transitions

Fe(3d64s2 5 ~ )

+

^hv⁺^{^F^e^'

+

e-1 5 ~ 0 , 5 ~ 0 ,

The number of channels is 9,6,9,10 for the symmetries 5 ~ , 5 ~ 0 , 5 ~ 0 , 5 ~ 0 , respective- ly. Our work is very limited : the LS-coupling scheme is not too well adapted to a heavy element like l?e and the effect of the neglected resonance series converging to

thresholds higher than the first 4 target states may be considerable. However, this

"simple" calculation, somewhat costly in CPU time, provides a first-step estimate of

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the "R-matrix" photoionisation cross section for neutral iron, illustrating the com- plexity of the problem.

Figure 1 shows the 3 partial photoionisation cross sections. At 0.584 Ryd., just above the ionisation threshold, the values are (in Mb) : 2.23(L), 1.77(V) for 5~

-

^5p0;

4.42(L),2.90(V) for 5~

-

^{5 ~ 0 ;}0.05(L),0.04(V) for 5~

-

^5~0.The overall 40 % discrepancy between length and velocity results is to be compared with the 10 % or less difference regularly obtained for light elements in R-matrix photoionisation calculations.

Figure 1.

c. Electron impact excitation of CR 111, Ar IV and K V.

The interpretation of forbidden lines in nebulae provides much valuable informa- tion when good observational and atomic data are available. Three of us have completed an extended calculation with a view to produce improved electron excitation rate coef- ficients for the f ine-structure transitions within the ground configuration 3p3 of Cl 111 (Butler and Zeippen 1987a, to be submitted), Ar IV (13) and K V (Butler, Zeippen and Le Bourlot 1987, to be submitted). Our study includes the seven energy terms of the spectroscopic configurations 3p3 and 3 ~ in the 3 tar ets. Employing 3 ~ ~ SUPERSTRUCTURE, we also use 6 correlation configurations : ~ ~3 ~ 3 ~ 3 % f , 5 , 3 p 2 a , 3p3d2, 3 p 2 a , 3p4% and we minimise the weighted sum of the term energies of interest, thus obtaining a discrepancy with experimental energies which is never more than 6 % (less than 2 % for odd-parity states).

The scattering problem is solved using the code IMPACT to estimate the contribution of partial waves up to l,R'<3 and the code DSTWAV that of higher partial waves.

All the possible symmetries of the total (e-

+

target) system are considered. Finally, the LS-coupling reactance matrices are converted to intermediate coupling by the code JAJOM (14) and fine-structure collision strengths are obtained. The present results differ by up to a factor of 5 from previous work (15) and should be accurate to much better than a factor of 2.

R Figure 2 illustrates the effect

of the new rates calculated on the

'1

⁼1(4741'5 a)n(4712'7 a)

fl

basis of the Dresent collision strengths in the case of an important line intensity ratio in Ar IV.

Present It is seen that for a given value of R, Ne is now found to be as much as a factor of 3 smaller than before in the density-sensitive range. Note Te = 20*000 O K that both curves were obtained using

the radiative transitjon ~robabili- - - -

3 4 5 6

;

ties calculated by (16) fbr forbidden

Density Ne (in Log) lines in the 3p3 configuration.

Figure 2.

d. .Contribution to the Opacity Project : the 0 I and F I isoelectronic sequences.

Considerable uncertainties affect existing opacity tabulations. In stellar atmospheres, opacities are determined by all possible radiative processes : bound-bound, bound-free, free-free, and important contributions come from elements other than H and He and which are not fully ionised (7, 17). An ambitious international effort named the Opacity Project, launched and coordinated by M.J. Seaton, aims at producing the very large set of accurate atomic data required for a more reliable estimate of stel-

lar opacities. The Project involves workers in Europe, the USA and Venezuela. All the n=2 isoelectronic sequences are being treated, plus specific ions of iron.

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CI-132 JOURNAL DE PHYSIQUE

Two of us (Butler and Zeippen 1987b, in progress) are in charge of the 0 I sequence, up to Fe. SUPERSTRUCTURE, RMATRX and the new Opacity codes are used. The targets include 8 spectroscopic terms : 2p3 4 ~ 0 , 2 ~ 0 , 2 ~ 0 ; 2 ~ 2 ~ 4 ~ P , ~ D , ~ s , ~ P ; 2p5 2 ~ 0 . 5 correlation configurations : 2.~2~3371, 2 ~ ~ 2 ~ ~ 3 7 1 , 2 ~ 2 2 ~ 2 G , 2 ~ 2 2 ~ % ~ , 2p4% and a minimisa- tion of the sum of the spectroscopic term energies yield good agreement with experimental energies. To illustrate the accuracy of the data produced, we take the photoionisation of the ground state of oxygen. Table 2 shows that the present cross section at threshold is close to the oldest and two most recent theoretical results in the literature. Note that the present difference between length and velocity values is less than 7 % and that all theoretical data lie within the error bars of the latest experiment. The fluorine sequence is treated in similar fashion (Butler and Zeippen 1 9 8 7 ~ ~

in progress). The present data and those computed by other collaborators to the Project will be published together in a special volume. Even though the primary aim of the work is to establish a firmer basis for stellar studies, much of the data being obtained will be of great use for other astronomy problems.

Table 2. Photoionisation cross section of o(~P) at threshold (ME).

Theory.

L

v

Present. 3~

-

^{3 ~ 0}3.21 3.08 3 ~ - 3 ~ 0 0.67 0.56 Total 3.88 3.64

(18) 4.4 3.6

(19) 4.1

(20) 4.0

Experiment.

(21) (4.0 +- 0.4)

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Acknowledgements.

The present calculations were performed on the NAS 9080 computer a t the CIRCE and the CRAY-I and CRAY-2 computers a t the CCVR (France) and on the CDC computers a t the Ludwig l l a x i m i l i a n ' s University, Munich, Ger- many. KLB and KB v i s i t e d Meudon w i t h support from the Observatoire de Paris. KB i s indebted t o the Royal Society f o r a European Science Exchange F e l l owship.