@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix skos: . vivo:departmentOrSchool "Science, Faculty of"@en, "Physics and Astronomy, Department of"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCV"@en ; dcterms:creator "Phelps, Daniel Holdsworth"@en ; dcterms:issued "2011-08-31T20:29:49Z"@en, "1966"@en ; vivo:relatedDegree "Doctor of Philosophy - PhD"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description """The electronic emission spectra of the OH and CH molecules in applied electric fields up to 68,000 v/cm have been observed. These spectra show Stark splittings, broadenings and field-induced, parity-forbidden lines. The electric dipole moment of the molecules has been determined for OH in the ²π electronic state and CH in both the ²π and ²∆ electronic states from Stark effects on transitions to the following levels: [formula omitted] Electric fields were determined from Stark splittings in hydrogen Balmer lines. The Stark spectra were produced in the high field region of a low pressure glow discharge. This technique is well suited for the study of short lived and chemically reactive molecules in both their ground and excited, electronic states."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/37046?expand=metadata"@en ; skos:note "STARK EFFECT ON EMISSION SPECTRA OF DIATOMIC MOLECULES by DANIEL HOLDSWORTH PHELPS B.A., Reed C o l l e g e , i960 M.A., Dartmouth C o l l e g e , 1962 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department o f PHYSICS We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 19^6 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f t he r e q u i r e m e n t s f o r an advanced deg ree at the 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 , I a g r e e t h a t t h e 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 a g r e e 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 o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i -c a t i o n o f 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 o f Physics The U n i v e r s i t y o f B r i t i s h Co lumbia Vancouver 8, Canada Date May 12, 1966 The University 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 of DANIEL H. PHELPS B.A., Reed College., 1960 M„A„, Dartmouth College., 1962 THURSDAY, MAY 12, 1966, AT 2:30 P.M. IN ROOM 303, HENNINGS COMMITTEE IN CHARGE Chairman: D. H. Chitty A. J, Barnard R„ A. Nodwell A. M. Crooker E. A. Ogryzlo F. W. Dalby R„ D. Russell External Examiner: A. V. Jones University of Saskatchewan . at Saskatoon Research Supervisor: F. W. Dalby STARK EFFECT IN EMISSION SPECTRA OF DIATOMIC MOLECULES ABSTRACT The infuence of an external e l e c t r i c f i e l d on atomic or molecular spectra, known as the Stark e f f e c t , t y p i c a l l y leads to s p l i t t i n g s , s h i f t s , broadenings and changes of i n t e n s i t y i n spectral l i n e s . The Stark e f f e c t on the e l e c t r o n i c emission spectra of the OH and CH molecules was studied for external e l e c t r i c up to 68,000 volts/cm. The Stark spectra were produced i n the high e l e c t r i c f i e l d region of a low pressure glow discharge. (The e l e c t r i c f i e l d s were determined from Stark s p l i t t i n g s i n hydrogen Balmer l i n e s . ) From ob-servations of the Stark e f f e c t on the molecular spectra the e l e c t r i c dipole moments were determined for the OH 2 ~TT* molecule i n the TT e l e c t r o n i c state and for the CH 2 - 2 molecule i n both the TT a r l c j A e l e c t r o n i c states. From t r a n s i t i o n s to the following l e v e l s the values of the dipole moment were found to be: OH 2 \" ^ l / 2 3 J = 1/2, v = 0 1 .73 2 t 0.02 Debye 2TT3/2, J =. 3/2, v = 0 1 .637•+ 0.03 •2TTi/2. J = 1/2, V = 1 1 .69 2 T 0.04 CH 2TTi/2> J = 1/2, V = 0 1 .46 + 0.06 2 A 3 J = 7/2, V = 0 1 .13 t 1 5 ?° The f i r s t reported observation of resolved f i r s t order Stark e f f e c t s on the el e c t r o n i c spectra of a diatomic molecule resulted from this work. The tech-niques developed i n t h i s i n v e s t i g a t i o n are well, suited for the study of short l i v e d and chemically reactive molecules i n both t h e i r ground and excited e l e c t r o n i c states. GRADUATE STUDIES F i e l d of Study; Molecular Spectroscopy Elementary Quantum Mechanics Waves Quantum Theory of Solids Spectroscopy Molecular Spectroscopy Advanced Spectroscopy W. Opechowski J . Co Savage R. Barrie A. M„ Crooker F. W. Dalby A. J . Barnard PUBLICATIONS R.W. Christy and D.H. Phelps, \"Production of V3 i n KCL by X Rays\", Physical Review 1_24, 1053 (1961). D.H. Phelps and F.W. Dalby, \"Optical Observations of the Stark Effect, on OH\", Canadian Journal of Physics 43, 144 (1965) . D.H. Phelps and F.W. Dalby, \"Experimental Determina-t i o n of the E l e c t r i c Dipole Moment of the Ground El e c t r o n i c State of CH\", Physical Review Letters 16, 3 (1966) i i ABSTRACT The e l e c t r o n i c emission s p e c t r a of the OH and CH molecules i n a p p l i e d e l e c t r i c f i e l d s up to 68,000 v/cm have been observed„ These s p e c t r a show St a r k s p l i t t i n g s , broadenings and f i e l d -induced, p a r i t y - f o r b i d d e n l i n e s . The e l e c t r i c d i p o l e moment of the molecules has been determined f o r OH i n the ZTf e l e c t r o n i c s t a t e and CH i n both 'the 2 T T and 2/^ e l e c t r o n i c s t a t e s from Stark e f f e c t s on t r a n s i t i o n s - to the f o l l o w i n g l e v e l s ; OH 2 T T ! / 2 , J = 1/2, v - 0 1.732 * 0.02 Debye 2 t t 3 / 2 » j \" 3/2, v = 0 1 . 6 3 7 ± 0.03 CH 2 T T 1 / 2 , J = 1/2, v = 1 1.692 * ° » o i + 2 ^ l / 2 > J ™ i / 2 , v - 0 1.^6 ± 0.06 2A , J - 7/2, v - 0 1.13 1 15% E l e c t r i c f i e l d s were determined from Stark s p l i t t i n g s i n hydro-gen Balmer l i n e s . The Stark s p e c t r a were produced i n the high f i e l d r e g i o n of a low pressure glow d i s c h a r g e . This technique i s w e l l s u i t e d f o r the study of short l i v e d and c h e m i c a l l y r e a c t i v e molecules i n both t h e i r ground and excited, e l e c t r o n i c s t a t e s . i l l TABLE OF CONTENTS CHAPTER I: INTRODUCTION 1 Footnotes f o r Chapter I 5 CHAPTER I I * THEORETICAL PRELUDE 7 Energy of a di a t o m i c molecule In an e l e c t r i c f i e l d ... 7 M a t r i x elements of the p e r t u r b a t i o n 8 The p e r t u r b a t i o n and p a r i t y 9 V e c t o r model treatment of Hund 1 s c o u p l i n g case (a) ... 10 The s e c u l a r equation f o r lambda doublet l e v e l s lk Starlc e f f e c t spectrs. . . . • . • . • . . • • . . • • • » « . « « . « © o « . . « . . . 15 Rigorous treatment of matrix elements ................. 19 Coup l i n g intermediate between Hund's case (a) P a r i t y mixing and t r a n s i t i o n s between perturbed lambda dOUbletS » . o » o f t » « o o o O 0 . o » e . » e o . » . o w 0 « a . 0 o . . o . o » 27 Second order Stark e f f e c t s 31 Footnotes CHAPTER I I I : EXPERIMENTAL DETAILS % E l e c t r i c d i s c h a r g e tube 36. P r o d u c t i o n of OH and CH e l e c t r o n i c emission s p e c t r a ^0 Observing the St a r k e f f e c t ........................... 4-2 Determination of the e l e c t r i c f i e l d s t r e n g t h ......... 43 Footnotes f o r Chapter I I I ............................ 4-5 i v CHAPTER IV: EXPERIMENTAL OBSERVATIONS . 46 S t a r k e f f e c t on the OH, 22Z +~* 2 T T hand ................ 46 Stark e f f e c t on the CH, Z^~-*ZJJ band ................ 54 Stark s p l i t t i n g s i n . the atomic hydrogen Balmer St a r k e f f e c t on the CH, 2A~* 2 77\" band 58 Experimental c o n d i t i o n s f o r spectrograms .............. 62 Measurements 62 A n a l y s i s o f Stark e f f e c t s p e c t r a 69 Determination of e l e c t r i c d i p o l e moments .............. 77 Summary ..... o o . . « . . . . . . . . . . . . . . . . . « . . © . © . . © . . * . . » . . o . © 87 Footnotes f o r Chapter IV .............................. 90 CHAPTER V: CONCLUSION AND SUGGESTION FOR FURTHER STUDY .... 91 Suggestions f o r f u r t h e r work 91 V LIST OF TABLES TABLE I: TABLE I I : TABLE I I I : TABLE IV: TABLE V: TABLE VI: TABLE V I I : TABLE V I I I : TABLE IX: TABLE X: TABLE XI: Experimental C o n d i t i o n s f o r Spectrograms used i n F i g u r e s , Observed Stark S p l i t t i n g s i n OH, z£?-~ 277 Band and i n hydrogen Balmer H^ « o » e « « o o o Observed and C a l c u l a t e d P o s i t i o n s o f f i e l d -induced, p a r i t y - f o r b i d d e n l i n e s i n the 2 Z * ~ > 2 7 T , (0,0), band of OH ................ Observed Stark S p l i t t i n g s i n CH, 2Z~^2TT Band and i n hydrogen Balmer Hy ............. Simultaneously Observed Stark S p l i t t i n g s i n CH and OH -> TT* Bands Experimental C o n d i t i o n s f o r P l a t e s Used to Determine OH and CH E l e c t r i c D i p o l e Moments . OH E l e c t r i c Dipole Moments Derived from S'tfl.rk SpXi.*fc\"tintrs O 0 o o » » » « e t > « o » 6 e o » » « . # o * 6 * * « . C o r r e c t e d Stark S p l i t t i n g s i n OH z2?-> 2 7 T Band 0 O O O 6 0 O C 6 t> 4» « O « « « O a o a e o • o o © o Corrected Low D i s p e r s i o n Stark S p l i t t i n g s i n CH 2£--.*2T T Band ........ C o r r e c t e d , Simultaneous Observed Stark S p l i t t i n g s i n CH and OH 2 £ \" - » 2 T T Bands ... E l e c t r i c Dipole Moments f o r the OH and CH Molecules o o o o c o o e o o o o o « o O O 4 O 0 O O O O * ) < I © • o o 63 64 66 68 70 71 78 80 83 85 89 v i LIST OF FIGURES Figure 2 . 1 : Figure 2 . 2 ; Figure 2 . 3 : V e c t o r diagram of a diatomic molecule i n an e l e c t r i c f i e l d , Hund'a case (a) o o o e o o o o i i Stark e f f e c t on OH, P i 2 ( l ) and P i ( l ) l i n e s . Zero f i e l d and f i e l d - i n d u c e d , p a r i t y -f o r b i d d e n t r a n s i t i o n s a s s o c i a t e d with 0^(4) and Q 2 1 ( 4 ) l i n e s of OH o o o o o o o o o o o o o o o o o o o o e o Figure 2 . 4 ; Zero f i e l d and f i e l d - i n d u c e d , p a r i t y -F igure 2.5' Figure 3 . 1 : Fie-ure 4 . 1 : F i g u r e 4 . 2 : Figure 4 . 3 : Figure 4 . 4 : Figure 4 . 5 ? Figure 4 . 6 : F i g u r e 4 . 7 : F i g u r e 4 . 8 : Figure 4 . 9 : Figure 4 . 1 0 : f o r b i d d e n t r a n s i t i o n s between lambda d o u b l e t s . Stark e f f e c t on CH, Q l c ( 3 ) and Q l d ( 3 ) l i n e s M o d i f i e d Lo Surdo discharge tube e o e e o o e o o o 0 0 Allowed t r a n s i t i o n s to lowest r o t a t i o n a l l e v e l s i n OH 2yr and. 2rT 3 / s t a t e s ............ Stark e f f e c t on OH, 2 j r + - » 2 T T , ( 0 , 0 ) band . Stark, e f f e c t on OH . o o o o o o o e o o e u o o o o o o o w e f r Stark e f f e c t on OH, 2 ]T% 2 IT, ( 1 , 1 ) band ... Stark e f f e c t on CH, 2 £ ~ - * 2 T T . ( 0 , 0 ) band ... Stark e f f e c t on CH, 2 5 T ~ - > 2 T T , ( 0 , 0 ) band f o r t h r e e values of e l e c t r i c f i e l d S tark e f f e c t on hydrogen Baimer H y Stark e f f e c t on CH, ZA~* 2 T T b a n d 0 0 0 D 0 0 Q 4 0 0 0 e « o e » o o o o e o C o r r e c t e d Stark s p l i t t i n g , A V ' , v s . e l e c t r i c f i e l d s t r e n g t h , E, f o r OH, R 2 ( l ) , ( 0 , 0 ) l i n e F i r s t - o r d e r Stark s p l i t t i n g of CH, P 1 2 ( l ) l i n e v s . f i r s t - o r d e r S tark s p l i t t i n g of OH, R 2 ( l ) l i n e D O O O O O o o o o o t - o o e o o o o o e c o o 0 0 0 0 0 0 0 11 16 18 29 32 37 47 48 52 53 55 57 59 60 79 86 v i ACKNOWLEDGEMENTS I wish to thank P r o f e s s o r F . W. Dalby, ray re s e a r c h d i r e c -t o r , f o r h i s h e l p f u l a s s i s t a n c e and c r i t i c i s m throughout t h i s work. This work was supported by the N a t i o n a l Research C o u n c i l of Canada. CHAPTER I • INTRODUCTION The i n f l u e n c e of an e x t e r n a l e l e c t r i c f i e l d on atomic or molecular spectra, known as the Stark e f f e c t , t y p i c a l l y pro-duces s p l i t t i n g s , s h i f t s , broadenings and changes i n i n t e n s i t y i n s p e c t r a l l i n e s . This study w i l l be concerned w i t h the Stark e f f e c t on the e l e c t r o n i c emission s p e c t r a of diatomic molecules. Observations of the Stark e f f e c t on such molecular s p e c t r a provide a means of determining the e l e c t r i c d i p o l e mo-' ment of a molecule. The Stark e f f e c t on an atomic spectrum was f i r s t observed f o r hydrogen. I t was observed independently by S t a r k 1 and by LoSurdo 2 i n 1913. The Stark e f f e c t on the hydrogen Balmer l i n e s provided a s u c c e s s f u l t e s t f o r the Bohr theory of the hy-drogen atom. ^ The Stark e f f e c t on various atomic, s p e c t r a was studie d e x t e n s i v e l y u n t i l the mid-1930'e. (A review a r t i c l e by Ver l e g e r provides many references on t h i s subject.^) Several t h e o r e t i c a l s t u d i e s of the Stark e f f e c t on molec-u l a r band spectra were reported during the 1920'a. ^ I n 1931» i W. G. Penny published a t h e o r e t i c a l paper covering the Stark e f f e c t on both symmetric top and asymmetric top molecules.-' In h i s i n t r o d u c t i o n he s a i d t h a t w i t h the Increasing Importance of the subject of band spectra h i s study had been undertaken . in'the hope that the experimental d i f f i c u l t i e s i n v o l v e d i n t e s t i n g the r e s u l t s would soon be overcome.\"-' Penny s p e c i f -i c a l l y s tated i n h i s conclusion that f o r a diatomic molecule 2 In an e l e c t r o n i c s t a t e w i t h a component of angular momentum, along the I n t e r n u c l e a r a x i s ( i . e . a TT, A f e t c . s ta te ) and w i t h a non-van i sh ing e l e c t r i c d i p o l e moment \" . . . there w i l l be a s p l i t t i n g , quad ra t i c at f i r s t and l i n e a r as soon as the energy s h i f t s become la rge compared w i t h the n a t u r a l \\ - & o u ~ -bl ing I n t e r v a l s . \"5 Penny a l s o s p e c i f i c a l l y s t a ted tha t there would be no apprec i ab l e c o n t r i b u t i o n to the Stark e f f e c t from e l e c t r o n i c X s t a t e s ( f o r which there i s no component o f angu-l a r momentum a long the I n t e r n u c l e a r a x i s ) . !*:-r:.r--.;• Y I I J ^ . . ^ . . : . : . . ^ . . . Contemporary t o Penny's work, numerous exper imenta l s t u d -i e s were made o f the Stark e f f e c t on the band spec t r a of the 6-11 hydrogen molecule . The observed s h i f t s i n frequency obeyed a q u a d r a t i c r e l a t i o n s h i p to the a p p l i e d e l e c t r i c f i e l d . (The observed t r a n s i t i o n s d i d i n v o l v e an e l e c t r o n i c TT s t a te but s ince from symmetry the molecule can have no permanent e l e c -t r i c d i p o l e moment only a second order S ta rk e f fec t was ob-served . ) The 2 X - 2 £ (0,0) band at 39l4# and (0,1) band at 4278$ were observed i n e l e c t r i c f i e l d s up to 280 kV? no e p l i t -t i n g s were observed. (Not ice tha t the N 2 molecule can have no permanent e l e c t r i c d i p o l e moment. Thus i t i s not s u r p r i s i n g that no apprec iab le Stark e f f e c t was observed.) Experiments which c o u l d have shown a f i r s t order S ta rk e f f ec t were made oh the CO^ comet t a i l band® w i t h e l e c t r i c f i e l d s up to 280 kV/cm and on the CO b a n d s 1 2 at 4835, 4511, 4393, and 4123$ w i t h e l e c -t r i c f i e l d s of 115 kV/cm. Both of these experiments showed n e i t h e r d isplacements nor s p l i t t i n g s . These negat ive r e s u l t s cou ld be due to the r a the r low d i s p e r s i o n used. (The g rea te s t 3 d i s p e r s i o n repor ted was k&/aua used i n the study of the S t a rk ef-fec t on CO.) A l s o , f o r the CO molecule i t i s now known from microwave measurements that the d i p o l e moment i s only 0.112 Debye?-3 i n the ground s t a t e . H e r z b e r g 1 ^ i n d i s c u s s i n g the f i r s t o rder S tark e f f e c t used the example of a J = 1, 17T l e v e l ; an e l e c t r i c d i p o l e moment of , 1 Debye; and an e l e c t r i c f i e l d of 10 kV/em which corresponds to an o v e r a l l s p l i t t i n g of 0.168 c m \" 1 . He s a i d : \"No such s p l i t -t i ngs have yet been observed even though they are w i t h i n reach of o r d i n a r y s p e c t r o s c o p i c methods.\" The r e s u l t s r e p o r t e d here i n c l u d e the f i r s t r epor ted ob-s e r v a t i o n s of f i r s t order S ta rk s p l i t t i n g s i n molecu la r e l e c -t r o n i c s p e c t r a . 1 ^ This work p rov ided the on l y pub l i shed exper-imenta l va lue of the e l e c t r i c d i p o l e moment of the CH mole-c u l e . 1 ^ A l s o 9 at i t s time o f p u b l i c a t i o n the value o f the e l e c -t r i c d i p o l e moment o f the OH molecule determined from t h i s work 1 ' ' ' was more accura te than e a r l i e r va lues determined us ing microwave techn iques . Knowledge of the e l e c t r i c d i p o l e moment of a molecule i s important because o f fundamental In te res t and a l s o as a t e s t f o r t h e o r e t i c a l l y computed wave f u n c t i o n s . R e c e n t l y , knowledge of the e l e c t r i c d i p o l e moment o f molecules has a l s o become ; impor-tant to r a d i o astronomers. For example, to determine the d e n s i -ty of OH molecules from observed microwave a b s o r p t i o n 1 ^ i n the I n t e r s t e l l a r medium the e l e c t r i c d ipo l e moment must be known. The d ipo le i moment o f the CH molecule i s a l s o c u r r e n t l y of impor- : tance i n e s t ima t ing the s t r eng th \"of the lambda doublet t r a n s l -i . t i o n f o r the J « 1/2 l e v e l of the 2T7 e l e c t r o n i c ground s t a t e . Douglas and E l l i o t t 1 ? h a V e determined t h i s lambda d o u b l i n g to be 3,400 Mc/sec„ The Stark e f f e c t on the s p e c t r a . r e p o r t e d here was produced i n a m odified L o S u r d o 2 type discharge tube. This technique i s p a r t i c u l a r l y u s e f u l f o r studying the Stark e f f e c t on the s p e c t r a of short l i v e d and c h e m i c a l l y r e a c t i v e s p e c i e s : i n both t h e i r ground and e l e c t r o n i c a l l y e x c i t e d s t a t e s . M o l e c u l a r e l e c t r i c d i p o l e moments have been determined from measurements of d i e l e c -t r i c constant, from microwave•observations of the second order Stark e f f e c t on lambda doublet l e v e l s and from molecular beam experiments using resonance techniques. However, these conven-t i o n a l techniques are g e n e r a l l y a p p l i c a b l e o n l y to s t a b l e mole-cul e s i n t h e i r e l e c t r o n i c ground s t a t e . In a d d i t i o n to the work r e p o r t e d here the LoSurdo tech-nique has a l s o been s u c c e s s f u l l y a p p l i e d to determine the e l e c -t r i c d i p o l e moment o f the NH molecule i n three e l e c t r o n i c e x c i t -ed s t a t e s : 2 0 A 3TT, a X A , and c - ^ T T o P r e s e n t l y t h i s t e c h -nique i s being used to study the Stark e f f e c t on the s p e c t r a of the HCl molecule. C A-5 Footnotes f o r Chapter I 1. J . S t a r k , Ann. Phys ik j£,, 965 (1914). 2. A . Lb- Surdo, Al t - t i i . Accad. L l n c e l 22, 665 (1913). 3. See f o r example, E. U . Condon and G. H . S h o r t l e y , The Theory of Atomic Spec t ra (Cambridge U n i v e r s i t y P re s s , Cambridge, England , 1935), p . 397. 4. H . V e r l e g e r , E r g i b . e x a k t . Na tu rwis s . 18, 99 (193'9) . 5. W. G. Penny, P h i l . Mag. 11, 602 (1931). •? 6. J . K . L . . M c D o n a l d , P r o c . Roy. Soc. (London) 123, 103 (1929). 7. , P r o c . Roy. Soc. (London) 131, 146 (193D. 8. W. Rave, Z. P h y s i k ^ , 72 (1935). 9. H . S n e l l , Trans . Roy. Soc. (London) 234, 115 (1935). 10. H . Hasunuma, P r o c . Phys . -Ma th . Soc. Japan 18, 469 (1936). 11. J . S. F o s t e r , D . C . Jones, and S. M. Neamtam, Phys . Rev. 51, 1029 (1935). 12. B . Svenson, Z . Phys ik 107., 485 (1937). 13. C. A . Bur rus , J . Chem. Phys . 28, 427 (1958). 14. G. Herzberg , M o l e c u l a r Spec t r a and M o l e c u l a r S t r u c t u r e . I . Spec t ra of Diatomic Molecu les (D. Van Nostrand C o . , New Y o r k , 1950), Second e d i t i o n , p . 308. 15. D. H . Phelps and. F . W. Dalby , paper presented at the Sympo-sium on M o l e c u l a r S t ruc tu re and Spect roscopy, The Ohio State U n i v e r s i t y , Columbus, Ohio , June, 1963-16. D. H. Phelps and F . W. Da lby , Phys. Rev. L e t t e r s 16, 3 (1966). 17. D. H . Phelps and F . W. Dalby , Can. J . Phys . 4 ,^ 144 (1965). 18. S. Weinreb, A . H . B a r r e t t , M. L . Meeks, and J . C. Henry, Nature 200, 829 (1963). 19. A . E . Douglas and G .A . E l l i o t t , Can. J . Phys. 4 ,^ 496 (1965). 1 T. A. R. Irwin and F. W . Dalby, Can. J . Phys. 43, 1766 (1965). Mr. S . Y. Wong i s completing h i s M. Sc. t h e s i s at U.B.C. on t h i s t o p i c under the d i r e c t i o n of Dr. F. W. Dalby. CHAPTER I I THEORETICAL PRELUDE One observes tha t the S ta rk e f fec t a l t e r s both the f r e -quency and i n t e n s i t y of e l e c t r o n i c emiss ion s p e c t r a l l i n e s . A s we w i l l see, t h i s i s the consequence of a p e r t u r b a t i o n of the r o t a t i o n a l energy l e v e l s due to the i n t e r a c t i o n of the a p p l i e d e l e c t r i c f i e l d and the average va lue of the e l e c t r i c d i p o l e mo-ment i n the d i r e c t i o n of the e l e c t r i c f i e l d . A l l the observed fea tures of the S t a rk e f f ec t on the spec t r a of a d i a tomic mole-cu le can be p r e d i c t e d and the mathematical r e l a t i o n s h i p s needed to determine e l e c t r i c d i p o l e moments w i l l be obtained by answer-ing the f o l l o w i n g ques t i ons : 1) How does one desc r ibe the i n -t e r a c t i o n of the a p p l i e d e l e c t r i c f i e l d and the charge d i s t r i b u -t i o n o f the molecule? 2) T r e a t i n g t h i s i n t e r a c t i o n as a p e r t u r -ba t i on u s i n g quantum mechanics, when does t h i s i n t e r a c t i o n have a nonzero matr ix element? 3) How does the p e r t u r b a t i o n a l t e r the energy of the molecule? 4) How does the p e r t u r b a t i o n e f fec t the cha rac t e r of the molecu la r energy l e v e l s ? Energy o f a d ia tomic molecule i n an e l e c t r i c f i e l d The energy a s s o c i a t e d w i t h a d i s t r i b u t i o n o f e l e c t r o n s i n -t e r a c t i n g w i t h an e x t e r n a l e l e c t r i c f i e l d can be found by sum-ming the c o n t r i b u t i o n due to each charge. For the d i a tomic molecule l e t us take the co -o rd ina t e o r i g i n at the cen te r of p o s i t i v e charge. The p e r t u r b a t i o n energy w i l l be of the form: V = erj/1? , (2.1) 8 where e Is the e l e c t r o n i c charge, r\\ i s the p o s i t i o n of the i t h 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 s t r e n g t h . Equation (2.1) w i l l now be rexirritten i n terms of the e l e c t r i c d i p o l e moment. F i r s t , s i n c e the molecule i s a x i a l l y symmetric, on l y the compo-nent of the p o s i t i o n v e c t o r a l o n g the i n t e r n u c l e a r a x i s , ^ , w i l l c o n t r i b u t e to ex p r e s s i o n (2.1). Thus, the c o n t r i b u t i o n to the energy from an i n d i v i d u a l e l e c t r o n may be w r i t t e n : e f^n°Es where n i s a u n i t v e c t o r along the i n t e r n u c l e a r a x i s . Second, we a l s o see that equation (2.1) could be ev a l u a t e d by f i r s t sum-ming over er^, s i n c e the e l e c t r i c f i e l d v e c t o r may be taken as a constant, and then the dot product could be taken. T h e r e f o r e , equation (2.1) w i l l be w r i t t e n : V - ( - e ^ ^ ) n - E = -p-E . (2.2) We see t h i s e x p r e s s i o n i s c o n s i s t e n t with a d e s c r i p t i o n o f the — > i n t e r a c t i o n energy which uses a d i p o l e moment, Jd, of magnitude ( e ^ L ^ ) d i r e c t e d along the i n t e r n u c l e a r a x i s . Matrix elements of the p e r t u r b a t i o n energy The t o t a l wave f u n c t i o n d e s c r i b i n g an energy l e v e l can be taken as the product o f three f a c t o r s , one an e l e c t r o n i c eigen- • f u n c t i o n , one r e l a t i n g to v i b r a t i o n and one to r o t a t i o n . For the experimental problem s t u d i e d here the matrix elements of the p e r t u r b a t i o n w i l l be Important only when the s e p a r a t i o n of two otherwise a p p r o p r i a t e energy l e v e l s i s comparable to the p e r t u r -b a t i o n energy. Thus we conclude the matrix elements o f the per-t u r b a t i o n between two l e v e l s w i l l only be important i f . the two . l e v e l s belong to the same e l e c t r o n i c and v i b r a t i o n a l l e v e l . They then have the form: V12 - (feYv f r ± \\ ( - e l i ) S . E / f j ^ ) . (2.3) Taking the d i r e c t i o n of the e l e c t r i c f i e l d as the z - a x i s of a co -o rd ina t e system f i x e d i n space we can r ep lace the dot prod-u c t , n*E, by n z E , where n z i s the p r o j e c t i o n of the u n i t v e c t o r •» -> n a long the d i r e c t i o n of E , the e l e c t r i c f i e l d , and E i s the magnitude of the e l e c t r i c f i e l d . Not ing tha t the e l e c t r o n i c and v i b r a t i o n a l wave func t ions are the same i n the i n i t i a l and f i n a l s ta te equat ion (2.3) becomes: V 1 2 = < « v | ( - e l ) \\ ) n z E { %z) , (2.4) where the °< and the v c h a r a c t e r i z e the e l e c t r o n i c and v i b r a t i o n -a l s t a t e . The f i r s t f a c t o r i n express ion (2.4) Is the quantum mechanical express ion f o r the e l e c t r i c d i p o l e moment i n the par -t i c u l a r e l e c t r o n i c and v i b r a t i o n a l s t a t e . We w i l l be s tudy ing d ia tomic molecules f o r which there i s a net d i p o l e moment. For t h i s s i t u a t i o n equa t ion (2.4) i n d i c a t e s that the behav io r of the second f a c t o r , which Involves the quantum mechanical average of the z-component of a v e c t o r , w i l l determine whether a S ta rk ef-fec t w i l l be observed. The p e r t u r b a t i o n and p a r i t y The i n i t i a l and f i n a l r o t a t i o n a l l e v e l s i n d i c a t e d above must have opposi te p a r i t y f o r the mat r ix element of the p e r t u r -b a t i o n energy to be nonzero. For t h i s argument we can w r i t e the matr ix element as : V l 2 = ^ (tit ™* ©I Vz) , ( 2-5) 1 0 where © i s the angle between the e l e c t r i c f i e l d and the d i p o l e moment l y i n g along the i n t e r n u c l e a r a x i s . If.we now perform a r e f l e c t i o n through the o r i g i n , x becomes -x, y becomes -y, z be-comes - z , and cos © becomes -cos ©. That i s , cos © has negative p a r i t y . For the val u e of V 1 2 to be nonzero i t must not change f o r such a r e f l e c t i o n . Thus we conclude that and ^ must have o p p o s i t e p a r i t y . The p e r t u r b a t i o n d i s c u s s e d here w i l l have the g r e a t e s t e f f e c t on r o t a t i o n a l l e v e l s which are degenerate with r e s p e c t to p a r i t y . Lambda doublet r o t a t i o n a l l e v e l s occur-r i n g f o r e l e c t r o n i c TT, A , e t c . s t a t e s c l o s e l y approximate such a s i t u a t i o n . V ector model treatment of Hund's c o u p l i n g case (a) Figu r e 2 .1 shows the v e c t o r model f o r Hund's c o u p l i n g case (a) f o r which the e l e c t r o n i c motion i s s t r o n g l y coupled to the i n t e r n u c l e a r a x i s . Using t h i s v e c t o r model the matrix elements shown i n equation (2.4) can be found c l a s s i c a l l y f o r a lambda doublet l e v e l . T h i s d i s c u s s i o n i s presented here s i n c e i t a l -lows us to e a s i l y a n t i c i p a t e the e s s e n t i a l f e a t u r e s of the Stark e f f e c t on the s p e c t r a o f a d i a t o m i c molecule. (The r e s u l t s found here w i l l be d e r i v e d r i g o r o u s l y l a t e r . ) In Figure 2 . 1 , \"T, the t o t a l angular momentum i s the v e c t o r sum of N, the r o t a t i o n a l angular momentum o f the n u c l e i and of —» jT, the angular momentum of the e l e c t r o n s taken along the i n t e r -n u c l e a r a x i s . J\\. i s composed of if, the p r o j e c t i o n o f the e l e c -t r o n i c s p i n angular momentum and of A , the p r o j e c t i o n of the e l e c t r o n i c o r b i t a l angular momentum, each taken along the i n t e r -11 Figure 2.1. V e c t o r diagram of a diatomic molecule i n an e l e c t r i c f i e l d , Hund's case ( a ) . 12 n u c l e a r a x i s . ( T h i s X should not be confused with the symbol f o r an e l e c t r o n i c s t a t e i n which the o r b i t a l angular momentum i s zero which corresponds t o an atomic S s t a t e . ) The v e c t o r d i a -gram a l s o shows y- , the e l e c t r i c d i p o l e moment, E, the e l e c t r i c —> - * - * f i e l d s t r e n g t h , and M, the component of J i n the d i r e c t i o n of E. Using t h i s v e c t o r model the p e r t u r b a t i o n energy w i l l be found as f o l l o w s . ( T h i s treatment i s s i m i l a r to Herzberg 1 s 1 d i s c u s s i o n of the Zeeman e f f e c t i n Hund's case (a).) The per-t u r b a t i o n energy i s the product o f the magnitude of the e l e c t r i c f i e l d s t r e n g t h , E, and.offy, the average v a l u e of the e l e c t r i c d i p o l e moment i n the d i r e c t i o n of the e l e c t r i c f i e l d . T h i s av-erage value of the d i p o l e moment i s found by f i r s t f i n d i n g the average value of j4 along ~J s i n c e Si (and}*) precess r a p i d l y about the d i r e c t i o n o f J . T h i s average v a l u e along J , ^ j , i s then averaged along the d i r e c t i o n o f E. Thus we w r i t e : 7 i j = ^ c o 8 ( j ? , J ) ^ _ ^ _ (2.6) /V£CG8( \" ' ^ I T T T ( 2 - 7 ) I f we now use equation (2.6) to re p l a c e the f a c t o r ^ i n equa-t i o n (2.7) we f i n d : 'T^fz r J ( J * I ) s i n c e the magnitude o f the v e c t o r J can be r e p l a c e d by ( J ( J + 1 ) ) \" 2 , ( i n u n i t s o f h/2n) J being the quantum number f o r the t o t a l angular momentum. U s i n g equation (2.8) we can now wr i t e the p e r t u r b a t i o n energy a s : Vi 2 = = ' (2.9) 13 Thus the p e r t u r b a t i o n energy can be found i n terms of the magni-tudes of the e l e c t r i c d i p o l e moment and o f the e l e c t r i c f i e l d s t r e n g t h ; and the quantum numbers f o r the t o t a l angular momentum and i t s p r o j e c t i o n s along the d i r e c t i o n of the . e l e c t r i c f i e l d and along the i n t e r n u c l e a r a x i s . From equation (2.9) we can conclude the f o l l o w i n g : The number o f Stark components w i l l i n c r e a s e w i t h i n c r e a s i n g angular momentum. (This i s due to the f a c t o r M which will.assume values J , J - l , . . ., -J.) The s e p a r a t i o n between adjacent S t a r k com-ponents of an energy l e v e l w i l l decrease due to the f a c t o r of J(J>1) i n the denominator of equation (2 .9 ) . Thus the S t a r k s p l i t t i n g s w i l l be r e s o l v e d o n l y f o r lower v a l u e s of J . We can a l s o conclude that an e l e c t r o n i c s t a t e h a v i n g no component of 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 - w i l l c o n t r i b u t e nothing to the f i r s t order Stark e f f e c t s i n c e t h i s s i t u a t i o n , corresponds to fi= 0. For example, i n an e l e c t r o n i c 2 are g i v e n i n equation (2.9). V 1 1 and V 2 2 are the e n e r g i e s of the two unperturbed lambda d o u b l e t s . I f we take the zero of energy as midway be-tween the two unperturbed l e v e l s and w r i t e t h e i r s e p a r a t i o n V l l ~ v 22 = ^ ' t h e 8 0 l u - t l o n t o equation (2.10) may be w r i t t e n as: £l = ± J ( V 2 ) 2 + ( V 1 2 ) 2 \" . (2.11) From t h i s s o l u t i o n we see that both l e v e l s of the lambda doublet w i l l s p l i t i n t o as many components as there are values of |M|. We may r e l a t e t h i s energy degeneracy f o r v a l u e s of M and -M to the appearance of a f a c t o r of M 2 under the square roo t due to the m a t r i x element of the p e r t u r b a t i o n being squared. T h i s M degeneracy i s a consequence of Kramers' theorem which s t a t e s that f o r a. system w i t h a h a l f I n t e g r a l value of the sum of the s p i n of the p a r t i c l e s i n an a r b i t r a r y e l e c t r i c f i e l d , a l l l e v -e l s must be doubly degenerate . . . . 1 , 2 Since a l l the mole-cule s s t u d i e d here were i n s t a t e s having t o t a l e l e c t r o n i c s p i n of 1/2, the Kramers' degeneracy i n M would remain even f o r an a r b i t r a r y e l e c t r i c f i e l d . Stark e f f e c t s p e c t r a The p e r t u r b a t i o n between a s s o c i a t e d lambda doublet l e v e l s of o p p o s i t e p a r i t y w i l l cause the perturbed energy l e v e l s t o be mixed. The extent of the mixing w i l l be d i s c u s s e d i n d e t a i l be-low, but f o r the present knowing that the p e rturbed l e v e l s have mixed p a r i t y we can p r e d i c t the e s s e n t i a l f e a t u r e of the Stark e f f e c t on the s p e c t r a of a d i a t o m i c molecule. A s t r i c t s e l e c t i o n r u l e f o r e l e c t r i c d i p o l e t r a n s i t i o n s i s that s t a t e s of p o s i t i v e p a r i t y combine only w i t h s t a t e s of nega-t i v e p a r i t y and v i c e v e r s a . The p a r i t y mixing due to the per-t u r b a t i o n r e s u l t i n g from the e l e c t r i c f i e l d w i l l l e a d to t r a n s i -t i o n s which are f o r b i d d e n i n the absence of the e l e c t r i c f i e l d . F i g u r e 2.2 shows two examples of p a r i t y f o r b i d d e n t r a n s i t i o n s which are induced by the e l e c t r i c f i e l d . The t r a n s i t i o n s shown i n the f i g u r e are f o r the OH molecule and c o r r e s p o n d i n g l i n e s 16 I, K = 0, J= '/2 F>2(l) T E=0 E=60kv/ c m n »/2 F[ (I) J =3/2 E=0 E = 60 kv/ c m F i g u r e 2.2. Stark e f f e c t on OH, Pi2 (D and P i ( l ) l i n e s . Broken l i n e s i n d i c a t e f o r b i d d e n t r a n s i t i o n s . Lambda doubling and Stark s p l i t t i n g s are drawn to the same s c a l e f o r both r o t a t i o n a l l e v e l s . show r e s o l v e d f i r s t o r d e r Stark s p l i t t i n g s . The s p l i t t i n g s are f i r s t o r d e r i n the a p p l i e d e l e c t r i c f i e l d because the p e r t u r b a -t i o n energy i s s e v e r a l times l a r g e r than the s e p a r a t i o n of the lambda doublet l e v e l s . T r a n s i t i o n s to r o t a t i o n a l l e v e l s with l a r g e r v a l u e s of J d i d not show r e s o l v e d S t a r k s p l i t t i n g s f o r the f o l l o w i n g reasons: As J i n c r e a s e s the lambda d o u b l i n g and the number of Stark components a l s o i n c r e a s e . Since the separa-t i o n of the Stark components decreases with i n c r e a s i n g J , the Stark e f f e c t w i l l g e n e r a l l y broaden a l l t r a n s i t i o n s except those to the lowest r o t a t i o n a l l e v e l s . When the lambda do u b l i n g be-comes somewhat l a r g e r than the p e r t u r b a t i o n , the lambda doublet components w i l l s t i l l be of mixed p a r i t y . Thus f o r h i g h e r r o t a -t i o n a l l i n e s the f o r b i d d e n l i n e w i l l appear q u i t e narrow and w e l l separated from the allowed l i n e . F i g u r e 2.3 shows an ex-, ample of the zero f i e l d and f i e l d induced t r a n s i t i o n s f o r the 0^(4) and Q 2 1 ^ ) l i n e s of the 2 Z T + - ^ 2 T T , (0,0) band of the OH molecule. The f i e l d - I n d u c e d , p a r i t y - f o r b i d d e n l i n e a s s o c i a t e d with the Q,2^(4) l i n e was obscured by the a l l o w e d component of the 0^(4) l i n e . In c o n c l u s i o n we see that the Stark e f f e c t w i l l r e s u l t i n r e s o l v e d s p l i t t i n g s , broadenings, and c l e a r l y separated f i e l d -induced, p a r i t y - f o r b i d d e n l i n e s f o r e l e c t r o n i c t r a n s i t i o n s i f e i t h e r the i n i t i a l or f i n a l l e v e l i s degenerate i n energy with r e s p e c t to p a r i t y . Before d i s c u s s i n g the Stark e f f e c t on spec-t r a r e s u l t i n g from t r a n s i t i o n s between e l e c t r o n i c s t a t e s f o r which both r o t a t i o n a l l e v e l s are degenerate, e.g. 2 A - » » 2 T T , the matrix elements f o r the p e r t u r b a t i o n i n v o l v i n g the e l e c t r i c F i g u r e 2.3. Zero f i e l d and - f i e l d - i n d u c e d } . p a r i t y - f o r b i d d e n t r a n s i t i o n s a s s o c i a t e d w i t h Q]_(4) and Q 2i(4) l i n e s of OH, 2\"s:+-* 2jr ( band. Broken l i n e s i n d i c a t e f i e l d induced t r a n -s i t i o n s . f i e l d and the e l e c t r i c d i p o l e moment w i l l be found r i g o r o u s l y * These r i g o r o u s l v a l u e s w i l l confirm the c o r r e c t n e s s of the v e c t o r model r e s u l t f o r the matrix elements. From the f o l l o w i n g s e c -t i o n we w i l l a l s o see what c o r r e c t i o n s are to be made when a r o -t a t i o n a l l e v e l does not belong to pure Hund's case (a) c o u p l i n g . Rigorous treatment of matrix elements In the i n i t i a l d i s c u s s i o n of the matrix elements f o r the p e r t u r b a t i o n energy of a molecule w i t h a permanent e l e c t r i c d i p o l e moment i n an a p p l i e d e l e c t r i c f i e l d were g i v e n by: V 1 2 a < « v | ( - e l i ) |*v><4£fn z Ej (2.4) We r e c a l l t h a t the f i r s t f a c t o r r e p r e s e n t s the e l e c t r i c d i p o l e moment f o r a p a r t i c u l a r e l e c t r o n i c and v i b r a t i o n a l s t a t e char-a c t e r i z e d by - < 2 ' 1 2 > We have a l r e a d y shown t h a t the i n i t i a l and f i n a l r o t a t i o n a l e i g e n - f u n c t i o n s must have opposite p a r i t y . We w i l l nowffind the remaining c o n d i t i o n s on these e i g e n - f u n c t i o n s f o r nonzero m a t r i x 20 elements. E s s e n t i a l l y we wish to determine when the quantum me-c h a n i c a l average of the z-component of a v e c t o r i s nonzero. The nonzero values of f n ) f o r Hund's c o u p l i n g case (a) w i l l now he Li d i s c u s s e d . In Hund's c o u p l i n g case (a) the e l e c t r o n i c motion i s s t r o n g l y coupled to the I n t e r n u c l e a r a x i s . The good quantum numbers f o r t h i s c o u p l i n g case are; ex , Ji, J , • M. = (/1J J n z | 71 J> M (SI J M I n z | y i J - l M ) = (71 JI n z | J - l ) y/(j2 _ M2) ( i l J - 1 M| n z | i l J M) = ( / i J - l | n z | / I j ) v / ( J 2 - M 2) ( 2 . 1 3 ) Although the p a r i t y of the s t a t e s i s not shown here e x p l i c i t l y , the i n i t i a l and f i n a l s t a t e must have op p o s i t e p a r i t y . The f i r s t r e l a t i o n s h i p w i l l be used f o r lambda doublets and the oth-er two w i l l be used i n f i n d i n g second order e f f e c t s due to n e i g h b o r i n g r o t a t i o n a l l e v e l s . The f a c t o r s i n equation (2.13) which depend only on J and Si are given by:^ (fLJ | n z | J\\ J> = . N 1 2 1 / J(J+ 1 ) (Jlj\\ n I Si J-l) = We can see f o r example that the v e c t o r model r e s u l t f o r the per-t u r b a t i o n matrix elements between lambda d o u b l e t s g i v e n i n equa-t i o n ( 2 . 9 ) i s c o r r e c t . The corresponding quantum mechanical r e -s u l t i s obtained from equation ( 2 . 1 2 ) u s i n g the f i r s t r e l a t i o n -s h i p i n equation ( 2 . 1 3 ) and (2.14) and one o b t a i n s : i n agreement with the v e c t o r model r e s u l t . In Hund's c o u p l i n g case (b) the e l e c t r o n i c s p i n a n g u l a r momentum i s weakly coupled to the i n t e r n u c l e a r a x i s . To f i n d the matrix elements of the p e r t u r b a t i o n f o r Hund's case (b) we need to know which quantum numbers are good and which s e l e c t i o n 23 rules apply specifically. The good quantum numbers are o( , A . K, S, J , M, and parity. As above; <* denotes the assembly of quantum numbers describing the electronic term with the excep-tion of A which corresponds to the projection of the electronic angular momentum on the internuclear axis; J is the total angu-lar momentum quantum number; and M corresponds to the projection of the total angular momentum along the direction of the applied electric field. The quantum number K denotes the total angular momentum apart from spin. K is composed of electron orbital angular momentum along the internuclear axis and angular momen-tum due to rotation of the nuclei. The total electron spin an-gular momentum is denoted by S. The selection rules given above for the general situation of electric dipole transitions and for both Hund's case (a) and case (b) can be immediately applied. Since we are only interest-ed: in the interaction of neighboring rotational levels which both correspond to case (b) coupling we only need the appropri-ate selection rule for K, i . e . :3 4 K = ±1, 0 except for 2 -2 transitions for which - 0 is forbidden. In complete detail the desired matrix element of n 2 for case (b) coupling would be written: . These matrix elements w i l l he found by f i r s t n e g l e c t i n g s p i n and then u s i n g the a p p r o p r i a t e formulas f o r f i n d i n g the matrix e l e -ments r e l a t i n g to the a d d i t i o n o f ; a n g u l a r momenta. C o n s i d e r i n g only TV and K the nonzero matrix elements a r e : ^ ( A K J n z | A R> = A K(K+l) (AKl nz\\J\\ K-l> - (A K - l l n z 1 A K > = (K - A ) (K +A ) (2.16) (2K - 1) (2K + 1) ' We w i l l be i n t e r e s t e d s p e c i f i c a l l y i n 2 £ \" e l e c t r o n i c s t a t e s which always obey case (b) c o u p l i n g . As noted above f o r such a £ - Z t r a n s i t i o n AK = 0 i s f o r b i d d e n and thus the f i r s t expres-s i o n i n ( 2 . l 6 ) i s a u t o m a t i c a l l y zero. T h i s agrees w i t h the vec-t o r model r e s u l t g i v e n above. For an e l e c t r o n i c X\" s t a t e , A. = 0 and the remaining e x p r e s s i o n i n ( 2 . l 6 ) reduces t o : = 1 ( 2.17) UM<- - 1 ) ' where y\\_ has been dropped. L e t us now i n t r o d u c e s p i n and f i n d the nonzero matrix elements i n terms of M , J , S, and K. These a r e : 6 (K S J M | n z | K - l S J M > = ^ K - l S J M | n z | K S J M ) = = M / ( J - S + K ) (J+S+K+l) ( S + K - J ) ( J * S - K > 1 ) ' 2 J ( J + 1 ) \\{kYL* - 1 ) ' (K S J M | n z | K - l S J - l M > = { K - l S J - l M | n z ) K S J M ) = = ft J 2 - M 2 ) \" j(J-S+K) (J+S+K+l) ( J - S + K - l ) (J*S+K)\" 2 J \\ | ( 4 J 2 - 1 ) ' l'- *PTT,/X) , *Y(2TTVx) < f i n t > 2 \" bWzfr,^ , t a f ( 2 7 f % ) (2.19) W2TT}i) a n d 27T3/ a) are pure'Hund's case (a) wave f u n c t i o n s . The upper signs i n equations (2 .19) are f o r r e g u l a r doublets and the lower signs are f o r i n v e r t e d doublets. The c o e f f i c i e n t s , a and b, i n equations (2.19) are given by:? (2 .20) where X - + + £ ) z + (A /BXA/B-4) \" . (2.21) A i s the s p i n c o u p l i n g constant and B i s the r o t a t i o n a l con-stant. For r e g u l a r doublets A / B i s p o s i t i v e and f o r i n v e r t e d doublets A / B i s negative. Hund's case (a) coupling corresponds to the r a t i o A / B becoming l a r g e . S p e c i f i c a l l y , as A/B-+ 00, a -# 1 and b-* 0 and we eee t h a t ! ^ i n t ) l ^ ^ 2 T T . A ) and ( V ^ t ^ ^ T T ^ ) ; as A/B-* -qo f a-* 0 and b-* 1 and t h i s corresponds to. ^ l n t ) l ^ T ^ ( 2 T T ^ ) ^ d ( f i n t ^ Y^2™/,.). I t was convenient to use Hund's case (a) wave fu n c t i o n s to t r e a t Intermediate ooupling as the appropriate matrix elements are a l -ready a v a i l a b l e . The d e s c r i p t i o n given here may also be used to trea t case (b) coupling by s e t t i n g the c o e f f i c i e n t s g i v e n i n equation (2.20): a - b - l / l T T . As a s p e c i f i c example, the ex-pressions a v a i l a b l e here w i l l be ap p l i e d t o an in v e r t e d ^ ' e l e c -t r o n i c s t a t e to evaluate the p e r t u r b a t i o n matrix elements f o r a lambda doublet r o t a t i o n a l l e v e l i n the 2 T T 3 / 4 s t a t e . The ap-pr o p r i a t e wave f u n c t i o n from equation (2.19) iss ( T ^ l n t h - a ^ H j / x ) + ^ Z V i / x ) (2.22) and the p e r t u r b a t i o n matrix element given i n equation (2.12) become! V 1 2 - -yz(*$izTr^ ) + * f?< 2 T7 J / A ) / n * | ^ 2 7 T v A ) * ^ < 2 T T > A J > (2.23) The s u b s c r i p t ± i n d i c a t e s the p a r i t y of the I n i t i a l and f i n a l s t a t e . As we have noted above, the combinations i n equation • (2.23) must obey the s e l e o t i o n r u l e , A£ - 0. Thus equation (2.23) reduces tos V 1 2 - -f f f a 2 ^ 2 ^ )l n z 1 T^<2T7ya )> ^ ^ T f ^ i ^ 1 ^ ( 2 % ) ) ] . (2.24) This expression can be evaluated f o r a s p e c i f i c r o t a t i o n a l l e v e l using expressions (2.1$) and (2 .20) . 27 There are two t o p i c s remaining i n t h i s chapter. The.Stark e f f e c t on s p e c t r a r e s u l t i n g from t r a n s i t i o n s between r o t a t i o n a l l e v e l s which are both degenerate w i l l be d i s c u s s e d , u s i n g the s p e c i f i c example of the CH 2/\\ -2TT band. Leading to t h i s the mixing o f lambda doublet l e v e l s w i l l be reviewed. The f i n a l t o p i c f o r d i s c u s s i o n w i l l be second order S t a r k e f f e c t s due to the i n t e r a c t i o n of neighboring r o t a t i o n a l l e v e l s . P a r i t y mixing and t r a n s i t i o n s between perturbed lambda doublets In d e s c r i b i n g a perturbed lambda doublet of mixed p a r i t y l e t us c a l l the lower unperturbed l e v e l \"1\" (one) and the upper unperturbed l e v e l \"2\" and l a b e l the corresponding unperturbed e i g e n - f u n c t i o n s as ^ and ^ . The perturbed l e v e l s w i l l be de-a s c r i b e d by the eigen-functions:° fupp \" bJi - < 2 ' 2 5 ) O where the c o e f f i c i e n t s a and b are given by:° a = .; i 2 2 J(A/2)Z + (V 1 2 ) 2 ' * = Ii2— f 1 - (X/2) . (2.26) |V12| | 2 27(A/2)2 i (V 1 2 ) 2 -\\ i s the s e p a r a t i o n of the unperturbed lambda doublet l e v e l s and V 1 2 i s the matrix element f o r the p e r t u r b a t i o n energy. The s i g n of the p e r t u r b a t i o n appearing .in equation (2.26) w i l l allow us to determine the r e l a t i v e s i g n of the e l e c t r i c d i -pole moment o f the CH molecule i n the i n i t i a l and f i n a l s t a t e 28 from o b s e r v a t i o n s o f the Stark e f f e c t on the 2A - 2 T T band. The p e r t u r b a t i o n c o n t a i n s the e l e c t r i c d i p o l e moment whose d i r e c t i o n i s f i x e d r e l a t i v e to the i n t e r n u c l e a r a x i s o f the molecule. The r e l a t i v e d i r e c t i o n of the d i p o l e moment w i l l determine the r e l a -t i v e s i g n of the p e r t u r b a t i o n which i n turn w i l l determine wheth-e r the c o e f f i c i e n t s • • • i. b are . p o s i t i v e or n e g a t i v e . I f the r e l a t i v e s p l i t t i n g s of the Stark components l e v e l s i n the upper and lower s t a t e are known, the observed Stark s p e c t r a a l -lows one to deduce whether the \"* .., coefficient';. -,: i b of one sta t e has- the same o r opposite s i g n as that'•'•>• i n the other s t a t e . Thus we are able to deduce the r e l a t i v e s i g n of the d i -pole moments i n the two s t a t e s . The t r a n s i t i o n s between two lambda doublet l e v e l s are shown i n Fig u r e 2.4 f o r zero e l e c t r i c f i e l d and i n the presence of an e l e c t r i c f i e l d f o r the same and o p p o s i t e r e l a t i v e s i g n s of the d i p o l e moment i n the upper and lower s t a t e . (This example i s g e n e r a l enough to be used l a t e r i n d i s c u s s i n g the p e r t u r b a -t i o n between n e i g h b o r i n g r o t a t i o n a l l e v e l s . ) The allowed t r a n -s i t i o n s i n Figure 2.4 are l a b e l l e d I and I I . The primes on the t r a n s i t i o n s i n the presence of the f i e l d i n d i c a t e f o r b i d d e n t r a n s i t i o n s . I f the d i p o l e moments have the same r e l a t i v e s i g n the s t r o n g component of the lower frequency allowed l i n e moves to h i g h e r frequency and the s t r o n g component of the h i g h e r f r e -quency allowed l i n e moves to lower frequency. ( T h i s c o n c l u s i o n assumes there are g r e a t e r Stark s h i f t s i n the upper s t a t e than the lower s t a t e which i s c o r r e c t f o r the GHJ/molecule.) • I f ' ' ' the r e l a t i v e signs of the d i p o l e moment are opposite i n the up-29 A . t B r + T Dipole Moments Dipole Moments Parallel Antiparallel Electric Field Zero Electric Field Applied Figure 2.4. Zero f i e l d and f i e l d - i n d u c e d , p a r i t y -f o r b i d d e n t r a n s i t l o n e between lambda d o u b l e t s . Broken l i n e s i n d i c a t e t r a n s i t i o n s w i t h lower i n t e n s i t y . 30 per and lower s t a t e s the strong Stark components move a p a r t . The i n t e n s i t i e s of the S t a r k t r a n s i t i o n s shown i n F i g u r e 2.4 can be given i n d e t a i l by f i n d i n g the perturbed wave func- . t i o n s . I f the s t a t e s have p a r i t y as shown i n the f i g u r e and the r e l a t i v e d i p o l e moments are the same i n the l e v e l s marked A and B the wave f u n c t i o n s are: f l o w = « A V 4 + f u p p = + * A W -•h (2.27) -The t r a n s i t i o n s l a b e l l e d I , I ' , I I , and I I ' w i l l have i n t e n s l -t i e s p r o p o r t i o n a l t o : I: ( a A a B + b A b B ) 2 i ' : ( a A b f i — b A a B ) 2 (2.2%) I I : ( a A a B + b A b B ) 2 I i ' : (-a Ab B - f b A a B ) 2 We expect that a A and b A w i l l be comparable t o a Band b B r e s p e c -t i v e l y . Thus, we see when the d i p o l e moments i n the two s t a t e s have the same r e l a t i v e s i g n the t r a n s i t i o n s l a b e l l e d I and I I w i l l be strong and the f o r b i d d e n t r a n s i t i o n s 1 1 and I I 1 w i l l be weak. A s i m i l a r argument can be made assuming the r e l a t i v e signs o f the d i p o l e moments i n the i n i t i a l and f i n a l s t a t e are o p p o s i t e . This i s e q u i v a l e n t to r e v e r s i n g the s i g n of the'b -co-e f f i c i e n t • i n the d e s c r i p t i o n o f one of the s t a t e s and r e s u l t s i n the r e v e r s i n g of the primes shown i n equation (2.28). Thus i f the r e l a t i v e s i g n s of the d i p o l e moment i n the two s t a t e s are 31 opposite the strong components move apa r t . F i g u r e 2.5 shows the Sta r k t r a n s i t i o n s f o r the Q, (3) and Q l d ( 3 ) l i n e s i n the CH 2 £ - 2T7 band. The observed Stark e f f e c t showed the l i n e s moving t o g e t h e r as i n d i c a t e d i n the f i g u r e . (Only the strong t r a n s i t i o n s a re i n d i c a t e d . ) The s p l i t t i n g s were computed using a value o f 1.0 Debye f o r the d i p o l e moment of the aZI s t a t e and 1.46 Debye f o r the XTT s t a t e and a v a l u e of 66kV/cm f o r the e l e c t r i c f i e l d s t r e n g t h . The lambda d o u b l i n g i n the ZA s t a t e i s e f f e c t i v e l y zero? and the lambda d o u b l i n g i n sta t e was taken as 0.38 cm~l. The f i g u r e shows that r e l a t i v e to the Q-xc(3) l i n e , f o r example, the g r e a t e s t i n c r e a s e i n frequency occurs f o r the H = 7/2-»M = 5/2 component. Second order Stark e f f e c t s T h i s f i n a l s e c t i o n w i l l d i s c u s s c o n t r i b u t i o n s to second order S t a r k e f f e c t s due to the i n t e r a c t i o n of n e i g h b o r i n g r o t a -t i o n a l l e v e l s . The d i s c u s s i o n i s based on the exp r e s s i o n f o r the second order c o r r e c t i o n i n energy, g i v e n by. *I , | V M : ' 2 ( 2 - 2 9 ) m E n \" Em This i s the c o r r e c t i o n f o r the l e v e l \"n\". The prime i n d i c a t e s the term f o r m = n i s to be omitted from the sum. E n and E m are unperturbed v a l u e s f o r the energies of the p e r t u r b i n g l e v e l s and V m n i s the matrix element f o r the p e r t u r b a t i o n energy be-tween the l e v e l s \"n\" and \"m\". The matrix elements to be used i n t h i s equation are those g i v e n above and we r e c a l l t h a t they are nonzero only between s t a t e s of opposite p a r i t y and f o r 2 A , K=3, J=/2 Q i c ( 3 ) Q,d(3) :n, K=3, J= \\ A M =0 A M = ± I F i g u r e 2.5. S t a r k e f f e c t on CH, Q l c ( 3 )'and Q l d ( 3 ) l i n e s , Only s t r o n g S t a r k t r a n s i t i o n s are shown. 33 A j = t i f o . Because of these r e s t r i c t i o n s on the matr i x e l e -ments we need c o n s i d e r only the e f f e c t s o f nei g h b o r i n g r o t a t i o n -a l l e v e l s . To e v a l u a t e such e f f e c t s i n the s t a t e the matrix elements f o r Hund's case (b) c o u p l i n g which are given i n equa-t i o n s (2.17) and ( . 2 . 1 8 ) can be a p p l i e d Immediately to equation (2.29). F o r 2 f T s t a t e s , the d i s c u s s i o n of p a r i t y mixing i n lambda doublets and t r a n s i t i o n s between them may be a p p l i e d t o g r e a t l y s i m p l i f y the e v a l u a t i o n of second order c o r r e c t i o n s g i v e n by equation (2.29)• Consider the s i t u a t i o n shown i n F i g u r e 2.4, where the lambda doublet l e v e l s now belong t o the same e l e c t r o n -i c and v i b r a t i o n a l s t a t e and d i f f e r by one i n J . I t i s s u f f i -c i e n t l y accurate f o r our purpose to take the s e p a r a t i o n between a lambda doublet l e v e l of one r o t a t i o n a l s t a t e and e i t h e r lamb-da doublet l e v e l o f the other s t a t e as the mean s e p a r a t i o n of the r o t a t i o n a l l e v e l s . The p a r i t y mixing o f lambda doublets f o r the same r o t a t i o n a l l e v e l i s g i v e n by equations (2.25) and (2.26). Since the p e r t u r b a t i o n between r o t a t i o n a l l e v e l s occurs between components w i t h the same value of M one need f i n d the p a r i t y mixing i n the two lambda doublets f o r only one v a l u e of |Mj at a time. The second o r d e r e f f e c t due to n e i g h b o r i n g r o t a t i o n a l l e -v e l s w i l l move both lambda doublet l e v e l s by the same amount. One can see that they move to g e t h e r from equations (2.29) and (2.28). A mixed lambda doublet component of one r o t a t i o n a l l e -v e l w i l l be pe r t u r b e d by both mixed lambda doublets of the other l e v e l . The energy d i f f e r e n c e In the numerator of equation (2 . 2 9 ) i s e s s e n t i a l l y the same f o r the t r a n s i t i o n s . From equa-t i o n (2 . 2 9 ) we a l s o see that the matrix elements are squared. The e x p r e s s i o n s i n (2.28) show these squared matrix elements to w i t h i n a f a c t o r . The e x p r e s s i o n s l a b e l l e d I and I ' sum to one (as do I I and I I ' ) . The f a c t o r of p r o p o r t i o n a l i t y f o r the ex-p r e s s i o n s i n (2.28) i s the square of the matrix element f o r ^ E n z between a r o t a t i o n a l l e v e l of one p a r i t y and the adjacent l e v e l of opposite p a r i t y . Thus j o i n t l y , both lambda do u b l e t s of one r o t a t i o n a l l e v e l push each lambda doublet component of the other r o t a t i o n a l l e v e l by the same amount. I f the r o t a t i o n a l l e v e l s correspond to c o u p l i n g i n t e r m e d i -ate between Hund's case (a) and case (b) equations (2.20) and (2.24) can be a p p l i e d . Pure Hund's case (b) can be t r e a t e d as an equal mixture o f pure Hund's case (a) wave f u n c t i o n s . 35 Footnotes f o r Chapter I I 1. G-. Herzberg, M o l e c u l a r S p e c t r a and M o l e c u l a r I S t r u c t lire.. -I. S p e c t r a of Diatomic Molecules.(D. Van Nostrand Co., New-York, 1950), Second E d i t i o n , p. 300. 2. L. D. Landau and E. M. L i f s c h l t z , Quantum M e c h a n i c s — N o n - r e l a t i v l s t i c Theory (Addison-Wesley P u b l i s h i n g Co., Reading, Massachusetts, 1958), p . 203. 3. Herzberg, p. 240-244. 4. Landau and L i f s c h i t z , p. 294-298. 5. Landau and L i f s c h i t z , p. 295. 6. Landau and L i f s c h i t z , p. 294-298 and p. 104-105. 7. G-. C. Dousmanis, T. M. Saunders and C. H. Townes, Phys. Rev. 100, 1735 (1955). 8. Landau and L i f s c h i t z , p. 139* 9. A. E. Douglas and.G. A. E l l i o t t , Can. J . Phys. 4^, 496 (1965). CHAPTER I I I EXPERIMENTAL DETAILS The Stark e f f e c t on the e l e c t r o n i c emission s p e c t r a of diatomic molecules r e p o r t e d here W&B produced i n an e l e c t r i c d i s c h arge tube s i m i l a r to that used by LoSurdo. The e l e c t r i c f i e l d i n the cathode dark space o f such a low pressure discharge tube produces the S t a r k e f f e c t . (In the cathode de&k space there i s a high d e n s i t y of slow moving p o s i t i v e ions which pro-duce a l a r g e drop i n p o t e n t i a l i n a small d i s t a n c e w i t h the r e -s u l t i n g l a r g e e l e c t r i c f i e l d . 1 ) The d i s c h a r g e tube not o n l y p r o v i d e d the e l e c t r i c f i e l d but a l s o s u p p l i e d the d e s i r e d mole-cule i n an e l e c t r o n i c e x c i t e d s t a t e . The r e s u l t i n g S t a r k e f f e c t s p e c t r a were observed p h o t o g r a p h i c a l l y . T h i s chapter w i l l d i s -cuss the experimental equipment and techniques used to produce the e l e c t r i c f i e l d and the e l e c t r o n i c a l l y e x c i t e d molecules. The o b s e r v a t i o n of the Stark s p e c t r a and the d e t e r m i n a t i o n of the e l e c t r i c f i e l d w i l l a l s o be d i s c u s s e d . E l e c t r i c discharge tube F i g u r e J.l shows a diagram of the d i s c h a r g e tube used i n t h i s study. The tube was blown from pyrex g l a s s . The plane window and c a p i l l a r y tube i n s u l a t i n g the cathode were b o t h qu a r t z . The window was sealed to the tube and the cathode was se a l e d i n the quartz c a p i l l a r y u s i n g deKhotinsky cement. Often the rubber stopper was sealed u s i n g an \"0\" r i n g formed from Aplezon \"Q\" compound. The o u t l e t of the d i s c h a r g e tube was con-3? To Pump Needle Valve H 2 0 Vapor To Spectrograph [ L J V * •Quartz Window 5 cm Rubber Stopper Quartz Tube v d e Khotinsky Cement ^Aluminum Wire (drawn to fit snug) F i g u r e 3.1. M o d i f i e d Lo Surdo d i s c h a r g e tube. 38 nected to a mechanical pump v i a a l i q u i d n i t r o g e n t r a p . The pressure i n the tube was measured with a McLeod guage l o c a t e d be-tween the discharge tube and the c o l d t r a p . The diagram i n d i -cates the d i r e c t i o n i n which gas flowed w h i l e using HgO vapour to produce OH molecules. (The gas i n l e t and pump connections were reversed f o r another a p p l i c a t i o n of the tube and remained that way when methyl a l c o h o l vapour was used to produce CH molecules.) The d i r e c t i o n of gas flow d i d not a p p a r e n t l y a l t e r the oper a t i o n of the d i s c h a r g e . When using carbon compounds to produce CH molecules a l i n e r was p l a c e d i n s i d e the d i s c h a r g e tube. In t h i s way the tube w a l l s could be q u i c k l y and e a s i l y cleaned when v i s -u a l o b s e r v a t i o n o f the di s c h a r g e became d i f f i c u l t . The l i n e r was a pyrex g l a s s c y l i n d e r f i t t i n g e a s i l y i n s i d e the d i s c h a r g e tube. The p o r t i o n o f the l i n e r i n f r o n t o f the side tube l e a d -ing to the quartz window was removed. The discharge tube was operated as a d i r e c t c u r r e n t glow. Under these c o n d i t i o n s most of the p o t e n t i a l d i f f e r e n c e between the cathode and anode appears a c r o s s the cathode dark space. For r e p r e s e n t a t i v e o p e r a t i n g c o n d i t i o n s of 4 k'V/ across the d i s -charge tube and 1 mm Hg t o t a l pressure the dark space would be about 1 mm and an e l e c t r i c f i e l d of about 40 kV/cm would be pro-duced. The d i s c anode was made of aluminum and the e l e c t r i c a l c o nnection was v i a a tungsten w i r e - g l a s s bead s e a l . The cathode was a w i r e , u s u a l l y 1 mm diameter aluminum. The wire was sealed i n a qu a r t z tube so th a t only the end was exposed i n s i d e the tube. The upper end of the cathode was u s u a l l y ground f l a t and f l u s h w i t h the end o f the quartz tube. (A more d e t a i l e d d i s c u s -39 s i o n o f c a t h o d e m a t e r i a l s i n v a r i o u s s i z e s a p p e a r s b e l o w . ) T h e a n o d e ( a n d p o s i t i v e t e r m i n a l o f t h e p o w e r s u p p l y ) w e r e g r o u n d e d . O t h e r w i s e , t h e d i s c h a r g e w o u l d a l s o g o t o g r o u n d v i a t h e p u m p . A b a l l a s t r e s i s t o r o f 5 0 , 0 0 0 o h m s w a s p l a c e d i n s e r i e s w i t h t h e d i s c h a r g e t u b e t o l i m i t t h e c u r r e n t . B p . s i c o p e r a t i n g p r o c e d u r e w a s d e t e r m i n e d b y f a c t o r s a f f e c -t i n g t h e s h o r t t e r m s t a b i l i t y a n d t h e u s e f u l l i f e t i m e o f t h e c a t h o d e . S h o r t t e r m s t a b i l i t y w a s l i m i t e d b y t h e a b i l i t y o f t h e c a t h o d e t o d i s s i p a t e h e a t . T o o m u c h p o w e r w o u l d d e s t r o y t h e u s e f u l p o r t i o n o f t h e c a t h o d e i m m e d i a t e l y . T h e u s e f u l l i f e t i m e o f t h e c a t h o d e w a s l i m i t e d b y s p u t t e r i n g w h i c h l o w e r e d t h e c a t h -o d e s u r f a c e ( a n d t h e h i g h f i e l d r e g i o n ) i n t o t h e q u a r t z t u b e . S i n c e t h e i n s i d e w a l l s o f t h e q u a r t z t u b e w e r e c o v e r e d w i t h o p a q u e s p u t t e r e d m a t e r i a l t h e h i g h f i e l d r e g i o n d i s a p p e a r e d f r o m v i e w a f t e r a f e w h o u r s a t m o s t . T h e d i s c h a r g e w a s s t a r t e d a t r e l a t i v e l y l o w v o l t a g e s a n d c u r r e n t s a n d r u n u n t i l a s m a l l p i t w a s b u r n e d i n t h e c e n t e r o f t h e c a t h o d e s u r f a c e . A b r i g h t c o n e i n t h e d i s c h a r g e e x t e n d i n g f r o m t h e p i t i n t o t h e p o s i t i v e c o l u m n w o u l d a p p e a r a l m o s t i m m e -d i a t e l y . W h e n t h e b r i g h t c o n e w o u l d r e m a i n s t a b l e a n d n a r r o w f o r i n c r e a s e d v o l t a g e s t h e a p p l i e d v o l t a g e c o u l d b e r a i s e d t o s o m e c h o s e n v a l u e a n d t h e p r e s s u r e i n c r e a s e d u n t i l t h e c u r r e n t c o r r e s p o n d e d t o t h e m a x i m u m s a f e p o w e r . ( T h e p o w e r d i s s i p a t e d i n t h e w h o l e t u b e w a s g e n e r a l l y l i m i t e d t o a b o u t 20 w a t t s t o i n s u r e s t a b l e o p e r a t i o n „ ) A l t e r n a t i v e l y , w h e n t h e d i s c h a r g e f i r s t b e c a m e s t a b l e a p r e s s u r e c o u l d b e c h o s e n a n d t h e n t h e v o l t a g e i n c r e a s e d . P r o d u c t i o n of OH and CH e l e c t r o n i c emission s p e c t r a R e l a t i v e l y s t r o n g and pure u l t r a v i o l e t OH emission s p e c t r a were observed when H 20 vapour was used .In the discharge tube. The vapour was s u p p l i e d from a t r a p c o n t a i n i n g c a r e f u l l y de-gassed l i q u i d H 20 and connected t o the d i s c h a r g e tube v i a a needle v a l v e . The vapour was c o n t i n u o u s l y flowed through the dis c h a r g e tube. The pressure of H 20 vapour In the d i s c h a r g e tube ranged from 0.5 to 4.0mm Hg. The p r e s s u r e was s e t by ad-Ju s t i n g the flow r a t e through the needle v a l v e . V a r i a t i o n s i n pressure due to changes i n the temperature of the l i q u i d H2O were reduced by u s i n g a water b a t h or by pumping on the l i q u i d u n t i l an e q u i l i b r i u m temperature was reached. Experiments were done wi t h aluminum cathodes 2 .0, 1.0,/and 0.5 mm In diameter and with a tungsten cathode 1.0 ram i n diame-t e r . The l a r g e s t cathodes were d i f f i c u l t t o use as l o c a l heat-ing on the cathode s u r f a c e o f t e n became e x c e s s i v e and the cen-t r a l p i t was de s t r o y e d . Tungsten was even more d i f f i c u l t to use as i t would of t e n evaporate from the cathode s u r f a c e and coat the q u a r t z tube i n s u l a t i n g the cathode. The evaporated c o a t i n g conducted e l e c t r i c a l l y and caused the c h a r a c t e r o f the discharge to change completely. The 1.0 mm diameter aluminum cathode was the e a s i e s t to use and produced e l e c t r i c f i e l d s up to 60 kV/cm. The l a r g e s t e l e c t r i c f i e l d i n the study of the OH molecule, 63 kV/cm, v/as produced u s i n g the 0.5 mm diameter aluminum cath-< ode. However, these small cathodes were d i f f i c u l t to use and o f t e n melted when the discharge was f i r s t s t a r t e d . In the study of the OH molecule the v o l t a g e across and cu r r e n t through the 41 d i s c h a r g e tube ranged from about 3-6 kV and 12 ma f o r 2 mm diam-eter: cathodes t o about 6.5 kV and 4.2 ma f o r 1 mm cathodes and about 3 kV and 2.4 ma f o r 0.5 mm cathodes. E l e c t r o n i c emission s p e c t r a from the CH molecule were pro-duced i n the di s c h a r g e tube u s i n g methyl a l c o h o l vapour. Helium or H 2 was sometimes used as a c a r r i e r gas. The best combination was CH^OH vapour and He gas w i t h a p a r t i a l p r e s s u r e of 0.2 to 0.4 mm Hg f o r the vapour and a t o t a l pressure of 1 to 3 mm Hg. The use of H 2 as a c a r r i e r gas was not v e r y s a t i s f a c t o r y even though i t sometimes enhanced the i n t e n s i t y of atomic hydrogen Balmer l i n e s which were used to determine the e l e c t r i c f i e l d s t r e n g t h . The r e s u l t i n g H 2 molecular l i n e s complicated the problem of i d e n t i f y i n g and s t u d y i n g a chosen CH molecular l i n e . For the p r e l i m i n a r y study of CH emission s p e c t r a the c a r r i e r gas when used flowed over a l c o h o l c o ntained i n a t r a p . The most s a t i s f a c t o r y arrangement, however, was to in t r o d u c e the a l c o h o l vapour and c a r r i e r gas through separate needle v a l v e s . In t h i s way the pressure of the two gasses could be set e a s i l y and inde-pendently. When CH^OH vapour and He were used the r e l a t i v e i n -t e n s i t y of the atomic hydrogen Balmer l i n e , Hy and the hel i u m l i n e at \\66?8& was observed v i s u a l l y . These o b s e r v a t i o n s were made through the side of the d i s c h a r g e with a prism spectroscope and v e r y much aided the adjustment of d i s c h a r g e c o n d i t i o n s be-for e o b s e r v i n g the molecular s p e c t r a . In f a c t , from such v i s u a l o b s e r v a t i o n s i t was p o s s i b l e to roughly estimate the e l e c t r i c f i e l d s t r e n g t h . The use of a hydrocarbon such as methane, propane, benzene or cyclohexane d i d not prove s a t i s f a c t o r y f o r the p r o d u c t i o n of CH emission s p e c t r a e i t h e r when used alone, with the a d d i t i o n of a c a r r i e r gas or'when mixed w i t h a l c o h o l w i t h or without the ad-d i t i o n of a c a r r i e r gas, Such substances i n the di s c h a r g e tube produced an e l e c t r i c a l l y conducting d e p o s i t on the cathode sur-face xirhich q u i c k l y destroyed the s t a b i l i t y o f the d i s c h a r g e . For studying the Stark e f f e c t on the s p e c t r a of the CH molecule, 1 mm diameter aluminum cathodes were g e n e r a l l y used. A p p l i e d v o l t a g e s ranged from 3»0 to 5.0 kV and c u r r e n t s ranged from 3-0 to 6.7 ma. When s t u d y i n g the Stark e f f e c t on the OH and CH molecules simultaneously CH^OH vapour and He gas was used i n the discharge tube and the experimental c o n d i t i o n s were es-s e n t i a l l y as d e s c r i b e d above except that the power d i s s i p a t e d :ln the discharge tube was kept at 15 watts o r l e s s . Observing the Stark e f f e c t The Stark e f f e c t was observed by f o c u s i n g the l i g h t from the r e g i o n of hig h e l e c t r i c f i e l d ontn the s l i t of a s t i g m a t l c spectrograph and photographing the s p e c t r a . (The hig h e l e c t r i c f i e l d i s i n the cathode dark space. The e l e c t r i c f i e l d i s zero at the cathode s u r f a c e and almost ze.ro again a m i l l i m e t e r or two above the cathode surface.) F o r the study of OH mol e c u l a r spec-t r a and. the p r e l i m i n a r y study of CH molecular s p e c t r a , a pair, of piano convex quartz l e n s having a combined f o c a l l e n g t h of about 15 cm was used. For the simultaneous study of OH and CH mole-c u l a r s p e c t r a , a p a i r of quartz-water achromatic lens w i t h a combined f o c a l l e n g t h of about 18 cm was used.. The mo l e c u l a r Stark s p e c t r a were photographed, w i t h a 3»4 meter Ebert s p e c t r o -graph equipped with a 30,000 l i n e p e r inch g r a t i n g . The OH band was photographed i n f o u r t h order with a r e s u l t i n g p l a t e d i s p e r s i o n o f 4.2 cm\"1/mm (0.39 S/mm). The CH band A3900$ was photographed i n second order with a d i s p e r s i o n o f 7.4 cm~l/mm (0.83 2/mm). When these OH and CH bands were observed s i m u l t a -neously the OH band was again photographed i n f o u r t h order and the CH band was photographed i n t h i r d order w i t h a p l a t e d i s p e r -s i o n of 4.0 cnrVmm (0 . 6 l X/ram). The CH \\ 4 3 0 o X band was photo-graphed i n t h i r d order with a d i s p e r s i o n of 2.8 cm\"\"1/mm (0.51 $/mm). Kodak 103a-0 p l a t e s were used f o r a l l photographs. Expo-sure times were u s u a l l y about two hours. P l a t e s were developed as recommended by the...Eastman Kodak Company. 2 Determination of the e l e c t r i c f i e l d s t r e n g t h In order to determine the e l e c t r i c d i p o l e moment of a molecule from the observed Stark s p l i t t i n g s i n the s p e c t r a one must know the corresponding e l e c t r i c f i e l d s t r e n g t h . For the study of the OH Stark s p e c t r a and the p r e l i m i n a r y study o f CH Stark s p e c t r a the e l e c t r i c f i e l d s t r e n g t h was determined from the Stark e f f e c t on atomic hydrogen Balmer l i n e s . The Stark s p l i t -t i n g s of the atomic hydrogen Balmer l i n e s were chosen because of the l a r g e observed s h i f t s i n frequency, t y p i c a l l y 40 to 60 cm - 1 on e i t h e r s i d e of the u n d i s p l a c e d l i n e . A l s o the Stark e f f e c t i n hydrogen has been s t u d i e d e x t e n s i v e l y and r e s u l t s obtained e x p e r i m e n t a l l y and t h e o r e t i c a l l y agree very w e l l . The r e l a t i o n between the a p p l i e d e l e c t r i c f i e l d and the observed Stark s p l i t t i n g s are known to terms i n the t h i r d power of the a p p l i e d f i e l d . (See f o r example, Condon and S h o r t l e y , The Theory of Atomic S p e c t r a , p. 3 9 7 . ) ^ The hydrogen Stark s p l i t t i n g s and molecular Stark, s p e c t r a were photographed simultaneously with the same s p e c t r o -graph. In t h i s way d r i f t s , i n the e l e c t r i c f i e l d and i n the molecular S t a r k s p l i t t i n g s , i f pr e s e n t , were averaged i n the same way. (During the study of OH s p e c t r a , hydrogen Stark s p l i t -t i n g s were sometimes a l s o observed through the w a l l of the d i s -charge tube and photographed with a H i l g e r medium quartz spec-trograph. However, i n only one case was i t necessary to use a. value f o r the e l e c t r i c f i e l d determined by t h i s means. Compar-isons i n o t h e r experiments showed that f i e l d s determined from prism and g r a t i n g photographs agreed to w i t h i n ! % . ) • When the Stark s p e c t r a of the CH ^3900$ band was observed i n t h i r d o r d e r i t was not p o s s i b l e to s i m u l t a n e o u s l y observe the Sta.rk s p l i t t i n g of a hydrogen Balmer l i n e . For t h i s reason OH S t a r k s p e c t r a and CH Stark s p e c t r a were observed s i m u l t a n e o u s l y using one spectrograph and the e l e c t r i c d i p o l e moment of the CH molecule was determined r e l a t i v e to that o f the OH molecule. 45 Footnotes f o r Chapter I I I 1. For a d i s c u s s i o n of low pressure glow d i s c h a r g e s see f o r example: F. A. Maxwell and R. R. Benedict , Theory of Gas-eous Conduction and E l e c t r o n i c s (McGraw H i l l Book Co., New York, 1941), pp. 311-325; or J . D. Cobine, Gaseous Conduc-t o r s , (Dover P u b l i c a t i o n s , New York, 1958), pp. 212-216. 2. Developing procedure used i s gi v e n i n : Kodak P l a t e s and Films f o r Science and Industry, Data Book P-9 (Eastman Kodak Co., Rochester, New York, I962). 3. E. U. Condon and G. H. S h o r t l e y , The Theory of Atomic Spec-t r a (Cambridge U n i v e r s i t y Press, Cambridge, England, 1935) P. 397. ' 46 CHAPTER IV EXPERIMENTAL OBSERVATIONS The Stark e f f e c t on the e l e c t r o n i c emission s p e c t r a of the OH and CH molecules was s t u d i e d f o r e l e c t r i c ^ f i e l d s i n the range: 35 kV/cm to 65 kV/cm. S p e c i f i c a l l y , the OH, 2 2 + ^ 2 77\"^ (0,0) and (1,1) hand, the CH, 2 2 --> 2TT, (0,0) band and the CH, 2 A - ^ 2 T T , (o,o) band were s t u d i e d . (The e l e c t r o n i c e mission s p e c t r a and the e l e c t r i c f i e l d c ausing the Stark e f f e c t were produced by a low p r e s s u r e d i r e c t current glow discharge tube.) From o b s e r v a t i o n s o f the Stark e f f e c t on these e l e c t r o n i c emis-sion s p e c t r a the e l e c t r i c d i p o l e moment was found i n the OH, 2TT, ground e l e c t r o n i c s t a t e , i n the CH, 2 T T f ground e l e c t r o n i c s t a t e , and i n the C H , 2 A , e x c i t e d e l e c t r o n i c s t a t e . To f a c i l i t a t e d i s c u s s i o n and comparison of the S t a r k on these emission specrtra the s i m i l a r aspects w i l l be p r e s e n t e d In the f o l l o w i n g o r d e r : 1) o b s e r v a t i o n s i n c l u d i n g r e p r e s e n t a t i v e spectrograms f o l l o w e d by a q u a l i t a t i v e d i s c u s s i o n of them, : 2) measured valu e s o f the observed Stark s p l i t t i n g s i n OH and CH l i n e s and the p o s i t i o n s of OH f i e l d - i n d u c e d , p a r i t y - f o r b i d d e n l i n e s observed i n the (0,0) band, 3) an a n a l y s i s of these data, and 4) the e x p e r i m e n t a l l y determined v a l u e s f o r the e l e c t r i c d i -pole moment of OH and CH. Stark e f f e c t on the 0H.. 2S*-» 2 T T band To i n t r o d u c e the OH spectrograms, F i g u r e 4.1 shows the a l -lowed t r a n s i t i o n s t o the lowest r o t a t i o n a l l e v e l of the ( K ) J (2) , (I) u (0) ^ J = '/> Q 9(D R,(l) Q,2(l) F| (I) J = 3/P Q,(l) 2 I + R,(l) R2 I(I) :n 3/2 F i g u r e 4 . 1 . Allowed t r a n s i t i o n s to lowest r o t a t i o n a l l e v e l i n OH 2 7 T i / A and 2TTyx s t a t e s . 32 314.2 cm - i 32 542 .0 cm - I F i g u r e 4.2. S t a r k e f f e c t on OH, 2 X + - » 2 T T , (0,0) band. Maximum f i e l d r e g i o n (63 kV/cm) l a near bottom of p r i n t . 49 and 2 T T v a e l e c t r o n i c s t a t e s o f the OH molecule. The f i g u r e i n -cludes the r e l e v a n t r o t a t i o n a l l e v e l s i n the 2 X + e l e c t r o n i c s t a t e from which the t r a n s i t i o n s o r i g i n a t e . (The diagram exag-gerates the A-type d o u b l i n g i n the 2 T T s t a t e and the s p i n dou-b l i n g ' i n the s t a t e . ) With t h i s diagram i n mind l e t us now turn to Figure 4 . 2 which i s an enlarged p o r t i o n of a photogra-phic p l a t e and shows a p o r t i o n of the OH, 21 ~* *1, ( 0 , 0 ) band, A3064A. Wave number frequency i n c r e a s e s to the r i g h t and the high f i e l d r e g i on i s at the bottom of the l i n e s . The maximum e l e c t r i c f i e l d i s 63 kV/cm. The simplest p a t t e r n of Stark s p l i t t i n g s occur f o r t r a n s i -t i o n s to the J = 1/2 l e v e l of the 2TTjjL s t a t e . These t r a n s i -t i o n s a re P 1 2 ( l ) , Q 2 ( l ) , % 2 ( l ) and R 2 ( l ) . For a J = l / 2 r o t a -t i o n a l l e v e l there i s . only one p o s s i b l e v a l u e of (M| f o r each lambda doublet l e v e l and the S t a r k e f f e c t w i l l produce d o u b l e t s . (This was shown i n F i g u r e 2 . 2 i n Chapter I I . ) The expected dou-blets appear i n the h i g h f i e l d r e g i o n f o r each o f the a p p r o p r i a t e l i n e s . . As seen from the energy l e v e l diagram i n F i g u r e 4 . 1 , the P 1 2 ( l ) and R 2 ( l ) t r a n s i t i o n s terminate at the upper lambda dou-blet l e v e l of the J = l / 2 , 2 TTy a s t a t e and as a r e s u l t the f o r -bidden components of the P]_ 2 ( l ) and R 2 ( l ) appearing i n the h i g h f i e l d r e g i o n are on the h i g h frequency s i d e of the r e s p e c t i v e allowed l i n e s (to the r i g h t ) . We a l s o see i n the p l a t e that the allowed components of the P 1 2 ( l ) and R 2 ( l ) l i n e s s h i f t to lower frequency i n the h i g h f i e l d r e g i o n . Since the allowed Q- 2(l) and Gv 1 2(l) t r a n s i t i o n s go to the lower lambda doublet l e v e l , the po-s i t i o n s o f the f o r b i d d e n and allowed components f o r these two 50 l i n e s w i l l be reversed, r e l a t i v e to those o f the P 1 2 ( l ) and R 2 ( l ) l i n e s , (The s l i g h t s e p a r a t i o n o f the Q 2 ( l ) and 0,^(1) l i n e s i n the absence of the e l e c t r i c f i e l d i s due to the s p i n s p l i t t i n g of 0.32 cm\" 1 ^ i n upper r o t a t i o n a l l e v e l , K - 1, 2 j r + . ) The t r a n s i t i o n s to the J - 3/2 (the lowest) l e v e l o f the 2 TT-i/z e l e c t r o n i c s t a t e are P x( 1) , % ( ! ) » Q 2 1 ( l ) , %(1) and H 2 i ( 1 ) * Since the values of |M| can be l / 2 and 3/2 each lambda doublet l e v e l of the J = 3/2 l e v e l w i l l y i e l d two Stark compo-nents and a qu a r t e t w i l l r e s u l t * (See again F i g u r e 2*2) fhe two low frequency components of the P ^ ( l ) l i n e are v i s i b l e be-side the broad aluminum l i n e on the l e f t . The 0 (^1) and (1) l i n e s each have S t a r k components wi t h the same r e l a t i v e separa-t i o n . However, f o r t h i s p l a t e the Stark p a t t e r n o f one l i n e f a l l s midway between that o f the other (because o f s p i n s p l i t -t i n g ) and one sees only a Very broad l i n e . The R ^ ( l ) and R^(l) l i n e s are more separated than the % ( l ) arid Q 2 ^ ( l ) l i n e s due to a g r e a t e r s p i n s p l i t t i n g , 0*47 c m \" 1 , ^ i n the upper s t a t e (ZX1, K = 2, J = 5/2, 7/2)* As a r e s u l t the three h i g h e r f r e -quency Stark components o f the R 2 ^ ( l ) l i n e f a i l on the th r e e lower frequency components of the R | ( l ) l i n e and the S t a r k com-ponents are c l e a r l y r e s o l v e d . (The lowest frequency S t a r k com-ponent of the R 2 1 ( l ) l i n e i s blended and t h e h i g h e s t frequency component of the R-^(l) was very f a i n t even on the o r i g i n a l spec-t r o g r a p h ^ p l a t e . F i g u r e 4*2 c l e a r l y shows s e v e r a l f i e l d * i n d u c e d v p a r i t y - f o r -bldden l i n e s completely s e p a r a t e d from the a s s o c i a t e d allowed l i n e * One a l s o sees the decrease i n Stark broadening w i t h i n -c r e a s i n g values o f J . These f e a t u r e s are r e l a t e d to the i n c r e a s -i n g number of Stark components w i t h I n c r e a s i n g values o f J and the corresponding decrease i n the s e p a r a t i o n of the Stark com-ponents and decrease i n the e f f e c t of the p e r t u r b a t i o n on the lambda d o u b l e t s . The l i n e s Q-^(l) to 0,-^ (5) show these f e a t u r e s . (When d i s t i n c t f o r b i d d e n i l i n e s appear the component a s s o c i a t e d with the Qgi l i n e i s overlapped by the allowed l i n e . ) A r e -d u c t i o n i n Stark broadening w i t h i n c r e a s i n g J can a l s o be seen i n the l i n e s , R 2 ( l ) \"to R 2 ( 4 ) . However, i n t h i s example the f o r -bidden components do not stand out s e p a r a t e l y because the lambda doubling In the 2TTy a s t a t e decreases f o r . the f i r s t few r o t a -t i o n a l l e v e l s and then i n c r e a s e s f o r s t i l l h i g h e r v a l u e s of J . 1 F i g u r e 4.3 shows an e n l a r g e d p o r t i o n of F i g u r e 4.2. (The maximum e l e c t r i c f i e l d i s 63 kV/cm.) The two l i n e s w i t h f o r -bidden l i n e s on t h e i r r i g h t t h a t are seen on e i t h e r s i d e of the R 2 ( l ) l i n e are Qa(4) and Qi(5)> from l e f t t o r i g h t . The broad-ening o f the P 1(2) l i n e i s v e r y apparent. The p r i n t a l s o shows the f o r b i d d e n components f o r the P 1 2 (U » Q 2 (D, Q ] ^ 1 ^ ' a n d R 2 ( l ) l i n e s more c l e a r l y than above. F i g u r e 4.4 shows a p o r t i o n of the OH, 2 X + - * 2 T T , (1,1) band. T h i s p l a t e was taken s i m u l t a n e o u s l y w i t h the p r e v i o u s two. The s p e c t r a are g e n e r a l l y f a i n t e r but s t i l l c l e a r l y show r e s o l v e d Stark s p l i t t i n g s , e.g. the P ^ d ) l i n e , Stark broaden-i n g , e.g. the P]_(2) l i n e , and f i e l d - I n d u c e d , p a r i t y - f o r b i d d e n l i n e s , e.g. the l i n e marked \"F\" on the l e f t o f the P-j_(2) l i n e . The two broad l i n e s that bend to lower f r e q u e n c i e s are due to the N 2 molecule, (The cathode s u r f a c e was t i l t e d s l i g h t l y t o -32314.2 CM-' 32415.5 CM-' F i g u r e 4 - 3 - S t a r k e f f e c t o n O H . M a x i m u m f i e l d r e g i o n i s n e a r b o t t o m o f p r i n t . ( T h i s i s a n e n l a r g e m e n t o f F i g u r e 4 . 2 , l e f t h a l f . ) 3 1 7 3 3 . 7 C M - I 3 I 8 9 3 . 0 C M - I F i g u r e 4.4. Stark e f f e c t on OH, 2 X t ' - * 2 TT ) (1,1) band. Maximum f i e l d r e g i o n (63kV/cm) i s near bottom of p r i n t . 54 ward the s l i t and the Doppler s h i f t r e s u l t e d because the e l e c -t r i c f i e l d moved the molecule.) Stark e f f e c t on the CH, 2 Z ~ - » 2 H b a n d F i g u r e 4.5 shows an e n l a r g e d p o r t i o n of a spectrogram of the CH, 2 Z _ J > 2 T T , (0,0) band, >3900$ taken i n t h i r d o r d e r . The e l e c t r i c f i e l d In the r e g i o n o f maximum s p l i t t i n g i s about 52 kV/cm. The CH l i n e s i n Figure 4.5 are broad because of the rath-e r h i g h pressure i n the d i s c h a r g e tube. P e c u l a r d i s c h a r g e c o n d i t i o n s caused the change of i n t e n s i t y i n the lower p o r t i o n of the l i n e s ; the unmarked l i n e s are due to the N 2 + molecule. Even so the p l a t e c l e a r l y shows the numerous f e a t u r e s due t o the Stark e f f e c t on t h i s CH band. A review of F i g u r e 4.1 which-shows the energy l e v e l s of the OH molecule w i l l a i d the understanding of the CH s p e c t r a i n the p l a t e i f the f o l l o w i n g p o i n t s are taken i n t o account: The upper s t a t e i n the CH molecule from which the observed t r a n s i -t i o n s o r i g i n a t e s i s a 2 £ \" s t a t e hence the r e l a t i v e p o s i t i o n f o r an allowed and f o r b i d d e n CH S t a r k component w i l l be r e v e r s e d from t h a t observed i n the OH s p e c t r a d i s c u s s e d above. See f o r example the OH, R 2 ( l ) l i n e i n F i g u r e 4.3 and the CH, R 2 ( l ) l i n e i n F i g u r e 4.5. The s p i n s p l i t t i n g i n the CH 2 £ *\" e l e c t r o n i c •,(2) s t a t e i s very s m a l l , l e s s than 0.3 cm~x even when K = 5. A l s q the CH 2TT e l e c t r o n i c s t a t e belongs n e a r l y to Hund's case (b) c o u p l i n g f o r which the s a t e l l i t e l i n e s are very weak. The other d i f f e r e n c e between the CH and OH molecule, although i t does not a l t e r the observed S t a r k e f f e c t , i s that the 2 T T s t a t e Q, Q 2 ^ 25617 cm\"1 H e 25807 cm\"1 I I I p T T T T 3 2 4 P2 7 6 5 4 3 I 2 1 Q l 1 I 13 1 12 11 3 10 13 12 1 211 3 10 4 F i g u r e 4.5. Stark e f f e c t on CH, 2T~-^ZTT, (0,0) band. Maximum f i e l d r e g i o n (52 kV/cm) i s near bottom of p r i n t . 56 in CH is regular while that in OH is inverted. Figure 4.5 shows that the CH P 2 ( l ) , a n d n2^ l l n e e resulting from transitions to the J = 1/2 level of the zTf>/x state, are doublets in the high field region. The R^(l) line shows a splitting into four Stark components as expected for a transition to the J = 3/2 level of the 27Tj/JJ state. For this particular plate the P 2 ( 2 ) Une showed four Stark components due to a transition to the J = 3/2 level of the 2TT'/a_ state. Also this plate shows very clearly the reduction in broadening and increase in separation of allowed and forbidden Stark components with Increasing values of J . See for example the lines: P^(l) to P-L(3), P 2 (D to P 2 ( 3 ) , R ^ D to % ( 4 ) , and R 2(l) to R 2 ( 4 ) . The relative location of the allowed and forbidden Stark compo-nents can be easily seen by comparing the P ^ ( 3), Q^(3), and R^(3) lines. Relative to the allowed line, the forbidden component is at lower frequencies for the P-j_ and R-j^ lines and at higher fre-quencies for the §1 line. The ^ ( l ) and Q 2 (l) lines obscured by the Helium line, \\3888.65$, appear in the center of Figure 4.6 (b). Figure 4.6 provides an opportunity to observe the Stark effect on the CH 2 r ~ - » 2 T 7 band for three different values of the electric field strength. The electric f ie ld increases going down the figure from (a) to (c). . The electric fields are: (a) 34 kV/cm, (b) 47 kV/cm, and (c) 68 kV/cm. The increase in splitting with electric field shows most clearly for the fy^1) line. These prints cover about the left three quarters of the previous plate (Figure 4.5) plus, from left to right, the 0,^8) 25 575 c m - 1 He 25756 cm\" P2(2) P,(l) P 2(l) Q 2(l) R,(l) F i g u r e 4.6. Stark e f f e c t on CH 2 x - - * 2 7 T (c,0) band f o r three values of e l e c t r i c f i e l d . (a) 34 kV/cm, (b) 4? kV/cm, (c) 68 kV/cm. Maximum f i e l d r e g i o n i s near bottom o f p r i n t . 53 and Q,2(8) l i n e s at the l e f t edge of the p r i n t s . This s e r i e s of pl a t e s a l s o shows th a t the fea t u r e s r e l a t e d to the Stark e f f e c t become more pronounced as the e l e c t r i c f i e l d Increases. Stark s p l i t t i n g s i n the atomic hydrogen Balmer l i n e Hy Figure 4.7 shows the Stark e f f e c t on the atomic hydrogen l i n e Hy, A4340.47$. The maximum e l e c t r i c f i e l d i s about 36 kV/cm and the s p l i t t i n g between the two 18rr components i s about 83 cm\"-1. The photograph was taken i n second order. (The discharge tube contained methyl a l c o h o l vapour thus producing CH molecular l i n e s . (The CH l i n e s appearing on t h i s p r i n t belong to the P branches of the 2A-+ 2TT , (0,0) band.) The (b) part of Figure 4.7 shows the l o c a t i o n o f the Stark components of the Hy l i n e . The l o c a t i o n s are drawn f o r an e l e c t r i c f i e l d of 36 kV/cm which corresponds to the maximum e l e c t r i c f i e l d on the p r i n t . The numbers 2,3,5, e t c . i n the drawing g i v e the displacement of a given component i n u n i t s of 0.0642 E cm\"1, where E i s the mag-nitude of the e l e c t r i c f i e l d s t r e n g t h i n kV/cm. (The r e l a t i v e i n t e n s i t i e s i n d i c a t e d i n the drawing are from Condon and Short-l e y , The Theory of Atomic Spectra, page 401.)^ The Stark s p l i t -t i n g s of the Balmer Hy l i n e were used to determine the e l e c t r i c f i e l d s t r e n g t h i n the study of the Stark e f f e c t on OH emission spectra end i n the p r e l i m i n a r y study of the Stark e f f e c t on the CH emission s p e c t r a . Stark e f f e c t on the CH 2 A •* 2 T T band Figure 4.8, the f i n a l spectrogram, shows the Stark e f f e c t 0 7T (b ) 18 15 12 F i e u r e 4 . 7 . Stark e f f e c t on hydrogen Balmer H Y. (a) Observed H y S t a r k s p l i t t i n g s Maximum e l e c t r i c f i e l d Is 36 kV/cm. ( M o l e c u l a r l i n e s are from CH J7T band.) (b) T h e o r e t i c a l s p l i t t i n g s and i n t e n s i t i e s . S p l i t t i n g s are drawn f o r 36 kV/cm (maximum f i e l d on p l a t e ) . Q,(2) Q,(3) Figure 4.8. Stark e f f e c t on CH 2 A bottom of p l a t e ) i s about 66 kV/cm. R,(l) 23329 cm -I II R,(3) R2(3) R,(4) R2(4) 2 T T band. (Part (b) Maximum .loins on e l e c t r i c t h e l e f t f i e l d (near of (a).) O N on a p o r t i o n of the CH 2 A\"*\" 2 n , (0,0). band, \\bJ00&. The l i n e s appearing i n the enlargements belong to the Q,^ , Q 2, R ,^ and R2 branches and extend from the 0^(2) l i n e s to the R 2( i0 l i n e s . (The (b) p o r t i o n of the f i g u r e extends t o the r i g h t ( h igher f r e -quencies) from the r i g h t end of the (a) p o r t i o n of the f i g u r e . ) The r e g i o n of maximum e l e c t r i c f i e l d i s a t the bottom of the l i n e s on the p r i n t . The maximum f i e l d i s about 66 kV/cm. ;The observed l i n e s r e s u l t from t r a n s i t i o n s from a lambda doublet > r o t a t i o n a l l e v e l i n the 2 A e l e c t r o n i c s t a t e t o one i n the 2 T 7 e l e c t r o n i c s t a t e . The lambda doubling i n the 2/\\ st a t e i s neg-l i g i b l e ^ while that i n the 2TT st a t e produces resolved doublets i n the absence of an e l e c t r i c f i e l d . Compare f o r example the l i n e s marked Q1(2) and 0^(3). For the CH 2A~* 2TT band the lambda doublets i n both the upper and lower s t a t e w i l l be perturbed by the e l e c t r i c f i e l d and a l a r g e number of Stark components w i l l r e s u l t even f o r a t r a n s i t i o n between l e v e l s with low values of J . (Figure 2.5 i n Chapter I I shows the strong Stark t r a n s i t i o n s f o r the CH Q-ic(3) and Q-ld(3) l i n e s . ) As we see from the p r i n t i n Figure 4.8 the Stark e f f e c t on the CH 2 A * 2 TT fcand d o e e C a U s e l i n e s to s h i f t and broaden but because of the l a r g e number of c l o s e l y spaced Stark components, no i n d i v i d u a l s p l i t t i n g s could be re s o l v e d . We a l s o see from t h i s p r i n t t h a t the Q]_c(3) and Qi d ( 3 ) ° l i n e s move together i n the high f i e l d region as has been p r e d i c t e d . This i s because the higher frequency Stark component of the low frequency l i n e , 0, (3), and the lower frequency Stark component of the high frequency l i n e , Q]_d(3), are the strong ones. Thus 62 these two l i n e s c r o s s i n the r e g i o n of h i g h e l e c t r i c f i e l d . We w i l l see below that the o b s e r v a t i o n o f the Stark e f f e c t on the CH Q i c ( 3 ) and Q. l d(3) l i n e s i s s u f f i c i e n t to determine the r e l a -t i v e s i g n of the d i p o l e moments i n the 2 A and ZJT s t a t e s and to determine the e l e c t r i c d i p o l e moment of the CH molecule i n i t s e x c i t e d e l e c t r o n i c s t a t e . Experimental c o n d i t i o n s f o r spectrograms To c l o s e the d i s c u s s i o n of the spectrograms, Table I i s i n c l u d e d and l i s t s the e s s e n t i a l experimental c o n d i t i o n s f o r the photographs appearing i n F i g u r e s 4.2 through 4.8. The t a b l e p r o v i d e s the f o l l o w i n g Information: The exposure number i s that marked on the o r i g i n a l photograph and on the d a t a book e n t r y . V i s the v o l t a g e ( i n k i l o v o l t s ) across the d i s c h a r g e tube. I i s the c u r r e n t ( i n mllliamperes) through the d i s c h a r g e tube. The t o t a l p r e s s u r e i n the discharge tube i s p ( i n mm Hg) and the ex-posure time to the nearest t e n t h of an hour i s t . The gas or gases used to produce the s p e c t r a and the cathode diameter and m a t e r i a l forming i t are a l s o g i v e n . The e l e c t r i c f i e l d s were determined from Balmer H y Stark s p l i t t i n g s f o r the OH p l a t e s and from CH or OH Stark s p l i t t i n g s f o r the o t h e r exposures used as i l l u s t r a t i o n s . Measurements Table I I l i s t s the measured values f o r the r e s o l v e d f i r s t order S t a r k s p l i t t i n g s observed i n the OH, 2 X \" f - * 2 H band and the corresponding Stark s p l i t t i n g s f o r the atomic hydrogen B a l -TABLE I F i g u r e Exposure Number* Experimental V I (kV) (ma) C o n d i t i o n s f o r Spectrograms used P + t (mm Hg) (hrs) gas i n F i g u r e s Cathode E l e c t r i c F (kV/cm) 4.2 F - 10 3-0 3.4 0.9 1.5 H 20 0.5mm A l . 63 4.3 it n II II II it n it it 4.4 n n ti n II it it 11 it 4.5 9/26/63 1 2.8 2.5 7.5 3.8 C H 3 O H , He 0.5mm A l 52 4.6a 6/19/65 1 2.6 3.5 1.9 2.0 C H 3 O H , He 1.0mm A l 3k 4.6b 8/25/63 1 3.6 3.0 0.5 2.6 CH 30H 1.0mm A l 47 4.6c 6/26/65 1 3.0 2.0 2.0 CH^OH, He 0.5mm A l 68 4.7 1/20/65 1 3-5 3.0 1.9 3-8 CH^OH, C 6 H 1 2 , He 1.0mm A l 36 4.8 6/28/65 u 3.6 1.9 2.8 1.3 C H 3 O H , He 0.5mm A l 66 * u = upper, 1 = lower + p i s t o t a l pressure i n d i s c h a r g e tube * diameter o f cathode i n m i l l i m e t e r s and metal used x E l e c t r i c f i e l d f o r CH 2 £ 2 7 T p l a t e s Is determined from Stark s p l i t t i n g of CH Q 2 ( l ) l i n e ; f i e l d f o r CH 2A~* 2 T T p l a t e i s determined from Stark s p l i t t i n g of OH P 1 2 ( l ) l i n e . I TABLE I I Observed Stark S p l i t t i n g s i n OH 22\" +~* 2 TT Band and i n hydrogen Balmer Hy l i n e Exposure No. R ? . ( D , (o,o) A~v(cm ) P l ? ( l ) , ( l , l ) AX(mm) -ax'(mm) ^ V C c n , \" 1 ) AX (mm) 4X(mm) E(kV/cm) 0.63/0.03 0 . 84 /0 . 0 2 34.9*0.8 0.91/0.04 1.19*0.06 49,2*2.4 0.97^0.03 ... t 52.9*0.5 0.91/0.03 1.32/0.01 54.8*0.5 0 . 9 8 /0 .02 1.45/0.03 '59.9*1.3 1 .03/0 . 0 2 X 1 .53*0.02 63.1*1.0 E-27 1 E-22 6/23/63 E-27 u 6/25/63 F-10 0.149*0.005 0.230*0.003 0.232*0.006 0.241*0.003 0.255*0.003 0.265*0.003 0.67^*0.02 1.043*0.01 1.04*0.02 1.09/0.01 1.15/0.01 1.20/0.01 0.176^0.012 0.242*0.003 0.251*0.003 0.276*0.003 0.285*0.003 0.72/0.05 1.00/0.01 1.04*0.01 1.09/0.01 1.18, to. 01 0.135*0.007 0.201-0.009 0.213*0.007 0.201*0.007 0.217 i0.004 0.228*0.004 *\" T h i s l i n e was very weak. The e r r o r has been increased by a f a c t o r of 5 to take care of p o s s i b l e systematic e r r o r s i n measurement. f F i e l d v a l u e from maximum Stark s p l i t t i n g of H y as measured on a prism cm -1 spectrogram. Observed s p l i t t i n g xfas H 2 « 2 ~ 1*0 * U s s s o n l y high f r e q u e n c y components. C o r r e c t i o n s are made f o r second order S t a r k e f f e c t s and changes i n d i s p e r s i o n w i t h frequency. O N mer l i n e Hg. The s p l i t t i n g s f o r the 1*2(1), (0,0) l i n e and the P 1 2 ( l ) > (1»1) l i n e are between the |M| = 1/2 components. The s p l i t t i n g s l i s t e d f o r the P i ( l ) , (0,0) l i n e are between the un-d i s p l a c e d l i n e and the low frequency /MJ = 3/2 component. These s p l i t t i n g s are given i n terms of the distance on the spectrogra-phic p l a t e measured i n m i l l i m e t e r s and a l s o i n terms of wave number u n i t s . The s p l i t t i n g s are the average of eight measure-ments on each l i n e . Four measurements were made by each of two observers. The R 2 ( l ) , (0,0) l i n e and the P ] ^ 1 ) l i n e were cho-sen because they were free of overlapping. The P 1 ( l ) , (0,0) was the only l i n e a r i s i n g from the lowest r o t a t i o n a l l e v e l of 2 e l e c t r o n i c s t a t e that had Stark components free of overlapping. The q u a n t i t y l i s t e d f o r the Balmer H y l i n e and quoted i n m i l l i m e t e r s corresponds to a u n i t s p l i t t i n g of 0.0642 E cm - 1, where E i s the magnitude of the e l e c t r i c f i e l d strength i n kV/cm. This u n i t s p l i t t i n g i s derived from measurements on f i v e or more u s u a l l y ten Stark components of Hy. The ten Hy Stark components were taken i n corresponding p a i r s about the c e n t r a l l i n e . In t h i s way second order Stark e f f e c t s c a n c e l l e d out and the small l i n e a r change i n wave number d i s p e r s i o n could be i g -nored. When only h a l f of the Stark pattern was observed, cor-r e c t i o n s were made f o r second order Stark e f f e c t s and f o r chang-ing d i s p e r s i o n . The u n i t s p l i t t i n g was converted to wave num-bers u s i n g a d i s p e r s i o n at Hy of 2.65 c m \" V m m . Table I I I g i v e s the observed and c a l c u l a t e d p o s i t i o n s of f i e l d i n duced-parity forbidden l i n e s observed i n the OH 2 Z V\"-* 2TT, (0,0) band. The measurements were made on a photo-TABLE I I I Observed and c a l c u l a t e d p o s i t i o n s of f i e l d - i n d u c e d p a r i t y , f o r b i d d e n - l i n e s i n the 2%+^ 2 T T , (0,0), band of OH* Pl( K ) Ql(K) C a l c u l a t e d ( c m - 1) Observed (cm-1) Calc.-obs. (cm- 1) C a l c u l a t e d (cm-1) Observed (cm-1) C a l c . -obs.. (cm - 1) 3 32 3^0.22 32 340.15 + 0.07 4 288.34 288.19 +0.15 32 424.41. 32 424.61 -0.20 5 234.68 234.72 -0.04 404.75 404.77 -0.02 6 179.11 179.03 + 0.08 382.71 382.77 -0.06 7 121.13 121.07 + 0.06 358.29 358.11 + 0.18 8 060.75 06O.4.3 + 0.32 331.05 331.39 -0.34 9 301.14 301.46 -0.32 10 268.00 11 232.01 231.97 + 0.04 \"\"These f o r b i d d e n l i n e s are a s s o c i a t e d with the allowed l i n e s : P 1(£) and Q - ^ K ) . The c a l c u l a t e d p o s i t i o n s have not been c o r r e c t e d f o r s h i f t s In energy due t o the Stark e f f e c t . \"'\"Measurements from exposure number F-10 which corresponds t o a n ' e l e c t r i c f i e l d of 63.I kV/cm at maximum. g r a p h i c p l a t e f o r which the maximum e l e c t r i c f i e l d waa (63.1 - 1»0') kV/cm. These f o r b i d d e n l i n e s correspond to the P.^ and Q,-|_ allowed l i n e s . The c a l c u l a t e d p o s i t i o n s were determined using the r o t a t i o n a l l e v e l s g i v e n by Dieke and C r o s s w h i t e 1 f o r 2 TT}/x s t a t e . The c a l c u l a t i o n i g n o r es the s m a l l s h i f t i n energy due t o the p e r t u r b a t i o n of the lambda do u b l e t s and makes the • c a l c u l a t e d p o s i t i o n f o r the l i n e s l i g h t l y higher than ob-served. (For example, the St a r k s h i f t would cause the d e v i a t i o n between c a l c u l a t e d and observed values to be about 0.2 c m - 1 f o r the Pi(3) and l e s s than 0.01 c m - 1 f o r the 0^(1).) Table IV l i s t s the Stark s p l i t t i n g s observed i n the CH 2 X ~ - ^ 2 T T > (0.0) band, A 3900$. These r e s o l v e d f i r s t order Stark s p l i t t i n g s were measured between the two )M| = l / 2 compo-nents of the ?2^) a n d ^2^1^ l i n e s . These S t a r k s p e c t r a were photographed i n second order s i m u l t a n e o u s l y w i t h the Sta r k e f -f e c t on the hydrogen Balmer l i n e Hy from which the e l e c t r i c f i e l d was determined. The CH S t a r k s p l i t t i n g s are g i v e n i n terms of the d i s t a n c e i n m i l l i m e t e r s measured on the s p e c t r o s c o -p i c p l a t e and i n terms of wave number u n i t s . The q u a n t i t y AX i s the average v a l u e f o r a u n i t s p l i t t i n g of 0.0642 E cm - 1, where E i s the magnitude of the e l e c t r i c f i e l d s t r e n g t h i n kV/cm. On t h i s p l a t e the d i s p e r s i o n f o r H y was (5.54 - 0.005) cm\"1/mm. Since the CH Stark s p l i t t i n g s were small (and subse-quently provided a value f o r the d i p o l e moment to only \"t 15$) the CH l i n e s were measured f o u r times each and the Hy S t a r k com-ponents were measured twice p a i r - w i s e about the c e n t r a l l i n e . From the data l i s t e d i n Table V a more accurate v a l u e o f TABLE IV O b s e r v e d S t a r k S p l i t t i n g s i n CH -*^V Band and i n hydrogen Balmer Hy. (Observed i n Second Order.) CH Stark S p l i t t i n g s : H Y S p l i t t i n g s P 2 (1) (1) Exposure No. 4x(mm) AX(mm) . ZV(cm-l) ^X(mm) E(kV/cm) 2/16/65 u 0.06^*0.01 0.51*0.08 0 . 0 5 0 * 0 . 0 1 0.44^0.08 0.326*0.01 27. 7*1.0 2/13/65 u 0 . 0 6 0 * 0 t 0 l 0.44±0.06 0.062*0.01 . 0.46*0,06 0.354*0.03 30 -*-3 2 7 7 , (0,0) band photographed i n second order, and (c) C H Stark s p l i t t i n g s i n the 2 £ - - * 2 T T , (o,0) band photographed s i m u l t a n e o u s l y i n t h i r d o r d e r with OH Stark s p l i t t i n g s i n the Z2L*-* ZTT, (0,0) i n f o u r t h order. The CH 2 A-* 2 T T , (0,0) band Stark s p e c t r a used to measure the e l e c t r i c d i p o l e moment of the CH ZA e l e c t r o n i c s t a t e were shown above as an i l l u s t r a t i o n i n F i g u r e 4.7. The experimental c o n d i t i o n s f o r that experiment are l i s t e d i n Table I. A n a l y s i s of Stark e f f e c t s p e c t r a In Chapter I I d e t a i l e d e x p r e s s i o n s were gi v e n f o r the s h i f t i n frequency o f a Stark, e f f e c t component i n e l e c t r o n i c emission l i n e s o f a d i a t o m i c molecule. In t h i s s e c t i o n the ob-served Stark s p l i t t i n g s and s h i f t s i n energy which we have jus t TABLE V Simultaneously Observed S t a r k S p l i t t i n g s i n CH and OH 2 J £ \"* 2 T T Bands (CH and OH bands were observed i n 3 r d and 4^ orders r e s p e c t i v e l y . ) CH, P 1 2 ( D OH, R 2 ( l ) •ft Exposure No. 4 X (mm') 4 V ( c n r1 ) AX (mm) A V(cm-1) 6/19/65 1 0.142^0.010 0.572*0.04 0.167*0.010* 0.702*0.04J 6/22/65 1 0.153-0.007 0 . 6 l 7 ± 0 . 0 3 0.167*0.012 0.71^*0.05 6/17/65 u 0.162-^ 0.005 0.651t0.02 0.174*0.007 0.745*0.03 6/23/65 u 0.190-0.005 0.767*0.02 1 0.220-0.009 0.940±0.04 u = upper, 1 = lower. OH, P 1 ? ( l ) 71 TABLE VI Experimental Conditions for Plates Used to Determine OH and CH Electric Dipole Moments (a) OH >3064^ band (4 t h-order), Hydrogen Balmer HY (3 r d order) Electric Exposure\"* Number V I P + t (kV) (ma) (mm Hg) (hrs) E-27 1 3.6 11.5 0.5 0.1 E-22 3.7 4.5 4.5 0.7 6/23/63 6.3 3.2 0.8 1.8 E-27 u 4.7 12.0 0.5 0.2 6/25/63 6.5 4.1. 0.9 2.3 F-10 3.0 2.4 0.9 1.5 gas H30 * Field cathode (icV/om) 2.0ram Al 1.0 1.0 2.0 1.0 0.5 w Al II II II 34.9 49.2 52.9 54.8 59.9 63.1 (b) CH A3900A5 band (2 n d order), Hydrogen Balmer H y (2nd order) 2/l6/65u 2/l3/65u 1/ 3/65m 12/3l/64m 1/20/6^1 1 / 3/65u 3.5 I'.O 5.0 3.5 4.0 T7T I*5 6.0 3.1 3.0 5.0 3.1 5.0 3.5 2.5 0.55 3.0 0.12 4.0 1 « 9 . 3.8 0.40 1.5 CHoOH, He 1.0mm Al CH^OH, He \" \" CH3OH • » CH3OH » • CH3OH, \\ \" \" C6H12, He) CH3OH \" \" 27.7 30 37.4 38.3 39.3 40.7 (c) CH >3900A> band (3 r d order), OH > 3064$ band ( 4 t h order) 6/19/651 6/22/6^. 6/17/65u 6/23/65u 2.6 3.1 1.9 2.1 CH?0H, He 1.0mm Al « ti 11 11 3.0 3.5 1.5 1.0 3.0 3.4 2.1 2.3 11 11 11 11 4.1 3.5 1.5 1.7 11 11 11 u 34. 7 36.1 37.6 ^7. x \"* u = upper, m = middle, 1 = lower1 * total pressure in discharge tube * Cathode diameter in millimeters and material used 72 seen w i l l be r e l a t e d to the a p p r o p r i a t e mathematical e x p r e s s i o n . The main purpose of the s e c t i o n w i l l be to provide an e x p r e s s i o n f o r the e l e c t r i c d i p o l e moment of a molecule i n a p a r t i c u l a r e l -e c t r o n i c s t a t e i n terms of the observed S t a r k s p l i t t i n g or s h i f t , the d e r i v e d value of the e l e c t r i c f i e l d s t r e n g t h , and the quantum numbers of the r o t a t i o n a l l e v e l s i n v o l v e d i n the t r a n s i -t i o n . F o r the OH 2 2TT, R 2 ( l ) , (0,0) and P i 2(l), (1,1) l i n e s and f o r the CH 2 Z _ - * 2 T 7 , (0,0) l i n e s : P 1 2 ( l ) , a n d R 2 ^ » the S t a r k s p l i t t i n g s correspond to the s e p a r a t i o n of two Stark components having the same value of |M| . We have seen i n Chap-t e r I I t h a t the energy of a lambda doublet Stark component r e l a -t i v e to the center o f the unperturbed doublet i s giv e n by: £l = t /(A/2)2+ ( V l 2 )2 , (2.11) where X i s the s e p a r a t i o n of the unperturbed doublet and V 1 2 i s the matrix element f o r the p e r t u r b a t i o n energy. The S t a r k s p l i t t i n g of i n t e r e s t corresponds to the d i f f e r e n c e of the p o s i -t i v e and negative v a l u e s of E 1 . That i s the observed s p l i t t i n g can be w r i t t e n : = 2 J(X/2)2+ ( V 1 2 ) 2 ' , (4.D A l l q u a n t i t i e s are i n wave number u n i t s . S o l v i n g f o r V 1 2 g i v e s : 2 V 1 2 = J ( A V ) 2 - x2 . (^ -2) For a 2 T T / 2 > J = 1/2 l e v e l , M = 1/2 and A = 1/2 and. 2 V 1 2 = 2|»E (M - V ( J ( J t 1)) becomes: 2 V i r 2 /3fE= J(AV)2 - )2 s ( 4 # 3 ) which w i l l be r e f e r r e d to as the c o r r e c t e d s p l i t t i n g . Since the 73 J = l / 2 l e v e l of the 2 T T y a s t a t e always belongs to pure Hund's case (a) c o u p l i n g there i s no c o r r e c t i o n f o r i n t e r m e d i a t e c o u -pling needed f o r e x p r e s s i o n (4 . 3 ) . I t i s convenient here to note the v a l u e s f o r the lambda s p l i t t i n g needed to evaluate equation (4.3) f o r the J = 1/2 OH and CH l i n e s l i s t e d above. For the OH 2T1^, J = 1/2 l e v e l the lambda doubling w a s taken as \\= 0.157 cm - 1 f o r OH i n both the v = 0 and v - l v i b r a t i o n a l s t a t e ; the lambda f o r the CH 2 TTi/ ; L , J - 1/2, v - 0 l e v e l \\fas taken as \\ - 0.1135 cm\" 1. The value of the lambda doubling chosen f o r CH was determined by Douglas and 4 E l l i o t t from h i g h d i s p e r s i o n o p t i c a l measurements of the CH band. The value chosen f o r the OH lambda d o u b l i n g was c a l c u l a t e d u s i n g data obtained by Dousmanls, Sanders and Townes^ from microwave a b s o r p t i o n measurements. Since Dieke and Cross-w h i t e 1 had obtained a value of 0.31 cm - 1 f o r the OH lambda dou-bling from measurements of the u l t r a v i o l e t spectrum an independ-ent d e t e r m i n a t i o n was mad.e even though the lambda d o u b l i n g com-puted from the microwave measurements was thought to be c o r r e c t . The d e t e r m i n a t i o n was made by measuring the Stark s p l i t t i n g f o r very s m a l l values of the e l e c t r i c f i e l d (at the top of the dou-b l e t ) . In the l i m i t of zero e l e c t r i c f i e l d the Stark s p l i t t i n g i s the lambda s p l i t t i n g . From observed S t a r k s p l i t t i n g s a value of X ° 0.15 - 0.03 c m - 1 w a s o b t a i n e d and thus the microwave value of the lambda doubling w a s chosen. For the e l e c t r i c f i e l d s used i n t h i s study second order Stark e f f e c t s caused by n e i g h b o r i n g r o t a t i o n a l l e v e l s do not a l -t e r the a n a l y s i s g i v e n above f o r s p l i t t i n g s between S t a r k compo-74 nents having the same value of |M| s i n c e b o t h components w i l l be s h i f t e d by the same amount. For example, i n the OH molecule sec-ond o r d e r e f f e c t s i n the 2 £ s t a t e w i l l cause a s l i g h t s h i f t and a v e r y s l i g h t s e p a r a t i o n o f the M = 1/2 and M = 3/2 compo-nents o f the r o t a t i o n a l l e v e l s . For the R2(l) l i n e , e f f e c t s i n the X s t a t e would broaden each doublet component by 0.007 cm - 1 with e s s e n t i a l l y no s h i f t at a l l . The R 2 ( l ) l i n e a r i s e s from the K = 2, J = 3/2 r o t a t i o n a l l e v e l . The o t h e r h a l f o f the s p i n doublet (K - 2, J - 5/2) does not r e s u l t i n t r a n s i t i o n s of ap-p r e c i a b l e i n t e n s i t y to the J = 1/2 ground s t a t e s i n c e mixing of the next lower ( 2 £ , K =» 1) l e v e l i s always l e s s than 1%. (These c a l c u l a t e d values f o r second o r d e r e f f e c t s do assume the d i p o l e moment o f the OH 22T s t a t e i s comparable to that found f o r the 2TT ground s t a t e . But even i f the d i p o l e moment i n the 2^r s t a t e were g r e a t e r by a f a c t o r of two the mixing would only be doubled and the broadening would s t i l l be l e s s than 0.03 cm - 1.) S i m i l a r l y one f i n d s that second o r d e r e f f e c t s due to the r o t a -t i o n a l l e v e l adjacent to the J = 1/2, 2TTy J L l e v e l are n e g l i g i -b l e . The s h i f t i n frequency i s the same f o r both Stark compo-nents of the lambda doublet and amount to o n l y 0.013 c m - 1 while the mixing of the J = 3/2 l e v e l o f the 2TT'/x. s t a t e i s always l e s s than 1.4$. Thus we can conclude that second o r d e r Stark e f f e c t s do not e f f e c t the d e t e r m i n a t i o n of the e l e c t r i c d i p o l e moment from the doublet s p l i t t i n g of the OH R g d ) l i n e . S i m i l a r l y second order S t a r k e f f e c t s w i l l not a l t e r the s e p a r a t i o n of the OH doublet s p l i t t i n g s which xvere used to de-termine the e l e c t r i c d i p o l e moment from t r a n s i t i o n s to the 75 J = 1/2, 2Tlfa l e v e l . The CH P j 2 ( l ) l i n e which was used f o r the more a c c u r a t e d e t e r m i n a t i o n of the e l e c t r i c d i p o l e moment w i l l be d i s c u s s e d as an example. The observed t r a n s i t i o n a r i s e s from a s i n g l e l e v e l ( 2 £ , K - 0, J = 1/2) which w i l l be s h i f t e d down by o n l y 0.016 cm~l and terminates at the lambda doublet (2TT&, » J = 1/2) which i s s h i f t e d down by only 0.014 cm\" 1. The s h i f t s which c o u l d be ign o r e d i n d i v i d u a l l y are e f f e c t i v e l y c a n c e l l e d . Mixing o f adjacent r o t a t i o n a l l e v e l s with the J = 1/2 l e v e l s w i l l not broaden the observed S t a r k d o u b l e t s . Thus we conclude that second order S t a r k e f f e c t s do not e f f e c t the a n a l y s i s of the CH St a r k d o u b l e t s observed here. The e l e c t r i c d i p o l e moment of the OH molecule i n the 2 T T 3 ^ e l e c t r o n i c s t a t e was determined from Stark s p l i t t i n g s observed i n the P - j ^ l ) , (0,0) l i n e . S i n c e f o r t h i s l i n e the s p l i t t i n g was measured between the allowed l i n e i n zero e l e c t r i c f i e l d and the low frequency, JM/ = 3/2, f o r b i d d e n Stark component the analy-s i s must i n c l u d e second order terms. The frequency of the P ^ d ) l i n e f o r zero f i e l d can be w r i t t e n as P-^l) = F 1 ( o ) - f ^ ( l ) , where F-j_(0) i s the term i n the 25L s t a t e and f ^ ( l ) i s the term f o r the lower lambda doublet l e v e l . In the presence of an e l e c -t r i c f i e l d the upper and lower l e v e l s f o r the observed S t a r k component a r i s e s a re: upper s t a t e term: ^ ( 0 ) -lower s t a t e term: f - ^ l ) + A/2 + i(\\/2)Z 1 ( V 1 2 ) 2 - 6 2 ^ The £ 2 and £ z are the second order s h i f t s . The square root i n the lower s t a t e term i s the per t u r b e d energy o f the upper lambda 76 doublet l e v e l ( t e r m i n a t i o n of forbidden t r a n s i t i o n ) measured from the center of the unperturbed lambda doublet; f ^ ( l ) * A/2 then i s the center of the unperturbed doublet. The forbidden t r a n s i t i o n w i l l have a frequency found by the d i f f e r e n c e of the two perturbed terms, i . e . : Fl<0) -8/ - (^(1) + A/2 + (|(A/2)2+ ( V 1 2 ) - £ * ) . The observed s p l i t t i n g i s the d i f f e r e n c e between t h i s expression and that g i v i n g the frequency of the zero f i e l d P ^ l ) l i n e . Thus we f i n d the s p l i t t i n g i s given by: J V t P i d ) ) = A/2 + |(A/2)2 + (v 1 2)2 + £ 2 . £2 ^ The value f o r the lambda doubling i n the J = 3/2, 2^*/x s t a t e i s X= 0.0 555 cm\"1 as determined by Ehrenstein^ et. a l . from micro-wave experiments. Since the lambda doubling i s much l e s s than the observed s p l i t t i n g the square root i n equation (4.4) was ex-panded using the bi n o m i a l expansion to give V 1 2 + (A2/8V12)» The small c o r r e c t i o n to V^ 2 was evaluated u s i n g the observed r a t h e r than the cor r e c t e d s p l i t t i n g . The e l e c t r i c d i p o l e moment •was found from equation (4.4) by f i n d i n g the corrected s p l i t -t i n g : ^ V ( P 1 ( l ) ) - ( c o r r e c t i o n s ) = V i 2 . The matrix element, V 1 2 was evaluated f o r intermediate coupling and. the expression y i e l d -i n g .the e l e c t r i c d i p o l e moment was: Corrected s p l i t t i n g , 4 V ' = V 1 2 = j 1 ' ^ ^ (3/5) JAE (4.5) The e l e c t r i c d i p o l e moment of the CH molecule i n the 2A e l e c t r o n i c state was determined from the maximum s h i f t In the high frequency component of the Q.]_c(3) l i n e r e l a t i v e to the un-di s p l a c e d l i n e . The observed S t s r k e f f e c t on t h i s l i n e can only 77 be e x p l a i n e d by assuming t h a t the d i p o l e moments i n the upper -and l o w e r s t a t e s have the same r e l a t i v e s i g n and t h a t the maxi-mum s p l i t t i n g i n the upper s t a t e i s s l i g h t l y g r e a t e r t h a n i n the l o w e r s t a t e . ( T h i s s i t u a t i o n was shown i n the diagram i n F i g u r e 2.5) The s h i f t i n f r e q u e n c y o f a S t a r k component r e l a t i v e t o the z e r o f i e l d l i n e i s g i v e n by: 4 V ( Q l c ( 3 ) ) = CV 1 2 ) A - J(A/2)2+ ( V 1 2 ) 2 ' + A/2. (4,6) The m a t r i x elements f o r the upper and l o w e r l e v e l s a re l a b e l l e d w i t h s u b s c r i p t s and \\ i s the lambda d o u b l e t s e p a r a t i o n i n the TT s t a t e . (The lambda d o u b l i n g In the ZA s t a t e i s e s s e n t i a l l y z e r o ^ and t h e r e f o r e does not appear i n e q u a t i o n (4.6). D e t e r m i n a t i o n o f e l e c t r i c d i p o l e moments The c o r r e c t i o n s g i v e n above were a p p l i e d t o the a p p r o p r i -a t e S t a r k s p l i t t i n g and the c o r r e c t e d s p l i t t i n g was p l o t t e d a g a i n s t the a p p l i e d e l e c t r i c f i e l d . The s l o p e was found u s i n g a l e a s t squares f i t to a s t r a i g h t l i n e t h r o u g h the o r i g i n . T h i s s l o p e i s p r o p o r t i o n a l t o the e l e c t r i c d i p o l e moment and p r o v i d e s the d e t e r m i n e d v a l u e . For example, F i g u r e 4.9. shows a . p l o t of c o r r e c t e d s p l i t t i n g v s . e l e c t r i c f i e l d f o r the OH R ? ( l ) l i n e i n the Y-'-**~TT , (0,0) band... I n t h e f i g u r e the l i n e a r r e l a t i o n -s h i p between the c o r r e c t e d s p l i t t i n g and the applied, e l e c t r i c f i e l d I s observed as expected. The s l o p e o f the l i n e I s (2/3J-0 i n u n i t s o f ( l / k V ) and i s c o n v e r t e d t o a d i p o l e moment i n Debyes by m u l t i p l y i n g by 3/2 and d i v i d i n g by 0.01679 (kV/Debye). Table V I I I l i s t s the o b s e r v e d and c o r r e c t e d S t a r k s p l i t -t i n g e and c o r r e s p o n d i n g e l e c t r i c f i e l d s f o r t h e R 2 ( l ) , (0,0); 78 P 1 2 ( l ) , (1,1) j and P ^ l ) , (0,0) l i n e s i n the OH, 2 2 T T band. From these data the f o l l o w i n g v a l u e s of the e l e c t r i c d i p o l e mo-ment of the OH molecule were obtained: TABLE V I I OH E l e c t r i c D i p o l e Moments Derived from Stark S p l i t t i n g s D i p o l e Moment (Debye) 1.732 1 ° » 0 2 I .637 ± °*°3 l . 6 9 2 ± o .o4 The e r r o r s quoted on the d i p o l e moments i n Table V I I are stand-ard d e v i a t i o n s determined from the f i t o f the p o i n t s t o the l i n e . On the b a s i s of the obs e r v a t i o n s one would expect t h a t only the P - ^ l ) , (0,0) l i n e would be e f f e c t e d by a s y s t e m a t i c e r -r o r . The observed Stark component of the OH P]_ ( l ) , (0,0) l i n e Is c l o s e to a broad aluminum impur i t y l i n e which might make the measured s p l i t t i n g too small and hence the d e r i v e d d i p o l e moment s l i g h t l y too s m a l l . A l s o the v a l u e of the e l e c t r i c d i p o l e mo-ment d e r i v e d from t h i s P]_(l) l i n e depends s l i g h t l y on the value assumed f o r the e l e c t r i c d i p o l e moment of OH i n the 2 ] ~ e l e c t r o -n i c s t a t e . I f a va l u e o f the 2 £ s t a t e d i p o l e moment had been taken as h a l f that o f the 2 T T s t a t e , the v a l u e d e r i v e d from the P-^l) l i n e would be about 0.02 Debye h i g h e r , j The R 2 ( l ) , (0,0) and P ^ g d ) , (1,1) l i n e s are completely f r e e of b l e n d i n g so there i s no apparent source of s y s t e m a t i c e r r o r i n the Stark s p l i t -t i n g s observed f o r these l i n e s . The e l e c t r i c d i p o l e moment of the OH molecule has been de-Line R 2 ( l ) , (0,0) P - L M ) , (0,0) P 1 2 ( l ) , ( 1 , 1 ) State 2TT, / a , v = 0 Z l T y x , v = 0 ZV,A , v - 1 7 9 Electric Field, E (KV/ c m ) F i g u r e 4 . 9 . C o r r e c t e d Stark s p l i t t i n g , >Ji v', v s . e l e c t r i c f i e l d s t r e n g t h , E, f o r OH, B 2 ( D , ( 0 , 0 ) l i n e . TABLE V I I I C o r r e c t e d Stark S p l i t t i n g s i n OH 2 T 2 T T Band* R 2 ( D , ( 0 , 0 / P 1 2 ( l ) , (l,l) f P 1 ( D , (0 ,0)* Exposure No. AV (cm - 1) AV(cm- 1) A l / f c n r 1 ) AV> (cm - 1) AV( cm - 1) E(kV/cm) E - 27 1 E - 22 6/23/63 E - 27 u 6/25/63 F - 10 0.67< i . o 4 3 i . 0 5 2 1.093 1.156 1.20 2 1.03i 1.040 1 .08 2 I .145 1.19i 0.72q I.OO3 0.71 2 0.99i O . 6 I 5 9*??i .9>?l6 0 . 9 8 0 1.03o 0,57 3 O.863 0,914 0,857 ? . ? 2 5 0.97e 34,9 49,2 52,9 54,8 5 9 . 9 63.I 1.040 1.094 1.18! 1.02g I . O 8 3 I . 1 7 i * Experimental u n c e r t a i n t i e s are the same as g i v e n i n Table I I . * C o r r e c t e d f o r X-type d o u b l i n g i n 2 T T ^ , J = l / 2 l e v e l u s i n g \\ = 0.157 cm~}-* C o r r e c t e d f o r X-type doubling i n 2TTy^ , J = 3/2 l e v e l u s i n g X = 0.0555 cm -and f o r second o r d e r e f f e c t s i n 2 2 \" and 2 7 T ^ s t a t e s assuming d i p o l e moment i n each s t a t e i s 1.7 Debye. co o termined from microwave measurements. For purposes of d i s c u s -s i o n the most a c c u r a t e value o f (1.660 - 0.010) Debye obtained by Powell and L i d e ^ w i l l be used. T h e i r value i s measured f o r the J = 7/2 l e v e l o f the 2 TTj/^ s t a t e . (The e a r l i e r , l e s s a ccu-rate microwave v a l u e s obtained by Meyer and Myers® and by Ehren-s t e i n ^ appear i n Table XI found at the end of t h i s chapter.) The e l e c t r i c d i p o l e moment of t h e OH molecule has been computed f o r the e l e c t r o n i c and v i b r a t i o n a l ground s t a t e by Cade and. Huo. 1 0 They obtained a value o f 1.780 Debye. Cade and Huo have a l s o computed the change i n the e l e c t r i c d i p o l e moment w i t h i n -t e r n u c l e a r d i s t a n c e . Using t h e i r computed v a l u e s , the d i p o l e moment Is found t o i n c r e a s e by 0.02 Debye f o r the 1.7$ i n c r e a s e i n i n t e r n u c l e a r d i s t a n c e i n g o i n g from v = 0 to v = 1. The change i n I n t e r n u c l e a r d i s t a n c e was found by using the formula given by Ramsey: 1 1 (4.7) where r i s the i n t e r n u c l e a r d i s t a n c e and r e i s that at e q u i l i b -rium, <*e i s the v i b r a t i o n a l c o r r e c t i o n at e q u i l i b r i u m and ^ e i s the e q u i l i b r i u m v i b r a t i o n a l c o n s t a n t . We may now compare the v a l u e s of the OH e l e c t r i c d i p o l e moment giv e n In Table VII with those found by Powell and L i d e and by Cade and Huo. We can say immediately on the b a s i s o f Cade and Huo's c a l c u l a t i o n , t h a t the value o f the e l e c t r i c d i -pole moment .determined from the Stark s p l i t t i n g of the P ^ 1 ) » (0,0) l i n e i s too l a r g e by at l e a s t 0.03 Debye, and t h a t the values obtained from the P.(1), (0,0) l i n e and P n _ ( l ) , (1,1) ap-82 pear i n the c o r r e c t r a t i o . In t u r n the s p e c t r o s c o p i c d a t a sug-gests t h a t the computed value of the OH d i p o l e moment i s about 0.1 Debye too l a r g e . The microwave value a l s o suggests t h a t the s p l i t t i n g measured i n the R 2 ( l ) , (0,0) l i n e i s too l a r g e . The standard d e v i a t i o n i n the d i p o l e moment g i v e n i s a r e a l i s t i c measure of the f i t of the Stark e f f e c t f o r R 2 ( l ) , ( 0 , 0 ) l i n e . T h e r e f o r e , i f the microwave value i s c o r r e c t , one must conclude the d i p o l e moment found, from the Stark s p l i t t i n g i n the R 2 ( l ) , (0,0) l i n e i s s y s t e m a t i c a l l y h i g h . However, the d i p o l e moment found from the R 2 ( l ) l i n e c ould be s a f e l y used to determine elec-t r i c f i e l d s from measured v a l u e s o f S t a r k s p l i t t i n g s i n that l i n e . The microwave value of the d i p o l e moment and those values found from the S t a r k s p l i t t i n g s of the P 1 ( l ) , ( 0 , 0 ) l i n e and the P 1 2 ( l ) , (1,1) l i n e a r e i n good agreement. (The s p l i t t i n g s i n the P]_(l) l i n e are s l i g h t l y low as a n t i c i p a t e d • a b o v e . ) The e l e c t r i c d i p o l e moment of the CH molecule i n the 2Tf e l e c t r o n i c ground s t a t e was found, by two independent e x p e r i -ments. The p r e l i m i n a r y value of the d i p o l e moment was found by measuring the Stark s p l i t t i n g s of the P 1 2 ( l ) , and Q 2(l)» (°»C) l i n e s o f the 2 X 2 T 7 band observed i n second order. The ob-served and c o r r e c t e d s p l i t t i n g s and. the corresponding e l e c t r i c f i e l d s are giv e n i n Table IX. The data were p l o t t e d and the slope o f a l i n e through the o r i g i n g i v i n g a l e a s t squares f i t was found. (The slope was 2/3/*.) The va l u e thus obtained f o r the e l e c t r i c d i p o l e moment of the CH molecule i n the 2TT^ s t a t e was 1.45 Debye ± 15#. A more accurate value o f the e l e c t r i c d i p o l e moment of the TABLE IX Corrected Low D i s p e r s i o n Stark S p l i t t i n g s i n CH 2] t 2 - T T Band P 1 2 (D Qp(l) Exposure No? A V (cm - 1 ) | hv\\cm-1) ^ V ( c m - l ) ) A V^cm- 1) E(kV/cm) 2/15/65 u 2/13/65 u 1/ 3/65 m 12/31/64 m 1/20/65 1 1/ 3/65 u 0 . 5 1 0 . 4 4 0 . 7 4 0 . 6 2 0.49c 0.42 8 0 . 7 3 2 0 . 6 l 4 0,44 0.46 0.54 0 . 9 0 0 . 6 9 < M 2 6 0 . 4 4 g O .89.3 0 . 6 8 ; 2? R T h e c o r r e c t e d s p l i t t i n g f o r each of these l i n e s i s 2/3j- J - l / 2 , v=l 1 . 6 9 ^ o . o 4 ti 11 2 TTvi> J= 7 / 2 , v=0 1 . 6 6 0 * 0 . 0 1 0 Powell and Lide ( 1 9 6 5 ) 7 2n, v =0 1 . 7 8 0 (computed) Cade and Huo ( 1 9 6 5 ) 1 0 CH 2 Fva' J - l / 2 , v=0 1 . 4 6 * 0 . 0 6 This work 2 TT, v =0 1 .57 (computed) Cade and Huo ( 1 9 6 5 ) 1 0 2 A . J= 7 / 2 , v=0 1.13 1 1 5 $ This work Footnotes f o r Chapter IV 90 1. G. H. Dieke and H. M. Crosswhite, Bumblebee Report No. 8? (John Hopkins U n i v e r s i t y , 1948) . 2. L. Gero, Z. Physik 118, 27 (19^1). 3. E. U. Condon and G. H. Sh o r t l e y , The Theory o f Atomic Spec-t r a (Cambridge U n i v e r s i t y P r e s s , Cambridge, England, 1935) p. 401. 4. A. E. Douglas and G. A. E l l i o t t , Can. J . Phys. 43, 496, (1965). 5. G.C..Dousmanis, T. M. Sanders, and C. H. Townes, Phys. Rev. 100, 1732 (1955). 6. G. E h r e n s t e i n , C. H. Townes, and M. J . Stevenson, Phys. Rev. L e t t e r s 2 , 40 (1959) 7. F. X. Powell and David R. L l d e , J r . , J . Chem. Phys. 42, 4201 (1965). 8. R. T. Meyer and R. J . Myres, J . Chem. Phys. J4, 1074 (1961). 9. Or. E h r e n s t e i n , Phys. Rev. 13_0, 669 (1963). 10. P r i v a t e communication: Paul E. Cade and W i n i f r e d Huo, Labor-atory of Mo l e c u l a r S t r u c t u r e and. Spectra, P h y s i c s Depart-ment, U n i v e r s i t y of Chicago, Chicago, I l l i n o i s . 11. N. F. Ramsey, M o l e c u l a r Beams (Clarendon P r e s s , Oxford, 1956), p. 231. 91 CHAPTER V CONCLUSION AND SUGGESTIONS FOR FURTHER STUDY T h i s work has r e p o r t e d the f i r s t s u c c e s s f u l o b s e r v a t i o n of l i n e a r Stark s p l i t t i n g s produced i n the e l e c t r o n i c s p e c t r a of a diatomi c molecule. The o b s e r v a t i o n s have a l s o shot^m broadenings and f i e l d i n d u c e d - p a r i t y f o r b i d d e n l i n e s r e s u l t i n g from the \\ Stark e f f e c t . A l l these f e a t u r e s are In agreement wi t h the t h e o r e t i c a l p r e d i c t i o n s f o r the St a r k s p e c t r a of a d i a t o m i c molecule having a permanent e l e c t r i c d i p o l e moment, when the ob-served e l e c t r o n i c t r a n s i t i o n s i n v o l v e at l e a s t one degenerate e l e c t r o n i c s t a t e . Derived v a l u e s are summarized at the end of the p r e v i o u s chapter. The e l e c t r i c d i p o l e moment of the OH molecule i n the 2 77 e l e c t r o n i c s t a t e and of the CH molecule i n the 2 7 T and ZA e l e c t r o n i c s t a t e s are g i v e n there. T h i s work has shown that the techniques used here provide a means of determining the e l e c t r i c d i p o l e moment f o r s h o r t l i v e d and c h e m i c a l l y r e a c t i v e s p e c i e s . Furthermore, w i t h these techniques the e l e c t r i c d i p o l e moment of a molecule i n e x c i t e d e l e c t r o n i c s t a t e s have been determined. Suggestions f o r f u r t h e r work The most i n t e r e s t i n g t o p i c f o r f u r t h e r study would be the fa d i n g of the f o r b i d d e n Stark components of s e v e r a l low J l i n e s observed i n the CH, 2^L~-~* 2 7 T , Ji3900^.band f o r an e l e c t r i c f i e l d exceeding 120 kV/cm. Such a study would probably i n v o l v e improv-ing the s t a b i l i t y o f the cathode i n the d i s c h a r g e tube. Per-92. haps an a l t e r n a t i v e technique f o r producing l a r g e e l e c t r i c f i e l d s could be developed. However, adapting the present spectrograph f o r p h o t o e l e c t r i c d e t e c t i o n may overcome the present low Inten-s i t i e s encountered at very h i g h e l e c t r i c f i e l d s . T h i s would allow s t u d i e s at h i g h e l e c t r i c f i e l d s w i t h the present d i s c h a r g e tube. F u r t h e r study o f the s l i g h t d i f f e r e n c e between the d i p o l e moments deduced from d i f f e r e n t t r a n s i t i o n s g o i n g to the same elec-t r b n i c ' • and v i b r a t i o n a l s t a t e i s advised f o r the OH, TT, R 2 ( l ) and P-LU) l i n e s and f o r the CH, 2 I 2 T T , P 2 ( D , and R 2 ( D l i n e s . In doing t h i s i t would be important t o give p a r t i c u l a r a t t e n t i o n to e l i m i n a t i n g sources o f Impurity l i n e s . e "@en ; edm:hasType "Thesis/Dissertation"@en ; edm:isShownAt "10.14288/1.0302505"@en ; dcterms:language "eng"@en ; ns0:degreeDiscipline "Physics"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "University of British Columbia"@en ; dcterms:rights "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en ; ns0:scholarLevel "Graduate"@en ; dcterms:title "Stark effect on emission spectra of diatomic molecules"@en ; dcterms:type "Text"@en ; ns0:identifierURI "http://hdl.handle.net/2429/37046"@en .