HAL Id: jpa-00227581
https://hal.archives-ouvertes.fr/jpa-00227581
Submitted on 1 Jan 1988
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
THEORETICAL SPECTRA OF Fe XXIII - Fe XIX IONS IN TWO CALCULATION METHODS
M. Cornille, J. Dubau, M. Loulergue, F. Bely-Dubau, P. Faucher, U.
Safronova, A. Shlyaptseva
To cite this version:
M. Cornille, J. Dubau, M. Loulergue, F. Bely-Dubau, P. Faucher, et al.. THEORETICAL SPECTRA
OF Fe XXIII - Fe XIX IONS IN TWO CALCULATION METHODS. Journal de Physique Colloques,
1988, 49 (C1), pp.C1-319-C1-321. �10.1051/jphyscol:1988167�. �jpa-00227581�
JOURNAL DE PHYSIQUE
Colloque C1, Supplement au n03, Tome 49, Mars 1988
THEORETICAL SPECTRA OF Fe XXIII - Fe XIX IONS IN TWO CALCULATION METHODS
M. CORNILLE, J. DUBAU, M. LOULERGUE, F. BELY-DUBAU', P. FAUCHER*, U.I. SAFRONOVA** and A.S. SHLYAPTSEVA"
Observatoire de Paris, F-92195 Meudon principal Cedex, France '~bservatofre de Nice, BP 139, F-06003 Nice Cedex, France
" ~ n s t i t u t e of Spectroscopy, Academy of Sciences of the USSR, Troistsk
1 4 2 0 9 2 ,USSR
Deux mdthodes dc calcul des parametres atomiques nhcessaires 2 llanalyse du spec- tre X des ions du Fe XXIII - Fe XIX (1.85
-
2 A) sont compardes. La comparaison est faite sur les raies satellites dielectroniques du type 1 ~ 2 ~ ~ 2 ~ "-
ls22sk2pn-1 (lon- gueurs d'ondc, probabilitds de transition radiative et dlautoionisation, facteurs de raics). Cette dtude a pour but llinterprdtation des spectres X dmis par les plasmas chauds et de faible densite (druptions solaires et plasmas de Tokamak).Abstract :
Two different calculation metbods are compared for Fe XXIII
-
Fe XIX spectra in the X-ray range between 1.85-
2 A, for transitions of the type 1s2sk 2pnWavelengths, radiative transition and autoionization probabilities as well as thein- tensity factors are compared. These parameters are given in order to diagnosis low density plasmas as found in solar flares and Tokamak devices.
The X-ray emission of highly ionized atoms in low density, hot plasmas such as observed in solar flares or Tokamak devices is'dominated by the resonance line emis-
sion of the H and He-like ions and their associated dielectronic satellites. The analysis of these satellite lines is of fundamental importance for the investigation of the physics of the highly ionized ions as well as for the interpretation in term of temperature and density diagnostics of the emitting plasmas. The most prominent satellite lines observed correspond to the transitions 2s2p-ls2s, 2p2-lszp, ls2s2p- ls22s, ls2p2-ls22p. That is the reason why the autoionization states of two and three electron systems have been the most well-studied in the past (1). On the con- trary, for autoionization states with four or more electrons, there are only few ob- servations (2, 3 ) , few calculations and practically no comparison. This is due to the complexity of the theoretical problem as well as the observational one. We pre- sent here a comparison between two different methods : the MZ method by Vainstein and Safronova
(4)
and the AUTOLSJ method by Dubau et al. ( 5 ) . The comparison is do- ne on Fe XXIII-
Fe XIX for transitions of the type 1 ~ 2- ~1s22sk2pn-1. Iron ~ 2 ~ ~ was chosen due to the possibility of comparison with observations.1) Calculation methods
A common feature of both methods is that the energy matrix is constructed on the basis of the L-S scheme and the relativistic corrections are included within the framework of the Breit-Pauli operator. The methods use a perturbational approach.
The main difference is in the choice of the monoelectronic wave functions used for building the unperturbed wave functions of the n-electron system. In the
MZ
method these monoelectronic wave functions are hydrogenic whereas in the SWERSTRUCTURE program (14) used by AUTOLSJ, the wave functions are calculated in a scaled Thomas Fermi Dirac potential, the scaling parameters are obtained by a sel: consistentener- gy minimization procedure. Another difference appears on the basis size of the un- perturbed wave functions. In the MZ method, the basis is complete including both bound and continuum states when in SUPERSTRUCTURE the truncated basis is limited to the most important bound states, the apparent restriction can be compensated by the minimization procedure.. In the MZ method the energy of a given state is calculated by diagonalization procedure of the energy matrix elements between the states of the same Laser complex, the contribution of all states belonging to the other complexes is introduced as a secc,>d order perturbation correction.Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988167
CI-320
JOURNAL DE PHYSIQUEI n t h e SUPERSTRUCTURE Trogram t h e d i a g o n a l i z a t i o n i s done f o r a l l t h e s t a t e s of t h e t r u n c a t e d b a s i s . The MZ method i s b e t t e r f o r systems w i t h few e l e c t r o n s s i n c e t h e h y d r o g e n i c o r b i t a l s a r e r e a l i s t i c and t h e method c a n b e c a r r i e d t o any o r d e r of p e r t u r b a t i o n o n a complete b a s i s . F o r s y s t e m s w i t h many e l e c t r o n s and a n a v e r a g e p o t e n t i a l b e i n g more r e a l i s t i c , SUPERSTRUCTURE c a n g i v e a c c u r a t e r e s u l t s f a s t e r t h a n MZ which becomes r a p i d l y u n t r a c t a b l e .
As mentioned above, i n b o t h a p p r o x i m a t i o n s t h e r e l a t i v i s t i c c o r r e c t i o n s w e r e t a - ken i n t o a c c o u n t w i t h i n t h e framework o f t h e B r e i t P a u l i o p e r a t o r . There a r e t h e one-body o p e r a t o r s a s mass, Darwin and s p i n - o r b i t and t h e two-body o p e r a t o r s a s s p i n - s p i n c o n t a c t , two-body Darwin, o r b i t - o r b i t , s p i n - o t h e r o r b i t and s p i n - s p i n .
I n b o t h methods e a c h of t h e o p e r a t o r s i s c a l c u l a t e d w i t h non r e l a t i v i s t i c f u n c t i - ons. The r a d i a t i v e p r o b a b i l i t i e s Ar and t h e a u t o i o n i z a t i o n p r o b a b i l i t i e s Aa a r e c a l - c u l a t e d i n b o t h schemes w i t h t h e u s e o f t h e v e c t o r c o u p l i n g c o e f f i c i e n t s o b t a i n e d upon d i a g o n a l i z a t i o n of t h e m a t r i x e n e r g y ( i n MZ w i t h t h e complex s t a t e s e t and i n AUTOLSJ w i t h t h e t r u n c a t e d b a s i s s e t ) .
I n t h e f o l l o w i n g s e c t i o n s we compare t h e w a v e l e n g t h s
A,
t h e r a d i a t i v e t r a n s i t i o f i s p r o b a b i l i t i e s A, and t h e l i n e f a c t o r Qd d e f i n e d zs :where XAr i s t h e t o t a l r a d i a t i v e p r o b a b i l i t y and CAa t h e t o t a l a u t o i o n i z a t i o n proba- b i l i t y f o r t h e upper l e v e l o f t h e t r a n s i t i o n .
2 ) R e s u l t s
F o r e a c h i o n a s e l e c t i o n o f t h e s t r o n g e s t l i n e s i s g i v e n i n t h e t a b l e . As f a r
T a b l e : D i e l e c t r o n i c s a t e l l i t e l i n e s ( n = 2) c a l c u l a t e d w i t h AUTOLSJ method ( a ) and
MZ
method (b)a s we a r e concerned w i t h low d e n s i t y plasmas we g i v e only t h e Qd f a c t o r correspon- d i n g t o d i e l e c t r o n i c recombination on t h e ground l e v e l of t h e recombining ion(FeXX1, Fe XX)
.
For FeXIX t h e r e i s no p o p u l a t i o n process by d i e l e c t r o n i c recombination from t h e lo- west l e v e l 1 ~ ~ 2 s ~ 2 p ' ~ S , , , of FeXX. For t h i s i o n we g i v e only t h e wavelengths and r a - d i a t i v e p r o b a b i l i t i e s .
O n e c a n s e e on t h e t a b l e t h a t t h e r e i s a s y s t e m a t i c d i f f e r e n c e of s 0 . 0 0 3 A on t h e wa- v e l e n g t h s . This d i f f e r e n c e seems t o d e c r e a s e f o r FeXX t h a t i s when t h e number of e l e c t r o n s i s growing up. This tendancy can be explained by t h e f a c t t h a t f o r system w i t h many e l e c t r o n s an average p o t e n t i a l i s more r e a l i s t i c .
For t h e two o t h e r parameters Ar and Qd t h e agreement between t h e two methods i s qui- t e good f o r l a r g e v a l u e s of t h e s e parameters. More important d i s c r e p a n c i e s appear when t h e s e v a l u e s a r e s m a l l e r . The f u l l s e t of d a t a w i l l be published l a t e r i n J . Phys. B.
REFERENCES
(1) A g l i t s k i , E.V., Safronova, U . I . , A u t o i o n i z a t i o n s t a t e s spectroscopy of atomic systems, 1984, Energoatomizdat. Moscow.
(2) Lemen, J.R., P h i l l i p s , K.J.H., Cowan, R.D., Hata, J . , Grant, I . P . , 1984, Astron.
Astrophys.
135,
313 (Paper 1 1 ) .(3) B i t t e r , M., Von Goeler, S . , H i l l , K.W., Horton, R., Johnson, D . , Roney, W . , S a u t h o f f , N , , S i l v e r , E . , S t o d i c k , W . , 1981, Phys. Rev. L e t t .
67,
921.(4) V a i n s t e i n , L.A., Safronova, U . I . , 1978, Atomic and n u c l e a r Data T a b l e s ,
2,
49.(5) Dubau, J . , G a b r i e l , A.H., Loulergue, M., Steenman C l a r k , L . , VolontB, S., 1981, Mon. Not. R. A s t r . Soc.
