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Measurement of radiative lifetimes of electronic states in neon Van Andel, Hendrikus Willem Helenius 1966

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MEASUREMENT OF RADIATIVE LIFETIMES OF ELECTRONIC STATES IN NEON by HENDRIKUS WILLEM HELENIUS VAN ANDEL B . S c , The U n i v e r s i t y of B r i t i s h Columbia, 1962 M.Sc., The U n i v e r s i t y of B r i t i s h Columbia, 1963 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of PHYSICS We accept t h i s t hesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1966 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study,, I fur t h e r agree that permission., f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s representatives, I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Department of PhyjloB The U n i v e r s i t y of B r i t i s h Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY HEMDRIKUS WILLEM HELEMIUS VAN ANDEL B.Sc, The U n i v e r s i t y of B r i t i s h Columbia, I962 14.Sc., The U n i v e r s i t y of B r i t i s h Columbia, 1963 FRIDAY, SEPTEMBER l 6 , 1 9 6 6 , at 3:30 P.M. IN ROOM 301, HENNINGS BUILDING COMMITTEE IN CHARGE External Examiner: W. Lochte-Holtgreven Dir e c t o r I n s t i t u t e f o r Experimental Physics K i e l U n i v e r s i t y West Germany Research Supervisor: R. A. Nodwell of Chairman: P. A. Dehnel A. J. Barnard A. V. Bree F. L. Curzon F. W. Dalby R. A. Nodwell T. J. Ulrych MEASUREMENT OF RADIATIVE LIFETIMES OF ELECTRONIC STATES IN.NEON ABSTRACT Radiative l i f e t i m e s were measured f o r a number of e l e c t r o n i c states i n neon I. The values of the l i f e t i m e s were obtained from a measurement of the time dependence of the i n t e n s i t y of l i g h t emitted by the neon gas while i t returned spontaneously to i t s ground state from a state of excitation,. The e x c i t a t i o n i n the gas was produced by a pulsed electron beam, A monochromator of high r e s o l u t i o n and l i g h t gathering power was designed and b u i l t f o r the purpose of i s o l a t i n g l i g h t from sin g l e t r a n s i t i o n s . The time resolved measurements on the l i g h t i n t e n s i t y were made using a photomultiplier and sampling o s c i l l o s c o p e . The l i f e t i m e of the 2p-j_ (Paschen notation) l e v e l i n neon was measured to be 15 .2 ± 0 . 2 x 1 0 ° ^ seconds, with a possible systematic error estimated at l e s s than 5 percent. The l i f e t i m e of the 2 s 2 state was found to be 9^-»5± ^ x 10"9 seconds. -Preliminary measurements of l i f e t i m e s were made f o r a number of other l e v e l s i n neon. The r e l a t i v e values of several t r a n s i t i o n p r o b a b i l i t i e s i n neon were determined from r e l a t i v e i n t e n s i t y measurements. GRADUATE STUDIES F i e l d of Study: Physics Quantum Mechanics Waves Electromagnetic Theory Plasma Physics Spectroscopy Special R e l a t i v i t y Plasma dynamics Related Studies: E l e c t r o n i c s Wo Opechowski J. C„ Savage G. M. Volkoff L. de Sobrino A. M. Crooker A. J. Barnard H. Schmidt F. L. Curzon W. A„ G. Voss - i i -A B S T R A C T R a d i a t i v e l i f e t i m e s w e r e m e a s u r e d f o r a n u m b e r o f e l e c t r o n i c s t a t e s i n n e o n I . T h e v a l u e s o f t h e l i f e t i m e s w e r e o b t a i n e d f r o m a m e a s u r e m e n t o f t h e ; t i m e d e p e n d e n c e o f t h e i n t e n s i t y o f l i g h t w h i l e t h e n e o n g a s r e t u r n e d s p o n t a n e o u s l y t o i t s g r o u n d s t a t e f r o m a s t a t e o f e x c i t a t i o n . T h e e x c i t a -t i o n i n t h e g a s w a s p r o d u c e d b y a p u l s e d e l e c t r o n g u n . A m o n o c h r o m a t o r o f h i g h r e s o l u t i o n a n d l i g h t g a t h e r i n g p o w e r w a s d e s i g n e d a n d b u i l t f o r t h e p u r p o s e o f i s o l a t i n g l i g h t f r o m s i n g l e t r a n s i t i o n s . T h e t i m e ; r e s o l v e d m e a s u r e m e n t s o n t h e l i g h t i n t e n s i t y w e r e m a d e u s i n g a p h o t o m u l t i p l i e r a n d s a m p l i n g o s c i l l o s c o p e . T h e l i f e t i m e o f t h e 2p^ s t a t e ( P a s c h e n n o t a t i o n ) i n n e o n w a s m e a s u r e d t o b e 1^.2 ±0.2 x 10 s e c o n d s , w i t h a p o s s i b l e s y s t e m a t i c a l e r r o r e s t i m a t e d a t l e s s t h a n 5%. T h e l i f e t i m e o f t h e 2s^ s t a t e i n n e o n w a s f o u n d t o b e 9lw3> ±. h x 10"9 s e c o n d s . P r e l i m i n a r y m e a s u r e m e n t s o f l i f e t i m e s w e r e m a d e f o r a n u m b e r o f o t h e r l e v e l s i n n e o n « T h e r e l a t i v e v a l u e s o f s e v e r a l t r a n s i t i o n p r o b a b i l i t i e s i n n e o n w e r e d e t e r m i n e d f r o m r e l a t i v e i n t e n s i t y m e a s u r e m e n t s . - i i i -T A B L E O F C O N T E N T S C H A P T E R I I n t r o d u c t i o n 1 C H A P T E R I I T h e o r y h A . L i f e t i m e m e a s u r e m e n t s h 1 . I n t r o d u c t i o n h 2. P r o c e s s e s l e a d i n g t o a c h a n g e i n p o p u l a t i o n d e n s i t i e s i n a ' w e a k l y e x c i t e d g a s 5 a . S p o n t a n e o u s e m i s s i o n 5 b . A b s o r p t i o n 5 c . S t i m u l a t e d e m i s s i o n 8 d . I n e l a s t i c a t o m - a t o m c o l l i s i o n s 9 e . I n e l a s t i c e l e c t r o n - a t o m c o l l i s i o n s 10 f . D i f f u s i o n 11 3 . G e n e r a l e q u a t i o n g o v e r n i n g t h e t i m e d e p e n d e n c e o f t h e p o p u l a t i o n d e n s i t i e s 11 k» S o l u t i o n f o r t h e g e n e r a l e q u a t i o n f o r t h e 2p^  l e v e l i n n e o n 12 5>. T h e o r e t i c a l d e t e r m i n a t i o n o f t r a n s i t i o n p r o b a b i l i t i e s 20 B . R e l a t i v e i n t e n s i t y m e a s u r e m e n t s 21 C H A P T E R I I I E x p e r i m e n t a l m e t h o d a n d a p p a r a t u s 23 A . L i f e t i m e m e a s u r e m e n t s 23 1. S u m m a r y o f t h e m e t h o d 23 2 . L i g h t s o u r c e 26 - iv -a. E l e c t r o n gun 26 h. Vacuum system 3it 3 . Monochromator 37 It. Photomultiplier I48 5 . Sampling system 5>0 6 . -Linearity and expected accuracy of the method 5'S> 7. Counting method 6 l B. Relative i n t e n s i t y measurements 62 CHAPTER IV Results and discussion 66 A. Lifetime measurements 66 B. Relative i n t e n s i t y measurements 80 CHAPTER V Conclusions and comparisons 82 APPENDIX I Maximum l i k e l i h o o d f i t of the data 86 APPENDIX I I Preliminary measurements of l i f e t i m e s of a number of 2p states in neon 89 APPENDIX I I I C a l i b r a t i o n of the s p e c t r a l response u : r of a monochromator 9% REFERENCES 99 - V -T A B L E OF I L L U S T R A T I O N S Figure 1. P a r t i a l term diagram of neon I 13 2. Sequence of events i n i n t e n s i t y measuring system 21) 3. Schematic diagram of the apparatus 25 k. D e t a i l s of the ele c t r o n gun 27 5. E q u i p o t e n t i a l surfaces of a p a r a l l e l e l e c t r o n beam 27 6. D e t a i l s of the cathode assembly 3U 7. Schematic diagram of the vacuum system 35 8. Optics of the monochromator L|2 9. Schematic diagram of the sine bar arrangement hh 10. Pulse height d i s t r i b u t i o n i n a photomultlplier k9 11. Schematic diagram of e l e c t r o n i c sampling system 53 12. E l e c t r o n i c sequence of events $h 13. Graphical i l l u s t r a t i o n of two types of superposition errors 59 l i u to 20. Computer p l o t s of the decay of i n t e n s i t y of the 5852 A t r a n s i t i o n i n neon at various pressures 68 - 7k 21. Computer p l o t of the decay of i n t e n s i t y of the 6ii02 A t r a n s i t i o n i n neon 91 22. Computer p l o t of the decay of i n t e n s i t y of the 6ll[3 A t r a n s i t i o n i n neon 92 - vi -LIST OF TABLES Table I Lifetimes of the 2p^ state i n neon 75 Table I I Lifetimes of the 2s^ state i n neon 76 Table I I I Goodness of f i t test on computed curves 78 Table IV Ratios of transition probabili t ies together with calibration data 80 Table V Measured values for the 2p^ lifetime i n neon 82 Table VI Measured ratios of transition probabili t ies for five pairs of transitions i n neon 85 Table VII Lifetime measurements for 2p levels i n neon 90 - v i i ~ ACKNOWLEDGEMENT I w i s h t o e x p r e s s m y s i n c e r e t h a n k s t o D r . R . A . N o d w e l l f o r h i s g u i d a n c e a n d e n c o u r a g e m e n t d u r i n g t h e c o u r s e o f t h e e x p e r i m e n t a l w o r k a n d t h e p r e p a r a t i o n o f t h i s t h e s i s . T h a n k s a r e a l s o d u e t o D r . A J i . C r o o k e r f o r h i s h e l p i n t h e d e s i g n a n d b u i l d i n g o f t h e m o n o c h r o m a t o r , a n d D r . J . H . W i l l i a m s o n f o r h i s a s s i s t a n c e i n c o m p u t e r p r o g r a m m i n g . T h e h e l p o f D r . F . W . D a l b y , D r . F . L . C u r z o n a n d D r . A . J . B a r n a r d i n r e a d i n g a n d i m p r o v i n g t h i s t h e s i s i s m u c h a p p r e c i a t e d . M y t h a n k s a l s o t o D r . B a r n a r d f o r t h e u s e o f h i s c o m p u t e r p r o g r a m m e t o c a l c u l a t e t r a n s i t i o n p r o b a b i l i t i e s . T h e t e c h n i c a l a s s i s t a n c e o f M r . J o h n L e e s i n t h e g l a s s b l o w i n g f o r t h e v a c u u m s y s t e m , M r . J a c k B o s m a i n t h e b u i l d i n g o f t h e m o n o c h r o m a t o r , M r . T o n y K n o p p i n t h e c o n s t r u c t i o n o f t h e e l e c t r o n g u n , a n d M e s s r s . W a l t e r R a t z l a f f a n d J o o p D o o y e w e e r d i n t h e d e s i g n a n d b u i l d i n g o f t h e e l e c t r o n i c a p p a r a t u s i s m u c h a p p r e c i a t e d , I s h o u l d a l s o l i k e t o e x p r e s s m y g r a t i t u d e t o m y c o l l e a g u e s R o b e r t 0 r t h , f o r t h e u s e o f h i s c o m p u t e r p r o g r a m m e f o r m a x i m u m l i k e l i h o o d f i t t i n g , a n d S a n d y R o b i n s o n , f o r h i s a s s i s t a n c e i n t h e r e l a t i v e i n t e n s i t y m e a s u r e -m e n t s . T h e g i f t o f a s a m p l e o f C a t h a l l o y A-33 n i c k e l f r o m t h e S u p e r i o r T u b e C o m p a n y o f Norrlstown, Pa., U., S. A. i s g r a t e f u l l y acknowledged. M y t h a n k s g o o u t t o t h e N a t i o n a l R e s e a r c h C o u n c i l f o r t h e i r f i n a n c i a l a s s i s t a n c e i n t h e f o r m o f s t u d e n t s h i p s t h r o u g h o u t t h e c o u r s e o f t h i s w o r k , T h i s w o r k i s s u p p o r t e d b y a g r a n t f r o m t h e A t o m i c E n e r g y C o n t r o l B o a r d o f C a n a d a . - 1 -: CHAPTER I INTRODUCTION Tr a n s i t i o n p r o b a b i l i t i e s f o r spontaneous r a d i a t i v e t r a n s i t i o n s between e l e c t r o n i c states i n atoms are of fundamental i n t e r e s t i n many branches of physics. P a r t i c u l a r l y i n the study of plasmas, p h y s i c i s t s often need the values of .these t r a n s i t i o n p r o b a b i l i t i e s to determine parameters of the p l a s -ma that are of i n t e r e s t , such as temperature or population density d i s t r i -bution. In astronomy, much knowledge about a star i s obtained from the study of the star's spectra, and these can often be interpreted quantita-t i v e l y ojily i f the t r a n s i t i o n p r o b a b i l i t i e s associated with the observed s p e c t r a l l i n e s are known. The recent development of the l a s e r has caused a renewed i n t e r e s t i n the determination of t r a n s i t i o n p r o b a b i l i t i e s i n rare gases ( see f o r example Bennett e t a l . ( 1 ) ), since the r a t i o of t r a n s i t i o n p r o b a b i l i t i e s f o r upper and lower states gives a c r i t e r i o n f o r l a s e r action between these s t a t e s . An extensive bibliography on the determination of t r a n s i t i o n p r o b a b i l i -t i e s was prepared by the National Bureau of Standards i n 1>62 ( 2 ). Although p h y s i c i s t s f o r more than t h i r t y years have been attempting to measure t r a n s i t i o n p r o b a b i l i t i e s , by a large v a r i e t y of methods, the values f o r a s u r p r i s i n g l y large number of well known and important t r a n s i t i o n s are not a v a i l a b l e , or i f a v a i l a b l e , show a large spread, i n measured values. Neon I i s a case i n p o i n t . As one can see from Table V i n Chapter V of t h i s t h e s i s , the values of the t r a n s i t i o n p r o b a b i l i t y f o r the 5852 A t r a n s i t i o n i n neon as reported by eight d i f f e r e n t authors vary by a f a c t o r of f i f t e e n . This t r a n s i t i o n i s one of the strongest t r a n s i t i o n s of the neon I spectrum. Not u n t i l 196U, which i n c i d e n t a l l y was a f t e r t h i s work was s t a r t e d , d i d the measured v a l u e s of the t r a n s i t i o n p r o b a b i l i t y f o r t h i s t r a n s i t i o n show any s i g n s :of c o n v e r g i n g . Because the measurements showed such a l a r g e s p r e a d , i t was deemed u s e f u l t o t r y t o measure the t r a n s i t i o n p r o b a b i l i t y f o r t h i s , t r a n s i t i o n and p o s s i b l y o t h e r t r a n s i t i o n s i n t h e neon s p e c t r u m , u s i n g a d i r e c t method i n v o l v i n g t i m e r e s o l v e d s p e c t r o s c o p y . A n o t h e r r e a s o n f o r our i n t e r e s t i n neon was t h a t our d e t e r m i n a t i o n o f an a b s o l u t e v a l u e f o r a t r a n s i t i o n p r o b a b i l i t y would e n a b l e o t h e r a b s o l u t e v a l u e s t o be computed from r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s p r e v i o u s l y measured i n our l a b o r a t o r y by I r w i n ( 3 ) and R o b i n s o n ( I4 ) . The method which we used t o d e t e r m i n e the a b s o l u t e v a l u e s o f t r a n s i t i o n p r o b a b i l i t i e s c o n s i s t e d o f the measurement o f the time dependence of the i n t e n s i t y o f l i g h t e m i t t e d w h i l e the gas r e t u r n e d s p o n t a n e o u s l y t o i t s ground s t a t e from a s t a t e o f e x c i t a t i o n . Under s u i t a b l e c o n d i t i o n s , t h e ti m e c o n s t a n t a s s o c i a t e d w i t h t h e e x p o n e n t i a l decay o f the i n t e n s i t y a t a p a r t i c u l a r w a v e l e n g t h i s e q u a l t o the i n v e r s e of the t r a n s i t i o n p r o b a b i l i t y f o r t h e t r a n s i t i o n c o r r e s p o n d i n g t o t h a t w a v e l e n g t h . Hence a d e t e r m i n a t i o n o f the time dependence of i n t e n s i t y g i v e s a measure o f the t r a n s i t i o n .proba-b i l i t y . I n C h a p t e r I I of t h i s t h e s i s a d e s c r i p t i o n i s g i v e n o f the p r o c e s s e s t h a t may i n f l u e n c e t h i s time dependence. The f o r m o f the time dependence un d e r s p e c i a l c o n d i t i o n s i s d i s c u s s e d , and i t i s shown how the d e s i r e d r e -s u l t s may be o b t a i n e d . I n Chapter. I l l a d e t a i l e d , d e s c r i p t i o n o f t h e a p p a r a -t u s and e x p e r i m e n t a l methods i s g i v e n , and i n C h a p t e r I V and V the m a i n r e -s u l t s a r e summarized. I t was o r i g i n a l l y i n t e n d e d t o measure the a b s o l u t e v a l u e s o f t r a n s i t i o n p r o b a b i l i t i e s f o r more t h a n one t r a n s i t i o n , b u t i t t u r n e d o u t t h a t e x p e r i -m e n t a l d i f f i c u l t i e s l i m i t e d o ur d e t e r m i n a t i o n s t o o n l y one t r a n s i t i o n , namely the 2 p n > 1^ t r a n s i t i o n ( P a s c h e n n o t a t i o n ) i n neon a t a - 3 -wavelength of 5 8 5 2 A. Although the l i f e t i m e s of a number of other states i n neon were measured, i n t e r p r e t a t i o n a l d i f f i c u l t i e s which are explained i n Appendix 2 made t h e i r measured values subject to doubt. I t i s possible that these; d i f f i c u l t i e s may be overcome by a thorough study of these t r a n s i t i o n s under various e x c i t a t i o n conditions, but this was deemed-to be beyond the scope of the present work. The values obtained f o r these t r a n s i t i o n s are l i s t e d as preliminary data i n Appendix 2 . The r e l a t i v e i n t e n s i t i e s of several l i n e s i n neon I were measured with our apparatus. The r e l a t i v e values of t r a n s i t i o n p r o b a b i l i t i e s of t r a n s i -tions fr,om a common upper l e v e l were determined from these measurements. This work was done i n c o l l a b o r a t i o n with Robinson ( h ), who needed these values i n order to co r r e l a t e h i s measurements of r e l a t i v e t r a n s i t i o n proba-b i l i t i e s of t r a n s i t i o n s having a common lower s t a t e . Therefore Chapter I I , I I I , and IV are divided i n t o sections A and B dealing with l i f e t i m e and r e l a t i v e i n t e n s i t y measurements r e s p e c t i v e l y . - k -CHAPTER I I THEORY . A. : L i f e t i m e Measurements 1. I n t r o d u c t i o n The p r o b a b i l i t y p e r u n i t t i m e t h a t an atom i n the s t a t e j w i l l make a spontaneous t r a n s i t i o n t o some l o w e r s t a t e k i s the E i n s t e i n c o e f f i c i e n t f o r spontaneous e m i s s i o n , A k . T h a t i s , t h e number o f t r a n s i t i o n s t h a t t a k e p l a c e i n a gas p e r u n i t t i m e p e r u n i t volume from t h e s t a t e j t o the s t a t e k, i f t h e p o p u l a t i o n d e n s i t y o f the s t a t e j i s n . , i s g i v e n b y The i n t e n s i t y of r a d i a t i o n a t some p o i n t o u t s i d e the s o u r c e a t the f r e q u e n c y V j ^ c o r r e s p o n d i n g t o t h e t r a n s i t i o n j —*• k i s where c i s a s u i t a b l e f a c t o r d e p e n d i n g on the f r e q u e n c y and the geometry. Thus t h e time dependence o f the i n t e n s i t y i s d e t e r m i n e d b y t h e t i m e depen-dence o f n.., p r o v i d e d , o f c o u r s e , t h e r e i s no t i m e dependent a b s o r p t i o n . Hence i f we hope t o measure t r a n s i t i o n p r o b a b i l i t i e s b y m e a s u r i n g the ti m e dependence o f i n t e n s i t i e s , we must d e t e r m i n e what f a c t o r s i n g e n e r a l , and how t r a n s i t i o n p r o b a b i l i t i e s i n p a r t i c u l a r , a f f e c t the time dependence o f the. p o p u l a t i o n d e n s i t i e s . T h i s w i l l be done i n the n e x t f e w s e c t i o n s . F o r a good g e n e r a l r e f e r e n c e , see M i t c h e l l and Zemansky ( 5 ). - 5 -2 . P r o c e s s e s l e a d i n g t o a change i n p o p u l a t i o n d e n s i t i e s i n a w e a k l y  e x c i t e d g a s , a . Spontaneous e m i s s i o n F o r a gas i n w h i c h the p o p u l a t i o n d e n s i t y o f the s t a t e j i s a f u n c t i o n o f t i m e , n . ( t ) , the r a t e o f change o f t h i s p o p u l a t i o n d e n s i t y due t o the p r o c e s s o f spontaneous e m i s s i o n a l o n e , i s g i v e n i n terms o f the above d e f i n e d . t r a n s i t i o n p r o b a b i l i t y A , 3 k djn>. I d t Upon. k<j I* tern. = "IT A j k njft) (3) N o r m a l l y one d e f i n e s t h e t o t a l t r a n s i t i o n p r o b a b i l i t y f o r t h e s t a t e j as Aj =Z A j k C4-) and the l i f e t i m e o f the s t a t e as I n terms,, of t h e s e q u a n t i t i e s e q u a t i o n ( 3 ) i s w r i t t e n sf>ont.€.m. J J ' X b . A b s o r p t i o n I t i s w e l l known t h a t i n t h e p r e s e n c e o f a r a d i a t i o n f i e l d an atom i n the s t a t e k can a b s o r b a p h o t o n o f f r e q u e n c y V j ^ , r e s u l t i n g i n an atom i n the s t a t e ,-j. The r e q u i r e m e n t on the f r e q u e n c y " ^ j K ^ s t h a t pr pr V •. = ,) K . where E • and E. a r e the e n e r g i e s o f the s t a t e s j K ' j k j and k r e s p e c t i v e l y , arid h i s P l a n c k ' s c o n s t a n t . The p r o b a b i l i t y t h a t t h e atom i n the s t a t e k w i l l make such a t r a n s i t i o n i s g i v e n b y 6>v<j P ^ "^j k) > where B ^ i s the E i n s t e i n c o e f f i c i e n t f o r a b s o r p t i o n , and p ( V j fe. ) i s - 6 -the energy density of r a d i a t i o n at the frequency V j ^ . The rate at which atoms are excited to the state j by t h i s process i s thus given by £t Lbs. =Z B k ) 9 C v j O (6) k<rj J In the absence of external sources, the r a d i a t i o n density p (VjyO i s due to r a d i a t i o n emitted by neighboring atoms i n the state j making a t r a n s i -t i o n to the lower state k. Hence one' may describe the absorption process equivalently by computing the p r o b a b i l i t y T ( "£> ^ JK.) that a photon of frequency ^ J K emitted, by an excited atom w i l l penetrate.a distance i n the gas, before being reabsorbed. This p r o b a b i l i t y , together with the dimensions of the l i g h t source, i n d i c a t e s the importance of the absorption process. The p r o b a b i l i t y T ( - £ , ^j^) defined above was calculated by H o l s t e i n ( 6 ) f o r the case where Doppler broadening dominates over any other broade-ning process. He obtained, the followi n g , V - V ( ? ) where _ — (~^r) > (8) c i s the v e l o c i t y of l i g h t , V j ^ i s the centre frequency of the Doppler r 2. RT1 d i s t r i b u t i o n of frequencies f o r the t r a n s i t i o n j — » k, AT 0 •=» /— i s the average v e l o c i t y of the atoms of gram molecular weight M i n the gas at temperature T, i s the absorption c o e f f i c i e n t , and g j , g k are the s t a t i s t i c a l weights of the upper and lower states r e s p e c t i v e l y . In these formulae the subscript k i s used to denote the.lower s t a t e , from which absorption takes p l a c e , and j designates the upper s t a t e . The expression f o r T ( Lt V ) s i m p l i f i e s considerably f o r two s p e c i a l cases which are of i n t e r e s t , namely i ) when k Q l i s much l e s s than one, and i i ) when k Q 1 i s much greater than one. For case i ) we expand the integrand of T(^- ;V) i n equation ( 7 ) and in t e g r a t e : T ^ . v ) = J k « / x > e " n * ^ - 2 j l 4 K ^ ( m , ^ { ^ ^ / ! i ^ = | _ ^  oOc.*f Oo) This case corresponds to a very small amount of s e l f absorption. For strong s e l f absorption, k 1 i s much greater than one, and the c a l c u l a t i o n i s more d i f f i c u l t . H o l s t e i n ( 6 ) shows that i n t h i s case the r e s u l t i s I which i s much less than one, which means that over the distance 4- v i r -t u a l l y a l l r a d i a t i o n i s reabsorbed. For a l i g h t source of s u f f i c i e n t l y large dimension 4- , r a d i a t i o n due to a t r a n s i t i o n f o r which -4-' i s much l a r g e r than one, i s said to be completely trapped due to s e l f absorp-t i o n . Under these conditions one can, f o r a p a r t i c u l a r geometry, c a l c u l a t e the time dependence of the population density of the upper state of t h i s t r a n s i t i o n . H o l s t e i n has done t h i s , and obtains - 8 -where >^ i s the f r a c t i o n of emitted, photons that escape the v e s s e l . The quantity'c i n ( 13 ) i s a constant of order u n i t y which depends on the geo-metry of the source. Again, when kQ L* i s much greater than one, ^ i s much less than one, and the e f f e c t i s to decrease the e f f e c t i v e t r a n s i t i o n p r o b a b i l i t y of the state by a large f a c t o r . A consequence of t h i s f a c t i s that the l i f e t i m e of a state that i s op-t i c a l l y connected to a strongly absorbing state ( f o r example the ground, state ), as w e l l as to states from which absorption i s n e g l i g i b l e , i s com-p l e t e l y determined by the t r a n s i t i o n p r o b a b i l i t i e s to these nonabsorbing s t a t e s . While the upper state i n such a case can make t r a n s i t i o n s to a l l lower s t a t e s , the rate at which i t s p o p u l a t i o n density i s depleted i s determined only by t r a n s i t i o n s to the non-absorbing s t a t e s , since atoms i n the.absorbing states immediately replenish the upper state population density by absorbing the photons emitted by neighboring atoms. The e f f i c i e n c y of the s e l f absorption process, and hence the degree of r a d i a t i o n trapping, i s cf course a function of the pressure, as i s evident from the dependence of k 0 on the population density i n equation ( 9 ) . c. Stimulated emission. In a r a d i a t i o n f i e l d , t r a n s i t i o n s can be induced from a higher state to a lower state i n a manner analogous to the absorption process, described i n the previous s e c t i o n . The process i s known as stimulated emission. The corresponding rate of change of population density of the state j i s given by - 9 -where B i s the E i n s t e i n c o e f f i c i e n t f o r s t i m u l a t e d e m i s s i o n . I t may be j k shown t h a t d. I n e l a s t i c Atom - Atom C o l l i s i o n s I t i s p o s s i b l e f o r an atcm i n t h e e x c i t e d s t a t e j t o g i v e up p a r t o r a l l of i t s e x c i t a t i o n e n e r g y t o a n o t h e r atom b y means o f i n e l a s t i c c o l l i s i o n s . The t y p e s o f c o l l i s i o n p r o c e s s e s t h a t may o c c u r a r e many, and a r e d i s c u s s e d i n d e t a i l i n many b o o k s , ( e . g . M a s s e y and Burhop ( 7 ) ) The most i m p o r -t a n t c o l l i s i o n p r o c e s s f o r our p u r p o s e s i s the one i n w h i c h an atom c o l l i d e s w i t h an atom i n t h e ground s t a t e . The r e a c t i o n c o u l d be d e s c r i b e d as f o l l o w s : Me. -f- Ne — N e +• He ± E (\6) Here Ne^ r e p r e s e n t s a neon atom i n t h e s t a t e j . The r a t e a t w h i c h the popu-l a t i o n d e n s i t y o f t h e s t a t e j i s b e i n g d e p l e t e d b y s u c h a p r o c e s s i s 5t I atom ell. = ^ Q j < "° ^ ^ ( ' ? ) where i s t h e c o l l i s i o n c r o s s - s e c t i o n f o r t r a n s f e r o f e x c i t a t i o n by means o f t h e above i n t e r a c t i o n , and v i s an a v e r a g e r e l a t i v e v e l o c i t y between c o l l i d i n g atoms. P r o c e s s e s s u c h as t h i s were r e c e n t l y s t u d i e d b y P a r k s and J a v a n ( 6 ) who measured c o l l i s i o n c r o s s - s e c t i o n s f o r e x c i t a t i o n t r a n s f e r between two l e v e l s i n neon. S t u d i e s on s i m i l a r i n t e r a c t i o n s i n h e l i u m were c a r r i e d o u t much e a r l i e r b y L ees and S k i n n e r ( 9 ), and M a u r e r and W o l f ( 10 ). The l a t t e r c o n f i r m e d t h a t the t r a n s f e r o f e x c i t a t i o n b y c o l l i s i o n s i s p r e -stim.£.m. - 10 -dominantly due to c o l l i s i o n s with the ground s t a t e , as described i n equation ( 16 ). In order to assess the importance of the process one must know the value of Q .,. • rt e • I n e l a s t i c Atom - E l e c t r o n c o l l i s i o n s . J Free electrons i n a gas c o l l i d i n g with atoms can cause changes i n the states of e x c i t a t i o n i n these atoms. In p a r t i c u l a r , electrons c o l l i d i n g with atoms i n the ground state can excite these i n t o higher states provided.the electrons carry enough k i n e t i c energy. Normally any free electrons which may be present i n the gas at room temperature do not have enough k i n e t i c energy to ex c i t e atoms from the ground, s t a t e . However, i f one passes an ex-t e r n a l l y generated e l e c t r o n beam through the gas, one can cause appreciable e x c i t a t i o n to take p l a c e . The process can be described as follo w s : H t 1 U.o*. - ^ e ^ o Q o j (18) In t h i s expression N g corresponds to the number of electrons traversing the gas per u n i t area per u n i t time. Q Q. i s the c o l l i s i o n cross-section f o r e x c i -t a t i o n by electrons of atoms from the ground state to the state j . C o l l i s i o n s with electrons i n an el e c t r o n beam may also cause atoms to become i o n i s e d . The i o n i s a t i o n process creates free electrons which i n turn may c o l l i d e with atoms i n excited s t a t e s , p o s s i b l y changing t h e i r state of e x c i t a t i o n . The l a t t e r process can be described by the equation dm di- Coll. where n g i s the number of free electrons i n the gas due to i o n i s a t i o n , v g i s an average r e l a t i v e v e l o c i t y between the electrons and. the gas atoms, e and Q ^ i s the c o l l i s i o n c r oss-section f o r transf e r of e x c i t a t i o n by means of electron-atom c o l l i s i o n s . - 11 -f . D i f f u s i o n T h e , p o p u l a t i o n d e n s i t y o f t h e s t a t e j m a y b e d e p l e t e d a t a p a r t i c u l a r p o i n t i n s p a c e b y m e a n s o f d i f f u s i o n o f a t o m s i n t h i s s t a t e t o s u r r o u n d i n g r e g i o n s . I f t h e r e g i o n o f t h e g a s i n w h i c h t h e e x c i t e d a t o m s a r e p r e s e n t i s s u r r o u n d e d b y a c o n t a i n e r , t h e n e x c i t e d a t o m s d i f f u s i n g o u t o f t h i s r e g i o n w i l l g e n e r a l l y l o s e t h e i r e x c i t a t i o n e n e r g y u p o n c o l l i s i o n s w i t h t h e w a l l s o f t h e c o n t a i n e r . T h e e q u a t i o n g o v e r n i n g t h e d i f f u s i o n o f a t o m s i n t h e s t a t e j t h r o u g h a t o m s i n t h e g r o u n d s t a t e m a y b e w r i t t e n a s A c c o r d i n g t o P h e l p s ( 12 ) , f o r d i f f u s i o n t o t h e w a l l s o f a c o n t a i n e r , w e c a n w r i t e t h i s e q u a t i o n a s o f t h e . o r d e r o f t h e d i m e n s i o n s o f t h e c o n t a i n e r . 3 • G e n e r a l e q u a t i o n g o v e r n i n g t h e t i m e d e p e n d e n c e o f t h e p o p u l a t i o n . d e n s i t i e s . I f w e c o m b i n e a l l t h e s e p a r a t e p r o c e s s e s d e s c r i b e d i n t h e p r e c e d i n g s e c t i o n s , w e o b t a i n o n e e q u a t i o n g o v e r n i n g t h e t i m e d e p e n d e n c e o f t h e p o p u -l a t i o n d e n s i t y o f t h e s t a t e j . T h e d i f f e r e n t t e r m s a r e d e s i g n a t e d a s t o t h e i r o r i g i n . w h e r e D i s t h e d i f f u s i o n c o e f f i c i e n t , a n d A i s a n e f f e c t i v e d i f f u s i o n l e n g t h . T h e v a l u e o f A d e p e n d s o n t h e s h a p e o f t h e c o n t a i n e r a n d i s (stimutaUd emission) ( a l o w -AtovvN c o l l i 4 1 o n i ) C c ( 2 1 ) A g e n e r a l s o l u t i o n t o t h i s e q u a t i o n would be v e r y d i f f i c u l t t o o b t a i n ; i t would have t o be s o l v e d s i m u l t a n e o u s l y w i t h s i m i l a r e q u a t i o n s d e s c r i b i n g t h e r a t e o f change o f p o p u l a t i o n d e n s i t i e s o f the o t h e r e x c i t e d s t a t e s . E v e n i f t h i s were p o s s i b l e , one would need t o know th e v a l u e s o f the many c o n s t a n t s s u c h as c o l l i s i o n c r o s s - s e c t i o n s and a b s o r p t i o n c o e f f i c i e n t s i n o r d e r t o o b t a i n t h e t r a n s i t i o n p r o b a b i l i t i e s from t h e measured p o p u l a t i o n decay r a t e s . The e x p e r i m e n t d e s c r i b e d i n t h i s t h e s i s i s d e s i g n e d so t h a t a l l t h e .terms i n the above e q u a t i o n may be n e g l e c t e d e x c e p t the f i r s t t h r e e . T h i s w i l l be shown i n the n e x t s e c t i o n , where we d i s c u s s the s p e c i a l t r a n s i -t i o n s t u d i e d . U. S o l u t i o n t o the g e n e r a l e q u a t i o n f o r the 2p-^ l e v e l i n n a o n The t r a n s i t i o n s t u d i e d i n t h i s e x p e r i m e n t was the 5852 .5 A t r a n s i t i o n between the 2p^and ls2 l e v e l s o f neon. F o r t h e sake o f o r i e n t a t i o n , a p a r t i a l e n e r g y l e v e l diagram o f neon I i s g i v e n i n f i g u r e ( 1 ) . The 2p 2 2 5 s t a t e s c o r r e s p o n d t o the e l e c t r o n c o n f i g u r a t i o n I s 2s 2p"jp, w h i l e t h e I s - 13 -736 A ( to the ground state ) Figure ( 1 ) Partial terra diagram of neon I. - l U -2 2 5 s t a t e s r e p r e s e n t the l e v e l s i n the I s 2s 2p 3s c o n f i g u r a t i o n , life c a n d e s c r i b e the terms of neon i n two c o u p l i n g schemes, namely t h e LS c o u p l i n g scheme, o r the j l c p u p l i n g scheme. N e i t h e r scheme i s a v e r y good a p p r o x i m a t i o n t o t h e a c t u a l c o u p l i n g scheme t h a t e x i s t s f o r t h e I s and 2p s t a t e s . T h i s p o i n t w i l l be d i s c u s s e d f u r t h e r i n a l a t e r s e c t i o n . I n the LS c o u p l i n g scheme th e t r a n s i t i o n s t u d i e d i s d e s i g n a t e d ^ p " " ^ > 3 s 1P 1, w h i l e i n t h e j l c o u p l i n g scheme we w r i t e 3p' ( | r ) 0 — • 3s' ( 2 ) The ground s t a t e i n neon I i s a 1 S Q s t a t e , w i t h e l e c t r o n c o n f i g u r a t i o n 2 2 5 I s 2s 2p . I t i s c l e a r t h a t the 2p^ s t a t e from w h i c h the 5852 A t r a n s i t i o n o r i g i n a t e s , i s n o t o p t i c a l l y c o n n e c t e d t o the ground s t a t e . N o t o n l y i s the t r a n s i t i o n f o r b i d d e n b y t h e p a r i t y change s e l e c t i o n r u l e ( p a r i t y i s e ven f o r b o t h s t a t e s ) , b u t a l s o a J=-0 — * J= 0 t r a n s i t i o n i s s t r i c t l y f o r b i d d e n f o r a l l r a d i a t i o n . I n o r d e r t o see why a l l b u t t h r e e terms i n e q u a t i o n ( 21 ) may be n e g l e c t e d , we must a n t i c i p a t e some of t h e e x p e r i m e n t a l d e t a i l s o f our l i g h t s o u r c e . The l i g h t s o u r c e c o n s i s t e d of neon gas a t p r e s s u r e s r a n g i n g from 20 t o 200 m i c r o n s o f Hg. I t was p e r i o d i c a l l y e x c i t e d b y a f a s t b u r s t o f , e l e c t r o n s w h i c h was g e n e r a t e d i n an e l e c t r o n gun. The p h y s i c a l d i m e n s i o n s o f the s o u r c e were o f the o r d e r of c e n t i m e t e r s . The e l e c t r o n c u r r e n t u s e d 2 t o e x c i t e the neon gas was a b out 25 m i l l i a m p e r e s p e r cm , and t h e e n e r g y o f the e l e c t r o n s 50 eV. A l l measurements on the s o u r c e were made i n t h e time i m m e d i a t e l y f o l l o w i n g the e x c i t a t i o n b u r s t o f e l e c t r o n s . .The w i d t h o f t h e e x c i t a t i o n p u l s e was h x 10"^  s e c o n d s . C o n s i d e r now the a b s o r p t i o n terms i n e q u a t i o n ( 21 ).as i t a p p l i e s t o the 2p^ s t a t e i n neon. The importance o f t h i s t e r m was s e e n t o be go v e r n e d b y t h e v a l u e o f k o l ' , where k Q i s the a b s o r p t i o n c o e f f i c i e n t g i v e n b y e q u a t i o n , ^ 9 ) , and 1' i s t h e p a t h l e n g t h t h a t t h e r a d i a t i o n must t r a v e l i n -15 -o r d e r t o e s c a p e t h e c o n t a i n e r . T h e c o e f f i c i e n t k Q d e p e n d s o n t h e p o p u l a t i o n d e n s i t y o f t h e a b s o r b i n g s t a t e . I t i s o b v i o u s t h a t t h e g r o u n d s t a t e h a s t h e l a r g e s t p o p u l a t i o n d e n s i t y , s o t h a t o n e w o u l d e x p e c t t h e a b s o r p t i o n f r o m t h e g r o u n d s t a t e t o b e t h e m o s t i m p o r t a n t . H o w e v e r , s i n c e r a d i a t i v e t r a n s i t i o n s t o t h e g r o u n d s t a t e f r o m t h e 2p^  s t a t e a r e f o r b i d d e n , we d o n o t h a v e a b s o r p t i o n f r o m t h e g r o u n d s t a t e t o t h i s p a r t i c u l a r l e v e l . O t h e r p o s -s i b i l i t i e s a r e a b s o r p t i o n f r o m e x c i t e d s t a t e s . F o r e x a m p l e , we c a n h a v e a b s o r p t i o n c a u s i n g t r a n s i t i o n s f r o m t h e 1&2 s t a t e t o t h e 2p^  s t a t e ($852 A ) , l e a d i n g t o a n i n c r e a s e i n p o p u l a t i o n d e n s i t y o f t h e 2p^  s t a t e , o r a b s o r p t i o n f r o m t h e 2p^  s t a t e i t s e l f t o . a h i g h e r s t a t e , l e a d i n g t o a d e c r e a s e i n p o p u l a t i o n d e n s i t y o f t h e 2p^  s t a t e . I n o r d e r t o e s t i m a t e k Q f o r t h e s e t r a n s i t i o n s , we m u s t m a k e a n e s t i m a t e o f t h e p o p u l a t i o n d e n s i t i e s o f t h e v a r i o u s e x c i t e d s t a t e s . T h e d o m i n a n t p r o c e s s o f p o p u l a t i n g t h e s e s t a t e s i s d i r e c t e x c i t a t i o n b y m e a n s o f e l e c t r o n i m p a c t , o r i n d i r e c t e x c i t a t i o n b y m e a n s o f t r a n s i t i o n s f r o m o t h e r e x c i t e d s t a t e s w h i c h i n t u r n t h e m s e l v e s w e r e e x c i t e d b y e l e c t r o n i m p a c t . I f we c a l c u l a t e t h e p o p u l a t i o n d e n s i t i e s u n d e r t h e a s s u m p t i o n t h a t i t i s e n t i r e l y d e t e r m i n e d b y e l e c t r o n i m p a c t , a n d n e g l e c t a l l d e p o p u l a t i n g p r o c e s s e s , i t m a y b e s a f e l y s a i d t h a t t h e c a l c u l a t e d p o p u l a t i o n d e n s i t y o f t h e e x c i t e d s t a t e s r e p r e s e n t s t h e o r d e r o f m a g n i t u d e o f t h e m a x i m u m p o s s i b l e p o p u l a t i o n d e n s i t i e s o f t h e s e s t a t e s . T h a t i s —8 w h e r e t i s e q u a l t o h x 10 s e c o n d s . T h e v a l u e s o f Q o j w i l l d i f f e r f o r e a c h l e v e l . S o m e o f t h e s e c r o s s - s e c t i o n s h a v e b e e n m e a s u r e d f o r n e o n . F o r e x a m p l e , R e v a l d ( 11 ) q u o t e s Q ^ ^ I O c m 2 . A t 100 m i c r o n s o f H g . p r e s s u r e , a n d r o o m t e m p e r a t u r e , t h e g r o u n d s t a t e p o p u l a t i o n d e n s i t y i s g i v e n b y - 16 -Y \ Q = 3 x l O cm" ? n 7 and a current density of 25 ma per cm corresponds to 1.5 x 10 ' electrons per cm2sec. Hence n . / >, the maximum population density of the excited j \IT12QC / states, i s approximately equal to •nj < r n a ^ =C3x\oSXi.-Sx\o7)( \ x » o " ^ ) ( 4 x j o ' S )^ l0 7 c * > T 3 I f we put this into equation ( 9 ) , assuming that X i s approximately 10"^  seconds, we have - 4 - -I k ~_ I x io cm o With 1' equal to a few centimeters at most, the approximation for T ( k 0 l ' ) given by equation ( 10 ) holds, and the absorption from the excited states i s seen to be negligible. For excitation pulses that are very much longer, this may not be so, especially for levels that are metastable. Because the absorption terms are negligible, the terms describing stimulated emission w i l l also be negligible , since they are of the same order of magnitude ( c . f . equation ( 15 ) ). The terms dealing with.atom-atom col l is ions w i l l be discussed next.. In order to assess their importance, we sha l l compare them with the terms describing spontaneous emission, since these are of the same form, ife must then compare the order of magnitude of Q n 0 v with A, the Einstein t ransi-tion probabil i ty . Again, detailed values for the cross-sections Q: are not available for the levels involved. However, they have been measured for a few isolated co l l i s ion interactions i n noble gases. For the transfer of energy between levels that are very close together, these cross-sections can become very high. For example, Maurer and Wolf ( 10 ) have measured for the interaction i n Helium (s V.) + Wc6 'So) — Uc6'^ +^e& 'D.V.003 CV (23) t o b e 5 x l O " " 1 " ^ c m 2 . F o r l e v e l s n o t s o c l o s e t o g e t h e r , t h e c r o s s - s e c t i o n s b e c o m e c o n s i d e r a b l y s m a l l e r . P a r k s a n d J a v a n ( 8 ) h a v e r e c e n t l y m e a s u r e d t h e c r o s s - s e c t i o n f o r t h e r e a c t i o n - l 6 2 a n d f o u n d i t t o b e 2.3 x 10 c m . A g e n e r a l r u l e o f t h u m b q u o t e d b y B e n n e t t e t a l . ( 1 ) i s t h a t f o r e n e r g y d i f f e r e n c e s o f m o r e t h a n a f e w -20 2 k T , t h e c r o s s - s e c t i o n s a r e 10 cm o r l e s s j f o r e n e r g y d i f f e r e n c e s o f t h e o r d e r o f k T , t h e c r o s s - s e c t i o n s a p p r o a c h t h e g a s k i n e t i c c r o s s - s e c t i o n ( a b o u t 1 0 ~ ^ > c m 2 ) , w h i l e f o r e n e r g y d i f f e r e n c e s l e s s t h a n t h a t t h e c r o s s -s e c t i o n s m a y b e c o m e a s h i g h a s 1 0 - ^ c m ^ . A n e n e r g y d i f f e r e n c e o f .03 e V c o r r e s p o n d s t o k T a t r o o m t e m p e r a t u r e . F o r t h e 2p^ l e v e l , w h i c h i s o f i n t e r e s t i n t h i s d i s c u s s i o n , t h e n e a r e s t l e v e l i s t h e 2p2 l e v e l , w h i c h i s ,2i| e V l o w e r . T h e r e f o r e we m a y t a k e t h e c o l l i s i o n e n e r g y t r a n s f e r c r o s s --20 2 s e c t i o n a t a p p r o x i m a t e l y 10 cm . T h i s t h e n g i v e s u s S i n c e t h e o r d e r o f m a g n i t u d e o f A t h a t we e x p e c t i s a t l e a s t 10^ s e c " ' ' " , we c a n s a f e l y n e g l e c t t h e s e c o l l i s i o n t e r m s f o r t h e 2p^ l e v e l a t t h e a b o v e q u o t e d p r e s s u r e s . F o r s i m i l a r r e a s o n s t h e r a t e o f c h a n g e i n t h e p o p u l a t i o n d e n s i t y o f t h e 2p-|_ s t a t e d u e t o c o l l i s i o n ? w i t h f r e e e l e c t r o n s i s n e g l i g i b l e . T h e d e n s i t y o f f r e e e l e c t r o n s i n t h e g a s c a n b e e s t i m a t e d f r o m a k n o w l e d g e o f t h e i o n i -s a t i o n c r o s s - s e c t i o n f o r c o l l i s i o n w i t h e l e c t r o n s i n t h e e l e c t r o n b e a m . We h a v e ( s e e e q u a t i o n ( 2 2 ) ) , - 18 -r4Alo ie.c a s s u m i n g W ^ ^ \ O <=>v> . The aver a g e v e l o c i t y o f the e l e c t r o n s a t room t e m p e r a t u r e i s a p p r o x i m a t e l y 5 x 10^ cm/sec. Hence ' » • e <•? e fe ,6 ^e. » \ x \o Q J V < 7 e - - 7 2 F o r t h i s t o be comparable t o A 10 we need Q j k a? C m w h i c h i s very-u n l i k e l y . I t i s r e a d i l y s e e n t h a t t h e term due t o d i f f u s i o n may a l s o be n e g l e c t e d . T h i s term a g a i n i s of t h e same fo r m as t h o s e f o r spontaneous e m i s s i o n , and we must compare w i t h A, The d i f f u s i o n c o e f f i c i e n t D was measured b y P h e l p s ( 12 ) f o r e x c i t e d neon atoms d i f f u s i n g t h r o u g h n e u t r a l neon atoms, He o b t a i n e d D - 5.5 x 10 cm s e c . The e f f e c t i v e d i f f u s i o n l e n g t h i s of t h e o r d e r o f t h e d i m e n s i o n s o f t h e l i g h t s o u r c e , so t h a t we o b t a i n r> S x i o - 1 * 3 — S - T ~ I X I O 7 Compared t o the v a l u e o f A o f about 10 , we see t h a t t h i s c o e f f i c i e n t , and t h e r e f o r e t he d i f f u s i o n p r o c e s s , i s n e g l i g i b l e . I n v i e w o f the above c o n s i d e r a t i o n s , i t c a n be c o n c l u d e d t h a t f o r t h e 2p^ s t a t e i n neon u n d e r our c o n d i t i o n s , t h e e q u a t i o n i s a v e r y good a p p r o x i m a t i o n t o e q u a t i o n ( 21 ) . The l a s t terra c o r r e s p o n d s t o the i n c r e a s e i n p o p u l a t i o n d e n s i t y o f t h e 2p^ s t a t e b y means b y s p o n -taneous r a d i a t i v e t r a n s i t i o n s f r o m h i g h e r s t a t e s t h a n t h e 2p^ s t a t e w h i c h - 1 9 -t e r m i n a t e i n t h a t s t a t e . Of s p e c i a l i n t e r e s t i s the c a s e where t h e r e i s o n l y one s u c h h i g h e r s t a t e f e e d i n g t h e 2p^  s t a t e , w h i c h i t s e l f i s n o t f e d v b y s t i l l h i g h e r s t a t e s . As i t t u r n s o u t , t h i s i s a v e r y good a p p r o x i m a t i o n t o o u r case as i s e v i d e n c e d b y the d a t a o b t a i n e d . T h i s p o i n t w i l l be c l a r i -f i e d l a t e r , b u t f o r now we s h a l l s o l v e e q u a t i o n ( 25 ) f o r t h i s c a s e . I f t h e h i g h e r s t a t e i i s n o t f e d b y s t i l l h i g h e r s t a t e s t h e n we can w r i t e f o r t h i s s t a t e 0 ^ ) I f we now t u r n o f f t h e e l e c t r o n e x c i t a t i o n a t sane t i m e b e f o r e t •=• 0, t h e n we have = ^do) *xp(-Act) ( 2 7 ) and ai* = "Aj^j + Ai) *>±Lo)4Xp(-Ai±) {2.8) T h i s e q u a t i o n has t h e s o l u t i o n We c a n t h e r e f o r e x«*ite f o r t h e t i m e dependence o f i n t e n s i t y w h i c h i s o f t h e fo r m i a) = i, •+- -ks * ( 3 1 ) T h i s e q u a t i o n may be s o l v e d n u m e r i c a l l y f o r * 2» " ^ i ^ ^ I J p r o v i d e d t h e tim e dependence of I ( t ) i s known e x p e r i m e n t a l l y o v e r a s u i t a b l e t i m e r a n g e . - 2 0 -The q u a n t i t y o f i n t e r e s t , namely A., c a n th u s be d e t e r m i n e d . 5. T h e o r e t i c a l d e t e r m i n a t i o n o f t r a n s i t i o n p r o b a b i l i t i e s . As i s well known ( see for example Condon and Shortley ( 13 ) ), t h e electric dipole transition probability from the state j to a lower s t a t e k i s g i v e n b y an e x p r e s s i o n of t h e form .4 Mi< 3 ^ V ^ j (32) i s t he s o c a l l e d l i n e s t r e n g t h . The l i n e s t r e n g t h J6 where J<J s JO i s made up o f two p a r t s , Here «S i s a f a c t o r w h i c h depends on the p a r t i c u l a r c o u p l i n g o f t h e a n g u l a r momenta of t h e e l e c t r o n s m a k i n g up the two terms o f t h e t r a n s i t i o n , w h i l e C. i s g i v e n b y the e q u a t i o n .04 <ra = T J p T I l0 Y * > a (34) where i s t h e g r e a t e r o f t h e two a z i m u t h a l quantum numbers o f the two e l e c t r o n c o n f i g u r a t i o n s i n v o l v e d i n t h e t r a n s i t i o n , and R n ^ j ^ n ' l ' a r e ^ e r a d i a l wave f u n c t i o n s o f t h e l e v e l s . The q u a n t i t y d" x c a n be o b t a i n e d b y the coulomb a p p r o x i m a t i o n as p r o p o s e d b y B a t e s and Damgaard ( Ik ) . The a n g u l a r f a c t o r 5 depends on t h e t y p e o f c o u p l i n g t h a t may be c o n s i d e r e d v a l i d f o r the p a r t i c u l a r terms o f i n t e r e s t . F o r the 2p s t a t e s i i n e o n , i t i s n o t c l e a r w h i c h c o u p l i n g d e s c r i p t i o n i s more v a l i d , t h e R u s s e l l S a u nders LS c o u p l i n g , o r the j l c o u p l i n g scheme i n t r o d u c e d b y Racah ( 1$ ) . The l a t t e r seems t o be v e r y good f o r the h i g h e r s t a t e s i n n e o n , where the c h a r a c -t e r i s t i c d o u b l e t s t r u c t u r e a s s o c i a t e d w i t h t h i s c o u p l i n g scheme i s q u i t e apparent. For the lower e x c i t e d s t a t e s , however, nei t h e r scheme seems to f i t the spacing of the energy l e v e l s very w e l l . A l s o , t r a n s i t i o n s are observed which are forbidden by both d e s c r i p t i o n s . I t turns out, however, that f o r the t r a n s i t i o n ^Vj~**ls2 ^ e v a l u e °^ S i s u n i t y f o r both coupling schemes. This i s calculated f o r LS coupling by Shortley ( 16 ) while f o r j l coupling the c a l c u l a t i o n was made by Koster and Statz ( 17 ), The r e l a t i v e values computed by the above authors were put on an absolute basis using the sum r u l e s as given by Menzel ( 18 ) . The value of cr* was determined using values f o r R.^ as given by the Coulomb approximation of Bates and Damgaard ( lU )• The wave functions and the i n t e g r a l were computed with the aid of a computer program written by Dr. A . J . Barnard from our la b o r a t o r y . The r e s u l t f o r the t r a n s i t i o n array 3p - 3s i n neon i s S~z — 1 , 8 6 X \ O O r v We then obtain A " X , ° 7 ^ " ' (35) The corresponding l i f e t i m e of the 2p^ state i s therefore _ •"*-2L|B, = 1 5 * 1 0 /<«.«>M6 (36) B. Relative I n t e n s i t y Measurements As i s apparent from equation ( 2 ), the amount of r a d i a t i v e energy that i s emitted by the source per u n i t time per u n i t volume at a p a r t i c u l a r frequency i s p r o p o r t i o n a l to A. , the t r a n s i t i o n p r o b a b i l i t y . That i s Jk VjK JVC J< J or, in terms of the wavelength, ft K V ) = A j V c nj ( 3 8 ) If there exists some other transition from the state j to a lower state t then i t is clear that the ratio is independent of the population density of the upper state. Hence i f one can measure this ratio, one has a method of determining the relative values of the transition probabilities for transitions having a common upper state. Of course, one can never determine directly the relative amounts of energy given off at the two wavelengths. What can be measured is the relative strengths of the signals that the two transitions produce in a photomultiplier after having been passed through an optical system having a characteristic wavelength response. Hence the optical and electrical measuring system must be calibrated as a function of wavelength before the relative values of I can be obtained. This calibration can be. done with a tungsten ribbon lamp of known temperature and emissivity. In Chapter III i t is shown how this calibration was performed in our experiment, . An important condition which must be met i f one is to measure relative transition probabilities in this way is that self absorption of the source be negligible for the transitions studied. It is clear from our previous discussion of absorption that this is negligible in our light source, even though somewhat longer excitation pulses ( 200 nanoseconds ) were used to excite the gas. ( c . f . section ht equation ( 2 2 ) ) . 23 -CHAPTER I I I EXPERIMENTAL METHOD AND APPARATUS A. L i f e t i m e Measurements. 1, Summary o f the method. The e x p e r i m e n t a l method u s e d f o r m e a s u r i n g I ( t ) as g i v e n b y e q u a t i o n ( 31 ) was as f o l l o w s . Neon g a s , w h i c h was l e t i n t o a p r e v i o u s l y e v a c u a t e d v e s s e l , was p e r i o d i c a l l y e x c i t e d a t 500 c p s b y means o f a p u l s e d e l e c t r o n beam. The r e s u l t i n g r a d i a t i o n due t o spontaneous t r a n s i t i o n s i n the neon gas was p a s s e d t h r o u g h a monochromator, and m o n i t o r e d a t d i f f e r e n t w a v e l e n g t h s as a f u n c t i o n of time b y a p h o t o m u l t l p l i e r . The time r e s o l u t i o n o f t h e i n t e n -s i t y was o b t a i n e d b y means o f a s a m p l i n g o s c i l l o s c o p e s y s t e m , w h i c h sampled t h e o u t p u t of t h e p h o t o m u l t i p l i e r once e v e r y c y c l e a t a known d e l a y t i m e r e l a t i v e t o the s t a r t i n g time o f t h e e x c i t a t i o n p u l s e . Because the l i g h t l e v e l s e n c o u n t e r e d i n t h e e x p e r i m e n t were e x t r e m e l y l o w , t h e p r o b a b i l i t y t h a t the sample would f i n d an o u t p u t on t h e p h o t o m u l t i p l i e r ( due t o a'- s i n g l e p h o t o n ) , d u r i n g the s a m p l i n g time,was much l e s s t h a n one. Hence t h e o u t p u t o f the s a m p l i n g system was f e d i n t o a c o u n t e r , and t h e r e s u l t i n g c o u n t o f t h e p h o t o m u l t i p l i e r o u t p u t s o v e r a p e r i o d o f s e v e r a l m i n u t e s was i n t e r p r e t e d as a measure of t h e average number o f p h o t o n s r a d i a t i n g from t h e s o u r c e a t a p a r t i c u l a r t i m e r e l a t i v e t o t h e b e g i n n i n g o f the e x c i t a t i o n p u l s e . S i n c e t h i s number i s p r o p o r t i o n a l t o t h e i n t e n s i t y , t h e p h o t o n c o u n t as sampled a t s u c c e s s i v e d e l a y t i m e s i n t h e e x c i t a t i o n - d e e x c i t a t i o n c y c l e gave a measure o f t h e t i m e dependence of t h e i n t e n s i t y . F o r t h e sake of c l a r i t y , a t y p i c a l sequence o f e v e n t s i s g i v e n g r a p h i c a l l y i n f i g u r e ( 2 ) , w h i l e a s c h e m a t i c d i a g r a m o f t h e a p p a r a t u s i s g i v e n i n f i g u r e ( 3 ) . E x c i t a t i o n p u l s e A v erage l i g h t o u t p u t P o s s i b l e p h o t o m u l t i p l i e r o u t p u t S a m p l i n g g a t e S a m p l i n g o u t p u t e t c 1 1 1 1 J 1 1 1 r \ «r\ i i . i i L A A ! A 1 1 1 lil rx I i 1 ! fl i | i i 1 • i i 1. • 1 ! 1  -H A t — 1 1 i I A t - — — A t — — 1 A t 1 1 i 1 t i m e F i g u r e ( 2 ) Sequence o f e v e n t s i n i n t e n s i t y m e a s u r i n g s y s t e m . electron gun Figure ( 3 ) Schematic diagram of the apparatus. A number of general considerations •were of Importance in the choice and design of the apparatus. The fi r s t of these was one of time resolution. Anticipating the order of magnitude of our results, we knew that the decay of intensity would take place in about 10 nanoseconds, so that for proper reso-lution we would need a time resolution of a few nanoseconds. This meant that a l l electronic equipment used both for excitation and detection had to have a time response of that order. Secondly, i t was apparent from the start that we would be dealing with extremely weak signals. For this reason the optical light gathering power of the detection system had to be optimised, and the conversion efficiency of light intensity into electrical signal had to be made as large as possible. Finally, because the output signals had to be averaged over fairly long times ( a typical determination of one decay took about one hour ), i t was important that the source remain at the same pressure, free of impurities during that length of time. This meant ultra-high vacuum techniques had to be used in the preparation of the source. In the next sections, these considerations and the apparatus used will be considered in more detail, 2 .• Light Source a) Electron gun A drawing of the main features of the electron gun appears in figure ( ii ) . The gun was designed to,give a parallel beam of electrons of fairly well defined energy traversing a region in the gas which could be focussed on the entrance s l i t of the monochromator. The electrons were released from an.indirectly heated oxide coated cathode and accelerated to the grid by means of a potential difference. The grid and anode together formed a box as shown, and the electrons, once having passed the grid, drifted Figure ( E> .) Equipotential surfaces of a parallel electron beam t h r o u g h the f i e l d f r e e r e g i o n i n s i d e the box a t a c o n s t a n t s p e e d . The l i g h t x-jhich r e s u l t e d from e x c i t a t i o n b y t h e s e e l e c t r o n s was o b s e r v e d t h r o u g h a s l i t i n the anode b o x , as i s shown i n the d i a g r a m s . The shape o f t h e e l e c -t r o d e s was c h osen a c c o r d i n g t o d e s i g n c a l c u l a t i o n s made b y P i e r c e ( 2 D ) . He showed t h a t f o r a space c h a r g e l i m i t e d p l a n e p a r a l l e l beam o f e l e c t r o n s o f i n i t i a l e n e r g y 0 and f i n a l e n e r g y eV 0 , the e q u i p o t e n t i a l . s u r f a c e s i n the s p a c e o u t s i d e t h e beam i t s e l f have a shape as i n d i c a t e d i n f i g u r e ( 5> ) • I f we t h e r e f o r e make the s u r f a c e s o f the c a t h o d e and g r i d t o c o i n c i d e w i t h the e q u i p o t e n t i a l s u r f a c e s V = 0 and V = V r e s p e c t i v e l y , t h e n we w i l l have a p a r a l l e l beam of e l e c t r o n s . The phenomenon o f t h e r m i o n i c e m i s s i o n , on w h i c h t h e o p e r a t i o n o f t h e e l e c t r o n gun depends, has b e e n s t u d i e d i n g r e a t d e t a i l b y many w o r k e r s . An e x c e l l e n t r e v i e w of t h e s u b j e c t i s g i v e n b y N o t t i n g h a m i n Volume X X I o f Handbuch d e r P h y s i k ( 21 ) . O n l y t h e b a s i c e q u a t i o n s g o v e r n i n g the e m i s s i o n o f e l e c t r o n s u n d e r v a r i o u s c o n d i t i o n s w i l l be g i v e n h e r e . The maximum c u r r e n t d e n s i t y t h a t c a n be drawn f r o m any s u r f a c e a t t e m p e r a t u r e T a t moderate a c c e l e r a t i n g p o t e n t i a l s i s g i v e n b y t h e w e l l known R i c h a r d s o n e q u a t i o n , X = AT 2 jtw? C ) (4o) were A and are c o n s t a n t s d e p e n d i n g on t h e s u r f a c e m a t e r i a l o f t h e e m i t t e r . I n p r a c t i c e , t h e c u r r e n t t h a t c a n be drawn by a p o t e n t i a l d i f f e r e n c e m a i n t a i n e d by two o r more e l e c t r o d e s i s l i m i t e d t o a v a l u e l e s s t h a n t h a t g i v e n b y e q u a t i o n ( hO ) due t o t h e space c h a r g e t h a t t h e beam of e l e c t r o n s s e t s up between t h e e l e c t r o d e s . F o r the s p e c i a l geometry o f i n t e r e s t h e r e , v i z . c u r r e n t f l o w between two p a r a l l e l p l a t e s , t h e space c h a r g e l i m i t e d c u r r e n t d e n s i t y i s g i v e n b y where x i s t h e s p a c i n g between t h e e l e c t r o d e s i n cm, and V q t h e p o t e n t i a l d i f f e r e n c e i n v o l t s . I n o ur e x p e r i m e n t i t was i m p o r t a n t t h a t the c u r r e n t o b t a i n e d f r o m the gun be as l a r g e as p o s s i b l e , s i n c e the v a l u e o f t h i s c u r r e n t d e t e r m i n e s the i n i t i a l p o p u l a t i o n d e n s i t i e s i n t h e decay p r o c e s s , and hence t h e s t r e n g t h of the s i g n a l o b s e r v e d . A l t h o u g h i t may seem f r o m e q u a t i o n ( 1^0 ) t h a t t h e c u r r e n t may be made a r b i t r a r i l y h i g h b y r a i s i n g t h e t e m p e r a t u r e o f t h e e m i t t i n g s u r f a c e , i t i s o b v i o u s t h a t a t t e m p e r a t u r e s n e a r t h e m e l t i n g p o i n t of t h e e m i t t i n g m a t e r i a l s i g n i f i c a n t d e p a r t u r e s from e q u a t i o n ( U0 ) o c c u r . E v e n t h a t c o n s i d e r a t i o n a s i d e , i n p r a c t i c e one does n o t h e a t t h e cathode h i g h e r t h a n some t e m p e r a t u r e T s u c h t h a t t h e c u r r e n t I g i v e n b y e q u a t i o n s c ( h0 ) i s s u f f i c i e n t t o s u p p l y the c u r r e n t i g i v e n b y e q u a t i o n ( i j l ) o v e r the range o f v o l t a g e s t o be u s e d . S i n c e a l l m a t e r i a l s have t h e i r own c h a r a c t e r i s t i c A and , t h i s t e m p e r a t u r e i s d i f f e r e n t f o r d i f f e r e n t m a t e r i a l s . Common c a t h o d e m a t e r i a l s c h o s e n f o r t h e i r f a v o r a b l e v a l u e s o f A and <5^, , a r e f o r example t u n g s t e n , t h o r i a t e d t u n g s t e n , and n i c k e l a l l o y s c o a t e d w i t h o x i d e s o f t h e a l k a l i n e e a r t h s . F o r t h e f i r s t two m e t a l s , T g c l i e s between l £ 0 0 and 2^ 00 d e g r e e s C . f o r our e l e c t r o n gun d e s i g n and moder-at e o p e r a t i n g v o l t a g e s ( f o r example $0 v o l t s ) . However, f o r the o x i d e c o a t e d c a t h o d e , t h i s t e m p e r a t u r e i s a p p r o x i m a t e l y 1000 d e g r e e s c e n t i g r a d e . T h i s t e m p e r a t u r e i s so much l o w e r b e c a u s e the o x i d e c o a t e d n i c k e l a l l o y s have a much l o w e r work f u n c t i o n <^> t h a n the o t h e r m a t e r i a l s m e n t i o n e d . F o r o ur p u r p o s e s , t h i s r e l a t i v e l y l o w o p e r a t i n g t e m p e r a t u r e i s a d i s t i n c t advantage f r o m s e v e r a l p o i n t s o f v i e w . I n the f i r s t p l a c e , t h e b a c k g r o u n d r a d i a t i o n from t h e h e a t e d c a t h o d e i s much s m a l l e r a t l o w t e m p e r a t u r e s , w h i c h i n c r e a s e s our s i g n a l t o n o i s e r a t i o , and s e c o n d l y , the l o w e r power t o - 30 -be d i s s i p a t e d w i l l r educe t h e amount o f d e g a s s i n g f r o m t h e e l e c t r o d e s and the s u r r o u n d i n g g l a s s i n t o t h e vacuum s y s t e m . F o r t h e s e r e a s o n s i t was d e c i d e d t o use an o x i d e c o a t e d c a t h o d e . The s u r f a c e a r e a o f the c a t h o d e , w h i c h d e t e r m i n e s the c r o s s - s e c t i o n a l a r e a of t h e beam, and hence t h e s i z e o f t h e l i g h t s o u r c e , was c h osen t o be a r e c t a n g l e o f d i m e n s i o n s 2.5 cm. b y 1 cm. The l o n g e r d i m e n s i o n was c h o s e n t o j u s t c o v e r the l e n g t h of t h e e n t r a n c e s l i t o f the monochromator, w h i l e t h e s h o r t e r d i m e n s i o n was c o n v e -n i e n t from the p o i n t o f v i e w of:-heater d e s i g n . Because t h e p h o t o m u l t i p l i e r u s e d as a d e t e c t o r e f f e c t i v e l y i n t e g r a t e d t h e s i g n a l o v e r t h e l e n g t h o f t h e s l i t , s i g n i f i c a n t g a i n s i n s i g n a l c o u l d be made b y u s i n g s u c h an e x t e n d e d s o u r c e . T h i s p o i n t w i l l be f u r t h e r d e a l t w i t h i n the s e c t i o n on t h e o p t i c a l p a r t s of t h e a p p a r a t u s . A l t h o u g h o x i d e c o a t e d c a t h o d e s a r e made i n huge q u a n t i t i e s b y e l e c t r o -n i c tube m a n u f a c t u r e r s , t h e y a r e d i f f i c u l t t o o b t a i n i n s e p e r a t e f o r m . Not one o f a dozen e l e c t r o n i c s f i r m s c o n t a c t e d c o u l d s u p p l y u s w i t h c a t h o d e s t h a t were e v e n a p p r o x i m a t e l y t h e s i z e t h a t we r e q u i r e d . 1/fe t h e r e f o r e de-c i d e d t o make our own. S i n c e t h e a u t h o r was n o t f a m i l i a r w i t h the r a t h e r s p e c i a l i s e d t e c h n o -l o g y a s s o c i a t e d w i t h the p r e p a r a t i o n and o p e r a t i o n o f o x i d e c o a t e d c a t h o d e s , much e x p e r i m e n t a t i o n had t o be done b e f o r e a p r o c e d u r e was f o u n d w h i c h p r o d u c e d a f a i r l y r e l i a b l e c a t h ode s u r f a c e w h i c h c o u l d be u s e d r o u t i n e l y i n t h e e l e c t r o n gun w i t h o u t f r e q u e n t r e p l a c e m e n t . Of g r e a t h e l p was t h e e x c e l -l e n t M ,1 .T . Tube L a b o r a t o r y M a n u a l ( 22 ) . A l t h o u g h we d i d manage t o o b t a i n good c u r r e n t s from the c a t h o d e s p r e p a r e d , the c a t h o d e s had a s h o r t o p e r a t i n g l i f e . A f t e r l e s s t h a n t h i r t y o r f o r t y r u n s t h e c u r r e n t b e g a n t o d i m i n i s h , and n e a r l y a l l specimens showed b l i s t e r i n g o r p e e l i n g a f t e r r e p e a t e d o p e r a t i o n . I t i s l i k e l y t h a t - 31 -t h i s b l i s t e r i n g i n s p o t s made the e l e c t r o n beam uneven i n i t s c r o s s - s e c t i o n , b u t t h i s , was n o t i m p o r t a n t f o r our e x p e r i m e n t . A l t h o u g h much c a r e was de-v o t e d t o t h e p r e p a r a t i o n and o p e r a t i o n o f t h e c a t h o d e s , a complete s o l u t i o n f o r t h e d i f f i c u l t i e s m e n t i o n e d above was n o t f o u n d . I n s t e a d , a new cathode was p r e p a r e d e a c h time an o l d one became u n u s a b l e . The m a t e r i a l s and p r o c e -dures u s e d i n making t h e c a t h o d e s w i l l be d e s c r i b e d b e l o w . The base m a t e r i a l u s e d f o r t h e c a t h o d e i s . a n i c k e l a l l o y e s p e c i a l l y made b y the S u p e r i o r Tube Company f o r u s e i n o x i d e c o a t e d c a t h o d e s , and d e s i g n a t e d C a t h a l ] o y A 33. The S u p e r i o r Tube company was s o k i n d as t o send us a p i e c e o f t h i s m e t a l a t no c h a r g e . The c a t h o d e c o a t i n g m a t e r i a l was RCA Code 33-C-l8S>A o b t a i n e d f r o m t h e R a d i o C o r p o r a t i o n o f A m e r i c a . T h i s i s a cathode c o a t i n g l i q u i d w i t h a c t i v e i n g r e d i e n t (CaSrBa)CO^ and a NagCO^ p r e c i p i t a t i n g a g e n t . P r i o r t o c o a t i n g , the n i c k e l was p r e p a r e d by th e s o - c a l l e d C I A p r o c e s s ( 22 ) , w h i c h i s summarized b e l o w . 1. R i n s e i n A c e t o n e . 2 . B o i l f o r f i v e m i n u t e s i n a s o l u t i o n made up o f Sodium Carbonate ( I4.O grams p e r l i t e r ) Sodium H y d r o x i d e ( 13 grams p e r l i t e r ) Sodium C y a n i d e ( 13 grams p e r l i t e r ) 3. B o i l f o r f i v e m i n u t e s i n d i s t i l l e d w a t e r . It. R i n s e i n warm 5% a c e t i c a c i d . 5 . A g i t a t e i n t h r e e changes o f b o i l i n g d i s t i l l e d w a t e r . 6. R i n s e i n c l e a n m e t h y l a l c o h o l . 7 . D r y i n warm a i r b l a s t o r oven. B e f o r e t h e m e t a l was s p r a y e d w i t h t h e c o a t i n g l i q u i d , i t was f i r e d i n vacuum a t about 800 degrees C. The c o a t i n g m a t e r i a l was t h e n s p r a y e d on b y means o f a homemade g l a s s s p r a y gun, u t i l i s i n g n i t r o g e n from a compressed - 32 -gas c y l i n d e r t o f o r c e the s p r a y from a s m a l l n o z z l e . S e v e r a l c o a t i n g p r o c e d u r e s were t r i e d , and f i n a l l y s e v e r a l t h i n c o a t s were a p p l i e d i n s u c -c e s s i o n . T h i s p r o c e d u r e seemed t o p r o d u c e the m o st r e l i a b l e s u r f a c e s . The cathode c o a t i n g i s s p r a y e d on i n the f o r m o f a c a r b o n a t e , and o n l y becomes a c t i v e as an e l e c t r o n e m i t t i n g s u b s t a n c e a f t e r i t has been c o n v e r t e d i n t o an o x i d e b y t h e s o - c a l l e d p r o c e s s of " a c t i v a t i o n " . The cathode must be a c t i v a t e d i n vacuum i n i t s o p e r a t i n g p o s i t i o n , s i n c e once t h e cathode i s a c t i v a t e d , a i r a t a t m o s p h e r i c p r e s s u r e s w i l l " s p o i l " t h e c a t h o d e , and i t s e m i s s i o n o f e l e c t r o n s w i l l be s m a l l . F o r t h i s r e a s o n i t i s n e v e r p o s s i b l e t o u s e an o x i d e c o a t e d c a t h o d e f r o m some c o m m e r c i a l t u b e , u n l e s s one c a n a r r a n g e t o use i t w i t h o u t e x p o s i n g i t t o t h e a t m o s p h e r e . A l s o , i f f o r some r e a s o n the vacuum s y s t e m must be opened t o the a t m o s p h e r e , t h e c a t h o d e must be r e c o a t e d and r e a c t i v a t e d b e f o r e i t c a n be u s e d a g a i n . The a c t i v a t i o n p r o c e d u r e n o r m a l l y f o l l o w e d was t h a t o u t l i n e d i n t h e M.I.T. Tube L a b o r a t o r y M a n u a l ( 22 ) , and i t s m a i n f e a t u r e s are as f o l l o w s . The t e m p e r a t u r e o f t h e c a t h o d e s u r f a c e was r a i s e d s l o w l y i n s m a l l s t e p s b y means o f a t u n g s t e n f i l a m e n t . The r a t e a t w h i c h t h e t e m p e r a t u r e was a l l o w e d t o r i s e was d e t e r m i n e d e n t i r e l y b y t h e p r e s s u r e i n t h e vacuum s y s t e m , w h i c h was m o n i t o r e d b y means o f an i o n i s a t i o n gauge. A t no t i m e d u r i n g t h e a c t i v a t i o n was t h e p r e s s u r e a l l o w e d t o r i s e above 1 x 10"^ t o r r , w h i l e i n t h e e a r l y s t a g e s ( the f i r s t h a l f h o u r o r s o ) , t h e p r e s s u r e was k e p t b e l o w 1 x 10"^ t o r r . I n an unbaked s y s t e m o f moderate pumping speed t h i s p r e s s u r e r e q u i r e m e n t can cause t h e a c t i v a t i o n p r o c e d u r e t o t a k e d a y s , b u t w i t h a b a k e a b l e s y s t e m i t c a n be done i n a f e w h o u r s . R e g a r d l e s s o f t h e r a t e , hox^ever, one r a i s e s the t e m p e r a t u r e as f a s t as i s c o n s i s t e n t w i t h t h i s p r e s s u r e r e q u i r e m e n t , u n t i l t h e t e m p e r a t u r e o f the cathode s u r f a c e i s about 800 degrees C. A t some p o i n t p r i o r t o t h i s t h e e v o l u t i o n o f gas f r o m t h e - 33 -cathode shows a marked increase due to the actual conversion reaction taking place in the cathode coating. This evolution of gas stops quite suddenly as shown by a marked decrease in pressure. In order to make sure that the activation has gone to completion, one can heat the cathode to temperatures in excess of 1 0 0 0 degrees C. for very short times, keeping the pressure requirement in mind. After the pressure has dropped to a value -6 in the 1 0 torr range, current may be drawn from the cathode. Inmost cases the current starts out rather small, and increases with time until i t reaches an equilibrium value. The pressure usually rises a l i t t l e when the _7 current is f irst drawn, but later drops to less than 1 0 torr in a well baked system. Currents up to 2 0 0 ma. at 5 0 volts ware obtained with the electron gunj however, most runs were done at somewhat reduced cathode temperatures with currents of the order of 5 0 ma. The heater used to raise the temperature of the emitting surface to its operating level consisted of a ten thousandths of an inch tungsten wire wound in a spiral and fitted inside a Mullite tube, Mullite is a ceramic insulator capable of withstanding very high temperatures. The arrangement of the heater inside the cathode is shown in some detail in figure (6). The s l i t cut in the insulating tube near the coated surface allowed heat to pass preferably in that direction, so that the front surface of the cathode sleeve would be heated more than the rest of the assembly. The. whole gun assemblywas mounted on a small block of lava stone, which is a very workable insulating material capable of withstanding high temperatures. This lava stone, available from the American Lava Company, can be cut, machined and dri l led, and in its finished form may be fired at 2 0 0 0 degrees C. After f ir ing, the stone becomes very hard, and is well suited for use inside a vacuum system. The block of lava stone in turn was nickel alloy sleeve to f i t into housing top surface is coated with oxide tungsten wire to f i t into mullite tube. spiral is i J I diameter approximately toib turns • '. Figure ( 6 ) Details of the cathode assembly. mounted on two stainless steel rods which ware suspended from above from a demountable flange in the vacuum system, b. Vacuum System The, essential parts of the vacuum system are shown schematically in figure ( 7 ). The part that is inside the dotted lines could be baked at temperatures as high as li!?0 degrees C,. ^ In the design of the vacuum system, several factors were of importance. The f i r s t of these was that the vacuum system be capable of maintaining a -good vacuum independent of the pumps while the electron gun was in operation. The experiment had, to be done in pure neon at a fixed pressure, and i t was important that, during a run, contamination of the neon due to degassing of the gun or the walls of the system be kept to a minimum. In a conven-tional non bakeable vacuum system, this requirement is almost impossible to f u l f i l , especially when one uses a large cathode surface, and correspon-dingly high dissipation of heat inside the system. What one can do is to - 35 -pirar.i gauge _| , gas supply"" ionisation gauge 2" o i l diffusion pump liquid nitrogen trap backing pump Figure ( 7 ) Schematic diagram of the vacuum system keep pumping on the system and flush neon through at a constant rate at some equilibrium pressure, but the disadvantages of such a system are several. One may have to use very large quantities of neon, especially i f ., the runs take long, and changing the gas supply bottles frequently is impractical, since each time the system is opened to the atmosphere, the cathode surface must be recoated. A better solution to this problem, although somewhat more expensive, is to use a bakeable ultrahigh vacuum system. In such a system the degassing problems are reduced by a large , factor after baking, and the system can be operated independently of the external pumps with the electron gun operating, without significant intro-duction of impurities in the system. A bakeable system is useful from other points of view as well. As mentioned earlier, the i n i t i a l degassing and subsequent activation proce-dure of the electron gun can proceed at a much faster rate after the system has been baked, and the cleanliness of a baked system is likely to improve - 36 -t h e o p e r a t i o n and l i f e o f t h e c a t h o d e s u r f a c e . A l s o , i t i s p o s s i b l e t o o b t a i n : v e r y l o w u l t i m a t e p r e s s u r e s b e f o r e neon i s l e t i n t o t h e s y s t e m , w h i c h w i l l r educe t h e i m p u r i t y l e v e l - a s w e l l . , W i t h t h e s e c o n s i d e r a t i o n s i n m i n d , i t was d e c i d e d t o use b a k e a b l e p a r t s i n t h e vacuum s y s t e m , and t o b u i l d an oven s o t h a t t h e whole s y s t e m , a p a r t from the t r a p and t h e pumps, c o u l d be b a k e d a t i|00 de g r e e s C. The oven u s e d f o r b a k i n g the system c o n s i s t e d o f f o u r demountable w a l l s , e a c h s e p a r a t e l y w i r e d w i t h h e a t e r e l e m e n t s , and made o u t o f 2" t h i c k M a r i n i t e , an a s b e s t o s t y p e b o a r d m a t e r i a l w h i c h i s heat r e s i s t a n t . A 3.5" p l a t e o f the same m a t e r i a l was used f o r a r o o f , and t h e whole s y s t e m was mounted on a base p l a t e o f t h e same m a t e r i a l . The i n s i d e d i m e n s i o n s o f the oven, were 28" x 28"t'-x 2 8 " , and s i x 750 Watt, h e a t e r e l e m e n t s were u s e d t o h e a t i t . The t e m p e r a t u r e i n s i d e t h e oven was r e g u l a t e d b y a F e n w a l l t h e r m o e l e c t r i c s w i t c h and a s e t o f r e l a y s w h i c h c o n t r o l l e d t h e c u r r e n t t o the oven e l e m e n t s . U s u a l l y , t h e t e m p e r a t u r e o f t h e sys t e m was r a i s e d q u i t e s l o w l y b y i n c r e a s i n g t h e s w i t c h i n g t e m p e r a t u r e o f t h e t h e r m a l s w i t c h i n s m a l l s t e p s . I n t h i s way s t r e s s e s due t o l a r g e t e m p e r a t u r e g r a d i e n t s c a u s e d b y t o o sudden h e a t i n g were m i n i m i s e d . Two i n c h e s was c h o s e n as t h e n o m i n a l d i a m e t e r o f t h e pumping s y s t e m j t h i s p r o v i d e d adequate pumping spe e d a t moderate c o s t . A s t a i n l e s s s t e e l l i q u i d a i r t r a p was u s e d w h i c h p r o v e d t o be i n d i s p e n s i b l e f o r the o p e r a t i o n o f t h e s y s t e m . The t r a p a i d e d n o t o n l y i n pumping away t h e v a p o r s f r o m t h e s y s t e m , b u t a l s o i n t r a p p i n g t h e b a c k s t r e a m i n g o i l f r o m t h e d i f f u s i o n pump. On two s e p a r a t e o c c a s i o n s when t h e l i q u i d a i r t r a p warmed up i n a d v e r t e n t l y , w h i l e the s y s t e m was open t o the pumps, t h e cathode became c o n t a m i n a t e d w i t h o i l ^ v a p o r f r o m the d i f f u s i o n pump as i n d i c a t e d b y a b l a c k e n i n g o f t h e c o a t i n g s u r f a c e on h e a t i n g , and a co m p l e t e l a c k o f c u r r e n t a t n o r m a l o p e r a t i n g tern-- 37 -peratures. For t h i s reason the system was never exposed to the pumps without the trap being f i l l e d with l i q u i d a i r . The trap was only warmed up and pumped clean when the main valve to the system was c l o s e d . The pressure inside the vacuum system was monitored by two gauges, -3 an i o n i s a t i o n gauge f or the measurement of pressures l e s s than 10 t o r r , and a P i r a n i gauge f o r measuring pressures above t h i s value. The P i r a n i gauge was used i n p a r t i c u l a r to determine the neon pressure i n s i d e the system during the experimental runs. Both gauges were bakeable, of course, and had to be disconnected from t h e i r c o n t r o l u n i t s during bakeout. The c a l i b r a t i o n of the P i r a n i gauge f or neon was supplied by the manufacturer. The neon used f o r the experiment was supplied i n glass containers by the A i r Reduction Company, and had an impurity l e v e l of less than l£0 parts per m i l l i o n . The. valves, flanges and trap used i n the vacuum system were supplied by the G r a n v i l l e P h i l i p s Company, and-proved to be very r e l i a b l e , providing v i r t u a l l y troublefree use. 3 • Monochromator. Whenever i t i s necessary to i s o l a t e the r a d i a t i o n at any one wavelength from a l l other wavelengths by means of a monochromator or spectrograph, there is, always a severe l o s s i n the s i g n a l a v a i l a b l e at the p a r t i c u l a r wavelength of i n t e r e s t . The f r a c t i o n of s i g n a l retained i s of s p e c i a l s i g n i f i c a n c e when one i s working with si g n a l s so weak that meaningful measurements are d i f f i c u l t to make. I t i s i n s t r u c t i v e to see how the frac-. t i o n of .the s i g n a l available at the e x i t s l i t depends on the o p t i c a l s p e c i f i -cations, of the monochromator. Suppose the o p t i c a l arrangement i s as f o l l o w s . An extended source ( assumed here rectangular, of height h g and width - 38 -w , ) , i s focussed by means of a lens i n the plane of the entrance s l i t of a s monochromator as shown. monochromator Suppose that the monochromator has aperture and working distance f , and the objective lens has aperture d , and f o c a l length f . Assume that h , wg are much l e s s than 1, 1', and f m , and that o p t i c a l aberrations are n e g l i g i b l e . I t i s c l e a r that i n order t o use the l i g h t gathering power of the monochromator to the f u l l , we must have = U d. (42) where F i s the f-number of the monochromator. Assume now that the source puts out B Watts per u n i t area i n the frequency i n t e r v a l of i n t e r e s t ( e.g. a l i n e ). The t o t a l power that the source radiates i s then equal to da_ which i n our case we set equal to Bh w * ( We assume here Soa«rte s s that the power output of the source i s uniform over the area of the source; for the argument the assumption i s not c r i t i c a l . ) Then the radiant power that i s intercepted by the objective lens i s given by B L » ~v ^ J The l i n e a r magnification of the lens i s given by i ' - h = tHr • t ~ -Li WS Hence we c a n w r i t e ' 6 ' The image o f the s o u r c e i s a r e c t a n g l e o f d i m e n s i o n s h ± x vr± i n t h e p l a n e of the e n t r a n c e s l i t of t h e monochromator. Hence the r a d i a n t power f a l l i n g i n . t h i s p l a n e p e r u n i t a r e a i s g i v e n b y The r a d i a n t power e n t e r i n g t h e monochromator i s t h e n ' Fx * R.w = t l f - * - , where h i s the s l i t l e n g t h and w i s t h e s l i t w i d t h , p r o v i d e d , o f c o u r s e , C o n s i d e r now a monochromator w i t h a v e r y n a r r o w e n t r a n c e s l i t . I n t h e image p l a n e i n w h i c h the e x i t s l i t i s l o c a t e d , a s e r i e s o f n a r r o w l i n e s w i l l appear ( d e p e n d i n g on t h e s p e c t r u m ) . I f we wi d e n the e n t r a n c e s l i t , t h e s e image l i n e s w i l l w i d e n , and a t some s l i t w i d t h , a d j a c e n t l i n e s w i l l s t a r t t o o v e r l a p . I f we are o n l y i n t e r e s t e d i n i s o l a t i n g one l i n e from the n e x t , t h e n we may use s l i t s s o wide t h a t t h e n e a r e s t n e i g h b o r s o f t h e l i n e u nder s t u d y w i l l j u s t n o t o v e r l a p w i t h t h i s l i n e . I n the p l a n e o f the e x i t s l i t , l e t t h e c e n t r e t o c e n t r e d i s t a n c e t o t h e n e a r e s t n e i g h b o r be g i v e n b y , c o r r e s p o n d i n g t o some w a v e l e n g t h d i f f e r e n c e I t i s t h e n c l e a r t h a t we may widen the e n t r a n c e s l i t t o a w i d t h ^ b e f o r e o v e r l a p t a k e s p l a c e ( assuming t h e s y s t e m has u n i t m a g n i f i c a t i o n ) . F o r a p a r t i c u l a r monochromator A = ^ X * D , where D i s t h e l i n e a r d i s p e r s i o n o f the i n s t r u m e n t i n mm p e r A n g s t r o m . Hence the l a r g e s t s l i t w i d t h we c a n use - uo -w h i l e s t i l l i s o l a t i n g the l i n e u n d e r s t u d y i s g i v e n b y w = A U D (47) Thus t h e power t h r o u g h the monochromator, a p a r t f r o m p o s s i b l e r e f l e c t i o n and a b s o r p t i o n l o s s e s , i s g i v e n b y S o o t * F ^ A X D = 1 ^ T A T ) ( 4 8 ) We c a n w r i t e D, t h e l i n e a r d i s p e r s i o n as d e f i n e d a b o v e , as where i s t h e a n g u l a r d i s p e r s i o n o f r a d / A . Then we g e t u _ _B_ o x r a g ( S O ) A w e l l known g e n e r a l r e l a t i o n s h i p f o r b o t h g r a t i n g and p r i s m i n t r u m e n t s i s t h a t t h e o r e t i c a l r e s o l v i n g power =. a p e r t u r e x a n g u l a r d i s p e r s i o n . We c a n thus r e w r i t e e q u a t i o n ( 50 ) i n a v e r y c o n v e n i e n t f o r m B o u t = < U \ ( K . P . ) ( S \ ) where R.P. i s t h e t h e o r e t i c a l r e s o l v i n g power o f t h e i n s t r u m e n t . The p r a c -t i c a l r e s u l t i s t h a t f o r a monochromator t h e maximum amount o f s i g n a l one may p a s s f r o m a l i n e s o u r c e i s p r o p o r t i o n a l t o t h e r e s o l v i n g power o f t h e i n s t r u m e n t , and i n v e r s e l y p r o p o r t i o n a l t o t h e f-number. The r e s o l v i n g power e n t e r s i n , o f c o u r s e , due t o t h e f a c t t h a t i t d e t e r m i n e s how wide one may open t h e s l i t w h i l e s t i l l i s o l a t i n g a l i n e . An i m p o r t a n t r e q u i r e m e n t i n t h i s c a l c u l a t i o n i s t h a t the s o u r c e be l a r g e enough t o c o y e r the e n t r a n c e s l i t . F o r t h i s r e a s o n a l a r g e e x t e n d e d s o u r c e was u s e d i n t h i s e x p e r i m e n t . - l a -t - . . . . . . . . . . . . . It is clear that the best possible monochromator that we could use in this experiment was one which maximised the quantity - p , which we shall refer to as the figure of merit. Because monochromators with a large figure pf merit are not readily available, we decided to design and build our own monochromator with a large figure of merit. A diagram of the optical design of the monochromator is given in figure ( 8 ). The important parameters of the monochromator are as. follows: Grating : Bausch & Lomb 3 5 - 53 - 28 - 78. Rule area 6" x 8" plane rectangular. Blaze angle 26° U5* Blaze wavelength 3.0 microns in f irst order, i 300 lines per millimeter. Mirror: Diameter 16" Focal length IQ." The sl its used were continuously adjustable from 0 to 2000 microns, calibrated in 5 micron steps. An Ebert mounting was used as shown in figure ( 8 ), with the geometrical centres of the grating, mirror, and two slits a l l in the same horizontal plane. The grating was mounted in an aluminum block, which in turn was mounted on a 6 inch diameter bearing. The wave-length that passed through the exit s l i t was set by rotating the grating on this bearing to an appropriate angle. The bearing was embedded in a 10 inch wide U beam, and could be turned by means of a sine-bar arrangement ( see below ). The mirror was mounted in an aluminum casting which was hung by three adjustable bolts from an end plate fastened to one end of the U beam. The whole assembly was encased in a r ig id , light tight aluminum box. The instrument was used in f ifth order, at wavelengths of about 6000 Angstroms. In this mode of operation the theoretical resolving power is F i g u r e 8 O p t i c s o f the monochromator - U3 -equal to 300.000, and the linear dispersion is about li.5 Angstroms per millimeter. The effective aperture is limited by the grating and is such that the f-number of the instrument is about 6. Therefore the figure of merit of the instrument as defined above is equal to This figure compares very favorably with corresponding figures for commer-cial ly available monochromators. The s l i t widths at which the measurements were taken were usually 1,5 - 2 mm. This gives a wavelength spread at the exit s l i t of less than 10 Angstroms. The sine - bar drive which is used to turn the grating, and hence for setting the monochromator to pass a certain wavelength, deserves special attention. The geometry of the arrangement is shown in figure ( 9 ) . AB lies in .the plane of the front surface of the grating, and together with B0 and AO forms a horizontal plane. The so-called sine bar used to turn the grating face about a vertical axis through A is a bar of fixed length "a" s AB, with pivots at B and at'0. The pivot point 0 is constrained to move along the line AD, while the pivot point B is fixed to the grating mount. The point A is fixed on the vertical axis of the bearing on which the grating is mounted. It is seen that moving the pivot point 0 along the line AD ( to the point 0' , for example ) rotates the line AB about the ver-t ical axis through A from an i n i t i a l angle p ( to a final angle ^ ' • From the geometry Figure of merit - i i i s. so, ooo A o — 2.0. iuv. o< so that Figure ( 9 ) Schematic diagram of the sine bar arrangement - us -Consider now light incident on the grating at angle f> to the normal, and leaving the grating at an angle 0<- |S ( refer also to figure 8 ), For these particular directions, we must have, according to the well known grating equation, where n is the order of interference. When the grating is at-the.angle oi1 , we have ^ X 1 =. •2.CLSA*A.<*[ C O S f so that But by ( 5 2 ) , Therefore X. 5u^ o(' — SUA ot - Z £ U A - A =. ^ r v c u which we write as r X1 - x = * ( « ) The above formula means that the linear distance which the pivot point at 0 moves along the line AD is directly proportional to the difference in wavelength of the light leaving the grating at an angle |3 to the optic axis. Since the light which is focussed at the exit s l i t is always that which travels at angle ^ to the optic axis ( see figure (8 ) ), the - U6 -d i f f e r e n c e i n wa v e l e n g t h s r e a c h i n g the e x i t s l i t i s l i n e a r l y p r o p o r t i o n a l to t h e d i s t a n c e x moved a l o n g A D . I n o ur monochromator t h e p o i n t B i s f i x e d i n t h e g r a t i n g mount i n the p l a n e o f the f r o n t s u r f a c e o f t h e g r a t i n g . The d i s t a n c e " a " f r o m B t o t h e v e r t i c a l a x i s t h r o u g h A was c h o s e n t o be it.3368 ± .0005 i n c h e s . W i t h t h i s c h o i c e , ' and t h e c h o i c e o f (3 - 7°30" , the p r o p o r t i o n a l i t y c o n s t a n t i n e q u a t i o n (' 53 ) was g i v e n by 3.000 x 10 "^ . W i t h t h i s c h o i c e t h e l i n e a r d i s t a n c e , s c a l e c o u l d be c a l i b r a t e d c o n v e n i e n t l y i n terms o f w a v e l e n g t h as shown b e l o w . A 50 mm S t a r r e t t m i c r o m e t e r screw*was u s e d t o move t h e s i n e b a r p i v o t 0 a l o n g the A D d i r e c t i o n . One f u l l t u r n o f t h e m i c r o m e t e r s c r e w c o r r e s p o n d s t o a l i n e a r d i s t a n c e o f 0.5 mm j hence u s i n g t h e above p r o p o r t i o n a l i t y c o n s t a n t , one t u r n c o r r e s p o n d s t o a w a v e l e n g t h change o f l50.0/n A n g s t r o m s , where n i s t h e o r d e r number. A number o f gea r s were mounted on t h e m i c r o m e t e r drum a x i s w h i c h were u s e d t o d r i v e a Veeder c o u n t e r . The gea r s were c h o s e n and mounted i n s u c h a way t h a t w i t h the use o f a s i m p l e g e a r s h i f t l e v e r one c a n make t h e c o u n t e r r e a d Angstroms d i r e c t l y i n i t t h , 5 t h , o r 6th o r d e r . When i t i s d e s i r e d t o change o v e r from one o r d e r t o a n o t h e r , one may do so b y means o f c h a n g i n g t h e g e a r and r e - s e t t i n g the a b s o l u t e s c a l e o f t h e c o u n t e r . W i t h t h e p r e s e n t a n g l e f> , w i t h the m i c r o m e t e r drum a t 500 m i c r o n s , t h e c o u n t e r s h o u l d r e a d : 66 hit i n t h e i t t h o r d e r 53l5 i n t h e 5th o r d e r itit2° i n t h e 6th o r d e r . The w a v e l e n g t h s c a l e t h u s d i s p l a y e d on t h e c o u n t e r was c h e c k e d s e v e r a l t i m e s o v e r a h a l f y e a r p e r i o d u s i n g a neon s p e c t r u m . W i t h a 10 m i c r o n e n -t r a n c e and e x i t s l i t t h e p o s i t i o n s o f t h e neon l i n e s were r e a d o f f t h e cou n --hi -t e r e s t i m a t e d t o t h e n e a r e s t t e n t h A n g s t r o m , and l a t e r compared w i t h a l i s t o f known wa v e l e n g t h s of neon. The average e r r o r made i n p o s i t i o n i n g t h e l i n e s was l e s s t h a n 0 . 2 A n g s t r o m s , w h i l e the maximum error'made was O .J4 A n g s t r o m s , There i s a s l i g h t amount o f b a c k l a s h i n the s y s t e m , w h i c h o c c u r s m a i n l y i n the mi!scrometer s c r e w i t s e l f . T h i s b a c k l a s h amounts t o l e s s t h a n one Angstrom on t h e c o u n t e r , and can be a v o i d e d b y always t u r n i n g t h e drum i n t h e same d i r e c t i o n . M o s t b e a r i n g s u s e d i n t h e d r i v i n g mechanism were mounted under t e n s i o n t o a v o i d p o s s i b l e p l a y . The f o c u s o f the monochromator may be o b t a i n e d r o u g h l y b y a d j u s t i n g t h e mounting b o l t s on t h e m i r r o r h o u s i n g , and more p r e c i s e l y by moving t h e s l i t mounts b a c k and f o r t h b y t h e i r a d j u s t i n g s c r e w s . The b e s t f o c u s c a n be o b t a i n e d w i t h a c o m p l e t e l y s y m m e t r i c a l arrangement o f e n t r a n c e and e x i t s l i t s . The s i d e w a y s i n c l i n a t i o n o f t h e m i r r o r i s n o t v e r y c r i t i c a l f o r t h e f o c u s , b u t q u i t e i m p o r t a n t as f a r as t h e s c a l e o f t h e s i n e b a r i s c o n c e r n e d . I t i s c l e a r t h a t t h i s i n c l i n a t i o n d e t e r m i n e s the a n g l e |b f o r f i x e d s l i t p o s i t i o n s , and s i n c e t h i s a n g l e e n t e r s t h e p r o p o r t i o n a l i t y c o n s t a n t "k"1 i n e q u a t i o n ( 5 3 ) , i t i s i m p o r t a n t t h a t t h i s a n g l e be e x a c t l y r i g h t . I n o r d e r t o make s u r e t h a t the i n c l i n a t i o n i s c o r r e c t , i t must be a d j u s t e d a f t e r f o c u s u n t i l w a v e l e n g t h d i f f e r e n c e s a s shown on t h e c o u n t e r c o r r e s p o n d as c l o s e l y as c a n be d e t e r m i n e d t o t h e c o r r e s p o n d i n g d i f f e r e n c e s i n w a v e l e n g t h s of l i n e s o f some s t a n d a r d t e s t s o u r c e as, t h e y appear a t the e x i t s l i t . Changes i n i n c l i n a t i o n o f a f r a c t i o n , o f a degree make a q u i t e n o t i c e a b l e d i f f e r e n c e i n the w a v e l e n g t h s c a l e . The o r i g i n o f t h e w a v e l e n g t h s c a l e a l s o changes w i t h i n c l i n a t i o n o f t h e m i r r o r , b u t i t may be d e t e r m i n e d e a s i l y w i t h some s t a n d a r d l i n e once t h e " s l o p e " o f t h e s c a l e i s c o r r e c t . The v e r t i c a l i n c l i n a t i o n o f t h e m i r r o r c a n b e s e t b y means o f f o c u s i n g a p i n h o l e s o u r c e i n p l a c e o f t h e e n t r a n c e s l i t . - kQ k. Photomultiplier The photomultiplier used to convert the l i g h t s i g n a l i n t o an e l e c t r i c a l s i g n a l was a RCA type 7 2 6 5 . This i s a Ik stage tube with a S -20 s p e c t r a l response, e s p e c i a l l y designed f o r f a s t time response. Several design con-siderations l e d us to th i s choice of photomultiplier. Of a l l the types of surface a v a i l a b l e , the S -20 photosensitive surface has the greatest quantum e f f i c i e n c y i n the red wavelength region. The f a s t time response was r e -quired i n order to resolve the decay process, and a Ik stage model was chosen because the added gain f a c i l i t a t e d the handling of the pulses from single photon events. The photomultiplier was operated at an o v e r a l l poten-t i a l d ifference of 2^00 v o l t s with an output r e s i s t o r of 50 ohms. The poten-t i a l d i s t r i b u t i o n across the dynodes i s given i n the accompanying diagram. P o t e n t i a l d i s t r i b u t i o n of photomultiplier l o o K 2Sk 6«k 6fk <>M fa** MK, UlK fcf* V-H l-H 108 If I . H h H H , o o l .001 . o o l •; .o©2;: - o o s ^ t •2500V As mentioned e a r l i e r , the l i g h t s i g n a l to be studied was so weak, that i t could be observed only as separate single photon events i n the output of the p h o t o m u l t i p l i e r . I t i s therefore of i n t e r e s t to consider the operation and output of photomultipliers under such c o n d i t i o n s . I t i s we l l known that when a photon i s i n c i d e n t on the photocathode of a photo m u l t i p l i e r , there e x i s t s a well defined p r o b a b i l i t y that t h i s photon w i l l release - h9 -an e l e c t r o n from the cathode s u r f a c e . The operation of a photomultiplier depends on the f a c t that t h i s photoelectron, being accelerated by an exter-n a l l y applied p o t e n t i a l d i f f e r e n c e , can release several secondary electrons upon impact with a s u i t a b l e m e t a l l i c surface c a l l e d a dynode. The photo-m u l t i p l i e r u t i l i s e s a number of such dynodes i n s e r i e s , each at a higher p o t e n t i a l than the previous one, and the r e s u l t i s that the s i n g l e e l e c t r o n released from the photocathode causes an ever growing burst of electrons to pass fr a i i dynode to dynode to dynode, u n t i l f i n a l l y at the l a s t dynode t h i s burst of electrons appears as a current pulse i n a load r e s i s t o r . Because the m u l t i p l i c a t i o n process at each dynode i s s t a t i s t i c a l i n nature, the number of electrons f i n a l l y a r r i v i n g at the anode due to one e l e c t r o n released from the photocathode, and hence the height of the current pulse through the load r e s i s t o r , has a c e r t a i n d i s t r i b u t i o n depen-ding on the s t a t i s t i c s of the m u l t i p l i c a t i o n process. Lombard and Martin ( 23 ) have calculated t h i s d i s t r i b u t i o n using the assumption that the m u l t i p l i c a t i o n process at each stage follows Poisson s t a t i s t i c s . T h eir r e s u l t s show a d i s t r i b u t i o n i n pulse heights as i s shown i n figure ( 1 0 ) . - 50 -I t t u r n s o u t , as w i l l be e x p l a i n e d i n a l a t e r s e c t i o n , t h a t our i n t e n -s i t y measurements c o r r e s p o n d t o c o u n t i n g t h e number o f p u l s e s f r o m t h e p h o t o m u l t i p l i e r t h a t a r e g r e a t e r t h a n some v a l u e V"q. T h i s c o u n t c o r r e s p o n d s t o the shaded a r e a u n d e r n e a t h t h e c u r v e i n f i g u r e ( 10 ) . I f one c a n assume a l i n e a r r e l a t i o n s h i p between t h e average number of p h o t o n s i n c i d e n t on t h e p h o t o c a t h o d e , and the average number of p u l s e s out o f t h e p h o t o m u l t i p l i e r , t h e n i t i s c l e a r t h a t the c o u n t , x-Aiich i s a c o n s t a n t f r a c t i o n o f t h e t o t a l number o f o u t p u t p u l s e s f o r f i x e d V , i s a measure o f t h e i n t e n s i t y o f t h e o l i g h t . Gadsden ( 21; ) has shown e x p e r i m e n t a l l y f o r a c o n s t a n t i n t e n s i t y l i g h t s o u r c e , t h a t t h e s t a t i s t i c a l d i s t r i b u t i o n o f the number o f anode p u l s e s p e r u n i t time due t o s i n g l e p h o t o n e v e n t s i s P o i s s o n i n f o r m , w i t h a s t a n -d a r d d e v i a t i o n o f t h e c o u n t s e q u a l t o t h e square r o o t o f the a b s o l u t e v a l u e of t h e average c o u n t . A r c e s e (25 ) , h o w e v e r , shows on t h e o r e t i c a l grounds t h a t the. d i s t r i b u t i o n o f p u l s e s e x p e c t e d i s n o t q u i t e P o i s s o n , and t h a t t h e s t a n d a r d d e v i a t i o n on N c o u n t s i s more c o r r e c t l y e x p r e s s e d as J(\i"r\) N| , where T| i s t h e above d e f i n e d quantum e f f i c i e n c y . F o r o u r p h o t o m u l t i -p l i e r i s about .03, so t h a t f o r a l l p r a c t i c a l p u r p o s e s t h e s t a n d a r d de-v i a t i o n i s g i v e n b y . 5. S a m p l i n g System The o u t p u t f r o m the p h o t o m u l t i p l i e r was f e d i n t o a T e k t r o n i x 66 l S a m p l i n g O s c i l l o s c o p e . A s a m p l i n g o s c i l l o s c o p e works as f o l l o w s . G i v e n a p e r i o d i c i n p u t , i t w i l l sample s u c c e s s i v e c y c l e s o f t h i s i n p u t a t p r e -d e t e r m i n e d d e l a y s r e l a t i v e t o some f i x e d phase o f the c y c l e . The v o l t a g e a p p e a r i n g a t the i n p u t o f the o s c i l l o s c o p e a t t h e t i m e t h e sample i s t a k e n i s r e c o r d e d on the s c r e e n o f the o s c i l l o s c o p e b y means o f a s m a l l d o t . Many - 51 -modes of operation are p o s s i b l e . For example, one can arrange th a t the sampling of successive cycles i s done, at ever increasing delay times r e l a -tive to a f i x e d p o i n t i n the c y c l e . In t h i s mode the dots appearing on the oscilloscope screen trace out the v a r i a t i o n of the voltage during a cycle. We c a l l this mode f o r l a t e r reference the continuously varying delay mode. Once can also sample at some f i x e d delay time, i n which case the dots w i l l show the v a r i a t i o n of the voltage from one cycle to the next at one p a r t i c u l a r point i n the c y c l e . This mode we c a l l the f i x e d delay mode. Because one can set the delay at any desired value, i t i s c l e a r that one can manually scan through a whole cycle i n t h i s f i x e d delay mode. Another p o s s i b i l i t y i s to sample a non-repetitive s i g n a l r e l a t i v e to some r e p e t i t i v e external t r i g g e r p u l s e . This mode i s su i t a b l e f o r equally spaced sampling of randomly occurring s i g n a l s . The sampling i n the oscilloscope i s done i n t e r n a l l y by means of a diode gating c i r c u i t , which allows the s i g n a l at the input to be monitored f o r .35 x 10 ^ seconds. This gating time determines the time r e s o l u t i o n of the o s c i l l o s c o p e . The r e s u l t of a sample ( i . e . the strength of the input s i g n a l during the sampling time), i s also a v a i l a b l e on the os c i l l o s c o p e ( v e r t i c a l s i g n a l out ) as a d.c. l e v e l which i s maintained f o r the period of time be-tween successive samples. The way i n which the data were obtained using the sampling system w i l l now be explained. Please refer to f i g u r e s ( 11 ) and ( 12 ), A Tektronix type 110 Pulse generator was used to pulse the e l e c t r o n gun at a r e p e t i t i o n frequency of J485 cps. The pulse had a width of U0 nanoseconds, with r i s e and f a l l times of the order of one nanosecond. The current pulse of the elec t r o n gun, which had s i m i l a r r i s e and f a l l times, was used to t r i g g e r the sampling o s c i l l o s c o p e . The l i g h t output of the el e c t r o n excited l i g h t source - 52 -on the average shows a shape as i s shown on axis 2 of f i g u r e ( 12 ) . The actual output of the pho t o m u l t i p l i e r , however, did not look l i k e 2 ? but rather something l i k e 3, where the l i t t l e pulses indicate single photon events. Only when averaged over many cycles we would get an i n t e n s i t y v a r i a -t i o n as displayed i n 2 , Nevertheless, the photomultiplier was sampled at times a f t e r the times t D , which represent the s t a r t of each c y c l e . The sampling gate i n the constant delay mode i s shown on axis U» The c o r r e -sponding- output of the sampling oscilloscope i s non-zero whenever a photon pulse occurs at the photomultiplier output at the time the sampling gate pulse occurs. Axis 5 shows the output of the " v e r t i c a l s i g n a l out"' of the os c i l l o s c o p e , f o r input 3 and sampling gate h. The pulse used to drive the electron gun was also used to drive a chopper, which changed the continuous stair c a s e type s i g n a l displayed on axis 5 to a pulsed s i g n a l , as displayed on axis 6. This s i g n a l was amplified and passed through a d i s c r i m i n a t o r , which eliminated a l l pulses below a c e r t a i n voltage l e v e l V q , The d i s c r i m i -nator output pulses, displayed on axis 7, were fed to a counter. I f the sampling i s i n the constant delay mode, with delay time -£>t , then the count obtained over a f i x e d length of time represents the number of times an anode pulse greater than some minimum voltage V was present at the output o of the photomultiplier at the time t 0 + A " t _ i n the c y c l e . As p r e v i o u s l y discussed, t h i s number i s pro p o r t i o n a l to the number of times an anode pulse of any height was present at the photomultiplier output at the time £ e - * - A t . i n the c y c l e . This l a t t e r number on the average i s p r o p o r t i o n a l to the number of times a photon was inc i d e n t on the photocathode at t h i s time i n the c y c l e . This number of photons i s a measure of the average i n t e n s i t y of the l i g h t source at the time fcc 4- / i t i n the c y c l e . By changing ^ t we can obtain another count, which gives a measure of the i n t e n s i t y at some d i f f e r e n t delay time i n the c y c l e . The t o t a l decay curve of .intensity Pulse Generator Sampling Oscilloscope Chopper 60£L (trigger) son. tfXS-QSi (trigger) -O Photomultiplier -O O ' 7 O Discriminator Counter Figure ( 11 ) Schematic diagram of e l e c t r o n i c sampling system E l e c t r o n gun current pulse Average l i g h t i n t e n s i t y 3. Photomultiplier output (for example) 1). Sampling gate (constant dela; mode) 5. Sampling o s c i l loseope out-put Chopper output (dotted l i n e i$ d i s c r i m i n a t o r ^ l e v e l ) 7. Discriminator output |«t £ >ws — » j -"40MS ~lh -f/~ - / A 1 A ft A I J time Figure ( 12 ) E l e c t r o n i c sequence of events - 55- -can then be obtained by counting the number of outputs over f i x e d lengths t of time for a whole set of the delay times. In order to avoid any problems a r i s i n g from r e f l e c t i o n s o f signals due to impedance mismatches i n the c i r c u i t s , a l l cables used to transmit the very high frequency pulses were of $0 ohm impedance, terminated a t both ends by 5>0 ohm r e s i s t o r s . For t h i s reason a $0 ohm output impedance was used i n the p h o t o m u l t i p l i e r . The e f f e c t i v e output impedance was 2$ ohms, since the photomultiplier sees £0 ohms i n p a r a l l e l with the 5>0 ohm c a b l e . The type 110 pulse generator which was used to drive the e l e c t r o n gun uses a p a i r of mercury switches and an external delay l i n e to generate a square pulse. The width of the pulse can be chosen by i n s e r t i n g the appro-p r i a t e length of cable i n the external pulse forming delay l i n e . The output impedance of the pulse generator was 50 ohms. The current passing through the e l e c t r o n gun was monitored as shown i n f i g u r e ( 11 ) by means of a Tektronix CT-3 current probe. The time response of t h i s probe was better than 1 nanosecond, and i t s s e n s i t i v i t y £mv per ma when terminated i n a 5>0 -0. impedance. , 6, L i n e a r i t y and expected accuracy of the measurements. There i s a quite noticeable delay between the a r r i v a l of a photon at the photocathode of the photomultiplier, and the corresponding output pulse at the anode. Hence the pulses which were measured at a p a r t i c u l a r time a c t u a l l y correspond to photons which h i t the cathode some 20 to 30 nanoseconds e a r l i e r . However, since a l l photons are delayed equal amounts on the average, the only e f f e c t of t h i s delay i s to s h i f t the time axis a f i x e d amount. Of course, the s t a t i s t i c a l f l u c t u a t i o n s i n the t r a n s i t time of the electrons i n the photomultiplier are of importance. These determine the width of the anode pulse due to a s i n g l e photon event. The approximate width of the anode pulse - 56 -was measured f o r o u r p h o t o m u l t i p l i e r . I t i s p o s s i b l e t o make t h i s measure-ment b y u s i n g a weak l i g h t s o u r c e and t r i g g e r i n g the o s c i l l o s c o p e on t h e anode p u l s e s r e s u l t i n g from s i n g l e p h o t o n e v e n t s . The measurement was made on the s a m p l i n g o s c i l l o s c o p e as w e l l as on a T e k t r o n i x 585A O s c i l l o s c o p e . The measurement c a n n o t be made v e r y a c c u r a t e l y , s i n c e t h e p u l s e s due t o s i n g l e p h o t o n e v e n t s v a r y i n p u l s e w i d t h as w e l l as i n a m p l i t u d e . I t was f o u n d t h a t on the average t h e p u l s e s ware 5 t o 10 nanoseconds .wide. T h i s p u l s e w i d t h i n t h e f i n a l a n a l y s i s d e t e r m i n e s the u l t i m a t e t i m e r e s o l u t i o n . I t does n o t , h owever, l i m i t t h e a c c u r a c y t o w h i c h t h e e x p o n e n t i a l t i m e c o n -s t a n t s o f the decay c a n be measured. I f t h e i n t e n s i t y d e c a y , as we e x p e c t , i s g i v e n b y a sum o f e x p o n e n t i a l t e r m s , t h e n we c a n s a y t h a t the p r o b a b i l i t y t h a t a p h o t o n i s i n c i d e n t a t a t i m e t on t h e p h o t o c a t h o d e i s g i v e n b y Now suppose t h a t t h e p r o b a b i l i t y of g e t t i n g an o u t p u t c o u n t a t t h e t i m e •t + x g i v e n a p h o t o n i n c i d e n t a t t h e t i m e t i s °j Od) . Then the p r o b a b i l i t y t h a t we o b t a i n an o u t p u t c o u n t a t t h e time t i s T h i s c a n be w r i t t e n as 2 A * e " ^ " L ^ ^ 9 dX o p r o v i d e d , /t > XL* } t h e w i d t h o f g ("C)« I f we f u l f i l l t h i s c o n d i t i o n i n o ur measurement, t h e o b s e r v e d p r o b a b i l i t y i s s t i l l a sum o f e x p o n e n t i a l terms w i t h the same ti m e c o n s t a n t s , r e g a r d l e s s o f the shape o f g ( X ) . - 57 -The relative strengths of the different exponential components is changed only. In order to obtain the time constants, we do not need to know g neither do we have to correct for i t . The only requirement is that / — i we make our measurements at delay times greater than L , where c is the width of C~c) . The ultimate accuracy of the data obtained by our method is determined by the statistics of the counting process. As mentioned earlier, we expect the counts to have a Poisson distribution. What this means numerically is i .*" the following. Suppose that the mean rate at which anode pulses arrive at the output of the photomultiplier is given by X . Then the probability of getting k counts during a time interval t can be shown to be ( see for example Fry (26 ) ), = U f e ) In our case we take N samples of effective sampling width t , where t is s s the sum of the sampling gate width and the width of the photomultiplier anode pulse. Therefore the probability of getting k counts for the total counting time is . = ~ k j ( 5 7 ) This probability distribution has a mean value NVt . s , and standard de-I 1 viation JXAW^ . We let NiX"L s • n. In connection with the counting statistics i t is important to examine the linearity of the measuring system. We assume in our counting that each count corresponds to one anode pulse, and hence to one photon. This is only correct in the limit of low count rates, when the probability for the super-position of two anode pulses is small. We can work out a numerical criterion - 58 -f o r t h i s as f o l l o w s . The p r o b a b i l i t y of obtaining zero or one anode pulse during the time t^ i s given according to equation (57 ) by -At* - x t - * / \ Therefore the p r o b a b i l i t y of obtaining two or more anode pulses during t i s s - — / The p r o b a b i l i t y of obtaining two or more pulses divided by the p r o b a b i l i t y of g e t t i n g one pulse i s therefore ^ This r a t i o represents the f r a c t i o n of the counts obtained that may be i n e r r o r . I t i s a monotonic a l l y i n c r e a s i n g function of . Since N i s f i x e d , the l a r g e r n i s , the larger i s the e r r o r i n the count due to the superposition phenomena. In order to avoid serious e r r o r s , one must be sure that R i s much' less than one. As a numerical example, when i s .05, then R i s .025, and the e r r o r possible due to superposition i s 2,5$. While one might say at f i r s t s i g h t that one could c o r r e c t f o r t h i s kind of e r r o r , because the mean count rate p r e d i c t s the e r r o r , c l o s e r exami-nation of the way i n which the counts were obtained w i l l show that this i s not so. The sign of the c o r r e c t i o n depends on the discriminator s e t t i n g . I f the discriminator i s set t o r e j e c t the majority of counts, then the superposition phenomenon w i l l add counts that should not have been counted due to two anode pulses which, when superimposed, form a pulse j u s t large enough to surpass the discriminator l e v e l . On the other hand, when the discriminator i s set low, the count obtained may be too low due to two superimposed anode D u l s e s being counted as one, whereas they should be counted as two. The two eases are illustrated in figure ( 13 ) Case I Case 2 Discriminator setting is high; because of superposition the measured count is higher than the true count. . Discriminator setting is low; because of superposition the measured count is lower than the true count. Figure ( 13 ) Graphical illustration of two types of superposition errors. Although care was taken to keep the discriminator as low as possible compatible with the requirement that electrical noise on the oscilloscope input be eliminated, i t was fe l t that a mixture of the two errors was s t i l l present. Hence a correction could not be made with certainty. Therefore a l l count rates were kept so low, where necessary with the use of f i l t ers , that the maximum value of R was .025, and therefore the maximum possible error due to superposition of anode pulses was never larger than 2 ,$%,.• In practice this was usually smaller than the statistical fluctuations in the counts. • In order to check the linearity of the system under these conditions, the transmission of a neutral density f i l t e r was measured. The value ob-- 60 -tained.on several different occasions agreed within experimental error with the value obtained as measured on the absorption apparatus of Robinson ( h ). The transmission of a ,5D neutral density f i l t e r as measured on Robinson's apparatus at 6000 A was 27.9 %y while measured with our apparatus i t was found to be 29,2%, At 5852 A , the values measured with Robinson's and our apparatus were 27.8 and 28.1$ respectively. Since his apparatus is linear, this agreement provided a good check on the linearity of our ap-paratus . The linearity and accuracy of the time base of the sampling oscilloscope was measured with a Tektronix crystal controlled 180-A time^ m'ark signal generator, operated at 50 megacycles. It was found that the time base was accurate as far as one could t e l l from the wave form as displayed on the screen of the oscilloscope at a sweep speed of 20 nanoseconds per cm., which was the time base used for our measurements. An inaccuracy of 1% would have been easily noticeable on the screen of the oscilloscope, so that we can conclude that the time base was accurate to better than 1$, For a l l photomultipliers, a certain number of anode pulses are observed even with no light falling on the photocathode. This dark current, together with any, stray light from places other than our neon source, constituted a background for our measurements. In a l l cases the background was determined and subtracted from the signal. For some very weak signals at the end of the intensity decay, this, background became comparable to the signal. For the majority of cases, however,*" the background correction was less than 10$ of the signal. The value of the background was determined by monitoring the signal at very long delay times ( e.g. 10 microseconds ). By this time a l l the signal due to neon transitions had disappeared, and a l l that was left was the background signal. - 61 -7 . Counting method. As described above, the intensity of radiation at different times in the decay can be obtained by counting the number of output pulses per unit time at different fixed delay times. In fact, the f i r s t results obtained with this apparatus were obtained in this way. However, i t soon became apparent that this method was not the best because of drifts in the response'of the apparatus. This made meaningful comparison of a count obtained at one delay-time with a count obtained some fifteen minutes later at another delay time difficult. The change in the count due to drift in some cases amounted to 20$. In order to overcome this difficulty, we used the sampling oscilloscope in the continuously varying delay time mode. Although this meant that suc-cessive samples were not at exactly the same time in the decay, the rate at which the delay time changed was so slow, that an appreciable count could be obtained while the delay time shifted a few nanoseconds. In fact, the rates chosen were such that in one ten second count, the sampling pulse delay time had shifted eight nanoseconds. The next two nanoseconds of delay time shift were taken up in displaying the count, and resetting the counter. The re-setting was done automatically, and subsequently the counter started to count for the next ten seconds, covering the next eight nanoseconds in the decay. In this way the sampling pulse swept through the entire decay, ( in our case about 180 nanoseconds ), giving us 18 counts per sweep, ^he counts so obtained correspond to where 1^  ( t ) is the measured count for ten seconds starting at the sample delay time t^. - 62 -As soon as t h e sweep t h r o u g h the e n t i r e d e c a y was c o m p l e t e , t h e s a m p l i n g was r e s e t t o t h e b e g i n n i n g of t h e d e c a y , and a n o t h e r sweep was made. The f i n a l c o u n t s o b t a i n e d were t h e t o t a l s o f t h e c o u n t s a t t h e p a r t i c u l a r d e l a y t i m e s o b t a i n e d , i n t e n sweeps. I n t h i s way e r r o r due t o d r i f t was r e d u c e d . Background c o u n t s were o b t a i n e d a f t e r t he c o m p l e t i o n o f e a c h sweep. I t w i l l be shown ( see C h a p t e r I V A ) , t h a t f o r a time dependence o f i n t e n s i t y g i v e n b y a sum o f e x p o n e n t i a l s , t h e i n t e g r a t i o n o f t h e i n t e n s i t y as g i v e n i n e q u a t i o n ( 6l ) does n o t change the time c o n s t a n t s o f t h e e x p o n e n t i a l components, o n l y t h e i r r e l a t i v e i n t e n s i t i e s . Hence t h e time c o n s t a n t s o b t a i n e d from the c o u n t s were s t i l l c o r r e c t . B . •-. R e l a t i v e I n t e n s i t y Measurements As e x p l a i n e d i n C h a p t e r I I , s e c t i o n B, the r e l a t i v e v a l u e s o f t r a n s i -t i o n p r o b a b i l i t i e s f o r t r a n s i t i o n s o r i g i n a t i n g on t h e same u p p e r l e v e l were o b t a i n e d by m e a s u r i n g t h e r e l a t i v e i n t e n s i t i e s - o f l i n e s c o r r e s p o n d i n g t o t h e s e t r a n s i t i o n s . These r e l a t i v e i n t e n s i t i e s were o b t a i n e d u s i n g t h e a p p a r a t u s d e s c r i b e d i n S e c t i o n A o f t h i s c h a p t e r . I n s t e a d o f v a r y i n g t h e d e l a y s o f t h e s a m p l i n g p u l s e over t h e whole decay t i m e , as was done i n t h e a b s o l u t e measurements, the r e l a t i v e i n t e n s i t i e s o f two s p e c t r a l l i n e s were o b t a i n e d b y c o m p a r i n g the s i g n a l s o f t h e s e two l i n e s a t some f i x e d d e l a y t i m e , n e a r t h e b e g i n n i n g o f t h e d e c a y . The s p e c t r a l r e s p o n s e o f t h e system was measured u s i n g a G.E. t u n g s t e n s t r i p f i l a m e n t lamp. Care was t a k e n i n the c a l i b r a t i o n t o e n s u r e t h a t the. o p t i c a l systems u s e d f o r measurement and c a l i b r a t i o n were f o r a l l p r a c t i c a l p u r p o s e s i d e n t i c a l . The i n t e n s i t y o f a t u n g s t e n r i b b o n lamp as measured a t some p o i n t o u t -s i d e the, s o u r c e can be w r i t t e n as - 63 -where *2-&,T) i s t h e e m i s s i v i t y o f t u n g s t e n and J ( X,T ) i s t h e b l a c k b ody s p e c t r a l d i s t r i b u t i o n a t w a v e l e n g t h X and t e m p e r a t u r e T. The e m i s s i v i t y o f t u n g s t e n u s e d i n our c a l i b r a t i o n c a l c u l a t i o n s was t h a t measured as a f u n c t i o n of t e m p e r a t u r e and w a v e l e n g t h b y L a r r a b e e ( 2 7 ) . The tem p e r a -t u r e o f t h e lamp was d e t e r m i n e d b y m e a s u r i n g t h e b r i g h t n e s s t e m p e r a t u r e u s i n g a Hartmann and B r a u n f i l a m e n t p y r o m e t e r . From t h e s e measurements, t h e t r u e t e m p e r a t u r e was c a l c u l a t e d u s i n g t h e method o f R u t g e r s and De Vos ( 28 V. Hence t h e s p e c t r a l d i s t r i b u t i o n o f t h e c a l i b r a t i o n s o u r c e was known. I t i s shown b y R o b i n s o n ( k )• as o u t l i n e d i n A p p e n d i x 3 , t h a t t h e r a t i o o f the a c t u a l l i n e i n t e n s i t i e s i s r e l a t e d t o t h e r a t i o as measured b y a monochromator and p h o t o m u l t i p l i e r d e t e c t i o n s y s t e m , b y the e q u a t i o n . i < fx*) -Jvru. (M i c f \ 0 x m t c M f M D fx,) ? where / j - (xZ)T) ^ e r a , t i 0 °? "the a c t u a l i n t e n s i t i e s o f t h e t u n g s t e n lamp, -^mcX^i>"0/ / \ j _ s ^ e r a t i o o f t h e measured i n t e n s i -v e . (X^Tj y t i e s o f t h i s lamp w i t h the d e t e c t i o n s y s t e m , / P f X a . ) ^ s "the r a t i o of t he monochromator d i s p e r s i o n s a t t h e two w a v e l e n g t h s , and i s a c o r r e c t i o n f a c t o r f o r the v a r i a t i o n o f t h e s o u r c e and d e t e c t o r r e s p o n s e - 6h -o v e r t h e band p a s s o f the d e t e c t o r . The v a l u e o f ^ ^ 'Vte. (A^) d i f f e r s from u n i t y b y an amount much l e s s t h a n the e x p e r i m e n t a l e r r o r , s o t h a t i t s c o n t r i -b u t i o n may be n e g l e c t e d . Hence p u t t i n g i n t h e v a l u e f o r I c ( X,T ) as g i v e n b y e q u a t i o n (62 ) , we o b t a i n B y e q u a t i o n ( 39 ) I^OM) _ A M X* X c O ^ AC.KC) X, (65) and we may w r i t e CX.) ; . The r e l a t i v e l i n e i n t e n s i t y measurements were made a t p r e s s u r e s o f 100 m i c r o n s o f Hg. and 200 nanosecond wide p u l s e s were used t o e x c i t e t h e gas a t the same r e p e t i t i o n f r e q u e n c y (,I$5 cps ) as was u s e d f o r the l i f e t i m e meas-u r e m e n t s . A l l measur orients were made u s i n g C o r n i n g g l a s s f i l t e r s as an o r d e r s o r t e r f o r the monochromator. W i t h t h e s e f i l t e r s t he monochromator had an e f f e c t i v e bandpass between 5700 and 6600 a n g s t r o m s . The t u n g s t e n lamp was op e r a t e d a t 5 Amperes, w h i c h r e s u l t e d i n a b r i g h t n e s s t e m p e r a t u r e o f lii95 degrees C e n t i g r a d e . The i n t e n s i t y of t h e t u n g s t e n lamp a t th e d i f f e r e n t w a v e l e n g t h s was measured i n the same way as t h e i n t e n s i t y o f the neon s o u r c e , w i t h t h e s a m p l i n g d e l a y time r e l a t i v e t o the p u l s e n o r m a l l y u s e d t o e x c i t e t h e ne o n . Wherever n e c e s s a r y , the. s i g n a l from the t u n g s t e n lamp was r e d u c e d b y r e d u c i n g the s l i t l e n g t h s o t h a t t h e e r r o r due t o s u p e r p o s i t i o n o f p u l s e s d i s c u s s e d i n s e c t i o n 6 of C h a p t e r I I I was s m a l l . For. a l l measurements t h e e n t r a n c e s l i t o f t h e monochromator was opened t o 1.25 mm, w h i l e the e x i t s l i t was opened t o 1.75 mm. The s l i t s i z e s were - 65 -made u n e q u a l i n t h i s -way t o e n s u r e t h a t t h e whole l i n e image o f t h e e n t r a n c e s l i t would be i n t e r c e p t e d b y the e x i t s l i t . W i t h e q u a l s l i t s i z e s , s m a l l e r r o r s i n t h e w a v e l e n g t h s e t t i n g o f t h e monochromator c o u l d r e s u l t i n s e r i o u s e r r o r s i n t h e s i g n a l o b s e r v e d , due t o n o n - o v e r l a p p i n g o f e n t r a n c e , s l i t image and e x i t s l i t . I n o r d e r t o e l i m i n a t e the e f f e c t s o f d r i f t i n t h e a p p a r a t u s as much as p o s s i b l e . , t h e two i n t e n s i t i e s t o be compared were measured a l t e r n a t e l y a number o f t i m e s , and the r e s u l t s a v e r a g e d . The a c t u a l p r o c e d u r e f o l l o w e d was t o c o u n t I ( \ ) f o r 30 s e c o n d s , t h e n t h e b a c k g r o u n d f o r t h i r t y s e c o n d s , t h e n I f o r t h i r t y s e c o n d s , f o l l o w e d b y . a n o t h e r b a c k g r o u n d c o u n t , and t h e n a g a i n I ( ), f o r t h i r t y s e c o n d s , e t c . The t o t a l c o u n t i n g t i m e s f o r I ( X,), and I ( X* ) were 300 seconds e a c h , w i t h e q u a l c o u n t i n g t i m e f o r t h e b a c k g r o u n d . The t o t a l number o f c o u n t s o b t a i n e d i n 300 seconds would t y p i c a l l y v a r y between 1000 and 5000 o u t o f a t o t a l o f 150,000 s a m p l e s . - 66 -CHAPTER I V RESULTS AND DISCUSSION A« Lifetime measurments. In© time dependence of the intensity of the 5852.5 Angstrom line in neon was measured a t p r e s s u r e s o f 1 0 , 2 0 , 3 0 , 100, and 200 m i c r o n s of Hg, The e x p e r i m e n t a l d a t a f o r e a c h p r e s s u r e were i n t h e f o r m o f numbers p r o p o r -*_ ^ +• S v\4 t i o n a l t o the i n t e g r a t e d i n t e n s i t y - r / , \ _ ) X L*) c&z j nanoseconds. A p r e l i m i n a r y p l o t o f t h e s e numbers v e r s u s time on a l o g s c a l e i n d i c a t e d t h a t I™ ( t n- ) was o f the for m , Hence the d a t a p o i n t s were f i t t e d t o a n e q u a t i o n o f t h i s t y p e , w i t h t h e f i t t i n g p a r a m e t e r s b e i n g L ^ , I 2 m , and T 2 m , T h e s u b s c r i p t m i n d i c a t e s measured v a l u e s . The decay o f the 2 p ^ s t a t e p o p u l a t i o n d e n s i t y , and hence t h e i n t e n s i t y of the 5852 A t r a n s i t i o n , may have two e x p o n e n t i a l components as was shown i n s e c t i o n 3 of C h a p t e r I I A . T h i s p a r t i c u l a r case c o r r e s p o n d s t o one t r a n s i -t i o n f e e d i n g t h e 2p-^ l e v e l , w h i l e t h e l a t t e r l e v e l i s b e i n g d r a i n e d b y t h e 5852 A t r a n s i t i o n . From t h e f o r m o f t h e d a t a , t h e r e f o r e , i t was assumed t h a t t h i s was t h e case t o a good a p p r o x i m a t i o n . I f we t h e n assume t h a t t h e e m i t t e d i n t e n s i t y o f t h e 5852 A l i n e h a s the f o r m ( c . f . e q u a t i o n ( 31 ) ) " 1 ( A ) ( 6 8 ) - 67 -t h e n our measured and f i t t e d q u a n t i t i e s a r e r e l a t e d t o t h e q u a n t i t i e s i n e q u a t i o n ( 6 8 ) b y the e q u a t i o n s I*m = I x^t 1 " C70) "LJYVI - "C| ( 7 1 ) •"C a m = "Ca. Cta»0 6 \Y\ n a n o s e c o n d s ) (7£) Hence t h e r e l a t i v e i n t e n s i t i e s o b t a i n e d from our d a t a must be c o r r e c t e d b e c a u s e o f t h e i n t e g r a t e d measurements b u t t h e l i f e t i m e s a r e unchanged. T h e r e f o r e t h e l i f e t i m e s o b t a i n e d from the i n t e g r a t e d d a t a f i t t e d t o e q u a t i o n ( 67 ) are c o r r e c t . The d a t a p o i n t s were f i t t e d t o . t h i s e q u a t i o n u s i n g a computer program d e v e l o p e d b y O r t h ( 29 ) . The program u s e s t h e maximum l i k e l i h o o d method o f c u r v e f i t t i n g ( 38 ). I n t h i s method t h e f o u r f i t t i n g p a r a m e t e r s a r e v a r i e d i n s u c h a way as t o maximise t h e l i k e l i h o o d t h a t t h e d a t a w i l l have t h e f o r m as o b s e r v e d , assuming P o i s s o n s t a t i s t i c s . The d e t a i l s o f t h e method a r e g i v e n i n A p p e n d i x 1. The r e s u l t s o f the f i t t e d v a l u e s f o r the l i f e t i m e 1 , which i s t h e l i f e t i m e , o f the 2p-^ s t a t e , a r e g i v e n i n t a b l e I. Computer p l o t s o f t h e f o u r p a r a m e t e r f i t s o f t h e d a t a a r e g i v e n i n t h e n e x t few p a g e s . The c r o s s e s i n d i c a t e t he e x p e r i m e n t a l d a t a p o i n t s , w h i l e t h e s o l i d l i n e i s t h e f o u r p a r a -meter f i t t h r o u g h t h e s e p o i n t s . . ( c o n t i n u e d on page 75 ) DOO 69 o 1—s V J Q 'J ~ O O * ( i O •-_ J COUNTS i 2.000 Q Qo COO' 3. GOG 1 1 1 1 1 1 1 -.000 3.000 6.000 g.OOG 12.000 15.GOG 18.000 TIME (NSEC) (X10 1 ) F i g u r e u . Decay o f i n t e n s i t y o f the 5852 A t r a n s i t i o n i n neon a t 2 0 0 m i c r o n s Kg. p r e s s u r e . The s o l i d l i n e r e p r e s e n t s t h e f i t t e d c u r v e t o t h e d a t a ( c r o s s e s ) . -3.000 -.000 3.000 TIME 6.000 (NSEC) 9.000 (XlO 1 12.000 15.000 18-000 Figure 15. Decay of intensity of the 5852 A transition i n neon at 100 microns Hg, pressure. The so l id l ine represents the f i t ted curve to the data (crosses). o I -3.000 -.000 3.000 T I M E 6.000 ( N S E C ) 9.000 ( X l O 1 1 1 2 . 0 0 0 15.000 18,000 F i g u r e 16. D e c a y o f i n t e n s i t y o f t h e 58£2 A t r a n s i t i o n i n n e o n a t 100 m i c r o n s H g . p r e s s u r e . T h e s o l i d l i n e r e p r e s e n t s t h e f i t t e d c u r v e t o t h e d a t a ( c r o s s e s ) . 5.000 7 0 o o o =r — (LOG) l NO. OF COUNTS -i l.000 2.000 o Q O 1 3.000 1 -.000 1 1 3.000 6.000 TIME (NSEC) 1 ! 9.000 12.000 (X10 1 ) i i 15.000 18.000 Figure 17. Decay of intensity of the 5852 A transition in neon at 30 microns Hg. pressure. The solid line represents the fitted curve to the data (crosses). - « 3 ,000 T I M E 6.000 (NSEC 9 .000 ( X l O 3 15.000 . 8 .000 Figure 18, Decay of intensity of the 5852 A transition i n neon at 30 microns Hg, pressure. The solid line represents -the f i t t e d curve to the data (crosses). -0 -3.000 -.000 3.000 TIME 6.000 (NSEC) 9.000 ( X l O 1 ) 12.000 15.000 18,000 Figure 19. Decay of intensity of the 5852 A transition in neon at 20 microns Hg. pressure. The solid line represents the fitted curve to the data (crosses). CD r—• \ _ i Q 71 O f—• ^—i CD « O Q ' CD CD • -o " _ _ J COUNTS i 2.000 o + — — o • t— o f—• w o 1 3.000 ! 1 -.000 3.000 T I M E l 6.000 ( N S E C ) i 9.000 (X10 1 ) 1 t 1 12.000 15.000 18-000 Figure 20. Decay of intensity of the 5852 A transition in neon at 10 microns Hg. pressure. The solid line represents the fitted curve to the data (crosses). - 75 -Pressure Lifetime ; • 10 microns of Hg. 1U.80 ± 0.25 x 10" 9 sec. 20 microns of Hg. U . 3 8 ±- 0.37 x 1 0 " 9 sec. 30 microns of Hg. 15.20 ± 0.57 x IO"9 sec. 30 microns of Hg. 1U.6U ±. 0.33 x 10~9 sec. 100 microns of Hg. 15.70 ± 0.19 x 10"9 sec. . 100 microns of Hg. IU.8I4 ± 0.17 x 10~ 9 sec. . . 200 microns of Hg, 15.81 ± 0.19 x 10~9 sec. • TABLE I Lifetimes of the 2px state i n neon. These seven values were averaged, weighted according to t h e i r computed stan-dard deviations. The weighted mean of a number of quantities with standard deviations (T^ i s u s u a l l y defined as _ 2 : v< X = Z V<r> In t h i s way the mean of the l i f e t i m e of the 2p-^  state was computed to be - 9 There i s one other very weak t r a n s i t i o n which o r i g i n a t e s at the 2p-^  l e v e l and which ends i n the l s ^ l e v e l , at the wavelength 5U00 A , This t r a n s i t i o n has been observed i n strong neon sources, but was not observed i n our source This meant that the r a t i o of i n t e n s i t i e s of the two l i n e s i s at l e a s t 100 : because the s i g n a l t o noise r a t i o f o r the 5852 l i n e at the beginning of the decay was l a r g e r than 100. Correspondingly, the r a t i o of the t r a n s i t i o n p r o b a b i l i t i e s of the two l i n e s w i l l be of that order. Therefore we may conclude, that the 5852 A t r a n s i t i o n has a t r a n s i t i o n p r o b a b i l i t y very close to the inverse of the l i f e t i m e of the 2p^  s t a t e , t h a t i s - 76 -; W h i l e t h e r e may be some s y s t e m a t i c e r r o r i n the m e a s u r i n g s y s t e m , i t i s d i f f i c u l t t o a s s e s s i t s m a g n i t u d e . I n the d i s c u s s i o n on t h e l i n e a r i t y o f the m e a s u r i n g system i n s e c t i o n 6 o f C h a p t e r I I I we c o n c l u d e d t h a t t h e maximum c o u n t i n g e r r o r was 2 . 5 % } w h i l e t he maximum e r r o r i n the time base was 1%, On the b a s i s o f t h e s e c o n s i d e r a t i o n s , i t i s l i k e l y t h a t t he maximum s y s t e m a t i c e r r o r i s l e s s t h a n 5 $ . The time c o n s t a n t o f t h e second e x p o n e n t i a l component was a l s o d e t e r m i n e d b y the program and i t i s a l s o of i n t e r e s t , s i n c e i t r e p r e s e n t s t h e l i f e t i m e o f the s t a t e which f e e d s i n t o t h e s t a t e . T a b l e I I g i v e s i t s v a l u e as d e t e r m i n e d a t s e v e r a l p r e s s u r e s . P r e s s u r e L i f e t i m e 2 0 m i c r o n s 82 ± l l i x 10" 9 s e c . 30 m i c r o n s 71 ± 16 x 10~ 9 s e c . 30 m i c r o n s 7 0 ± 1 1 x 10~ 9 s e c . 1 0 0 m i c r o n s 102 ± 11 x 1 0 ~ 9 s e c . 1 0 0 m i c r o n s 90 ± 8 x 10" 9 s e c . 2 0 0 m i c r o n s 92 ± 9 x 10" 9 s e c . TABLE I I L i f e t i m e o f the 2 s 2 s t a t e i n Neon T h i s s e c o n d a r y e x p o n e n t i a l component i s p r o b a b l y due t o t h e l5231 i Angstrom, t r a n s i t i o n ( ^ s ^ - " • * 2p^ ) i n neon. W h i l e t h e r e a r e a f e w o t h e r t r a n s i t i o n s w h i c h t e r m i n a t e on the 2p-^ l e v e l , i t i s l i k e l y t h a t t h i s one w i l l be t h e s t r o n g e s t i n our s o u r c e . A c c o r d i n g t o B e n n e t t e t a l ( 1 ) , the 2s s t a t e s have l a r g e e x c i t a t i o n c r o s s - s e c t i o n s f o r c o l l i s i o n s w i t h e l e c t r o n s , and he s t a t e s t h a t t h e p r i n c i p a l c a s c a d i n g c o n t r i b u t i o n s t o - 77 -t h e 2p l e v e l s i n neon come f r o m t h e s e 2s s t a t e s . Of t h e t r a n s i t i o n s coming from the, 2s l e v e l s , and t e r m i n a t i n g on t h e 2p^ s t a t e , t h e l£23U Angstrom t r a n s i t i o n i s b y f a r t h e s t r o n g e s t , and the o n l y one a l l o w e d i n b o t h LS and j l c o u p l i n g . The 2 s 2 l e v e l i s o p t i c a l l y c o n n e c t e d t o t h e ground s t a t e b y means o f the u l t r a v i o l e t t r a n s i t i o n a t 630 Angstroms as o b s e r v e d b y Boyce ( 30 ) . Because t h i s i s a resonance t r a n s i t i o n , we e x p e c t , a t h i g h p r e s s u r e s a t l e a s t , t h a t t h i s r a d i a t i o n w i l l be c o m p l e t e l y " t r a p p e d " b y s e l f a b s o r p t i o n , and t h e l i f e t i m e o f t h e 2 s 2 s t a t e w i l l be d e t e r m i n e d b y o t h e r t r a n s i t i o n s . ( c . f . t h e d i s c u s s i o n o f a b s o r p t i o n i n s e c t i o n 2 b , C h a p t e r H A . ) . However, a t the p r e s s u r e s a t w h i c h o u r measurements were made, i t i s d e b a t a b l e whether t h e res o n a n c e r a d i a t i o n from t h e 2s s t a t e i s c o m p l e t e l y t r a p p e d . I f we s compute k Q , w h i c h i s t h e q u a n t i t y we d e f i n e d f o r a b s o r p t i o n i n e q u a t i o n ( 9 ) , we o b t a i n f o r t h i s p a r t i c u l a r t r a n s i t i o n , a t a p r e s s u r e o f 100 m i c r o n s o f Hg., u s i n g a v a l u e o f 1(P f o r A ( 2 s 2 _ _ » o) • T h i s i s on t h e b o t l e r l i n e f o r co m p l e t e r e s o n a n c e t r a p p i n g ; the r e q u i r m e n t was t h a t k Q£be much g r e a t e r t h a n one-. F o r p r e s s u r e s l e s s t h e n 100 m i r c r o n s o f Hg, t h i s i s c e r t a i n l y n o t t h e c a s e , s o t h a t we c a n e x p e c t c o n t r i b u t i o n s t o t h e l i f e t i m e o f t h e 2 s ^ s t a t e b y means o f the 630 Angstrom t r a n s i t i o n . The e f f e c t i s t o l o w e r t h e l i f e t i m e , because t h i s t r a n s i t i o n i s t h e n i n s t r u m e n t a l i n d e p l e t i n g t h e 2 s 2 p o p u l a t i o n d e n s i t y . The d a t a w h i c h a r e t a b u l a t e d i n t a b l e I I seem t o be c o n s i s t e n t w i t h the above c o n s i d e r a t i o n s . We see t h a t t h e v a l u e s a t t h e p r e s s u r e s b e l o w 100 m i c r o n s o f Hg. tend,to be l o w e r t h a n t h o s e a t 100 and 200 m i c r o n s o f Hg. W h i l e more d a t a w o u l d be r e q u i r e d t o w a r r a n t d e f i n i t e c o n c l u s i o n s , o u r d a t a a r e n o t i n c o n s i s t e n t w i t h the h y p o t h e s i s t h a t the r e s o n a n c e t r a p p i n g ' i s i n c o m p l e t e a t l e s s t h a n 100 f*- o f Hg. The v a l u e s a t 100 and 200 m i c r o n s of Hg. do not d i f f e r very much; t h i s means that the resonance trapping i s complete to a good approximation at pressures above 100 microns of Hg. The l i f e t i m e measured at these pressures therefore i s a measure 'of the t r a n s i -t i o n p r o b a b i l i t y f o r the 1523 i; A t r a n s i t i o n between the 2 s 2 and the 2p^ s t a t e . I f we" average the three values obtained with weights i n v e r s e l y p r o p o r t i o n a l to t h e i r variance, we get - - 9 This agrees very well with a value f o r t h i s state recently measured by Bennett e t a l . ( 1 ) of 96 nanoseconds. This determination of the l i f e t i m e of the 2 s 2 state i s an i n t e r e s t i n g byproduct of the main i n v e s t i g a t i o n of the l i f e t i m e of the 2p s t a t e , .2-A *X- t e s t of the f i t s as obtained by the computer program was made. The r e s u l t s for the seven determinations were as f o l l o w s . Pressure No. of of Degrees freedom p 10 microns 9.5 11 .6 20 microns 10.7 11 .5 30 microns 32.2 . 11 .01 30 microns 12 .95 100 microns • lit .8 12- .25 100 microns 9.5 12 .65 200 microns 2 5 . 9 12: .01 TABLE I I I Goodness of f i t t e s t on computed curves. - 79 -T h e A - d i s t r i b u t i o n i s t a b u l a t e d i n m a n y h a n d b o o k s o n s t a t i s t i c s , a n d c a n b e i n t e r p r e t e d a s a m e a s u r e o f t h e p r o b a b i l i t y t h a t t h e s p r e a d i n p o i n t s a b o u t a f i t t e d c u r v e w i l l b e w o r s e t h a n t h e o n e o b t a i n e d . T h e q u a n -t i t y P a s t a b u l a t e d a b o v e r e p r e s e n t s t h i s p r o b a b i l i t y f o r t h e v a l u e s o f A . t h a t w e o b t a i n e d , g i v e n t h e c o r r e s p o n d i n g n u m b e r o f d e g r e e s o f f r e e d o m i n t h e f i t . T h e n u m b e r o f d e g r e e s o f f r e e d o m i s e q u a l t o t h e n u m b e r o f d a t a p o i n t s u s e d i n t h e f i t m i n u s t h e n u m b e r o f p a r a m e t e r s o f t h e f i t . T h e c o m p u t e d *~X^ f o r t h e a b o v e r u n s a s s u m e d a n e x p e c t e d e r r o r i n t h e d a t a p o i n t s a s g i v e n b y P o i s s o n s t a t i s t i c s . W h i l e t h e 'X t e s t a s s u m e s t h a t t h e s e e r r o r s a r e n o r m a l l y d i s t r i b u t e d a b o u t t h e i r m e a n , i n s t e a d o f P o i s s o n , t h e d i f f e r e n c e b e t w e e n t h e t w o i s s m a l l f o r t h e m a j o r i t y o f o u r d a t a p o i n t s ( i . e . f o r l a r g e ri, t h e P o i s s o n d i s t r i b u t i o n b e c o m e s s y m m e t r i c a l ) . I t i s e v i d e n t f r o m t h e t a b u l a t i o n o f P t h a t f o r t w o o f t h e s e v e n r u n s t h e s p r e a d i n t h e v a l u e s i s m o r e t h a n m i g h t b e e x p e c t e d a c c o r d i n g t o P o i s s o n s t a t i s t i c s . A l i k e l y ; e x p l a n a t i o n f o r t h i s i s t h a t , a l t h o u g h a v e r a g i n g t e c h n i q u e s w e r e u s e d t o m i n i m i s e t h e e f f e c t s o f d r i f t i n t h e a p p a r a t u s , a c e r t a i n a m o u n t o f e r r o r , i n t h e c o u n t r a t e s c o u l d s t i l l r e s u l t f r o m a p p a r a t u s d r i f t . T h i s e r r o r i s n o t P o i s s o n d i s t r i b u t e d , b u t r e p r e s e n t s a c e r t a i n f r a c t i o n o f t h e c o u n t i r r e s p e c t i v e o f t h e a b s o l u t e v a l u e o f t h e c o u n t . E s p e c i a l l y w h e r e t h e c o u n t i s h i g h , t h i s e r r o r d u e t o d r i f t c a n b e s i g n i f i c a n t l y h i g h e r t h a n t h e e x p e c t e d e r r o r g i v e n b y t h e P o i s s o n d i s t r i b u t i o n . I t i s s e e n , h o w e v e r , t h a n i n t h e m a j o r i t y o f r u n s , P o i s s o n s t a t i s t i c s d o m i n a t e . O n e s c o u l d r e j e c t t h e t w o d e t e r m i n a t i o n s w i t h t h e r e l a t i v e l y l a r g e A - f o r t h i s r e a s o n , b u t i t w a s f e l t t h a t t h i s w a s n o t w a r r a n t e d i n v i e w o f t h e a b o v e c o n s i d e r a t i o n s , a n d a l s o , b e c a u s e t h e t w o v a l u e s o b t a i n e d f o r t h e l i f e t i m e s i n t h e t w o r u n s i n q u e s t i o n w e . r e n o t v e r y f a r f r o m t h e m e a n o f a l l s e v e n r u n s . W h a t w a s d o n e , t h e r e f o r e , w a s t o c o r r e c t t h e s t a n d a r d d e v i a t i o n s a s g i v e n b y t h e m a x i m u m l i k e l i h o o d m e t h o d b y a f a c t o r e q u a l t o - 80 -f o r t h e t w o r u n s i n q u e s t i o n , w h e r e NDF i s e q u a l t o t h e n u m b e r o f d e g r e e s o f f r e e d o m , T h e s t a n d a r d d e v i a t i o n s g i v e n i n T a b l e I a r e t h e c o r r e c t e d v a l u e s . • T h e r e s u l t o f t h i s c o r r e c t i o n i s t h a t t h e w e i g h t s u s e d i n t h e d e t e r -m i n a t i o n o f t h e m e a n o f t h e l i f e t i m e a r e a l t e r e d . B. Relative Intensity Measurements. F i v e sets o f r e l a t i v e i n t e n s i t i e s w e r e m e a s u r e d , g i v i n g u s - f i v e i n d e p e n -d e n t r a t i o s o f t r a n s i t i o n p r o b a b i l i t i e s . T h e r e s u l t s o f t h e m e a s u r e m e n t s a r e t a b u l a t e d i n T a b l e IV, t o g e t h e r w i t h t h e r e l e v a n t c a l i b r a t i o n d a t a . t r a n s i t i o n 1 t r a n s i t i o n 2 X, 76%) AcV) AM 2 P 2 - I s 3 2 p 2 - l s 2 ; 6161, 6599 .93U 6.hi 1.01 . 6 2 6 6.U9 .591 ± .025 2 p / r l s i t . 2 p i r l s 2 : 6096 6678 .913 17.5 1.02 .535 •10.8 .802 ± .036 2 p 7 - l s 5 2p 7 - i s ^ 6217 6383 .971; .5a 1.00 .832 1.83 • .21a. ± .015 2 P 7 " l s 5 2 p 7 - l s 3 . 6217 6533 .952 3.87 1.01 .711 3.95 .688 ± .053 2pg~l S£ 2p -Is . P 8 k 6331* 6506 .97 Li 1.63 1.00 .8324 2 . 3 2 .572 ± .032 T a b l e IV R a t i o s o f t r a n s i t i o n p r o b a b i l i t i e s ft C>0 A (KC) t o g e t h e r w i t h c a l i b r a t i o n d a t a . - 81 -The choice of these particular ratios for measurement was largely influenced by the fact that the value of these ratios had to be known in order to correlate relative measurements of transition probabilities made in this laboratory by Robinson ( k ). Although the f i r s t three ratios listed were sufficient to do this, the last two were also determined in order to provide a crosscheck on the data. The errors were estimated from the separate errors in the calibration quantities and the actual intensity ratio measure-ments , - 82 -CHAPTER V • CONCLUSIONS AND COMPARISONS We can conclude from t h i s experiment that the l i f e time of the 2p-^ -9 state in' Neon i s 15.2 ±. 0.2 x 10 seconds, and that the t r a n s i t i o n 7 - 1 p r o b a b i l i t y f o r the 2p^ - l s 2 t r a n s i t i o n i s 6 .57± 0.1 xlO sec . The estimated systematic er r o r i s less than $%. These values compare favor-ably with t h e o r e t i c a l c a l c u l a t i o n s made as described i n Chapter I I s e c t i o n -9 A5. The values obtained with the c a l c u l a t i o n s are "C = 15 x 10 7 -1 seconds, and A = 6.7 x 10 sec. The value of the 2p^ l i f e t i m e i n Neon has been measured before. For 1jhe sake of comparison, Table V shows the values obtained. L i f e time Date Author (nanoseconds) Method 1966 Present work 15.2 i 0.2 Sampling, e l e c t r o n gun . 1965 Klose ( 31 ) III.7 ±- 0.6 Delayed coincidence, e l e c t r o n gun 1965 Bennett at a l . ( 1 ) 1U.7 ±- 1 Delayed coincidence, e l e c t r o n gun 196.U F r i e d r i c h s ( 32 ) 17 S t a b i l i s e d arc emission 1963 Mac Lean ( 33 ) .3.8 Shock tube emission 1963 Doherty ( 3h ) 28 Shock tube emission I960 Osherovich ( 35 ) 51 D i r e c t measurement 193k Ladenburg ( '36 ) 8 Anomalous dispersion 193ii G r i f f i t h s ( 37 ) 39 D i r e c t measurement, phase s h i f t . Table V Measured values f o r the 2p n l i f e t i m e i n neon I t i s seen that our value shows e x c e l l e n t agreement with those of Bennett and Klose, and good agreement with the value obtained by F r i e d r i c h s . In general the emission experiments have the disadvantage that one must assume - 83 -a c e r t a i n p o p u l a t i o n d e n s i t y d i s t r i b u t i o n , and t h a t c o n s e q u e n t l y an a b s o l u t e v a l u e o f t h e t e m p e r a t u r e must be d e t e r m i n e d . T h i s t y p e o f measurement i s d i f f i c u l t and s u b j e c t t o e r r o r . The measurement o f the phase s h i f t b etween e x c i t a t i o n and e m i s s i o n p u l s e s u s e d b y G r i f f i t h s i s good i n t h a t i t does n o t n e c e s s i t a t e a b s o l u t e i n t e n s i t y measurements, b u t s u f f e r s t h e d i s a d v a n t a g e t h a t c a s c a d i n g components i n t h e decay c a n n o t be r e s o l v e d . The d e l a y e d c o i n c i d e n c e method used b y B e n n e t t , and. a l s o b y K l o s e , must be c o n s i d e r e d q u i t e r e l i a b l e from many p o i n t s o f v i e w . The f o r m e r has w r i t t e n an e x t e n s i v e r e v i e w a r t i c l e on the measurements o f f a s t decay r a t e s , i ( 1 ) , i n w h i c h a l l the f a c t o r s t h a t e n t e r i n t o s u c h measurements a r e t h o r o u g h l y d i s c u s s e d . The method a d o p t e d b y t h e above a u t h o r s w i l l be d i s c u s s e d b r i e f l y and compared w i t h o u r method. F o r f u r t h e r r e f e r e n c e t h e r e a d e r i s r e f e r r e d t o t he r e f e r e n c e s q u o t e d i n T a b l e V. The d e l a y e d c o i n c i d e n c e method u t i l i s e s a time t o p u l s e h e i g h t c o n v e r t e r and a m u l t i c h a n n e l p u l s e h e i g h t a n a l y s e r t o measure t h e ti m e d i f f e r e n c e between an e x c i t a t i o n p u l s e and t h e a r r i v a l o f t h e f i r s t p h o t o n p u l s e a t the anode o f the p h o t o m u l t i p l i e r . The measurement i s r e p e a t e d a t a r e p e t i t i o n f r e q u e n c y o f about one k i l o c y c l e , and t h e d e l a y t i m e measured f o r e a c h p u l s e i s s t o r e d i n t h e memory of t h e p u l s e h e i g h t a n a l y s e r . The s p e c t r u m o f d e l a y t i m e s t h u s o b t a i n e d , i s t h e r e f o r e the spec t r u m o f f i r s t p h o t o n a r r i v a l t i m e s , and i n t h e l i n i t o f l o w c o u n t r a t e s , t h i s s p e c t r u m i s e q u i v a l e n t t o t h e p r o b a b i l i t y t h a t a p h o t o n w i l l be e m i t t e d b y the s o u r c e a t c o r r e s p o n d i n g d e l a y t i m e s . I n o u r method we measured t h e average number o f t i m e s a p h o t o n a r r i v e s a t a p a r t i c u l a r d e l a y t i m e , i n s t e a d o f m e a s u r i n g time d e l a y s f o r t h e a r r i v a l o f the f i r s t p h o t o n . W h i l e t h e d e l a y e d c o i n c i d e n c e method i s l e s s w a s t e f u l o f i n f o r m a t i o n , i t i s s u b j e c t t o s a t u r a t i o n a t much l o w e r l i g h t l e v e l s t h a n our method. As i s p o i n t e d o u t i n s e c t i o n I I I A 6, s a t u r a t i o n o c c u r s - 6li -i n our method when th e p r o b a b i l i t y t h a t two p h o t o n p u l s e s a r r i v e a t t h e 'anode'"; a t the same ti m e i n the c y c l e i s comparable t o t h e p r o b a b i l i t y t h a t one a r r i v e s . The d e l a y e d c o i n c i d e n c e method shows s a t u r a t i o n when th e p r o -b a b i l i t y t h a t two o r more p h o t o n p u l s e s a r r i v e d u r i n g t h e e n t i r e d e c a y becomes comparable t o t h e p r o b a b i l i t y t h a t one a r r i v e s . The t i m e r e s o l u t i o n o f b o t h methods i s c o m p a r a b l e . I n the absence of a p p a r a t u s d r i f t , t h e a c c u r a c y o f t h e d a t a i n b o t h c a s e s i s d e t e r m i n e d b y c o u n t i n g s t a t i s t i c s . The l i f e t i m e o f t h e 2 s ^ s t a t e i n neon was f o u n d t o be 9lw5 ±- lj x 1 0 ~ 9 s e c o n d s , assuming resonance t r a p p i n g i s c o m p l e t e f o r t h i s l e v e l a t 100 m i c r o n s p r e s s u r e , , b u t n o t a t 30 m i c r o n s p r e s s u r e . T h i s v a l u e agrees w i t h i n e x p e r i -m e n t a l e r r o r w i t h t h a t o b t a i n e d b y B e n n e t t a t a l . ( 1 ) , who measured t h i s l i f e t i m e t o be 96 x I O - 9 s e c . R e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s were o b t a i n e d f o r s e v e r a l t r a n s i t i o n s i n neon; h a v i n g t h e same up p e r s t a t e s . The r e s u l t s o b t a i n e d a r e summarised i n T a b l e V I , where t h e y a r e compared w i t h r e s u l t s o b t a i n e d b y I r w i n ( 3 ), D o h e r t y ( 3k ) , and L a d e n b u r g ( 36 ) . The agreement w i t h t h e v a l u e s o b t a i n e d b y o t h e r w o r k e r s on t h e whole i s q u i t e g o o d , and t h e d i s c r e p a n c y i s n e v e r g r e a t e r t h a n 20$. Of t h e above d e t e r m i n a t i o n s , ours i s t h e o n l y one where e m i s s i o n s t u d i e s were done on a p u l s e d e l e c t r o n gun l i g h t s o u r c e . D o h e r t i j p s measurements were made u s i n g a s h o c k t u b e , w h i l e I r w i n and L a d e n b u r g u s e d a c o n t i n u o u s gas d i s c h a r g e as t h e i r l i g h t s o u r c e . A l l t h r e e u s e d p h o t o g r a p h i c d e t e c t i o n e q u i p m e n t , and had t o make c o r r e c t i o n s f o r s e l f a b s o r p t i o n f o r a number o f t h e l i n e s . S i n c e s e l f a b s o r p t i o n was n e g l i g i b l e i n our l i g h t s o u r c e , our' m e t h o d • i s i n h e r e n t l y more a c c u r a t e . - 8 5 -T r a n s i t i o n 1 Laden-ourg ( 3 6 ) , T r a n s i t i o n 2 ^ 2 AW Irwin (U) Doherty (3u) 2 p 2  2 P 2 Is ^  Is 2 6 l 6 I i 6 5 9 9 . 5 9 t .03 .6U . 6 5 .57 6 0 9 6 . 8 0 ± .Oli .68 .61 . 5 9 1 B 2 6678 P 7 6217 , 2 U ± .02 .23 .23 . 3 5 2P7 • l s t 6383 % Is 5 6217 .69 ± . 0 5 •51 . 5 0 .68 . Is 3 6533 2P 8 lss 6 3 3 U . 5 7 1 .03 .63 . 6 5 . 6 1 2 ? 8 . Is a 6506 Table VI Measured r a t i o s of t r a n s i t i o n p r o b a b i l i t i e s f o r 5 p a i r s of t r a n s i t i o n s i n neon. - 86 -APPENDIX I MAXIMUM LIKELIHOOD F I T OF THE DATA I f we assume t h a t t h e d a t a o b t a i n e d r e p r e s e n t P o i s s o n d i s t r i b u t e d c o u n t s a b out a mean v a l u e y ( t ^ ) w h i c h i s o f the form - _ t h e n the p r o b a b i l i t y P t h a t a t t h e time t k we o b t a i n a c o u n t N k i s g i v e n b y and the p r o b a b i l i t y o f h a v i n g t h e s e r i e s o f c o u n t s N^, N^, ... a t c o r r e s p o n -d i n g t i m e s t t 2 , f o r t h e whole decay i s g i v e n by P _ TT pK = ~TT ^ O, - ) k . D k ^ N f c 1 w h i c h w r i t t e n i n terms o f ott) o(Xj a»\d becomes P ( « ^ ^ = k U ^(-<,€. " - - ^ e * ) } j ^ j The c r i t e r i o n u s e d t o d e t e r m i n e t h e b e s t v a l u e o f «i > °<-i) rtj,, euvck <tf4 w i t h the g i v e n d a t a N -was t o maximise the p r o b a b l i t y P. T h a t i s 1>* The computer program o f O r t h ( 29 ) m a x i m i s e s t h e more c o n v e n i e n t f u n c t i o n b y s o l v i n g -cXy c^w «g»uj ^ K / - 87 -These e q u a t i o n s are t h e n of t h e f o r m T V — o (•77) I t i s c l e a r t h a t t h e s e e q u a t i o n s a r e n o n l i n e a r . The computer program t h e r e f o r e a d o p t s an i t e r a t i v e p r o c e d u r e f o r t h e i r s o l u t i o n u s i n g a f i r s t o r d e r T a y l o r e x p a n s i o n o f the f u n c t i o n s (77 ) a b o u t some i n i t i a l e s t i m a t e s I n g e n e r a l one may expand any f u n c t i o n t o f i r s t o r d e r as f o l l o w s C78) X., -&s, -etc A p p l y i n g t h i s t o t h e above e q u a t i o n s , we o b t a i n Hence the computer s o l v e s t h e system o f e q u a t i o n s ( 7 9 ) f o r J, 09) where The v a l u e s of cSj .are u s e d t o f i n d a new e s t i m a t e f or <Xj , and t h e whole p r o c e d u r e i s r e p e a t e d . I f t h e i n i t i a l e s t i m a t e s f o r <Xj a r e g ood, t h e p r o c e -dure c o n v e r g e s q u i t e r a p i d l y ( l e s s t h a n t e n i t e r a t i o n s w i l l g e n e r a l l y y i e l d - 88 -The intial estimates of the l i f e time can be fed into the computer from a graphical analysis of the data, or can be generated by the program itself by a rough iterative procedure using the well known method of least squares. It is shown by Orear ( 3 8 ) that the matrix H L j =- ( - C C J T " 1 ( s o ) represents the socalled error matrix of the iteration and its diagonal elements give the values of the variance of the corresponding parameters, i.e. The standard deviations used in our results are the square roots of the appropriate diagonal elements in this inverted matrix. - 89 -APPENDIX I I . PRELIMINARY MEASUREMENT OF LIFETIMES OF A NUMBER OF 2p STATES B l NEON I As i s a p p a r e n t from t h e d i s c u s s i o n i n C h a p t e r I I , i t i s o n l y under v e r y s p e c i a l c o n d i t i o n s t h a t measurements on t h e t i m e dependence o f l i g h t i n t e n s i -t i e s w i l l y i e l d unambiguous i n f o r m a t i o n r e g a r d i n g t r a n s i t i o n p r o b a b i l i t i e s between e x c i t e d s t a t e s . E v e n i f p r o c e s s e s s u c h as a b s o r p t i o n , s t i m u l a t e d e m i s s i o n , and atom-atom c o l l i s i o n s may be n e g l e c t e d , an i r i t e r p r e t a t i o n a l d i f f i c u l t y r e m a i n s because o f the " c a s c a d i n g " term (the t h i r d term) i n equa-t i o n (25). F o r the t r a n s i t i o n s t u d i e d i n d e t a i l i n t h i s work, namely t h e 2p>L - l s ^ t r a n s i t i o n i n neon, a t 58$2 A, t h e e f f e c t o f t h e c a s c a d i n g t e r m c o u l d be i n t e r p r e t e d r e l a t i v e l y e a s i l y because o f the f o r m o f t h e d a t a . I n t h i s c a s e c a s c a d i n g f r o m h i g h e r l e v e l s p r o v e d t o be a s m a l l p e r t u r b a t i o n on t he decay o f the 2p-^  l e v e l i t s e l f . The r e a s o n f o r t h i s i s p r o b a b l y t h a t the 2p-^  l e v e l has a r e l a t i v e l y l a r g e e x c i t a t i o n c r o s s - s e c t i o n f o r e l e c t r o n i m p a c t . I t i s i n t e r e s t i n g t o note t h a t t h e d e s i g n a t i o n o f t h i s s t a t e i n LS c o u p l i n g i s ^ Q > w h i c h i s t h e same as the ground s t a t e . Hence t h e a n g u l a r momentum of the e l e c t r o n i s unchanged i n the e x c i t a t i o n t r a n s i t i o n , w h i c h means t h a t t he e x c i t i n g e l e c t r o n need n o t s u p p l y o r c a r r y o f f any a n g u l a r momentum. E x c i t a t i o n b y t h i s p r o c e s s i s t h e r e f o r e f a v o r a b l e f o r t h i s . p a r t i -c u l a r s t a t e . T h i s i s n o t n e c e s s a r i l y so f o r the o t h e r 2p l e v e l s i n n e o n , and i n f a c t the e x p e r i m e n t a l d a t a i n d i c a t e t h a t f o r t h e s e l e v e l s t h e e x c i -t a t i o n c r o s s - s e c t i o n s a r e comparable t o t h o s e f o r t h e h i g h e r 2s s t a t e s . A two e x p o n e n t i a l f i t o f t h e d a t a f o r t h e s e l e v e l s i n d i c a t e s l a r g e c o n t r i -b u t i o n s t o the decay by c a s c a d i n g t r a n s i t i o n s . When t h i s o c c u r s , one must d e c i d e i f t h e decay i s b e t t e r d e s c r i b e d b y t h r e e o r more t e r m s . T h i s i s 90 d i f f i c u l t when the r e l a t i v e i n t e n s i t i e s of the exponential components become comparable, as i s the case f o r these other 2p l e v e l s . Consequently the r e -s u l t s obtained by means of a f i t t o two exponential terms must be treated with caution. For t h i s reason we report on them as preliminary r e s u l t s i n t h i s appendix, rather than l i s t them with the other r e s u l t s on the 2p^ s t a t e , which we consider quite r e l i a b l e . Table VII gives a l i s t of l i f e t i m e s obtained f o r a number of l e v e l s i n neon assuming that a two step decay scheme was dominant. The t r a n s i t i o n s used to study the l i f e t i m e s are l i s t e d . Some t y p i c a l p l o t s of the computer f i t s to the data are given i n the next pages. The r e s u l t s were obtained at a pressure of 100 microns Hg, 5 and with an e x c i t a t i o n pulse of width 4O nanoseconds, and height $0 v o l t s . For the sake of comparison, the r e s u l t s thaiv were obtained by Klose ( 3 l ) , Bennett e t a l , ( 1 ) and F r i e d r i c h s ( 32 ) are l i s t e d i n Table VII as w e l l . L evel T r a n s i t i o n Lifetime, (nanoseconds) Klose Bennett F r . 2 p 2 ( 6 1 6 3 A ) 2 5 . 1 * 2 .5 16 .5 19.2 17 2 p 3 (607i |A) 27.6 ± 1.8 23 2 P 5 ( 6 2 6 6 A ) 3U.7 ± 2.7 1 8 . 9 2 P 6 (61U3A) 27.1* ± 0.7 22 2 8 ( 6 3 8 3 A ) 33.8 t 20.3 2 p 8 (633 uA) 20.2 ±-1.8 2i i .3 2 p Q (6U02A) 28 , l i ± 1 . 0 2 2 . 5 Table VII Lifetime measurments f o r 2p l e v e l s i n neon -3.000 -.000 3.000 T I M E 6.000 9.000 , 12.000 ( N S E C ) ( X l O 1 ) 15.000 18.000 Figure 21. Decay of intensity of the 61(02 & transition in neon at 100 microns Hg. pressure. The solid line represents the fitted curve to ihe data (crosses). o o in~ o S 1 O 3 * " " ^ ^ ^ ^ ^ CD O --(LOG: COUNTS 2.000 o o o 1 3.000 1 1 1 1 1 I I - .000 3.000 6.000 9.000 , 12.000 15.000 18.000 TIME (NSEC) (X101 ) Figure 22. Decay of intensity of the 6llj3 A transition in neon at 100 microns Hg. pressure. The solid line represents the fitted curve to -the data (crosses). - 93 -One can, i n p r i n c i p l e , eliminate the e f f e c t s of cascading by a judicious choice of e l e c t r o n energy f o r e x c i t a t i o n . As i s well known, atoms can only be excited to a p a r t i c u l a r state by means of e l e c t r o n c o l l i s i o n s provided the electrons have s u f f i c i e n t k i n e t i c energy to supply the atom with the appro-p r i a t e e x c i t a t i o n energy. I f one can arrange to have electrons that are just energetic enough to excite atoms i n t o the state o f i n t e r e s t , but of i n s u f f i -c i e n t energy to excite atoms i n t o higher states which conceivably could feed the state of i n t e r e s t by means of r a d i a t i v e t r a n s i t i o n s , then the problem of cascading would not occur. However, there are severe experimental d i f f i c u l -t i e s associated with t h i s method. In the f i r s t p lace, one would require an e l e c t r o n gun of such design that the electrons obtained were monoenergetic to within a f r a c t i o n of an e l e c t r o n v o l t , since the spacings between the energy l e v e l s are quite small. While t h i s requirement could p o s s i b l y be met, a further problem occurs because of the dependence of the e l e c t r o n e x c i t a t i o n cross-section on the e l e c t r o n energy. I t turns out that f o r most s t a t e s , the cross-section f o r e x c i t a t i o n with electrons i s extremely small near the "threshold" energy f o r e x c i t a t i o n , and becomes only appreciable at energies well i n excess of t h i s value. The p r a c t i c a l r e s u l t i s that one must work with e l e c t r o n energies of about twice the threshold energies f o r e x c i t a t i o n , which means that a l l l e v e l s are excited at the same time. For t h i s reason our measurements were made with e l e c t r o n energies of about 50 e l e c t r o n v o l t s , even though the threshold energies f o r the 2p states are of the order of 18 e l e c t r o n v o l t s . Although the cascading to the l e v e l s l i s t e d above i s quite severe, t h i s does not mean that one cannot obtain u s e f u l information about these l e v e l s . , What can be done, f o r example, i s to see how the computed l i f e t i m e s u.sing a two step decay model vary as a f u n c t i o n of the d i f f e r e n t parameters - 9k ~ of the l i g h t source, such as pressure, pulse height and pulse width. By vary-ing the pulse height, one i s able to excite one or another l e v e l preferen-t i a l l y , as the d i f f e r e n t l e v e l s have a peak cross-section f o r e x c i t a t i o n by electrons at d i f f e r e n t e l e c t r o n energies ( see f o r example Hanle ( 39 ) ). By changing the pulse width, one may change the r a t i o s of population d e n s i t i e s at the beginning of the decay, because the rate at which population d e n s i t i e s b u i l d up during the e x c i t a t i o n part of the cycle i s governed by the same time constants as the decay process. What may be possible i s to f i t the data to a function with more than two exponential terms, since i n general the two term model i s only an approximation to what a c t u a l l y happens i n the gas during the decay. While some of these ideas were t r i e d f o r the determination of the l i f e t i m e s of the 2p l e v e l s , i t soon became apparent that r e l i a b l e r e s u l t s could only be obtained a f t e r a d e t a i l e d study, in v o l v i n g many runs. I t i s the opinion of the author that such a study would be worthwhile, not only to see i f the values of the other workers quoted i n Table VII can be substantiated, but also to study the cascading processes themselves. Be-sides getting, information on the l i f e t i m e s of the states i n question, one may also study the dependence of the e x c i t a t i o n functions on e l e c t r o n energy f o r the various l e v e l s , and the dominant paths cf cascading involved i n the decay of the gas to i t s ground s t a t e . The more r e l i a b l e r e s u l t obtained for the l i f e t i m e of the 2p^ state serves as an absolute basis for the very r e l i a b l e values of r e l a t i v e t r a n s i -t i o n p r o b a b i l i t i e s obtained i n t h i s laboratory by Robinson ( U ). Using these r e l a t i v e values, one can, i f so desired, compute the l i f e t i m e s of the other 2p states i n neon accurately. iSPPENDIX I I I CALIBRATION OF SPECTRAL RESPONSE OF A MONOCHROMATOR T h i s A p p e n d i x d e a l s w i t h t h e d e r i v a t i o n o f e q u a t i o n (63) i n C h a p t e r I I I . C o n s i d e r t h e case i n whi c h t h e i l l u m i n a t i o n on t h e e n t r a n c e s l i t o f a mono-chr o m a t o r i s o f u n i f o r m i n t e n s i t y , c o v e r i n g t h e e n t i r e s l i t o p e n i n g . The t r a n s m i s s i o n p a s s band o f t h e monochromator i s t h e n t r i a n g u l a r o r t r a p e z o i d a l , d e p e n d i n g on t h e r e l a t i v e s i z e s o f t h e e n t r a n c e and e x i t s l i t s . I f t h e monochromator i s s e t t o p a s s a w a v e l e n g t h ^ w t h e n an e x i t s l i t o f w i d t h we may p a s s a w a v e l e n g t h i n t e r v a l g i v e n b y where D(A ) i s t h e l i n e a r d i s p e r s i o n . I f t h e e n t r a n c e s l i t has a w i d t h w^ , t h e n t h e w a v e l e n g t h i n t e r v a l imaged i n the p l a n e o f t h e e x i t s l i t i s g i v e n b y A X ; -¥e assume i n t h i s d i s c u s s i o n t h a t A X g f so t h a t t h e t r a n s m i s s i o n t ( \ ^ i s t r a p e z o i d a l , as shown i n t h e accompanying d i a g r a m . u t(x,\J T r a p e z o i d a l t r a n s m i s s i o n f u n c t i o n . - 96 -The transmission of the monochromator reaches a maximum, T ( Xj^ i n the. region x ^ ^— ^ — ^ — The output measured by the detector due to r a d i a t i o n i n a small band of wavelengths dA , centred at X is d l „ = S L i C \ X m ) 5 a ) TLC*) d X where —^1. i s the e f f e c t i v e s o l i d angle subtended at the source by the monochromator, S (A) i s the s e n s i t i v i t y of the detector, and I (A) i s the i n t e n s i t y per u n i t s o l i d angle per u n i t wavelength i n t e r v a l of the source. Integrating over a l l wavelengths y i e l d s the t o t a l response, thus; Aw, —=r~ For a s p e c t r a l l i n e of width £ A « ^ X ; _ a n d wavelength X 1.^ ( X ^ = SLT(^)S(^)1C(^) iX^T^LX^) where the su b s c r i p t A. indicates l i n e r a d i a t i o n . Therefore two l i n e s z o f the same l i n e - width give For a continuous source, the v a r i a t i o n of I and S over ^ X ^ must be taken i n t o account. Introducing a new v a r i a b l e X1 -(A-X^^/^A* and w r i t i n g a Taylor seri e s expansion f o r I and S about X1 — o ; we get 160 ~ £ ( o ) + i ' f o ) \ * + .... 97 -S(x,s) , SCo) t s'cToVX1 + .. . Now r'M and i f only the f i r s t wo terms i n the expansions are retained, then Sfo ) [ I f (<r-i) X 1 ] with X(o) and the transmission i s given by <r = where C L = I -Equation ( 8JU ) then becomes or with x ^ d X ' but k ( X O ) «{ii.[,+ i ^ < r . , V a l - ^ V * - , ) ( r . , ) ] ] Therefore i f two wavelengths X j are compared, then ^ X e M D ( X ^ (87) - 98 -where D i s the l i n e a r d i s p e r s i o n , -Combining equations (85), (86), and (87), This equation i s the same as equation ( 63 ). - 99 -REFERENCES 1 . W.R. Bennett, P . J . Kindlmarai, and G.N. Mercer, implied Optics Supplement 2 , 3JU ( 1965) 2. B.M.- Glennon and W.L. Wlese, Bibliography on Atomic T r a n s i t i o n  P r o b a b i l i t i e s „ U.S:. Department of Commerce, MBS; Monograph $0 (l?S2) 3. J.C. Irwin, Ph.D 0 Thesis, U.B.C. (196$) ho AuM.. Robinson, Ph. D 0 Thesis;, U.B.C. (1956) 5 . A.C.G. M i t c h e l l and M.W. 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Journal 1 0 ^ , 126 (191+7) 2 0 . J.R. P i e r c e , Theory and Design of E l e c t r o n Beams , Van Nostrand ( l 9 u 9 ) - 100 -2 1 . W , N o t t i n g h a m , T h e r m i o n i c E m i s s i o n , Handbuch d e r P h y s i k X X I , S p r i n g e r V e r l a g (1956) 22. F . R o s e b u r y , MIT Tube L a b o r a t o r y M a n u a l , M.I.T. (1956) 23. F . J , Lombard and F . M a r t i n , R e v . o f S c . I n s t r . 3 2 , 2 0 0 (lS6l) 2k, M . Gadsden, A p p l i e d O p t i c s Jj , ll+L+6 (l?55) 2 5 , A. A r c e s e , A p p l i e d O p t i c s 3, I|35 (1961+) 26, T.C.. F r y , P r o b a b i l i t y and i t s E n g i n e e r i n g U s e s , Van N o s t r a n d , 1965 2 7 . R.D. L a r r a b e e , J . o f t h e O p t . S o c . o f Am. J+9, 6l9 (1959) 28. G.A.W. R u t g e r s and J.C. de V o s , P h y s i c a 2 0 , 715 (1951+) 2 9. , R. O r t h , P h . D. T h e s i s ( t o be p u b l i s h e d ) 30. J.C. B o y c e , P h y s . R e v . J£, 378 (1931+) 31. J.Z. K l o s e , P h y s . R e v . l l j l , 181 (1966) 3 2 . H. F r i e d r i c h s , Z. f u r A s t r o p h y i k 6 0 , 176 (1951+) 33. E . A . Mac L e a n , i n P r o c . o f t h e S i x t h I n t . C o n f . on I o n i s a t i o n Phenomena i n Gases ( P a r i s 1953), V o l . I l l , 389 3l+, L.R. D p h e r t y , P h . D. T h e s i s , U n i v e r s i t y o f M i c h i g a n (1952:) 3 5 . • f i . L . O s h e r o v i c h and G.M. P e t e l i n , S o v i e t P h y s i c s - D o k l a d y JJ., 1289, ( i 9 6 0 ) 36. R, Lad e n b u r g and S. L e v y , 2. f u r P h y s , 88, I4.61 (1931+) 37. J o H J E . G r i f f i t h s , P r o c . R o y . S o c , (London) A. ll+3, 588 0-931+) 38. J . O r e a r , U.C.R.L. R e p o r t 81a7 (1958) 39. W. H a n l e , Z l . f u r P h y s . 6£, 5 l 2 (1930) 

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