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Photoionization of positive ions of atomic oxygen
Volume 38A, n u m b e r 2
PHYSICS
LETTERS
17 J a n u a r y 1972
P H O T O I O N I Z A T I O N OF P O S I T I V E IONS
OF A T O M I C OXYGEN
D. W. MISSAVAGE and S. T. MANSCN Department of Physics, Georgia State University, Atlanta, Georgia 30303, USA Received 30 November 1971
The p h o t o i o n i z a t i o n c r o s s s e c t i o n of the K - s h e l l of a t o m i c o x y g e n and i t s p o s i t i v e i ons to 0 6+ h a s b e e n c a l c u l a t e d u s i n g H a r t r e e - S l a t e r w a v e f u n c t i o n s and c o m p a r e d w i t h h y d r o g e n - l i k e r e s u l t s . The i m p l i c a t i o n s fo r o t h e r s h e l l s and o t h e r a t o m s a r e d i s c u s s e d .
The photoionization of multicharged atomic ions is a process of importance in stellar and solar physics. Laboratory experiments on these ions are extremely difficult due to the very high temperatures needed to produce them in quantity; theoretical estimates have been made based only on the hydrogen-like model [i]. To test the accuracy of such estimates, we have performed more realistic photoionization calculations on the K-shell for the ground state of each stage of ionization of atomic oxygen from the neutral to 0 6+ using wave functions which are anti-symmetrized products of one-electron functions. The single particle functions for the initial (ground) state are non-relativistic Hartree-Slater * funct i o n s a s d e f i n e d b y H e r m a n a n d S k i l l m a n [2]; t h e final state continuum functions are taken as sol u t i o n s to t h e s a m e p o t e n t i a l a s t h e i n i t i a l s t a t e d i s c r e t e f u n c t i o n s , i . e . , no c o r e r e l a x a t i o n i s included. This model has been found, by a numb e r of w o r k e r s , to do w e l l f o r t h e p h o t o i o n i z a t i o n of n e u t r a l a t o m s [ 3 - 5 ] ; it s h o u l d b e e v e n better for positive ions since the electron-electron electrostatic interaction becomes less imp o r t a n t r e l a t i v e to t h e i n t e r a c t i o n w i t h t h e n u c l e u s a s e l e c t r o n s a r e r e m o v e d . T h e d e t a i l s of t h e m e t h o d of c o m p u t a t i o n a r e g i v e n in r e f . [3]. The calculated K-shell photoionization cross s e c t i o n s of t h e g r o u n d s t a t e s of t h e o x y g e n i o n s a r e s h o w n in fig. 1; a l s o s h o w n a r e t h e h y d r o g e n like results with effective charge z = 7.69 and outer screening [6] to reproduce the HartreeStaler binding energies. The striking feature of
* We use the " H a r t r e e - S l a t e r " r a t h e r than the p r e vious " H a r t r e e - F o c k - S l a t e r " since the f o r m e r m o r e accurately d e s c r i b e d these H a r t r e e functions with Slater exchange.
our results is that they all lie along the same g e n e r a l c u r v e w i t h only m i n o r v a r i a t i o n s (< 5%). T h u s t h e only e f f e c t of r e m o v i n g o u t e r e l e c t r o n s i s to s h i f t t h e K - s h e l l c o n t i n u u m t h r e s h o l d a n d shift some oscillator strength into the discrete w i t h e s s e n t i a l l y no c h a n g e in s h a p e of t h e o s c i l lator strength distribution. Agreement with the h y d r o g e n - l i k e r e s u l t s i s only f a i r a t t h e n e u t r a l oxygen threshold; it becomes excellent with inc r e a s i n g e n e r g y a t t h e K e d g e of 0 6 + a n d a t s t i l l higher energies. These results have several important implic a t i o n s . F i r s t , e x c i t e d s t a t e s of t h e a t o m o r its positive ions will hardly affect the K-shell c r o s s s e c t i o n e x c e p t to s h i f t t h e t h r e s h o l d i n a s -
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F i g . 1. C a l c u l a t e d K - s h e l l p h o t o i o n i z a t i o n c r o s s s e c t i on for the g r o u n d s t a t e s of n e u t r a l a t o m i c oxyge n and e a c h of i t s p o s i t i v e i ons +1 to +6. The v e r t i c a l l i n e s a r e the t h e o r e t i c a l K - s h e l l t h r e s h o l d s f o r e a c h c h a r g e s t a t e and the d a s h e d c u r v e is the h y d r o g e n i c r e s u l t .
85
Volume 38A, n u m b e r 2
PtlYSICS
m u c h a s i o n i z a t i o n h a s only this effect. Second, one n e e d s only c a l c u l a t e the K - s h e l l c r o s s s e c t i o n f o r t h e n e u t r a l a t o m a n d s h i f t t h r e s h o l d s to obtain same for the positive ions. Third. these r e s u l t s will a l s o hold even m o r e e x a c t l y for K s h e l l s of h e a v i e r e l e m e n t s ( a n d t h e i r i o n s ) s i n c e removing a single electron when there are more e l e c t r o n s will have a p r o p o r t i o n a l l y s m a l l e r effect. P r e l i m i n a r y r e s u l t s on t h e 2s a n d 2p s u b s h e l l s of o x y g e n i n d i c a t e a m u c h g r e a t e r d e p e n d e n c e on i o n i c i t y a n d p o o r e r a g r e e m e n t w i t h t h e hydrogen-like model, as one might expect. Furt h e r c a l c u l a t i o n s on o t h e r a t o m i c s p e c i e s a r e in p r o g r e s s a n d w i l l b e p u b l i s h e d e l s e w h e r e [7].
86
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17 J a n u a r y 1972
4
{ll I[.Itall, llev. Mod. P h y s . 8 (1!)36) 358. [21 F. l t e r m a n and S. Skilhnan, Atomic s t r u c t u r e c:d culations ( P r e n t i c e - H a l l . Englewood Cliffs. N.3.,
19(~3). I:tl 8. T. Matlsot? }/nd J. W. (;ooper. Phys. I{(!v. 1{;~) ( 19(IS} 178. Ill E . J . McGuire, P h y s . l{cv. 175 (1968) 120. 15] F. C o m b e t - F a r n o u x . ,l. d(~ Phys. 30 (1,<)69) 531. [r;] E . M e r z h : t e h e r an(I H . W . l , c w i s . in: ttandbuch der Physik. cd. S. Ftugge ( S p r i n g e r - V e r l a g . Berlin. 1!)58) p. 166. [71 D.W. M i s s a v a g e and S.T. Manson. to })e i)ublish(M.
PHYSICS
LETTERS
17 J a n u a r y 1972
P H O T O I O N I Z A T I O N OF P O S I T I V E IONS
OF A T O M I C OXYGEN
D. W. MISSAVAGE and S. T. MANSCN Department of Physics, Georgia State University, Atlanta, Georgia 30303, USA Received 30 November 1971
The p h o t o i o n i z a t i o n c r o s s s e c t i o n of the K - s h e l l of a t o m i c o x y g e n and i t s p o s i t i v e i ons to 0 6+ h a s b e e n c a l c u l a t e d u s i n g H a r t r e e - S l a t e r w a v e f u n c t i o n s and c o m p a r e d w i t h h y d r o g e n - l i k e r e s u l t s . The i m p l i c a t i o n s fo r o t h e r s h e l l s and o t h e r a t o m s a r e d i s c u s s e d .
The photoionization of multicharged atomic ions is a process of importance in stellar and solar physics. Laboratory experiments on these ions are extremely difficult due to the very high temperatures needed to produce them in quantity; theoretical estimates have been made based only on the hydrogen-like model [i]. To test the accuracy of such estimates, we have performed more realistic photoionization calculations on the K-shell for the ground state of each stage of ionization of atomic oxygen from the neutral to 0 6+ using wave functions which are anti-symmetrized products of one-electron functions. The single particle functions for the initial (ground) state are non-relativistic Hartree-Slater * funct i o n s a s d e f i n e d b y H e r m a n a n d S k i l l m a n [2]; t h e final state continuum functions are taken as sol u t i o n s to t h e s a m e p o t e n t i a l a s t h e i n i t i a l s t a t e d i s c r e t e f u n c t i o n s , i . e . , no c o r e r e l a x a t i o n i s included. This model has been found, by a numb e r of w o r k e r s , to do w e l l f o r t h e p h o t o i o n i z a t i o n of n e u t r a l a t o m s [ 3 - 5 ] ; it s h o u l d b e e v e n better for positive ions since the electron-electron electrostatic interaction becomes less imp o r t a n t r e l a t i v e to t h e i n t e r a c t i o n w i t h t h e n u c l e u s a s e l e c t r o n s a r e r e m o v e d . T h e d e t a i l s of t h e m e t h o d of c o m p u t a t i o n a r e g i v e n in r e f . [3]. The calculated K-shell photoionization cross s e c t i o n s of t h e g r o u n d s t a t e s of t h e o x y g e n i o n s a r e s h o w n in fig. 1; a l s o s h o w n a r e t h e h y d r o g e n like results with effective charge z = 7.69 and outer screening [6] to reproduce the HartreeStaler binding energies. The striking feature of
* We use the " H a r t r e e - S l a t e r " r a t h e r than the p r e vious " H a r t r e e - F o c k - S l a t e r " since the f o r m e r m o r e accurately d e s c r i b e d these H a r t r e e functions with Slater exchange.
our results is that they all lie along the same g e n e r a l c u r v e w i t h only m i n o r v a r i a t i o n s (< 5%). T h u s t h e only e f f e c t of r e m o v i n g o u t e r e l e c t r o n s i s to s h i f t t h e K - s h e l l c o n t i n u u m t h r e s h o l d a n d shift some oscillator strength into the discrete w i t h e s s e n t i a l l y no c h a n g e in s h a p e of t h e o s c i l lator strength distribution. Agreement with the h y d r o g e n - l i k e r e s u l t s i s only f a i r a t t h e n e u t r a l oxygen threshold; it becomes excellent with inc r e a s i n g e n e r g y a t t h e K e d g e of 0 6 + a n d a t s t i l l higher energies. These results have several important implic a t i o n s . F i r s t , e x c i t e d s t a t e s of t h e a t o m o r its positive ions will hardly affect the K-shell c r o s s s e c t i o n e x c e p t to s h i f t t h e t h r e s h o l d i n a s -
ELECTRONVOLTS 600 i
I
7D0 I
800
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I
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1000 i
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]-
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o,4[ +3
0.3 0.2
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i
40
I
-'~2-.
+4 ~,~.~ \ +5
\~
I
I
50
i
60 hv (RYDBEP,GS)
i
I
I
70
F i g . 1. C a l c u l a t e d K - s h e l l p h o t o i o n i z a t i o n c r o s s s e c t i on for the g r o u n d s t a t e s of n e u t r a l a t o m i c oxyge n and e a c h of i t s p o s i t i v e i ons +1 to +6. The v e r t i c a l l i n e s a r e the t h e o r e t i c a l K - s h e l l t h r e s h o l d s f o r e a c h c h a r g e s t a t e and the d a s h e d c u r v e is the h y d r o g e n i c r e s u l t .
85
Volume 38A, n u m b e r 2
PtlYSICS
m u c h a s i o n i z a t i o n h a s only this effect. Second, one n e e d s only c a l c u l a t e the K - s h e l l c r o s s s e c t i o n f o r t h e n e u t r a l a t o m a n d s h i f t t h r e s h o l d s to obtain same for the positive ions. Third. these r e s u l t s will a l s o hold even m o r e e x a c t l y for K s h e l l s of h e a v i e r e l e m e n t s ( a n d t h e i r i o n s ) s i n c e removing a single electron when there are more e l e c t r o n s will have a p r o p o r t i o n a l l y s m a l l e r effect. P r e l i m i n a r y r e s u l t s on t h e 2s a n d 2p s u b s h e l l s of o x y g e n i n d i c a t e a m u c h g r e a t e r d e p e n d e n c e on i o n i c i t y a n d p o o r e r a g r e e m e n t w i t h t h e hydrogen-like model, as one might expect. Furt h e r c a l c u l a t i o n s on o t h e r a t o m i c s p e c i e s a r e in p r o g r e s s a n d w i l l b e p u b l i s h e d e l s e w h e r e [7].
86
LETTERS
R~'rc~cc
17 J a n u a r y 1972
4
{ll I[.Itall, llev. Mod. P h y s . 8 (1!)36) 358. [21 F. l t e r m a n and S. Skilhnan, Atomic s t r u c t u r e c:d culations ( P r e n t i c e - H a l l . Englewood Cliffs. N.3.,
19(~3). I:tl 8. T. Matlsot? }/nd J. W. (;ooper. Phys. I{(!v. 1{;~) ( 19(IS} 178. Ill E . J . McGuire, P h y s . l{cv. 175 (1968) 120. 15] F. C o m b e t - F a r n o u x . ,l. d(~ Phys. 30 (1,<)69) 531. [r;] E . M e r z h : t e h e r an(I H . W . l , c w i s . in: ttandbuch der Physik. cd. S. Ftugge ( S p r i n g e r - V e r l a g . Berlin. 1!)58) p. 166. [71 D.W. M i s s a v a g e and S.T. Manson. to })e i)ublish(M.