Volume 23, number 7 P H Y S I C S L E T T E R S 14 November 1966 h~2(1 ~ 2) is v e r y s i m p l e a n d i s g i v e n by
A~(1 ~ 2 ) f~(1 ~ 3 ) . ~2(3 ~ 2)
= f~(1 - - 3 ) + f ~ ( 3 - - 2 ) " (3) T h i s e x p r e s s i o n i s v a l i d f o r e a c h t o t a l a n g u l a r m o m e n t u m L t of t h e s y s t e m (ion + e - ) . T h e e x p r e s - s i o n (3) h a s b e e n p o i n t e d out r i g o r o u s l y by G a i l i - t i s , b u t it is p o s s i b l e to o b t a i n (3) t h r o u g h the s a m e p h y s i c a l a r g u m e n t s t h a t A. B u r g e s s u s e d in his p a p e r on r e c o m b i n a t i o n [5].
L e t us l o o k at the s p e c i f i c p r o b l e m of t h e Ca II e x c i t a t i o n by e l e c t r o n i m p a c t . T h i s p r o b l e m i s a s i x - c h a n n e l p r o b l e m if one r e d u c e s C a II to i t s f i r s t t h r e e l e v e l s : 4 s , 3d and 4p. F o r a g i v e n t o t a l a n g u l a r m o m e n t u m L t, the s i x a s s o c i a t e d c h a n - n e l s a r e :
2 4s; l 1 L t
1 ~ k l ; =
2 k2; 3d; 12 = L t - 2 2
2 3d; l 3 L t
3 = k2; =
2 3d; l 4 L t + 2
4 -- k2; =
5 = k 2. 5' 4p; 15 = L t - 1
2 4p; 16 L t + 1 ,
6 -= k5; =
k 2 and l: b e i n g the e n e r g y and t h e a n g u l a r m o m e n - tu~m of t~e a d d i t i o n a l e l e c t r o n a s s o c i a t e d w i t h t h e c h a n n e l i. One s e e s t h a t i n t r o d u c t i o n of t h e l e v e l 4p c o r r e s p o n d s to two n e w c h a n n e l s in the s c a t - t e r i n g p r o b l e m . It f o l l o w s t h a t (3) is no l o n g e r v a l i d . S i n c e t h e i n t e r a c t i o n p o t e n t i a l b e t w e e n the c h a n n e l s 5 and 6 is q u a d r u p o l a r , and by no m e a n s w e a k , it is p o s s i b l e to s h o w t h a t the f o l l o w i n g i s a g o o d a p p r o x i m a t i o n (i =2, 3, 4):
A~2 (1 ~ i) = f~(1 ~ 5 ) . f~(5 ~ i) + ~2(1 --~ 6 ) . ~2(6 ~ i)
j<5 j < 5 (4)
T a k i n g the R m a t r i x e s c o m p u t e d by D. P e t r i n i , who u s e d the C o u l o m b - B o r n a p p r o x i m a t i o n [6], we h a v e c o m p u t e d ~ 2 ( 4 s ~ 3 d ) .
T a b l e 1 s h o w s t h e r e s u l t s f o r e a c h t o t a l a n - g u l a r m o m e n t u m L t. T h e s e r e s u l t s s h o w that t h e e f f e c t s of the n o n - d i r e c t e x c i t a t i o n a r e not n e g l i g i b l e at a l l . R o u g h l y s p e a k i n g , one c a n a s - s u r e that Q (4s ~ 3d) is m u l t i p l i e d by 2 b e t w e e n t h e l e v e l s 3d and 4p.
In c o n c l u s i o n we c a n s a y that e a c h t i m e one h a s to d e a l w i t h a w e a k t r a n s i t i o n c r o s s s e c t i o n one h a s to w o r r y a b o u t the e f f e c t s t h a t t h e s t r o n g c o u p l e d t r a n s i t i o n s c o u l d i n t r o d u c e to the w e a k t r a n s i t i o n c r o s s s e c t i o n t h r o u g h t h e p r o c e s s m e n - t i o n e d a b o v e . T h e p a r t i c u l a r l y i n t e r e s t i n g c a s e of F e XIV is u n d e r i n v e s t i g a t i o n now.
R e f e r e n c e s
1. O.Bely, D.Moores and M.Seaton, in: Atomic Colli- sion P r o c e s s e s , ed. M . R . C . M e D o w e l l (North-Hol- land Publ. Co., A m s t e r d a m , 1964) p. 304.
2. O.Bely, Ann. d'Astrophysique 27 (1965) 599.
3. M.Seaton, Proc. Phys. Soc.88 (1966) 801.
4. M.Gailitis, Sov. Phys. J E T P 44 (1963)1974.
5. A . B u r g e s s , Astrophys. J. 139 (1964) 776.
6. D. Petrini, C . R . A . S . 2 6 0 (1965) 4929.
N O T E S O N T H E S U B M I L L I M E T E R L A S E R E M I S S I O N F R O M C Y A N I C C O M P O U N D S
W . P R E T T L and L . G E N Z E L
P h y s i k a l i s c h e s I n s t i t u t d e r U n i v e r s i t t i t F r e i b u r g i. B r . , G e r m a n y Received 13 October 1966
F r o m C H 3 C N a n d f r o m a m i x t u r e of C H 3 C N a n d ( C B 3 ) 2 S O 4 l a s e r e m i s s i o n additional to that a l r e a d y r e - p o r t e d in the literature h a s b e e n f o u n d at 119/2, 310.4 it, 310.5/2, 311.512, 334.4 ~ a n d 334.8 p.
S e v e r a l a u t h o r s h a v e r e p o r t e d f a r - i n f r a r e d l a s e r e m i s s i o n f r o m c y a n i c c o m p o u n d s [1-6]. We o b s e r v e d w i t h a p u l s e d e l e c t r i c d i s c h a r g e t h r o u g h C H 3 C N t h e w e l l - k n o w n s t r o n g l i n e s at 337/2 and 310/2. F u r t h e r m o r e we found u n d e r a p p r o p r i a t e
c o n d i t i o n s , s t r o n g l y d e p e n d e n t on v a p o r p r e s s u r e , a s p l i t t i n g of the 310/2 l i n e into t h r e e l i n e s at 310.4 p, 3 1 0 . 5 / 2 , 3 1 1 . 5 ~ and a new l i n e g r o u p at 334.4/2 and 3 3 4 . 8 / 2 . T h e s p l i t t i n g of 337 p e m i s - s i o n f i r s t r e p o r t e d by Kneubtihl et a l . [4] c o u l d be p r o v e d .
443
V o l u m e 23, n u m b e r 7 P H Y S I C S L E T T E R S 1 4 N o v e m b e r 1 9 6 6
T a b l e I
Output p e a k W a v e l e n g t h O p t i m u m p r e s -
V a p o u r (/2) s u r e ( T o r r ) e n e r g y p e r p u l s e (J)
CH3CN
CH3CN +(CH3)2SO4
310.4 l 1 0 - 6
310.5 0.3 10 -6
311.5 10 - 7
334.4 I 1 0 - 6
334.8 0.5 10_ 6
CH3CN : 0.01 10 -5
119.0
(CH3)2SO 4 : 0.8
± 0.1,~
In a m i x t u r e of C H 3 C N and ( C H 3 ) 2 S O 4 w i t h p a r t i a l p r e s s u r e s of 1 0 - 2 T o r r and 0 . 8 T o r r r e s p . , a s t r o n g l i n e at 119/2 w a s o b t a i n e d . T h i s o s c i l l a - t i o n o c c u r r e d o n l y if the e l e c t r i c d i s c h a r g e w a s f i r s t a p p l i e d f o r a f e w m i n u t e s to C H 3 C N o n l y and t h e n ( C H 3 ) 2 S O 4 w a s a d d e d . With p u r e C H 3 C N o r p u r e ( C H 3 ) 2 S O 4 an e m i s s i o n of t h i s w a v e l e n g t h c o u l d not be o b s e r v e d . A l l l i n e s a r e l i s t e d in t a b l e 1.
The l a s e r c a v i t y w a s a g l a s s tube 5 . 8 5 m l o n g h a v i n g an i n t e r n a l d i a m e t e r of 7.2 c m c l o s e d at one end by a p l a n e a l u m i n i z e d m i r r o r and at the o t h e r end by a p l a n e c o p p e r m e s h . T h e p r o p e r t i e s of t h i s m e s h w e r e [7, 8]: g r a t i n g c o n s t a n t = 3 5 / 2 , g r a t i n g c o n s t a n t to s t r i p h a l f b r e a d t h r a t i o = 8 and r e f l e c t i o n = 0 . 9 7 , t r a n s m i s s i o n = 0 . 0 2 a l l at 3 3 0 t t w a v e l e n g t h . The r a d i a t i o n w a s c o u p l e d t h r o u g h the m e s h to the o u t e r d e t e c t o r s y s t e m c o n s i s t i n g of a F a b r y - P e r o t - i n t e r f e r o m e t e r [9] to s e p a r a t e the
i i i I , i
,, , i~210.5u~
' I , I
I i '
i i b
~ - . 7 l O . g u ~ I i
[ ~ i i I I
I
Fig. 1. I n t e r f e r o g r a m of CH3CN. T h r e e l i n e s at 310.4/2, 310.5~t, 311.5/2. T h e d a s h e d l i n e s m a r k the 21~t-reso -
n a n c e s .
1
/2.-
Fig. 2. Left: I n t e r f e r o g r a m of CH3CN. T w o l i n e s at 334.4/2 and 334.8/2. With an e x t e r n a l F P I t h e s e r e s o - n a n c e s w e r e p r o v e d to be p r o d u c e d by t w o l i n e s a n d n o t by o n e l i n e at 167 ft. Right: I n t e r l e r o g r a m of CH3CN a n d
(CH3)2SO 4. One line at l l g t t .
d i f f e r e n t l i n e g r o u p s and a b o l o m e t e r . T h e b o l o m - e t e r w a s c a l i b r a t e d to m e a s u r e the e n e r g y p e r r a - d i a t i o n p u l s e . The w a v e l e n g t h of the l i n e s w e r e d e t e r m i n e d b y the i n t e r f e r o m e t r i c p r o p e r t i e s of the l a s e r c a v i t y . T h e i n t e r f e r o g r a m s a r e s h o w n in f i g s . 1 and 2.
T h e e l e c t r i c p u l s e s w e r e p r o d u c e d by a 17 k V d. c . - s o u r c e and a 0.1 ~tF c o n d e n s e r p e r i o d i c a l l y d i s c h a r g e d t h r o u g h the v a p o u r in the c a v i t y . T h e r e p e t i t i o n f r e q u e n c y w a s 1 c p s .
RefeYe~zces
1. H, A. Gebbie, N . W . B . S t o n e a n d F. B. F i n d l a y , N a t u r e 202 (1964) 685.
2. L, E. S. M a t h i a s , A. C r o c k e r and M. S. w i l l s , E l e c t r . L e t t e r s 1 (1965) 45.
3. F . K . Kneubfihl, J. - F . M o s e r , H, Stel'len a n d W. T a n d - l e r , Z . A n g e w . Math. P h y s . 16 (1965) 560.
4. M. C a m a n i , F . K . KneubtihI, J. - F . M o s e r and H. S t e f - fen, Z. Angew. Math. P h y s . 16 (1965) 562.
5. H . S t e f f e n , J. Steffen, J , - F . M o s e r and F . K . K n e u - biihl, P h y s . L e t t e r s 20 (1966) 20.
6. H. Steffen, J. Steffen, J. - F . M o s e r a n d F. K. Kneubiihl, P h y s . L e t t e r s 21 (1966) 425.
7. K. F. R e n k a n d L. G e n z e l , Appl. O p t i c s 1 (1962) 643.
8. P. V o g e l a n d L. G e n z e l . I n f r a r e d P h y s . 4 (1964) 257.
9. R. Ulrich, K. F. R e n k a n d L. G e n z e l , I E E E T r a n s a c - tions M T T iI (1963) 363.
444
