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Dipole moment of the 3P state of HN as determined from optical observations of the Stark effect Irwin, Timothy Alexander Ready 1965

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THE DIPOLE MOMENT OP THE - 'TT STATE OP NH AS DETERMINED PROM OPTICAL OBSERVATIONS OP THE STARK EFFECT * y TIMOTHY ALEXANDER READY IRWIN B . S c , U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1961 A THESIS SUBMITTED I N P A R T I A L FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n t h e d e p a r t m e n t o f PHYSICS We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF B R I T I S H COLUMBIA A p r i l 1965 I n p r e s e n t i n g 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 r e q u i r e m e n t s 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 t h a t 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 r e f e r e n c e and s t u d y , I f u r t h e r agree t h a t p e r -m i s s i o n f o r e x t e n s i v e c o p y i n g 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 g r anted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood t h a t , c o p y i n g 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 g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n * Department of Physics The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada Date March 2, 1965 A B S T R A C T T h e v a l u e o f t h e d i p o l e m o m ent , y U , o f NH i n t h e s t a t e was f o u n d t o b e 1 .31 - . 0 3 D e b y e . T h i s v a l u e was d e t e r m i n e d f r o m d a t a o n t h e S t a r k e f f e c t m e a s u r e d f r o m 3 T — . o s p e c t r o g r a m s o f t h e A T T - X ° l , 3360 A, b a n d t a k e n o n a 3.U m e t e r g r a t i n g s p e c t r o g r a p h i n t h i r d o r d e r g i v i n g a r e s o l u t i o n o f a b o u t 1 0 0 , 0 0 0 . T h e t h e o r y o f t h e S t a r k 5 e f f e c t i n m o l e c u l e s was t a k e n f r o m p a p e r s b y W. G. P e n n y Q a n d V a n V l e c k a n d H i l l . T h e m a g n i t u d e o f t h e e l e c t r i c f i e l d was d e t e r m i n e d f r o m t h e S t a r k s p l i t t i n g o f t h e h y d r o g e n l i n e H^ a c c o r d i n g t o t h e t h e o r y g i v e n i n T h e T h e o r y o f A t o m i c S p e c t r a . I n t h e n e a r f u t u r e I s h o u l d b e a b l e t o c o m p l e t e w o r k o n t h e c V - ^ a 1 / ! , 321(0 A, b a n d a n d g i v e t h e v a l u e s o f t h e d i p o l e m o m e n t s f o r s t a t e s c a n d a a s w e l l . T h u s i t w i l l b e p o s s i b l e t o d e t e r m i n e h o w t h e d i p o l e moment c h a n g e s w i t h e l e c t r o n i c c o n f i g -u r a t i o n . i i i T A B L E OP CONTENTS I n t r o d u c t i o n 1 E x p e r i m e n t 3 A p p a r a t u s 3 M e t h o d 5 R e s u l t s 5 D a t a 9 D e t e r m i n a t i o n o f t h e d i p o l e moment 11 T h e S t a r k e f f e c t o n d i a t o m i c m o l e c u l e s 11 D e t e r m i n a t i o n o f t h e e l e c t r i c f i e l d 15 T h e R Q 2 1 ( 0 ) l i n e 17 C o r r e c t i o n s 23 M i x e d c o u p l i n g 23 S e c o n d o r d e r e f f e c t s 2k E r r o r s 25 S u m m a r y 26 B i D l i o g r a p h y 27 Table I Table II Data Refined Data V P L A T E S AND F I G U R E S P l a t e 1, T h e 32U0 A B a n d a n d H p 6 P l a t e 2, T h e 336O A B a n d 7 P l a t e 3, T h e R Q 2 1 ( 0 ) L i n e 8 F i g u r e 1, S o u r c e U F i g u r e 2, V e c t o r M o d e l 1U F i g u r e 3, S t a r k E f f e c t i n H y d r o g e n 16 o F i g u r e I4, E n e r g y L e v e l s , 3360 A B a n d 1 8 F i g u r e 5, R ^ 2 1 ( 0 ) 19 F i g u r e 6, i{6 + A ) v s E 2 21 v i ACKNOWLEDGEMENTS I am p l e a s e d t o a c k n o w l e d g e t h e g e n e r o u s a s s i s t a n c e o f P r o f e s s o r P. W. D a l b y a n d D. H. P h e l p s w h o s e a d v i c e o n m a t t e r s o f t e c h n i c a l a s w e l l a s t h e o r e t i c a l i m p o r t a n c e t o t h i s w o r k w a s i n v a l u a b l e . T h i s w o r k w a s s u p p o r t e d j o i n t l y b y 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 o f C a n a d a a n d T h e P r e s i d e n t ' s F u n d o f t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a . INTRODUCTION The study of the dipole moments of diatomic hydrides was undertaken at the University of B r i t i s h Columhia i n 1962 by Professor P. W. Dalby i n order to; a) provide information concerning dipole t r a n s i t i o n moments i n diatomic molecules so that the concentrations of these molecules i n the i n t e r s t e l l a r gas might be determined, b) check the assumptions made i n the th e o r e t i c a l c a l -culations of dipole t r a n s i t i o n moments. The NH molecule i s not known to exist i n the i n t e r s t e l l a r gas but i s int e r e s t i n g from a t h e o r e t i c a l point of view. There are several methods of determining dipole moments. The most di r e c t of which i s spectroscopic observations of the Stark e f f e c t . Microwave spectros-copy while very accurate i s l i m i t e d to measurements of the ground state of a molecule. Optical spectroscopy while not quite so accurate can be used to investigate the excited states as well as the ground state of a molecule. For these reasons the technique of o p t i c a l observations on the Stark e f f e c t was used to measure the dipole moment. The dipole moment of the A^fT state was determined •z f i r s t because: a) the ground state, ¥r , exhibits no f i r s t order Stark e f f e c t , b) of the s i x known states of NH this i s the only one f o r which transitions to the ground state are known, c) there should be no complica-tions due to both upper and lower states s p l i t t i n g . 2 I s h a l l discuss f i r s t the experimental method and then the analysis of the data and the theory of the Stark e f f e c t . 3 EXPERIMENT APPARATUS One of the a t t r a c t i v e f e a t u r e s of t h i s experiment was the s i m p l i c i t y of the apparatus r e q u i r e d . To do the experiment i t was necessary only to focus the l i g h t from the high f i e l d r e g i o n of a Lo Surdo type discharge tube (see f i g u r e l ) running i n ammonia on the s l i t of a s t i g -matic spectrograph of r e s o l u t i o n around 1009000. The bottom of the glas s discharge tube was sealed by means of a l a r g e rubber stopper with the cathode passing through i t . This provided f o r easy i n s p e c t i o n , changing, and c l e a n i n g of the cathode. The cathode i t s e l f was an aluminum wire f i t t e d as t i g h t l y as p o s s i b l e i n s i d e a quartz c a p i l l a r y tube i n such a way that the top of the aluminum wire was f l u s h with the top of the quartz cap-i l l a r y tube. A f l a t d i s k anode was permanently mounted i n the top of the discharge tube about eight inches from the cathode. Ammonia was passed through the discharge tube from a needle valve to a l i q u i d a i r cooled trap and a vacuum pump. The pressure c o u l d be c o n t r o l l e d by adjust-i n g the needle v a l v e which c o n t r o l l e d the ra t e at which ammonia entered the discharge tube. In t h i s way the pressure could be s e t at any value between .01 and 2 mm of mercury. The l i g h t from the high f i e l d r e gion of the discharge was passed out of the discharge tube by a quartz window and then focused by a quartz lens system of 15 cm f o c a l l e n g t h on the s l i t of a 3.U meter J a r r e l l SOURCE TO L IOUID A I R T R A P A N O D E C A T H O D E TO NEEDLE V A L V E •Q U A R T Z WI NDO W R U B B E R S T O P P E R F l G U R E I P L A T E I T H E 3 2 4 0 A B A N D AND H p 3 2 4 0 A 3 2 7 8 1 U ' 1 1 - i i • it i li 1 1 1 1 P B R / K N C ; H 2 5 f i 5 2 • 3 ' T 1 l 5 € • r e » 1 0 Q B R j N C H R B R A N C H 4 3 > 1 [ 10 6 . 6 4 0 4 6 8 1 0 P L A T E T H E RQ 2 | ( 0 ) l i n e s a r e a l s o s p l i t . T h e y a r e P 2 ( 2 ) a n d Q 2 ^ ( 2 ) a n d t h i s i s t h e o n l y e x p o s u r e o n w h i c h t h e y s h o w u p . T h e v a r i o u s c o m p o n e n t s o f t h e l a t t e r t w o l i n e s a r e o v e r l a p p e d s o t h a t n o r e l i a b l e d a t a may h e t a k e n f r o m t h e m . I m m e d i a t e l y t o t h e l e f t , l o n g e r w a v e l e n g t h , o f t h e Q 2 ^(0) l i n e i s a w e a k e r l i n e t h e p o s i t i o n o f w h i c h i s a f u n c t i o n o f f i e l d s t r e n g t h . T h i s l i n e i s t h e f i e l d i n d u c e d l i n e o r i g i n a t i n g f r o m t h e o t h e r l e v e l o f t h e l a m b d a d o u b l e t AHT. J = l . F o r e x p o s u r e s 2 a n d 20 t h e p o s i t i o n s o f t h e t h r e e c o m p o n e n t s o f t h e Q 2 - j ( 0 ) l i n e w e r e m e a s u r e d a t t h e s a m e h e i g h t , s a m e f i e l d s t r e n g t h , a n d t h e d i f f e r e n c e s b e t w e e n e a c h s i d e c o m p o n e n t a n d t h e c e n t e r c o m p o n e n t a r e g i v e n i n t h e d a t a . I t was n o t p o s s i b l e t o r e s o l v e a l l t h r e e c o m p o n e n t s o n e x p o s u r e s 1 8 , 1 9 t o p , a n d 1 9 b o t t o m t h e r e f o r e o n l y t h e d i s t a n c e f r o m t h e f i e l d i n d u c e d l i n e t o t h e c e n t e r c o m p o n e n t i s g i v e n f o r t h e s e e x p o s u r e s . T h e h y d r o g e n l i n e Hp s e e n i n p l a t e 2 s p l i t s i n t o • e i g h t w e l l r e s o l v e d c o m p o n e n t s . T h e t h e o r y p r e d i c t s t h a t t h e s e w i l l b e d e v i a t e d b y £ 1 0 , - 8, - 6, - k} i n u n i t s o f 0.06i(.2 E , cm""'', w h e r e E i s t h e f i e l d s t r e n g t h i n k V / c m . I n o r d e r t o n u l l i f y a n y s e c o n d o r d e r e f f e c t s t h e d i s t a n c e b e t w e e n p a i r s o f c o m p o n e n t s was m e a s u r e d . T h u s f o u r v a l u e s o f 0.06U2 E w e r e a v a i l a b l e f r o m e a c h e x p o s u r e . T h e v a l u e s o f E g i v e n a r e t h e a v e r a g e s o f t h e f o u r v a l u e s . D ATA I n t h e f o l l o w i n g d a t a t a b l e s t h e e r r o r s g i v e n a r e t h e s t a n d a r d d e v i a t i o n s o f s e v e r a l m e a s u r e m e n t s . 10 DATA EXPOSURE NUMBER 2 20 18 19 top 19 bottom ,-1 SPLITTINGS IN CM LEFT RIGHT COMPONENT COMPONENT 1 .25 1 .02 0 .63 1 .Ok 1.18 - .Ok 0.5k - .05 0.97 i .ok 0.87 - .Ok 0.89 1 .Ok FIELD STRENGTH IN kV PER CM x 10° 112 - 2 9U.8 ± 2 6 9 - 1 U8 t 2 5 8 - 2 11 . DETERMINATION OF THE DIPOLE MOMENT In order to determine the d i p o l e moment from the data given i t i s necessary to i n v e s t i g a t e the e f f e c t of an e l e c t r i c f i e l d on the molecule. The theory of the Stark e f f e c t on molecules i s given i n Penny's paper . The r e s u l t s of the theory a p p l i e d to diatomic molecules can he found i n Herzherg's "book'*'. We s h a l l present here the theory of the Stark e f f e c t on diatomic molecules. THE STARK EFFECT ON DIATOMIC MOLECULES Let a complete s e t of a t t r i b u t e s of a diatomic molecule be represented by the f o l l o w i n g quantum numbers; J , t o t a l angular momentum; M, component of J i n the f i e l d d i r e c t i o n ; X L , angular momentum along the i n t e r n u c l e a r a x i s ; P, p a r i t y ; y v , e l e c t r o n i c angular momentum along the i n t e r n u c l e a r a x i s ; S, s p i n angular momentum; i ., component of S along the i n t e r n u c l e a r a x i s ; and , remaining e l e c t r o n i c quantum numbers. The s t a t e of a diatomic molecule can then be represented by ^^XJMS A 1 IT- P \. I t i s assumed that the e f f e c t of the e l e c t r i c f i e l d i s suf-f i c i e n t l y small that we may regard i t as a p e r t u r b a t i o n on the f i e l d f r e e s t a t e s of the molecule. The v a l i d i t y of t h i s assumption i s demonstrated by the general agree-ment between p r e d i c t e d and measured Stark e f f e c t s . The p e r t u r b a t i o n h a m i l t o n i a n i s of the form H' = i er -E ( l ) where e i s the charge of the e l e c t r o n , r^ i s the p o s i t i o n v e c t o r of the i th e l e c t r o n and E i s the e l e c t r i c f i e l d 12 vector. Since diatomic molecules are a x i a l l y symmetric t h i s can be written more simply by l e t t i n g 3^  be the component of "r\ along the internuclear axis and © the angle between E and the internuclear axis. Thus H' = £e S cE cos © (2) In determining the energy change due to the perturbation i t w i l l be necessary to evaluate matrix elements of the form (c< JMSAInP| 1 e BL E cos e|dljMSU A-Pl> (3) which can be written E<V| lei l L|<* /^JMSAin.P | cos©| JMSALlip ) (U) This i s of the same form as dipole t r a n s i t i o n moments f o r AM = 0 . Thus we can use the previously derived selection rules found i n Herzberg^ on pages 2U0 to 2A4.5. We give below the s e l e c t i o n rules f o r the more common coupling schemes. 1) AJ = - 1, 0 ; J = O ^ J = 0 2) AM = O0± 1 3) Symmetric terms combine only with symmetric terms and the converse k) only lev e l s of opposite p a r i t y combine 5) odd states i n t e r a c t only with even states and the converse Selection rules which apply only to Hund's coupling cases ( a ) and ( b ) 1) A A= - 1> 0 2) A S = ° Selection rules which apply only i f both states are coupled according to Hund's case ( a ) 1) 0 2) A.XL= - 1, 0 3) A J = 0 i s forbidden f o r XI = 0 -^XL = 0. It can be seen that the matrix elements (k) w i l l be non zero between the two lambda doublets of a p a r t i c u l a r diatomic molecular l e v e l and further the mutual perturbation between a p a i r of lambda doublets w i l l be much larger than the perturbation between neighbouring r o t a t i o n a l l e v e l s . To a f i r s t order of accuracy then, we need consider only the perturbation between a pa i r of lambda doublets. (1+) i s now of the form S<C*|£e S;J<*) -^JMSAiXiP \ cose \ JMSAlJH-P 1 ) (5) The l e f t portion of which i s the dipole moment,^ , i n the state represented byO(and the right hand portion i s the average value of cos© which may i n general be determined c l a s s i c a l l y from the vector model (f i g u r e 2 ) . Thus (5) becomes Letting £ be the perturbed energy and and W2 the unperturbed energies of the lambda doublets of the molec-ular state. We can write (see page 15 of Herzberg^"). Solving (7) we get = 0 (7) V E C T O R M O D E L I E M fe 0 F I G U R E .2 15 £ = i(W 1 +W 2) ± i(Wx-W2) / 4 J 2^J E MX-L \ 2 ' ( g ) I f A = 0, no lambda d o u b l i n g , or i f the r o t a t i o n a l l e v e l s are c l o s e t o g e t h e r .then the p e r t u r b a t i o n between n e i g h -b o u r i n g r o t a t i o n a l l e v e l s w i l l be of s i g n i f i c a n c e . The ener g i e s due to t h i s p e r t u r b a t i o n are given by Van V l e c k and H i l l 9 . E _ S ^ J 2 ( l j | 7 M 2 ) ( j f - X l 2 ) _ ( ( J + l ) 2 - M 2 ) ( ( j ; l ) 2 - . p - 2 ) ) ( } ~ 2TT B \ J ^ ( 2 J + l ) ( 2 J - l ) ( J + l ) 3 ( 2 J+l ) ( 2 J + 3 ) J I f e e l i t i s wise at t h i s p o i n t to e x p l a i n the u n i t s used i n the above formulae. The energies £ , W^ , W2, and -1 -1 B are i n cm . E i s i n v o l t s p e r cm.^u i s i n v o l t s The quantum numbers J , M, and X i are of course u n i t l e s s . These u n i t s are not standard, but are convenient from an experimental p o i n t of view. DETERMINATION OP THE ELECTRIC FIELD Before going on to an e v a l u a t i o n of J J f o r the "^ TT^ J = 1 s t a t e i t w i l l be necessary to know the f i e l d s t r e n g t h . I s h a l l t h e r e f o r e g i v e a b r i e f resume of the St a r k e f f e c t on hydrogen as found i n Theory of Atomic S p e c t r a ^ . The s t a t e of a hydrogen atom can be d e s c r i b e d by: n, p r i n c i p l e quantum number; m, magnetic quantum number; k^ and k 2 , quantum numbers i n p a r a b o l i c c o - o r d i n a t e s determined from the r e l a t i o n s n = k 1+k 2+|m|+l k ± ^ 0 (10) The f i r s t order energy change, A v> , due to an i n t e r a c t i o n with an e l e c t r i c f i e l d E i n kV/cm i s g i v e n by AY = - 0.061+2 n ( k 1 - k 2 ) E ( l l ) S T A R K E F F E C T IN H Y D R O G E N T T H P 0 T 12 8 4 2 4 6 ~E r 10 14 F I G U R E 3 17 The correct expression f o r A? including second order effects i s A?= - a E + b E 2 The constants a and b may be found i n the Theory of Atomic Spectra . By measuring the separation of corresponding pairs of components we measure the quantity (a E + b E 2 ) - (-a E + b E 2 ) = 2 a E i n which second order terms have been eliminated. The f i r s t order Stark pattern f o r Hp> i s shown i n figure 3. The s p l i t t i n g i s i n units of 0.06lj.2 E and the lengths of the l i n e s are proportional to the t h e o r e t i c a l i n t e n s i t i e s . The p o l a r i z a t i o n of the component i s indicated by drawing i t i n the T T , p a r a l l e l to E , or CT, perpendicular to E , h a l f plane. l21( THE R Q Q 1 ( 0 ) LINE Let us apply the foregoing to the Q 2 ^(0) l i n e . This l i n e (shown i n figures U and 5) i s the r e s u l t of a tran-7 -2. _ s i t i o n from Tf ]_ J = 1 to J = 1. In the lower state, ^£_~ J = 1, there i s no f i r s t order Stark e f f e c t since J\ = 0 ( no lambda doubling) and_TL= 0 . Most of the Stark s p l i t t i n g i s i n the upper, T f ^ J = 1, Level. For this l e v e l J = 1,S1 = 1, M = 0,1. The M = 0 l e v e l s are un-perturbed i n f i r s t order and the M = 1 l e v e l s are s h i f t e d apart by an ammount £-. Thus l e t t i n g the energy of the unperturbed RQ 2^ ( 0 ) l i n e *>e zero and the lambda doubling be _A_ and substituting these values i n ( 8 ) ; £• i s given by E N E R G Y L E V E L S 3 3 6 0 A B A N D 18 0 3-TT, 0 N 1 J 3 i J 3 2 : 0 3 N" 3: Q _ O fa OJ a OS pi cr .0 J": - 3 4 :?3 =0< F I G U R E 4 R Q 2 , ( 0 ) 19 4-J ' = l _ J» = | |M| I 0 0 F I E L D I N C R E A S ING REGION.OF MAXIMUM FIELD E N E R G Y F IGURE 5 20 or . * ( 1 3 ) With reference to the data and plate 3 , £• i s the smaller of the two s p l i t t i n g s measured and (6- + A ) the larger. The Stark e f f e c t on this l i n e i s shown i n figu r e 5. Using the data from exposures 2 and 20 we can determine £ and A « Using the value of A so determined, values of £ can be determined from the data from exposures 18, 19 top, and 19 bottom and i n this way a value o f d e t e r -mined from these exposures. The average value o f ^ i s O.63 - .02 cm~\ This i s i n good agreement with the value 0.61+ cm-"*" determined 3 + from the graph i n Dixon's paper . Using .A = 0 . 6 3 - .02 cm"^ " we derive the following from the data. REPINED DATA EXPOSURE £ ( + A ) E 2 NUMBER IN CM - 1 (VOLTS/CM)2 X 1 0 8 2 0.78 - .06 125 - h 20 0.6U - .07 9 0 - k 18 0 .33 1 .17 hi ± 2 19 top 0 .21 - .12+ 22 - k 19 bottom 0 .23 - .1U 3k 1 U £ (6 +A-) i s plotted as a function of E i n figure 2 — 2 6. The slope o f this graph, ~ $ i n volts , was deter-mined by the method of least squares f i t t i n g and the value o f J j so obtained i s X) = .960 - .03 Debye e ce + A ) vs E 2 F I G U R E 6 Of the seven l i n e s with TT]_ J = 1 f o r an upper l e v e l only the l i n e Q 2 1(0) i s s u f f i c i e n t l y f a r from other l i n e s to allow a measurement of the s p l i t t i n g s . Therefore the only a v a i l a b l e value of}> f o r this state i s the one just given. A rough measurement of the s p l i t t i n g s f o r the li n e s P 2 (2) and PQ 2^ (2) was i n reasonable agreement, 20^, with this value of JJ . It i s unfortunate that the dipole moment may only 3 be determined f o r the IT ^  J = 1 state. It i s f e l t however that p i s e s s e n t i a l l y independent of jfland J and i s therefore the same for a l l l e v e l s of the A state. 23 CORRECTIONS MIXED COUPLING T h e v a l u e of y J i n (1U) i s the apparent d i p o l e moment 3 d e r i v e d from data on the T T ^ J = 1 l e v e l . This l e v e l i s "-not a pure s t a t e hut i s mixed s l i g h t l y w i t h the ^TTQ J = 1 level„ The c o r r e c t wave f u n c t i o n i s t h e r e f o r e of the form a ( 5 T T 1 J=l) + b(V Q J=l) where () i n d i c a t e s the pure wave f u n c t i o n of the s t a t e i n d i c a t e d * The f a c t o r s a and b may be determined by formula ( V, 78 ) i n Herzberg from the matrix elements f o r the i n t e r a c t i o n between the two s t a t e s given by Van 9 V l e c k and H i l l and shown below. 3 l f 1 B(X+1) B(2X ) 2 3 l f 0 B(2X)^ B(X+1)-A (15) X=*J(J+l) ( 1 6 ) A i s the s e p a r a t i o n of the and ^TTQ s t a t e s . B i s the r o t a t i o n a l c onstant f o r the ^TT" s t a t e , a = .8572 (17) b = .5150 (18) The average value of cos & i s {a( 3-Tr i,J=l)+b( 3- Tr 0 SJ=l)|cose | a ( 3 - T r i SJ=l)+b( 3-rr 0 ?J=l)yi9) Which i s of the same form as a d i p o l e t r a n s i t i o n moment f o r fa M = 0, The onl y non zero term i s t h e r e f o r e < a 2 ( 3 f f 1 ? J = l ) | c o s © j ( 3 i r r J = l ) ) (20) 2k 2 Thus the c o r r e c t i o n f a c t o r a = .73k7 must "be a p p l i e d to the o l d value ofjj „ Therefore the c o r r e c t e d value of J j i s / J =. = 1.31 1 .03 Debye. (21) SECOND ORDER EFFECTS There i s a second order Stark e f f e c t on "both the J7T^ J = 1 and the ^ J = 1 s t a t e s . There i s of course a mutual Stark p e r t u r b a t i o n between a l l r o t a t i o n a l l e v e l s . In general t h i s p e r t u r b a t i o n i s very much l a r g e r f o r neighbouring r o t a t i o n a l l e v e l s and so we s h a l l determine the p e r t u r b a t i o n only between neighbouring r o t a t i o n a l l e v e l s . The i _ J = 1 s t a t e i s the lowest r o t a t i o n a l s t a t e . Any second order e f f e c t w i l l t h erefore cause a s h i f t to lower energies. The M = 0 l e v e l w i l l be s h i f t e d s l i g h t l y more than the M = 1 l e v e l . The e f f e c t of t h i s i s to s h i f t a l l components of the R Q 2 1 ( 0 ) l i n e toward higher energies and to s l i g h t l y broaden them. These e f f e c t s were e l i m i n a t e d from the data by measuring a l l the com-ponents at the same height ( f i e l d strength) on the p l a t e . The second order e f f e c t s on the n f j J = 1 l e v e l are as f o l l o w s . The M = 0 l e v e l s are s h i f t e d down by an ammount The M = 1 l e v e l s are s h i f t e d down by an ammount A ? ( M = 1) , k * f w ^ ( 2 3 ) 2 2 1 E~>0 Thus the outer components are s h i f t e d x -jp^fg— l e s s 25 than the center component. This difference i n the s h i f t s w i l l have a d i r e c t e f f e c t on the measured values of A , £ , and + A . . Evaluating this difference using jj = 1»3 Dehye, E = 111,000 Volts/cm, and B = l6„3 cm"1 we get which i s not s i g n i f i c a n t compared to the errors i n measurment. ERRORS A l l errors quoted are standard deviations. Assuming; the theory of the Stark e f f e c t and the mixed coupling correction are accurate this i s a r e a l i s t i c measure of the possible error i n the dipole moment. 1_ = 0.0025 cm' (2h) 26 SUMMARY The value of the d i p o l e moment of NH i n the A 3Tf J = 1 s t a t e i s 1«31 - <>03 Debye, I t would he of i n t e r e s t to check the dependence ofjO on J and the v i b r a t i o n a l quantum number, v 0 To do t h i s i t would be necessary to use a spectrograph of greater d i s p e r s i o n and a discharge tube g i v i n g g r e a t e r e l e c t r i c f i e l d s . , The d e t e r m i n a t i o n of the d i p o l e moment i n the c hr -i 0 and a A 4 s t a t e s from data on the 32U0 A band should be completed i n the near future„ T h i s w i l l g i v e an id e a as to how the d i p o l e moment changes with e l e c t r o n i c con-figuration„ 27 B I B L I O G R A P H Y l o H e r z o e r g , G., M o l e c u l a r S p e c t r a a n d M o l e c u l a r S t r u c t u r e , I S p e c t r a o f D i a t o m i c M o l e c u l e s , New Y o r k , V a n N o s t r a n d , (1950). 2„ P e a r s e , R„ W„ B. , 321+0 B a n d o f NH. P r o c e e d i n g s o f t h e R o y a l S o c i e t y , 11+3, 112, (193U). 3 . D i x o n , R o N. , T h e 0-0 a n d 1-0 B a n d s o f t h e A ( ^ H T ) - X ( 3'fc) S y s t e m o f NH, N a t i o n a l R e s e a r c h C o u n c i l N u m b e r 5353. k. F u n k e , G„ W B, D i e NH B a n d e n b e i X 3 3 6 0 > Z e i t s c h r i f t F u r P h y s i k , 99 , 7 8 7 , ( 1935) . 5. P e n n y , W. G. , T h e S t a r k E f f e c t i n B a n d S p e c t r a , P h i l o s o p h i c a l M a g a z i n e , 11, 602, (1931) . 6. C o n d o n , E„ U. a n d S h o r t l e y , G. H., T h e T h e o r y o f A t o m i c S p e c t r a , C a m b r i d g e , C a m b r i d g e U n i v e r s i t y P r e s s , (1963) . 7. J e v o n s , W„, R e p o r t o n B a n d S p e c t r a o f D i a t o m i c M o l e c u l e s , T h e P h y s i c a l S o c i e t y , C a m b r i d g e , C a m b r i d g e U n i v e r -s i t y P r e s s , ( l 9 3 2 ) o 80 V a n V l e c k , J . H., T h e T h e o r y o f E l e c t r i c a n d M a g n e t i c S u s c e p t i b i l i t i e s , O x f o r d , O x f o r d U n i v e r s i t y P r e s s , ( l 9 3 2 ) o 9. V a n V l e c k a n d H i l l , On t h e Q u a n t u m M e c h a n i c s o f t h e R o t a t i o n a l D i s t o r t i o n o f M u l t i p l e t s i n M o l e c u l a r S p e c t r a , P h y s i c a l R e v i e w , 3 2 , P. 250 - 272, (1928) . 10o S y m b o l s , U n i t s , a n d N o m e n c l a t u r e i n P h y s i c s , P h y s i c s T o d a y , ( J u n e 1962). 

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