A NEW AID FOR INTERPOLATING AND ASSESSING COLLISION STRENGTHS AND RATE COEFFICIENTS

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A NEW AID FOR INTERPOLATING AND

ASSESSING COLLISION STRENGTHS AND RATE COEFFICIENTS

A. Burgess, H. Mason, J. Tully

To cite this version:

A. Burgess, H. Mason, J. Tully. A NEW AID FOR INTERPOLATING AND ASSESSING COLLI-

SION STRENGTHS AND RATE COEFFICIENTS. Journal de Physique Colloques, 1988, 49 (C1),

pp.C1-107-C1-110. �10.1051/jphyscol:1988122�. �jpa-00227442�

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JOURNAL DE PHYSIQUE

Colloque C1, Supplement au n03, Tome 49, Mars 1988

A NEW AID FOR INTERPOLATING AND ASSESSING COLLISION STRENGTHS AND RATE COEFFICIENTS

A. BURGESS, H.E. MASON and J.A. TULLY*

Department of Applied Mathematics and Theoretical Physics, Silver Street. GB-Cambridge CB3 9EW, Great-Britain

"~bservatoire de Nice, BP 139, F-06003 Nice Cedex, France

RESUME: On propose une methode n o u v e l l e permettant

a

des non s p e c i a l i s t e s de l a physique atomique d ' u t i l i s e r commod6ment l e s donnees r e l a t i v e s il 1 'e x c i t a t i o n des i o n s posi t i f s p a r choc e l e c t r o n i q u e d i sponi b l e s dans 1 a 1 i t t e r a t u r e

.

C e t t e m6thode permet

a

l a f o i s ( i ) de d e t e c t e r d ' @ v e n t u e l l e s e r r e u r s dans des t a b l e s publiees ( f a u t e s de frappe ou e r r e u r s de c a l c u l ) , ( i i ) d ' i n t e r p o l e r e t d ' e x t r a p o l e r l e s d o n n e s e x i s t a n t e s en f o n c t i o n de l ' e n e r g i e e t de l a temperature e t , ( i i i ) de s i m p l i f i e r considerablement l e stockage e t l e t r a n s f e r t des donn6es sans p e r t e d ' i n - f o r m a t i o n s i g n i f i c a t i v e . On procede t o u t d'abord I l a r e d u c t i o n des valeurs des f o r c e s de c o l l i s i o n n(E) dont on dispose (mesur6es ou c a l c u l 6 e s ) . On p o r t e e n s u i t e s u r un graphe l e s v a l e u r s a i n s i obtenues en f o n c t i o n de l ' e n e r g i e r e d u i t e d e f i n i e de t e l l e s o r t e que l e domaine (0,m) s o i t r a p p o r t 6

a

l ' i n t e r v a l l e ( 0 , l ) . Pour une t r a n s i t i o n donn6e l e graphe correspondant 2i 0 r e d u i t e peut a l o r s e t r e represents avec une bonne p r e c i s i o n

-

normalement mieux qu'un pourcent

-

par une f o n c t i o n s p l i n e

a

moindres carres p o r t a n t sur seulement 5 noeuds. Plus de d e t a i l s sont donn6s dans (1). Par des techniques s i m i l a i r e s on peut egalement o b t e n i r des forces de c o l l i s i o n thermiques u p s i l o n ( T ) pour n ' i m p o r t e q u e l l e temperature e l e c t r o n i q u e T dans 1 'i n t e r - v a l l e (0,-). Un programme i n t e r a c t i f avec t r a i t e m e n t graphique (2) f a c i l i t e 1 ' a p p l i - c a t i o n de l a methode. Pour i l l u s t r e r c e t t e procedure commode nous 1 'appliquons au t r a i t e m e n t de

n

pour l a t r a n s i t i o n optiquement permise 2s + 2p dans ArXVI.

ABSTRACT: A new way o f c r i t i c a l l y assessing and compacting d a t a f o r e l e c t r o n impact e x c i t a t i o n o f p o s i t i v e i o n s i s proposed. This method a l l o w s one ( i ) t o d e t e c t p o s s i b l e p r i n t i n g and computational e r r o r s i n t h e p u b l i s h e d tables, ( i i ) t o i n t e r p o l a t e and e x t r a p o l a t e t h e e x i s t i n g data as a f u n c t i o n o f energy o r temperature, and ( i i i ) t o simp1 i f y considerably t h e storage and t r a n s f e r of data w i t h o u t s i g n i f i c a n t l o s s o f information. T h e o r e t i c a l o r experimental c o l l i s i o n s t r e n g t h s n(E) are scaled and then p l o t t e d as f u n c t i o n s o f t h e c o l l i d i n g e l e c t r o n energy, t h e e n t i r e range o f which i s conveniently mapped onto the i n t e r v a l (0,l). For a given t r a n s i t i o n the scaled

n

can be a c c u r a t e l y represented

-

u s u a l l y t o w i t h i n a f r a c t i o n o f a percent

-

by a 5 p o i n t l e a s t squares s p l i n e . F u r t h e r d e t a i l s are g i v e n i n (2). S i m i l a r techniques enable t h e r m a l l y averaged c o l l i s i o n s t r e n g t h s u p s i l o n ( T ) t o be o b t a i n e d a t a r b i t r a r y tem- peratures i n the i n t e r v a l 0 < T <

-.

A p p l i c a t i o n o f ' t h e method i s p o s s i b l e by means o f an i n t e r a c t i v e program w i t h graphical d i s p l a y ( 2 ) . To i l l u s t r a t e t h i s p r a c t i c a l procedure we use t h e program t o t r e a t n f o r the o p t i c a l l y allowed t r a n s i t i o n 2s -+ 2p i n 9rXVI.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988122

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N u c l e a r Charge = 18 Charge on I o n = 15 Energy L e v e l s : Lower(cm-1) = 0

Upper (cm-1) = 274027 Di f f

.

^(cm-1)⁼²⁷⁴⁰²⁷

T r a n s i t i o n Type = 1 g f v a l u e = 0.1681 T r a n s i t i o n : Rrgon+15 2s-2p

D a t a source: Mann DW, w i t h 7 p t s . r e p l a c e d b y H e n r y CC

Omega 9.680E-1 9.800E- 1

1.020EO 1.027EO 1. ObOEO l.098EO l.lbOE0 1.201EO 1.266EO 1.340EO 1.330EO 1.410EO 1.698EO 1.590EO 1.893EO 1.991EO 2.087EO 2.lBlEO 2.273EO 2.362EO

Table 1. Example o f raw data f o r a type 1 t r a n s i t i o n . The c o l l i s i o n s t r e n g t h s t o be processed by t h e program are taken from (3,4). E j i s t h e energy of t h e c o l l i d i n g e l e c t r o n a f t e r e x c i t a t i o n . Note t h a t t h e values o f omega f o r I = 11, 12 and 14 were computed i n a 5 - s t a t e c l o s e c o u p l i n g approximation ( 4 ) .

DATA REDUCTION

Ered = 1

-

I n C / l n ( E j / E i j

+

C) nred = n / l n ( E j / E i j + e) E i j = t r a n s i t i o n energy C = a d j u s t a b l e parameter

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F i g u r e 1. P l o t o f reduced data. I n t h i s example t h e c a l u e C = 4 has been chosen t o o p t i m i s e t h e d i s t r i b u t i o n o f data p o i n t s . The 3 values o f nred r e f e r r e d t o i n Table 1 a r e seen t o d e v i a t e from the general t r e n d o f t h e o t h e r s . They were t h e r e f o r e

replaced by Mann's d i s t o r t e d wave r e s u l t s ( 3 ) before proceeding t o t h e s p l i n e f i t . The h i g h energy l i m i t p o i n t a t Ered = 1.0 i s given by fired = 4pf(13.60eV/Eij).

0 . 0 0.2 0 . 4 0.E 0.8 1.0

Ered

F i g u r e 2. S p l i n e f i t t o the reduced data. The values o f Qred a t t h e 5 knots a r e t a b u l a t e d t o t h e r i g h t o f t h e graph. Note t h a t t h e 3 dubious p o i n t s i n F i g u r e 1 have been replaced by more r e l i a b l e ones. The l e a s t squares s p l i n e f i t has an r.m.s.

e r r o r of l e s s than 0.3%.

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F i g u r e 3. Graphical comparison of the t a b u l a t e d c o l l i s i o n s t r e n g t h s (+) and t h e s p l i n e f i t (----).

CONCLUDING REMARKS

The example presented here i s f o r an o p t i c a l l y al&wed t r a n s i t i o n . The program can a l s o be used f o r forbidden and i n t e r c o m b i n a t i o n t r a n s i t i o n s which a r e t r e a t e d i n a s i m i l a r fashion.

There e x i s t s an opt-ion f o r e v a l u a t i n g u p s i l o n from omega s p l i n e .

When n e x h i b i t s resonance s t r u c t u r e i t i s customary t o evaluate and t a b u l a t e u p s i l o n as a f u n c t i o n o f temperature. The program can be used t o analyse T(T) i n a manner analogous t o t h a t used f o r n(E).

I n conclusion we can summarise some o f t h e advantages of t h e method as f o l l o w s : 1) The user does not; need t o be an e x p e r t i n atomic c o l l i s i o n theory.

2) There a r e o n l y 6 f i t t i n g parameters f o r each t r a n s j t i o n .

3 ) These a r e obtained by an i n t e r a c t i v e program from the o r i g i n a l t a b u l a t e d data.

4 ) The h i g h energy o r temperature behaviour o f t h e c o l l i s i o n s t r e n g t h i s t r e a t e d c o r r e c t l y by t h e program.

5 ) E r r o r s i n t h e o r i g i n a l data can be detected v i s u a l l y .

REFERENCES

1. Burgess A. and T u l l y J.A. 1988 ( i n p r e p a r a t i o n ) .

2. Burgess A. 1988 Comput. Phys. Commun. ( t o be published).

3. Merts A.L., Mann J.B., Robb W.D. and Magee J r . N.H. 1980 Los Alamos S c i e n t i f i c Laboratory Report No. LA-8267-MS, Los A1 amos, New Mexico, U .S.A.

4. Gau J.N. and Henry R.J.W. 1977 Phys.Rev. A16, 986.