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The measurement of transition probabilities of atomic neon Robinson, Alexander Maguire 1966

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THE  MEASUREMENT OF TRANSITION  PROBABILITIES OF ATOMIC NEON  Alexander Maguire B.Ao  Sc.,  M. S c . ,  University  University  Robinson  of British  of B r i t i s h  Columbia,  Columbia,  1961  I963  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE  REQUIREMENTS FOR THE DEGREE OF  Ph.  D.  i n t h e Department of Physics  We a c c e p t t h i s required  THE  t h e s i s as conforming t o t h e  standard  UNIVERSITY OF B R I T I S H COLUMBIA September,  I966  In presenting  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s  f o r an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h Columbia, I 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 study.  f o r reference  agree  and  I f u r t h e r agree t h a t p e r m i s s i o n , f o r e x t e n s i v e c o p y i n g o f t h i s  t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by t h e 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 .  I t i s understood that  copying  or 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 n o t be a l l o w e d w i t h o u t my w r i t t e n  permission.  The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8 , Canada  THE UNIVERSITY OF BRITISH. COLUMBIA FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of ALEXANDER MAGUIRE ROBINSON B . A . S c , The U n i v e r s i t y o f B r i t i s h Columbia, 1961 M.Sc,  The U n i v e r s i t y of B r i t i s h Columbia, 1963  WEDNESDAY, SEPTEMBER lk,  1966 a t 3 : 3 0 P.M.  IN ROOM 3 0 1 , HENNINGS BUILDING COMMITTEE IN CHARGE Chairman:  B. A. D u n e l l  A. M. Crooker F. L„ Curzon A. J . Barnard External  T. J . U l r y c h W. F. Slawson R. A. Nodwell  Examiner:  Professor York  R. W. N i c h o l l s  of Physics University  Research S u p e r v i s o r :  R. A. Nodwell  THE MEASUREMENT OF TRANSITION PROBABILITIES OF ATOMIC NEON ABSTRACT The t r a n s m i s s i o n o f neon l i n e r a d i a t i o n through the p o s i t i v e column o f a neon dc glow d i s c h a r g e has been measured. S i x l e n g t h s o f the column were used and a g r a p h i c a l comparison o f the t h e o r e t i c a l and e x p e r i m e n t a l t r a n s m i s s i o n s were made. This permitted a d e t e r m i n a t i o n o f the a b s o r p t i o n c o e f f i c i e n t o f the g a s f o r t h e case o f Doppler~broadened s p e c t r a l l i n e s , „The r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s f o r t r a n s i t i o n s w i t h the same lower l e v e l were o b t a i n e d from t h e v a l u e s of t h e a b s o r p t i o n c o e f f i c i e n t s . R a d i a l v a r i a t i o n o f the d e n s i t y o f a b s o r b i n g atoms and the p r e s e n c e o f i s o t o p e s i n the column were taken i n t o account. ?  The r e l a t i v e i n t e n s i t i e s o f s e v e r a l p a i r s o f spectral, l i n e s e m i t t e d by neon gas e x c i t e d by a p u l s e d e l e c t r o n beam have been measured. The neon was a t a low p r e s s u r e (.1 mm Hg) and e x c i t e d f o r a s h o r t time (200 nsec) t o supress s e l f ~ a b s o r p t i o n o f the e m i t t e d r a d i a t i o n . The r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s f o r l i n e s w i t h the same upper l e v e l were determined from t h e i n t e n s i t y measurements, A weighted a v e r a g i n g technique was used t o connect the r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s o f the a b s o r p t i o n • and e m i s s i o n measurements and a complete s e t o f r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s was o b t a i n e d . The p r o b a b i l i t i e s were p l a c e d on a n a b s o l u t e s c a l e u s i n g t h e r e s u l t s o f a l i f e t i m e measurement r e c e n t l y made by van A n d e l ,  GRADUATE STUDIES  F i e l d of Study: Molecular  Physics  Spectroscopy  Magnetohydr odynaiaic s  Special  Dalby  F. L. Curzon P. R. Smy  Relativity  Plasma P h y s i c s  Related  F. W.  P.  Rastall  L. G. de Sobrir;o  Studies:  E l e c t r o n Dynamics  G.  B. Walker  PUBLICATION The Measurement o f L i n e A b s o r p t i o n o f E x c i t e d Gases, R„A„ Nodwell and A. M. Robinson, P r o c e e d i n g s of the Seventh I n t e r n a t i o n a l Conference on Phenomena i n I o n i z e d G a s e s Beograd 19&5 ( i - p r e s s ) . n  s  9  ii  ABSTRACT  The t r a n s m i s s i o n o f n e o n l i n e positive Six of  radiation  through t h e  c o l u m n o f a n e o n dc glow d i s c h a r g e h a s b e e n m e a s u r e d .  l e n g t h s o f t h e c o l u m n were u s e d the t h e o r e t i c a l  and e x p e r i m e n t a l  and a g r a p h i c a l comparison t r a n s m i s s i o n s were  made.  This permitted a determination of the absorption c o e f f i c i e n t of the gas, f o r the case o f Doppler-broadened relative lower  transition probabilities  l e v e l were o b t a i n e d  coefficients. and  from  Radial variation  the presence  spectral  f o r transitions  lines.  with  The  t h e same  the values of the absorption of the density of absorbing  o f i s o t o p e s i n t h e c o l u m n were t a k e n  atoms  into  account. The r e l a t i v e lines  e m i t t e d by neon gas e x c i t e d  have b e e n m e a s u r e d . and  intensities  excited  of several pairs  by a p u l s e d e l e c t r o n  The n e o n was a t a l o w p r e s s u r e  f o r a short time  of the emitted  ties  f o r l i n e s w i t h t h e same u p p e r l e v e l were intensity  radiation.  (.1 mm  transition determined  a v e r a g i n g t e c h n i q u e was u s e d  Hg)  probabilifrom  t o connect  o f t h e a b s o r p t i o n and  and a complete s e t o f r e l a t i v e  was o b t a i n e d .  an a b s o l u t e s c a l e recently  The r e l a t i v e  transition probabilities  e m i s s i o n measurements probabilities  beam  measurements.  A weighted the r e l a t i v e  spectral  (200 n s e c ) t o supress, s e l f - a b s o r p -  tion  the  of  The p r o b a b i l i t i e s  using the results  made by v a n A n d e l  transition  were p l a c e d o n  of a l i f e t i m e  measurement  iii  TABLE OF CONTENTS  Abstract,  o o o o o o o  o  oo  c o ou o o o o  Table of Contents  O O O  Index of Tables..  o o o o o ©  Index of Figures. Acknowledgements  0  O O 0 OO'  ©o o o o o  o o o  o o o o  o  o o o o o o o o o o o  © © ©  oo o o o o o  9 0 0 0 0 oo  iii  ooo  ooo © o* © © o « © © .  CHAPTER  2  1?!E£EiOSYo  2o1  A.'b.SOI^t  O O O  l0Hs  JjYXifOGO.S NOin."** XJXX i f O  ooo, © oooooooo «o. ooooooo ooooo ooooooo  o o o o o .  O O O O O O O O O O O  Xltl'PHOIDTJC'P XOM  vi  O O O  oo  O O O  O O O  ooo  o o  O, O O  o o o  900  o o o o  O O O O O O O O O O O  o o o o o o o o o o  1  o o o © © © • • oeoooo 7  ooooooooo oooo ooooooo 7 « « « • oooo ooooooooo ooooo 7 9; « « « o © o o o • o, © oooooooo o  oo  oo  X  o o o o  oooo  O  GfllS  o  00  tt  2*1*3 2.1.4  Hyp erf Ine Structure© © © © © © © © © ©. © •13 © o ©«© • A n a l y s i s o f Data©©©o©• «•«•.••©-••©©o*©«• 16  2.2  Sill  3  ABSORPTION EXPERIMENT.. . . . . . . . . . . . . . . .  3.1 3.1.1 3.1.2  Apparatus o  !LS S 3. OX1 oooooooooo  e «o  oo o  O O O O  © » ©  O O O  © •  oo oooo oo oo e* o  O O O O O O O O  ooo  0 0 , 0 0 0 ©  1.8 21 21  Background Light Source and Modulator. Absorpt ion Tubes and Apertures.......'. Monochromator..... . . . . . « . . <>..0» Phot omul t i p l 1 er . . . . . . . . . . . . Amplifier and Phase-Sensitive Detector  23  Experimental M e t h o d 6 . . . . . . . . . . . . . . . . . . 3,2 3 . 2 . 1 Circular A p e r t u r e s . . . . v . . . . . . . . . . . . . . . . . . . . . . .. p . o e . . . . . . . . 3 e 2 © 2 Annul1«e . . .  33 33 36  3.1.3 3.1.^ 3.1.5  0  0  a  0  CHAPTER  o o O O O O  vlii  1  CHAPTER  ooo  o o© oo oo oo © o o o o  CHAPTER  2.1.2  o'o'oo  ii  o ooo o o oo o o o o © o © o © ©  o o o ©  0  .  .  .  .  .  .  .  .  .  .  .  .  0  .  .  24  .  .  27  .  .  28  0  29  EMISSION EXPERIMENT...... . . . . . . . .  37  Measurement of Relative Intensities...  37  4.2  Preliminary Intensity Measurements....  3?  ^.3 ^.3.1  Final Intensity Measurements.......... Apparatus © 0 0 . 0 . « . « . . . «. . . . . . . .  ^3  4  0  0 . •  44  iv  TABLE OF CONTENTS  CHAPTER  CHAPTER  k  (cont'd)  (cont'd) kk  .1  Sampling  .2  Monochromator..  « . . . . o . . . . . . . « • > » • . . . .  fh5  .3  Spectral Calibration,...............  ^5  *K3.2  Experimental Method.................  ^7  5  RESULTS AND DISCUSSION..............  52  3.1  Neon  52  5„2  Absorption-Circular A p e r t u r e s . . . . . $ k  5.2.1  Cross-Sectional of Transmission.....  Technique...............*\.  Spectrum........so.............  Curv© FAttin££©©  -3 © 2 « 2  ,5.2.3  ©o© © © • © * • ©  ©•«©  ©«•©  © © ©  ' Relative O s c i l l a t o r Strengths.......  5*3  Absorption—Annulio.........  5.^-  D i s c u s s i o n o f R e s u l t s and E r r o r s o f  . o . o . « o . .  5^ 5^  58 64-  A b s o r p t i o n Method...............  68  5J^.1  F i c t i t i o u s Line-Shapes..............  68  5.^.2  D i s c u s s i o n of E r r o r s . . . . . . . . . . . . . . . .  71  .1  Stimulated Emission.................  72  .2  T r a n s m i s s i o n Accuracy...............  72  .3  Curve F i t t i n g and S l o p e s . . . . . . . . . . . .  73  ,k  O p t i c a l Alignment............. •  73  .5  End-Window Reflections....».........  7^  .6  Uniform  75  .7  E n d - E f f e c t s o f A b s o r p t i o n Column....  76  .8  Estlmated E r r o r s . . . . . . . . . . . . . . . ......  79  EmiSS 1 On .  81  3  b  5  •  Discharge C o n d i t i o n s . . . . . . . .  . . . s o o .  o . o o o o .  . . . . . .  o o . o . . .  5*5*1  Relative Transition Probabilities...  81  5.5.2-  Discussion of Errors................  82  il  Intensity-Ratio Error...............  82  .2  E m i s s l v i t y and Temperature E r r o r . . . .  82  .3  P i l e — U p E r r o r . . . . . . . . . . . . . . »••««....  8^  .k  Radiation Trapping..................  85  V  CHAPTER 5 (cont/d) 5.6 5 o 6 .1 5e6 2 0  5.6.3  Absolute Transitions Probabilities "Multi-Path" Method of Relative Transition P r o b a b i l i t i e s . . . . . Lifetime M e a s u r e m e n t . . . . . « . . . . . . . . Comparison and Discussion of Absolute P r o b a b i l i t i e s . . . . . . . . . 0  88 89 94 97  CHAPTER 6  CONCLUSIONS...  APPENDIX 1  ISOTOPE CORRECTION  APPENDIX 2  EVALUATION OF TRANSMISSION EQUATION 107  APPENDIX 3  SELF-ABSORPTION CORRECTION FACTOR.. 109  APPENDIX 4  RELATIVE INTENSITY MEASUREMENT OF..  O  0 0  O «  0 0  i o o o o  OQ  0 0 0  0 0  * o o « « «  0 0 0 0 0 0  0.  o • o o o o o  SPECTRAL L I N E S . . . . . . . • • • • . . « « 0  APPENDIX 5  99  101  112  CURVE-FITTING OF NON-DOPPLER SPECTRAL DISTRIBUTION TO DOPPLER DISTRIBUTION  APPENDIX 6 REFERENCES  117  END CORRECTION A T T E M P T S . . . . . . . . . . . . 124-  o « o t > Q © o « o » e o e o  © © © © • • •  * « « o © o o o Q O O © »  v e o o e v o o o o  130  vi  INDEX OF TABLES TABLE 1.  PAGE Circular Aperture Determination of f  2.  r e l  :s  2  Lines, c Line S .  e  e o . o o . o . e o . o . . . . . o « . o . . o o . '  ^4 ^l^®^•  • • • • • • • • • . . . . . . . . o .  cc• S^QJTICL  ^Li2i.©so«o* ••»«•«•  •• •••«•«  re  Annulus Determination of  65 k  Q  ,  ats^jS^,  and s^  95  Comparison of Relative Transition Probabilities.  13.  93  Comparison of Absolute Transition Probabilities.. . . . . . . . . . . . . . . . .  12.  92  Relative and Absolute Neon Transition Probabilities and Oscillator Strengths.  11.  83  Estimated Errors of Transition Probabilities (Emission and Absorption).  10.  80  Relative Transition Probabilities From Intensity Measurements...  9,  66  Estimated Errors of Relative Oscillator Strengths...............................  • 8.  62  Annulus Determination of f -^: s^,s^, and s^  Lines. 7.  61  Circular Aperture Determination of  Lines 6.  60  Circular Aperture Determination of  •  5.  59  >  ^rel*^3 k  . . . . . . . . . . . . . . . .  Circular Aperture Determination of k _ . CC • S /s O * C  3.  .  Comparison of Upper Level Lifetimes  96 98  vii  TABLES (cont'd)  A3.  Self-Absorption Correction Factors For a One and Two Isotope  G a s .  0  o o . . . « o . . . . . . . . . .  A5.1  Self-Absorbed Doppler Line-Shape Fit  A5.2  Calculation of k- ( r e l ) for self-Absorbed Doppler Line-Shapes  Ill  . . . 120 121  A5.3  Voigt Line-Shape Fit  .  120  A6.1  End-Correction Attempt # 1 . . . . . . . . . . . . . . . . . . . . 128  A6.2  End-Correction Attempt #2.  128  viii  INDEX OP FIGURES  FIGURE  PAGE  1.  Plot  2.  Geometry o f A b s o r b i n g  3.  Plot  10  o f F^ a s a F u n c t i o n o f k i . , a . . . . o o *  o f (1/1 + a ) ( F ( k i , 0  12,  Column................. o  a) +  aF (bk ,a)) 0  0  as a F u n c t i o n o f k 4.  Schematic o f Absorption Apparatus..  22  5.  Absorption  25  6.  P h o t o m u l t i p l l e r and A m p l i f i e r C i r c u i t . . .  30  7.  Phase-Sensitive  31  8.  Polynomial  9.  R e l a t i v e I n t e n s i t y o f M.6096,6678............ 42  10.  Partial  Tubes a n d A n n u l u s . . . . . . . . . . . . . . . . .  Detector  Circuit  3^  F i t of R T. 2  Term  D i a g r a m o f Neon f o r I n t e n s i t y  Measurements 11.  kQ  ...  R e l a t i v e Response o f I n t e n s i t y - M e a s u r i n g 50  Circuit 12.  Neon Term  Diagram?  F i r s t and Second E x c i t e d 53  State Configurations.... 13.  Transmission  14.  Curve F i t t i n g . .  a s a F u n c t i o n o f R,............. o . . . . . . . .  ^rel  a  sa  ^  u  n  c  ^l°  n  °^  57  o  15. R . • • . « • o . • • • «  55  63  16.  Photograph o f D i s c h a r g e . . . . . . . . . . . . . . . . . . o . . .  77  17.  End-Effects o f Discharge..............  78  18.  T r a n s i t i o n Array  90  Al.  Isotope  Splitting  f o r " M u l t i - P a t h " Method..... Error.........  105  Ix  FIGURES  (cont'd)  A*r„  Pass-Band o f Monochromator„« ...... • • . . . . . . 1 1 3  A6.1  Geometry  A6.2  P a r t i a l l y Blocked-Off Annulus................ 1 2 6  0  o f Ends o f A b s o r b i n g C o l u m n . . . . . . . . 0  125.  ACKNOWLEDGEMENTS  I would like to sincerely thank Dr. R. A. Nodwell for his helpful guidance and assistance to me in this work, and to other members of the plasma physics group for their helpful  discussions  t o t h e members  and suggestions. Thanks is also given  of the physics workshop for assistance in con-  struction of equipment. I am indebted to my committee members Drs. P. L. Curzon, A. J . Barnard, and A. M. Crooker for suggestions regarding my research and the writing of this thesis. Special acknowledgement is given to Mr. H. W. H. van Andel for making available the apparatus used for measuring intensities and his assistance given in performing them.  CHAPTER 1  INTRODUCTION  It was In 1 9 1 6 and 1 9 1 7 that Einstein / ! / published his classic papers In which he Introduced transition probabilities Since that time much effort has been expended in the theoretical and experimental determination of these probabilities or the associated oscillator strengths because of their Importance in many fields of basic scientific research. For example, transition probabilities are essential in astrophysics.  Here, research is restricted to analysis of  radiation emitted and absorbed by stellar bodies.  Measurement  of spectral intensities can in principle determine such variables as electron density and temperature, number density of atoms and degree of ionization, and the abundance, of the elements in the universe but these determinations depend explicitly- on the transition probabilities,,  In the field of plasma physics a  similar situation exists.  Of course the scientist is not con-  fined to mere observation of electromagnetic radiation and can to some degree control his experimental environment.  Neverthe-  less transition probabilities are needed for virtually a l l spectroscopic diagnoses of plasmas.  The recent interest in  lasers has produced a spate of research In excitation and deexcltatlon processes In connection with excitation decay rates and population inversions in solid and gaseous materials.  A  knowledge of probabilities is imperative for both experimental and theoretical studies of these processes. Although quantitative values of transition probabili-  -2-  t i e s are essential  i n these f i e l d s of research, the actual  number of values known accurately Is extremely small.  The need  for a d d i t i o n a l and more accurate values i s apparent and has led to marked Increase i n work i n t h i s d i r e c t i o n (for a recent b i b liography of t r a n s i t i o n p r o b a b i l i t i e s , see Glennon and Wlese / 2 / ) . T h e o r e t i c a l l y , the t r a n s i t i o n p r o b a b i l i t y can be c a l culated from the eigenfunctions  of the atom, and the  eigenfunc-  tions may be obtained from the p o t e n t i a l acting on the electron(s) involved i n the radiative t r a n s i t i o n .  The simplest atomic system  i s the hydrogen-like atom whose eigenfunctions may be found exactly because the electron moves i n a simple Coulomb f i e l d . Thus for these atoms, t r a n s i t i o n p r o b a b i l i t i e s may be computed, as has recently been done by Karzas and Latter / 3 / and Herdon and Hughes /4/.  However, for more complicated atoms, exact  analytic solution of Schroedinger's equation i s not  possible  and thus t h e o r e t i c a l calculations involve some degree of approximation.  The most widely used approximation method i s due to  Bates and Damgaard / 5 / which uses asymptotic solutions of a Coulomb p o t e n t i a l .  Because these approximations are somewhat  doubtful there i s some uncertainty i n the computed values, and hence i t i s desireable to determine the values  experimentally.  The experimental techniques f a l l into two general classes.  The f i r s t class measures the rate of decay of atom  populations d i r e c t l y .  This method can provide accurate deter-  minations under appropriate experimental conditions but i t  is  usually d i f f i c u l t to know the rate at which the upper l e v e l i s being populated.  In a d d i t i o n , i f the upper state decays to  more than one lower level individual probabilities cannot be determined by lifetime measurements alone.  For most elements,  this means absolute transition probabilities can be obtained from lifetime measurements for a few transitions only.  The  second general technique is less direct and measures parameters related to the transitions probabilities.  For example, measure-  ments of emission and absorption of radiation can lead to estimates of transition probabilities.  To obtain absolute  values the absolute population densities of the two levels must be known.  Values of population densities of sufficient accuracy  are not usually available.  However measurements involving  relative emission and absorption can be made accurately, so that relative transition probabilities can be a c q u i r e d . T h e lifetime methods usually yield at least one (absolute .transition probability so when combined withthe more numerous relative values, accurate absolute probabilities can be obtained. In the experiment reported in this,thesis the relative transition probabilities have been measured for most of the transitions between the 2p%s and 2p^3p configurations of Ne I.  This gas was chosen for several reasons.  Neon appears  in the hotter stars and in some cases is as abundant as oxygen / 6 / , making i t an interesting subject for astrophysical research and i t is often used for high-temperature shock tube work in plasma research so that a knowledge of neon transition probab i l i t i e s is important.  From an experimental point of view,  neon is rich in spectral lines in the visible region.  Finally,  there are some significant discrepancies in previous evaluations  of neon transition probabilities and a new determination is highly desireable. Transitions between the above mentioned configurations of neon have been the subject of several experimental investigations In the past four decades.  One of the f i r s t was  performed by Ladenburg, et a l . / ? / who measured the relative transition probabilities from the anomalous dispersion of the gas by the Roschdestwensky "hook method" / 8 /  8  This technique  was recently repeated by Pery-Thorne and Chamberlain /9/. Doherty /10/ determined the absolute transition probabilities from absolute intensity measurements using a shock tube. Frledrichs / l l / also measured absolute intensities, but with a stabilized arc as a source.  More recently, relative values for  these lines have been determined by Irwin /12/ using l i n e reversal and relative intensity methods. The method of determining the time dependence of populations of the excited states was f i r s t attempted on some of these neon levels by Griffiths /13/ who estimated the lifetimes by measuring the phase lag between periodic excitation and emission.  Other direct measurements of lifetimes has been  performed by Bennett / l V , et a l . and KLose A 5 A  l  n  which the  decay of the radiative intensity is measured by sampling. There is considerable disagreement amongst the values of the transition probabilities obtained by these workers.  The  presence of self-absorption in some of the experiments and other limitations on the accuracy of the measurements prompted the undertaking of the experiment described in this thesis.  -5-  The experiment reported here consists of two separate parts, an absorption experiment which relates probabilities of transitions having a common lower level, and an emission or intensity experiment which relates probabilities of transitions with a common upper level.  Combining the results of these two  experiments allows one complete set of relative values to be obtained. The absorption experiment employs a modification and extension of a method due to Bamberger / l 6 / , who measured; the transmission of a plasma to intensity-modulated hydrogen radiation to determine the density of excited atoms as a function of time.  In the experiment described in this thesis, the trans-  mission of the positive column of a neon dc glow discharge is measured.  Use of six absorption lengths enables a graphical  comparison of the theoretical and experimental transmissions to be made to determine the absorption coefficient of the gas, assuming Doppler-broadened spectral lines.  The values of the  absorption coefficients of appropriate spectral transitions allows calculation of relative transition probabilities.  Radial  variations of the density of excited atoms is observed and compensated for by varying the diameter of the incident beam or by using an annular cross-sectional beam.  The presence of  isotopes is also taken into account. The emission experiment measures relative intensities of several pairs of neon spectral lines by a method not believed to have been used previously.  The radiation is emitted by a  neon source excited by a pulsed electron beam and the intensity  -6-  Is determined by counting the photons with a photo-electric counting device.  The pressure of the gas is low (.1 mm Hg) to  eliminate self-absorption.  The apparatus was developed by  van Andel / l ? / for lifetime measurements but was readily adapted for this experiment. The values of the transition probabilities obtained by this method are estimated to be the most accurate to date and should prove to be valuable for future spectroscopic diagnosis of neon. The theory of the experiment is developed in Chapter 2.  Starting with the general laws of total absorption of a  spectral line in a uniform gas, the specific case of Doppler broadened lines is considered.  Non-uniformity in a radial  direction of a cyllndrlcally symmetric system is next considered, and two methods overcoming this difficulty are discussed.  The  equations necessary to account for the presence of isotopes in the source and absorber are given. developed and discussed.  Finally emission theory is  Chapter 3 describes the experimental  apparatus and procedure of the absorption experiment while Chapter 4 does the same for the emission experiment.  The  results of the work are given in Chapter 5 and discussed; attempts are made to account for broadening other than pure Doppler in the absorption experiment and errors in absorption and emission are investigated.  The chapter is concluded with  a presentation of the absolute transition probabilities based on a lifetime measurement by van Andel / l ? / . are contained in Chapter 6.  The conclusions  -7-  CHAPTER 2  THEORY  The theory developed In this chapter indicates how relative transition probabilities may be determined from a measurement of the absorption and emission of radiation by a gas.  2 1 8  Absorption The absorption coefficient  integrated over a spectral  line is proportional to the transition probability (see for example, Garbuny  The theory given in this section  /18/).  calculates the transmission of Doppler-broadened spectral radiation through a gas and relates the absorption coefficient and hence the transition probability to the transmission measurements.  2.1.1  Uniform Gas  When a plane-parallel beam of monochromatic radiation at frequency "0 passes through a uniform gas of length  ^ , the  intensity of the beam is decreased because of absorption.  The  fraction of the energy transmitted per second, or the transmission T, is given by e absorption coefficient  v  '  where k ( V ) is called the  of the gas.  If the incident beam consists of a single spectral line of small but finite width, integration over the line yields the transmission, thus:  -8-  £  T =  Jkwl  '  A-__1_J  ...(2.1)  where 1 ( 9 ) Is the intensity of the incident beam at frequency\> The absorption coefficient  is a parameter of the  absorbing gas and depends on the transition probability.  In  principle the absorption coefficient may be determined from a measurement of the transmission of a beam of light of known spectral distribution,,  The transition probability may then be  determined from the absorption coefficient. In this experiment conditions are chosen such that both the source and the absorber have predominantly Dopplerbroadened lines.  For a source and an absorber having tempera-  tures T_ and T respectively, and a spectral line of centres  a  f r e q u e n c y 9 the emission intensity and the absorption coefficient are given by (see for example, Mitchell and Zemansky /19/)  where  O =  Av = • — / — K  '  .6M>  S  = Doppler width of the  -9-  spectral line of the source, and a = VTs/Ta .= ratio of the Doppler widths of the source and the absorber. When stimulated emission is negligible, as i t is in this experiment, the value of the absorption coefficient at the centre of the spectral line, k , Is given by Q  a - /"^Ntj-  -  K  3j Ni An  ,  2 2 )  where N^ = the number density of atoms in the lower state of the transition, and 'f^j and Aj^ are the oscillator strength and the transition probability respectively, for the absorption transition 1—*J (i s lower level, J • upper level). Equation (2.1) then becomes.  Fig. 1 is a plot of F as a function of k i? Q  Q  for several values  of a. 2.1.2  Non-Uniform Gas  A modification of equation (2.1) Is necessary when  -li-  the density or the temperature of the absorbing gas is not constant perpendicular to the axis of the beam (but uniform along the axis) because the absorption coefficient w i l l vary with radial position and an integration over the transverse area is necessary.  Equation (2,1) then becomes  T=  For an absorbing column with axial symmetry and an annular cross-sectional beam (with inner and outer radii R and i  R respectively) centred on the axis of the column,  T=  where r is the radial distance from the axis.  (2.5)  Pig. 2 shows the  -12-  geometry of the system.  INCI DENT RADIATION  Pig. 2 Geometry of Absorbing Column If R Q - ^  is small enough so that k("v> ,r) is nearly  constant over the annulus, then the form of T becomes identical with equation  (2.1).  If Ro is treated as a variable so that T becomes a function of R , an expression depending only on the parameters Q  2  at r = R may be obtained by differentiating (R Q  2  respect to R ; Q  d(Rl)  ^ IMCK>-  Q  2  - R^T with  -13-  For Doppler broadened lines this beomes  For a circular beam (R^ = 0) equation (2.6) becomes finally  where R has been written instead of R for simplicity. Q  enables the absorption coefficient  This  to be related to the trans-  mission as the beam diameter is varied.  2.1.3  Hyperfine Structure  So far only spectral lines having a simple Doppler profile have been considered.  Many lines possess a structure,  which can lead to error i f ignored.  The fine structure of neon  is large enough to separate easily with a spectrograph,;, but the hyperfine structure of the spectral lines is not and must be accounted for in the analysis.  In neon, the hyperfine struc-  ture of the lines is due solely to the mass difference of the isotopes, since the nuclear angular momentum of the predominant  -14-  Isotopes Is zero /20/. Naturally occurlng neon Is composed approximately of 91% atomic mass 20, 9% mass 22, and „3# mass 21.  The quantity  21  of Ne  is so small that the effect of its presence w i l l be  negligible in this experiment, making neon essentially a twoisotope gas.  For a two-isotope gas, the total profile of a  spectral line is the sum of the profiles of two components. Each individual profile is centred on  a slightly different  frequency and i f the splitting is large enough the total line w i l l have two peaks or even two separate components.  In neon  the isotope of mass 22 only contributes about 10$ of the emission energy but in absorption the effect of this isotope can be predominant. To see qualitatively the effect of this Isotope in absorption consider a neon source and absorber whose spectral lines have two isotope components with profiles completely or almost completely non-overlapping. Because of the non-overlapp20  ing condition, the Ne  component in the absorber w i l l absorb  20  only the Ne  component emitted by the source, with a similar 22  situation existing for the Ne portion of the spectral l i n e . The energy entering the absorber w i l l be predominantly from the 20  Ne  isotope.  However this isotope has a correspondingly  large absorption coefficient  and the transmission varies  exponentially with absorption coefficient,  not linearly.  That  i s , the gas is more transparent to the weaker component of the radiation.  With strong absorption the energy transmitted  by the absorber can be almost completely due to the less  -15-  abundant Isotope Ne  .  Gf course If the line-width of the  components are. larger than the isotope separation, the two components blend into one line and the isotope effect is not so significant. A quantitative analysis has been made relevant to the conditions in this experiment.  Only the results are given  here and the detailed calculations and discussion reserved for Appendix 1.  The main postulate of the analysis is that the  spectral profile may be represented by two separated Doppler curves.  Experimental conditions are such that this is a good  approximation, as shown in the appendix. For a uniform gas the transmission is shown to be  where F Is defined in equation (2.3) and Q  a = K VM/M* « ,094 b =  K VMVM  = aM'/M  «  .104  K = relative abundance of the two isotopes « .099 M = mass of greatest-occurring isotope = 20 atomic mass units M* = mass of least-occurring isotope = 22 atomic mass units The numerical values given pertain to neon. The two terms on the right hand side of equation (2.8) represent contributions to the transmission from the two isotopes.  The relationship between this equation and the  qualitative discussion of the previous paragraphs may be seen with reference to Fig. 1.  F is close to 1 for small k i Q  Q  but  -16-  decreases rapidly with increasing k £ Q  . a and b are approxi-  mately equal and small i f one of the isotopes is not very abundant.  Therefore for small absorpt ion ( i . e . , k l Q  the f i r s t term dominates, but at large k i Q  small)  , the argument in  the second term is s t i l l small because of the factor b and the second term dominates. Equation (2.8) is plotted in Fig. 3.  For comparison  F (k J2 , a) is plotted for several values of a (dotted line). 0  Q  The calculations of these functions is discussed in Appendix 2, The equation corresponding to equation (2.7) is  =  2.1.4  ^[F (4(R)^(R))-f-aF (b4(R)iM(R))J 0  0  - ~  { 2  '  9 )  Analysis of Data  If ko and a can be determined from measurement of T, the relative probabilities (or oscillator strengths), temperatures and populations can be calculated as can be see from consideration of equation  (2.2).  For measurements made on a  single spectral line the relative temperature and number density of the lower state may be determined as a function of radial position;  FIG. 3. Plot of  ( I /I + a)(F (k l,a) +aF (bk l,a)) B  0  0  0  as a function of k l 0  and a  •18-  TJR')  L<*(R).  N,-CR)  =  H(R')  MB)  Its)  A(R')  ~^ '>  ...(2.10)  R  where R» is some arbitrary reference radius. But more important, i f two spectral lines having a common lower level are compared at the same radius,  is the  same for both and  « • « (2eH )  At a . /\  2.2  K 9,  Emission  Einstein / l / showed that the power spontaneously emitted by a group of atoms is proportional to A^h-p where  -19-  Aj^ is the spontaneous transition probability and "9 is the frequency of the emitted radiation.  For Nj atoms per unit  volume in the upper state j emitting in a layer of thickness !  the energy flux due to spontaneous emission is proportional  to  NjAjjhtfi  .,,(2.13)  Thus relative transition probabilities may be calculated from a determination of the relative intensities of lines with a common upper level since Nj is equal for both transitions and hence  If the density of atoms i n the lower state is nonzero, there is a finite probability of emitted photons being reabsorbed with a consequent decrease of output intensity.  This  radiation imprisonment is largest for resonance line since most of the atoms are in the ground state.  Ladenberg and Levy / 7 /  derived for a one-isotope gas a correction factor to be applied to the measured intensity for Doppler lines. They showed that the intensity of a finite layer of the luminous gas is equal to the intensity of a layer of unit thickness in the absence of self-absorption multiplied by the factor J^S, where  20  S =  2 Co+Oi/rvTT  (2.15)  When two isotopes are present,-equation (2.15) must be modified to i  with  where a and b are defined in equation (2;8) and - f l  is the  frequency separation between the isotoplc components, in units of 60 The derivation of equation (2.16) as well as a table of numerical values is given'in Appendix 3•  -21CHAPTER 3  3.1  ABSORPTION EXPERIMENT  Apparatus The detecting apparatus used in these studies is  based on a method described by Hamberger /16A  A brief  description of the apparatus is given with the help of Fig. 4 which Illustrates schematically the experimental arrangement. Radiation from a neon-filled Geissler tube passes through a pinhole and is rotating disk chopper.  intensity-modulated at 210 cps by a It is then collimated by a lens;.and  passed through a cylindrical neon-filled absorption tube.  The  absorption tube has four internal electrodes so that six different discharge lengths may be obtained. then focused  The radiation is  on the entrance s l i t of a monochromator set to  pass the spectral line under investigation.  The cross-sectional  area of the transmitted beam is controlled by apertures placed in the collimated beam at both ends of the absorption tube. The intensity of the light is measured at the exit s l i t of the monochromator by a photomultiplier and a narrow-band amplifier centred at 210 cps.  The resultant signal is then fed into a  phase-sensitive detector which receives a reference signal of the same frequency.  The detector only accepts signals coherent  with the reference signal and eliminates unwanted signals due to emission of radiation from the absorption tube and noise in the photomultiplier and amplifier.  The dc signal from the  detector is measured with a chart recorder and is proportional  CHOPPE  LENS-  PINHOLE/  SOURCE GRATING  MONOCHROM-  PHOTO - DETECTOR'  ATOR  4 - E L E C T R O D E  ABSORPTION  TMBE-  PHOTOMULT1PLIER-  REFERENCE  SIGNAL  PHASE-SENSITIVE DC  RECORDER  F \ 6 . 4- S C H E M A T I C  DETECTOR  OF  ABSORPTION  AMPLIFIER  APPARATUS  i  to to 1  -23to the Intensity of the modulated beam f a l l i n g on the photomultiplier.  Thus the apparatus provides a means of separating  the background light from the absorption tube and furnishes several absorbing lengths so that it' is possible to calculate k  Q  and a using equation (2„9) The apparatus w i l l now be discussed in detail.  3.1.1  Background Light Source and Modulator The source used was a neon-filled Geissler tube 10 cm  long and approximately 2 mm inner diameter.  The tube was  operated from a 600v dc power supply and current regulator. The current regulator was necessary to stabilize the intensity of the emitted radiation.  The direct current through the tube could be  varied upwards from 2 ma and was operated at a maximum of 9 ma. The tube did not heat up and remained essentailly at room temperature. The modulator was a seven-slotted circular disk placed between the Geissler tube and the collimatlng lens.  It was  mounted on the shaft of a Bodine Electric Co. 1/25 hp, 30 cps synchronous motor, chopping the beam at a frequency of 210 cps. The modulating frequency of 210 cps was chosen to avoid harmonics of 60 cps. It was found that best overall performance was attained when the motor was driven by a 60 cps crystal oscillator and power amplifier, rather than using power from the mains.  The  frequency of both the oscillator-amplifier source and the mains voltage was measured with a d i g i t a l counter.  The variation of  the frequency had a standard deviation of 9 x 10 former source and 12 x 10  % for the latter.  % for the  This larger  -24deviation resulted in a 5% variation of the output signal measured on the chart recorder.  This was because the frequency  of the modulated light did not remain at the centre-frequency of the pass-band of the amplifier.  The variation of the output  signal with the oscillator-amplifier source was less than \%.  3.1.2  Absorption Tubes and Apertures  The absorbing neon for this experiment was the plasma of a positive column dc discharge contained in a cylindrical absorption tube.  Two absorption tubes were used for this  experiment and are Illustrated in Fig. 5.  Both were constructed  with glass tubing of 5 ° cm length, one with 25 mm inside diameter and the other 13 mm. mounted on each end.  Optically flat windows were  Four side-arms containing electrodes were  spaced along the length of the tube so that absorption lengths of 10, 15, 20, 25, 35, and 45 cm could be obtained.  The  electrodes were partially hollowed aluminum cylinders joined to a tungsten wire sealed through the glass.  The dimensions of  the electrodes are given in Fig. 5« The glow discharge was maintained by applying 600v dc across the pair of electrodes corresponding to the discharge length desired.  For both the absorption and emission tubes, the  discharge was Initiated with a Tesla c o l l . Before f i l l i n g , the tubes were baked at 400°C for -9  several hours and then evacuated to a pressure of 10 ' mm Hg on a high-vacuum system built by van Andel / 2 1 / before being  13mm  ~«  10  cm  — »  15  cm  2 0 cm 1/2  25 mm  FIG. 5. ABSORPTION  TUBES  AND  ANNULUS  -26-  filled and  w i t h r e s e a r c h grade  A i r c o n e o n t o a p r e s s u r e o f 2,mm  Hg  sealed o f f . C e n t r e d on e a c h end o f t h e n a r r o w a b s o r p t i o n t u b e  were aluminum h o l d e r s i n t o w h i c h aluminum w i t h c i r c u l a r  could  h o l e s i n them.  i n g d i a m e t e r , a beam o f c i r c u l a r  slide  short  strips of  By u s i n g h o l e s o f v a r y -  c r o s s - s e c t i o n o f known  p a s s e d down t h e a x i s o f t h e a b s o r p t i o n t u b e .  diameter  Mounted a t e a c h  end  o f t h e l a r g e r d i a m e t e r t u b e was a b r a s s s h e e t f r o m w h i c h  cut  an annulus.  and  2.14 cm i n n e r d i a m e t e r t o p a s s  The  dimensions  T h i s a l l o w e d a beam o f 2.2 cm o u t e r  o f t h e a n n u l u s was g o v e r n e d  operating conditions. for  through t h e tube,  was  diameter ( s e e F i g . 5)  by experimental  The w i d t h o f t h e a n n u l u s  h a d t o be s m a l l  c o n d i t i o n s t o be a p p r o x i m a t e l y c o n s t a n t i n t h e a n n u l a r beam.  T h i s meant t h e d i a m e t e r c o u l d n o t be t o o s m a l l , c r o s s - s e c t i o n a l area o f t h e annulus the l i g h t  from t h e background  signal-to-noise  r a t i o low.  otherwise the  and hence t h e i n t e n s i t y o f  s o u r c e w o u l d be s m a l l a n d t h e  As w e l l ,  the less  highly  absorbing  gas w e l l away f r o m t h e a x i s o f t h e a b s o r p t i o n t u b e was o f interest  and l e d t o t h e above c h o i c e o f a n n u l a r  dimensions.  B e c a u s e t h e d i a m e t e r o f t h e a n n u l u s was l a r g e r t h a n t h a t  of the  narrow a b s o r p t i o n tube, t h e a n n u l ! were o n l y u s e d w i t h t h e l a r g e a b s o r p t i o n tube. It experiment this  i s obvious that  is critical  the o p t i c a l alignment  for this  and s p e c i a l c a r e i s n e c e s s a r y .  r e a s o n a P r e c i s i o n T o o l and Instrument  b e n c h w i t h x, y , a n d z v e r n i e r m o t i o n  For  Co. 2-meter  optical  s a d d l e s was u s e d i n  c o n j u n c t i o n w i t h a S p e c t r a - P h y s i c s He-Ne l a s e r .  The l a s e r was  -27-  i n i t i a l l y lined up along the axis of the monochromator and defined the optic axis for alignment of tubes, leases, annuli\,  etc.  Correct alignment of each component was estimated to be within . 25 mm.  3.1.3  Monoohromator The monochromator used for the absorption experiment  was built in this laboratory.  It Incorporated an f/15  3-meter  spherical mirror, 10 cm diameter, and a 3-meter concave grating, 10 cm diameter. worth  The arrangement was in a standard, Wads -  mount with the exit s l i t mountedon ways perpendicular  to the centre of the grating.  The spectrum was observed In the  f i r s t order and gave a reciprocal dispersion of an almost constant 22.4 AVW over the total wavelength region observed (5800A - 7300A). The maximum signal-to-noise resulted from maximum' width of entrance and exit s l i t s .  Ideally the exit s l i t would  be set exactly at the exit. plane position corresponding to the spectral line under investigation.  The s l i t s (assuming  unit magnification) could then be opened to a width equal to the distance between the centre of this spectral line and the centre of the nearest strong adjacent spectral line and the two spectral lines would then be contiguous.  However because  the exit s l i t cannot be positioned exactly there is danger of some radiation from the.wrong, line passing through the exit slit.  To safeguard against this the width of the entrance s l i t  28«  was made smaller than the exit s l i t by a factor of about 2/3. Care must be taken in deciding which weak adjacent lines produce effects small enough to ignore and so can be encompassed  by the exit s l i t ;  by the same reasoning as given  in Chapter 2, a line which is very weak in emission can also be weak in absorption and with strong absorption of the main line, a large proportion of the energy transmitted may be due to the weak line.  For this reason the spectrum from the  Geissler tube was examined with a high resolving power 3.5meter Ebert mount grating spectrograph and the approximate relative intensities of a l l weak lines near the main lines were measured.  The criterion was set that the weak lines must have  intensity less than 1% of the main line.  For most lines the  exit s l i t width was 1 mm or wider, although some had widths as small as 350 microns.  3.1.4  Photomultlplier  Affixed directly behind the exit s l i t in a lighttight brass container was a Philips 150 CVP end-on photomultiplier.  The circuit is shown In Fig. 6.  Because the  spectral response of the photomultlplier peaked in the near Infra-red, the dark current was found to be excessively large at room temperature.  By surrounding the brass container with  crushed dry ice, the noise was reduced by a factor of approximately 50, giving an acceptable signal-to-noise ratio of approximately 5 for the less intense lines.  Depending on the humidity,  -29-  a small stream of a i r blowing on the edges of the exit s l i t was sometimes necessary to keep ice from forming on the edges,  3.1»5  Amplifier and Phase-Sensitive  Detector  The signal from the photomultiplier was fed into a four-stage amplifier with a twin-tee feed-back circuit /22/ from stage 4 to stage 2,  The resulting amplifier had a one-  half amplitude bandwidth of 13 cps centred at 210 cps and a gain at this frequency of approximately 32,000.  The output  signal was tapped off. a potentiometer and reduced in amplitude so the resulting signal into the phase-sensitive detector was never larger than ,.25v peak-to-peak to ensure linearity.  The  circuit diagram is shown in Pig. 6. The phase-sensitive detector is the same as that described by Schuster /23/ and the circuit is drawn in Pig. 7. Essentially i t operates by having a sine-wave reference voltage turning one triode on and the other off on each half cycle;  a  signal with the same frequency is fed through the cathodes and alters the anode currents, but with opposite polarities in each anode c i r c u i t .  Upon rectification, the resulting dc  voltage depends sinusoldally on the phase difference between the reference voltage and the signal.  The phase difference  was set to 0° or 180° for a maximum output.  The dc output was  then monitored on a Heathkit model EUW - 20A chart recorder. The RC time constant in the rectifying unit indicated in Pig. 7 was chosen to obtain a response time appropriate to the signal-  —I  ooo V oc  7k  t-3oov D C  >  ^  IOOK  2!OK  <\if.< olS>f  I2AX7  12.AX7 i  41t<  ~7  1/p  -°5>  IZAU7A  ~7.  f  I—"W  ZS/<f I 3«>ff  TWIN-TEE  150  AMPLIFIER  CVP PHOTOMULTIPLIER  Fig. 6. Photomultiplier  and Amplifier  Circuit  + 3<=»ov P^-  /  V\r 50 K 5W  r t AU7A _ 33*  33*  vwjgsRp—'W  1 j  -1- M X  r—  41H  I  1  1  \M 1  1 •  1  1 1  1  V*  1 v  4-1  1  4--7H  M  '/lW _ J RC  Fig.7  Phase-Sensitive  Detector  NETWORK  Circuit  CWVRT I RECORDER.  1  Sot.  5V IOTURW  -32to-noise ratio at the output of the amplifier.  Thus the  detector acts essentially as a frequency-mixer which f i l t e r s out a l l the resulting signals except the difference-frequency signal, which in this case happens to be a dc signal. The reference voltage was generated by a 6v tungsten lamp Illuminating a Philips OCP-71 photo-transister.  The  intensity was strong enough to saturate the photo-transister making the output voltage Independent of variation of lamp illumination.  The two components were mounted as a unit, but  with the rotating disk intervening and modulating the light, as indicated in Pig. 4.  The resulting square-wave signal was  sent through a low-pass f i l t e r and re-shaped into a 1.4v rms sine-wave before entering the phase-sensitive detector.  The  phase difference between the reference signal and the signal from the amplifier could be adjusted for maximum detector output by mechanically rotating the lamp-photo-transister unit around the axis of the disk.  One-seventh of a revolution was  necessary for a phase-shift of 3^0°. The linearity of the intensity - measuring circuit (photomultlplier, amplifier, phase-sensitive detector, and chart recorder) was measured using a 6-step neutral density f i l t e r which had transmissions varying from .06 to 1.  For maximum rms  voltages Into the amplifier and phase-sensitive detector of 4 mv and 90 mv respectively, the system was linear to within 2%. The entire system, including the intensity of radiation from the Geissler tube, was stable to within 3% over periods of 5 minutes or more.  -33-  3.2  Experimental Method  The procedure followed in determining absorption coefficients  and oscillator strengths is outlined in the  following paragraphs.  3.2.1  Circular Apertures  The circular apertures were used in conjunction with the 13 mm inner diameter absorption tube and the transmission of the gas determined for the six lengths at each diameter of aperture.  The diameters were varied from 3 mm to 13 mm In steps  of 1 mm. For a particular discharge length the transmission is determined as the ratio of the intensity of the modulated light from the source when the gas in the absorption tube is excited to the intensity when the gas is not excited.  Prom this data  2  of T as a function of R, R T can be plotted as a function of R from which is to be calculated the slope d(R T)/d(R ) at 2  2  some value of R.  2  For this purpose, an IBM 7040 d i g i t a l compu-  ter was employed to process the data and determine a leastsquares f i t of a second-order polynomial to the experimental points.  The slope of this curve determined d(R T)/d(R ).  A  second order polynomial was chosen as i t fitted the points f a i r l y well and was simple;  an example is shown in Fig. 8 of  the experimental points and the calculated polynomial.  -35This procedure is repeated  for a l l six discharge 2  2  lengths and a plot at a particular R of d(R T)/d(R ) against log ( 1 ) prepared.  This differs from a plot of equation ( 2 , 9 )  as a function of log (k I ), as shown in Pig, 3» "by the Q  v  additive constant log (k ). Q  their  abscissae  By shifting the two plots along  the theoretical curve may be found which best  f i t s the experimental points.  The curve found in this manner  determines a, and the origin shift determines k . Q  Thus the  problem of determining the two unknowns from equation ( 2 . 9 ) solved by using more than one length;  is  six lengths allows a  quick averaging graphical solution. In this manner k^ and a were measured for each of the o four series of lines; common lower level.  a series consists of those lines with a The excitation current in the absorption  tube had values varying from 2 to 12 ma during the course of these t r i a l s while the current in the source was kept at a constant 7 noa. Some of the lines were extremely highly absorbing with transmissions as low as 2%, For these lines the accuracy of the measurement of T was increased by the use of an optical attenuator.  This consisted of Kodak Wratten gelatin "neutral  density" f i l t e r s which were used to attenuate the background signal when no absorption was taking place.  The sensitivity  of the chart recorder was then changed u n t i l f u l l deflection was achieved.  When absorption occurred upon switching on  the excitation current in the absorption tube, the f i l t e r s were removed increasing the otherwise small deflection of the  -36-  recorder due to the transmitted light. The f i l t e r s were not truly neutral and the transmission had to be measured at each wavelength for which they were used, 3.2,2  Annull  Using the circular apertures, the transmission of some of the highly absorbing spectral lines was less than 2%„ Most of the absorption occurs near the axis of the discharge tube where the atom density is higher (see section 5.2.1), For such lines, the annulus method is useful because the region near- the axis is avoided.  Conversely, more accurate measure-  ments may be performed on weakly absorbing lines by using the circular apertures.  As well, use of the annul!  affords a  means of confirming the values of the transition probabilities measured with the circular apertures. The larger diameter absorption tube was used with an annulus at each end and determinations of k^ made. o  Over a  number of measurements the current in the absorption tube was varied from 1 to 10 ma, and the current in the source, from 5 to 9 ma.  For a given set of conditions the transmission was  measured 3 times for each wavelength and an average transmission calculated.  The procedure followed to analyse the data using  the annull was simpler than with the circular apertures; a plot of T against log (!.)  was compared with the theoretical curves,  eliminating the necessity of measuring slopes from the experimental T's.  -37-  CHAPTER 4  4.1  EMISSION EXPERIMENT  Measurement o f R e l a t i v e I n t e n s i t i e s  In m e a s u r i n g a b s o r p t i o n may  be  intensities  eliminated  a b s o r p t i o n when t h e v a l u e known  (see f o r example,  density  so t h e  the  e i t h e r by  Irwin /12/),  the  variation  taken  spectral variation.  G(X)  f o r the of the  S(\)  PU)  geometry o f the detector,  wavelength can  of the  required  source  is  the  gas  allowed  d e t e c t i n g apparatus "Non-flat"  a standard  with  response  lamp o f known strip  filament  T the by  ratio  be  P's  p h o t o m u l t l p l i e r can  system, S r e p r e s e n t s  i t may  be  written  the  accounts  sensitivity  transmission  of the  monochromator,  the  I f two  different  source.  o f t h e i r power o u t p u t s  d e t e r m i n e d by  a t two  be  where G i s a f a c t o r w h i c h  photPmultiplier'out,puts without  is  lowering  case a tungsten  from the  TU)  compared, t h e  ratio  coefficient  been e l i m i n a t e d o r  i n t o account.  In t h i s  output  P t h e power e m i t t e d are  self-  used. The  «  o r by  i n response of the  requires a c a l i b r a t i o n against  1U)  self-  self-absorption is negligible.  w a v e l e n g t h must be  lamp was  to  correcting for  of the a b s o r p t i o n  Once s e l f - a b s o r p t i o n has for,  e r r o r due  measuring the knowledge o f  different  measured  at a ratio  sources particular of  S o r T.  P ratio  the  If  w a v e l e n g t h s o f one  i f the  and  f o r the  the  source other  i s known. Absolute  c a l i b r a t i o n o f a l i g h t - d e t e c t o r and  deter-  -38-  mination of spectral output of a continuous light source has been described by Christensen and Ames /24/,  Their theory  relevant to intensity determinations is given in Appendix 4, with modification for unequal monochromator entrance and exit slits.  The results of the analysis show that i f the relative  response of the detector at two wavelengths to the line radiation is designated for  (X-pJig) and the corresponding ratio  a continuous source is R (X^jXg) then  RjtlA.^O  =  I A ) ^ c ( ^ K ( x Q DfoQ  ...(4.1)  where I«I. and Ic are the intensities of the line and continuous sources, respectively, D is the dispersion of the monochromator, and K is a correction factor defined in the appendix which accounts for spectral variation of the continuous source, photomultiplier, and the monochromator transmission over the pass-band of the monochromator.  In this experiment, K differs .  from one by an amount less than the estimated experimental error. The intensity Ig  includes the effect of self-absorption, i f  present, and must be corrected later. For a tungsten lamp I  can be written c  where £  is the emissivity of tungsten, t  is the transmission  of the glass envelope surrounding the tungsten strip,  T. Is  -39-  the temperature of the tungsten s t r i p , and J is the blackbody spectral intensity.  V changes very l i t t l e over the range of  wavelengths considered here and w i l l be treated as a constant. Values of £  have been measured for tungsten by de Vos /25/  and Larrabee /26/ for different X and T . t  Although the values  given in these two references differ by a few percent the ratios  £ (X^Tj. ) / £ ( X » T ) agreed to within .5^, and in fact 2  t  were at most about 2% from the value of unity over the wavelength range 5800A'  -  7000A\  Thus equation (4.1) becomes  Rlf*o>Q  _  Ijfo.) H(h^Jt)  T(^Tt)  D(%)  ...(4.2)  from which I g (X-^J/l^ (X ) may be calculated. 2  4.2  Preliminary Intensity Measurements  I n i t i a l l y it was thought that the Intensity measurements could be made using the absorption tube as an emitting source, with corrections for self-absorption being determined from the measured values of k . Q  Apart from the fact that the  optical arrangement required for these measurements was extremely c r i t i c a l with respect to alignment, i t turned out that the uncertainty in the value of k factory (see section 5.4.1).  Q  rendered the results unsatis-  -40-  The alternate method of using a discharge tube with no self-absorption was then attempted but it was found that self-absorption could not be eliminated.  This preliminary  experiment is described here, for although no "true" relative intensities resulted, i t pointed out the difficulties involved In making Intensity measurements. Two neon sources were used.  One was a discharge  tube similar to the narrow absorption tube but with windows mounted perpendicular to the axis so that the discharge could be viewed transversely. This gave a discharge thickness of about 1 cm.  The other source was the Geissler tube used as a  background source in the absorption experiment. The source was mounted behind the modulating chopper and imaged on the s l i t of the spectrograph.  Beyond the source  was a General Electric "Sun Gun" photographic tungsten lamp for calibrating the. spectral response of the system. Only one pair of spectral lines was investigated thoroughly.  It was chosen because of the low absorption of  each line, and because both transitions started from the same upper level (see equation (2.14)).  The lines were X.6678 and  X6096. First the side-on tube was used and the centre of the discharge investigated.  As the discharge current was reduced  from 5 ma to 1 ma in steps of 1 ma the relative response to the two spectral lines was measured at each step.  If self-  absorption was not present, the relative response should be independent of current.  The relative response of the equipment  -41-  to the continuous radiation source was measured at these two wavelengths after each pair of line  measurements, A change in  this ratio would indicate a variation somewhere in the apparatus. No significant change was observed. Two other procedures were attempted.  The discharge  tube operated at a current of 3 ma was moved perpendicular to the optic axis after each measurement so that succeeding measurements "saw" regions of the discharge further from the centre and nearer the cylindrical edge. the discharge is less dense as  Towards the outer regions, well as being of smaller  thickness. Because of this, the extreme edge of the discharge was examined where the discharge thickness is minimum as the current was again reduced in steps. The Geissler tube was investigated in a similar manner except that only the centre of the tube was examined. Also the discharge extinguished at low currents and the Intensities were measured only down to a current of 2 ma. The reproducibility of a l l the measurements was extremely good.  A variation between similar measurements  never exceeded 2% and in most cases was less than 1%. It was observed in a l l the above tests that the apparent relative intensities varied monotonically as the current or position of the discharge was changed. variation was approximately 10$.  The total  Pig. 9 shows a plot of the  relative intensity as a function of current and discharge position. The observed variation could have been due to the  RELATIVE. INTENSITY 1(6678) ^1  1}  fj)  —  •  P  r> < m  o> -  *-  z 1  I t  I  H </ >  2. en  §  H  a .n i  -<  0  o  —-  o  z.  c  y  N  0  -  '" 0»-  0\ GN  Nl  CD 0  o M  TI z  H c o» •m  c n ;» o 3 >  o  pi  i X I  m  effect  of self-absorption  showed t h a t to  100  stimulated  ma u s i n g  Ladenburg /7/  or stimulated  emission  emission,  i s n e g l i g i b l e for currents  a d i s c h a r g e tube s i m i l a r t o t h e s i d e - o n  came t o t h e same c o n c l u s i o n  tube comparable t o t h e G e i s s l e r  the  with  a b s o r b i n g o f t h e two l i n e s . increase  than f o r  tube used here.  X.6096  Thus t h e It i s also  (see  the table  b e i n g t h e more  highly  A decrease o f the s e l f - a b s o r p t i o n  the intensity of  X.6678  \6096  by a l a r g e r  of self-absorption  proportion factors In  3).  Appendix  The  inablility  to eliminate  self-absorption  i n the  s o u r c e s prompted t h e u s e o f a d i f f e r e n t t y p e o f s o u r c e . details  4.3  o f t h e ensuing experiment  Final Intensity  The  w h i c h had o n l y  are given  was t o measure t h e e m i s s i o n f r o m l o w d e n s i t y been i n t h e e x c i t e d  state  density  combined w i t h t h e s h o r t  the  excited  state population  was  of absorption  f o r a short  time.  e x c i t a t i o n time ensured  d e n s i t i e s was s m a l l .  neon The that  Thus t h e  o f r a d i a t i o n by atoms i n a n e x c i t e d  small. Because t h e d e n s i t y  also  below.  adopted t o ensure t h e absence o f  low  probability  The  Measurements  procedure f i n a l l y  self-absorption  state  tube,  the variation of r e l a t i v e intensity i s i n  direction consistent  would  up  about a d i s c h a r g e  o b s e r v e d e f f e c t must be due t o s e l f - a b s o r p t i o n . to be noted that  /12/  Irwin  i s low, t h e e m i s s i o n i n t e n s i t y i s  low and t h e problem c o n s i s t s  of counting  i n d i v i d u a l photons.  -44-  The  average  requires  photon  flux  i s equal to the  somewhat s o p h i s t i c a t e d  are described  4.3.1  apparatus and  The  counting  techniques  which  below.  Apparatus  This p a r t i c u l a r have b e e n d e v e l o p e d who  intensity.  given  .1  him  the general techniques  f o r l i f e t i m e measurements by v a n  helped perform t h i s  c r i b e d by  apparatus and  experiment.  in detail,  /17/  Andel  As t h e a p p a r a t u s  i s des-  only a cursory description w i l l  be  here.  Sampling  An  Technique  e l e c t r o n gun  h i g h vacuum s y s t e m was  s i t u a t e d w i t h i n a bakable,  used  t o e x c i t e t h e n e o n gas w h i c h  a pressure of  .1  with a  d u r a t i o n o f 200  pulse  mm  Hg.  ultra-  The  p u l s e d 485  gun was  n s e c , and  was  times per  r a d i a t i o n from  second  the  e m i t t i n g n e o n was  o b s e r v e d w i t h a g r a t i n g m o n o c h r o m a t o r and  photomultiplier.  The  m o n i t o r i n g RCA  7265  resultant  s a m p l i n g was  p h o t o m u l t i p l i e r was  which  performed  sampled  w i t h a T e k t r o n i x 66l  p u t s out a v o l t a g e p r o p o r t i o n a l  sampled  photomultiplier  d i s c r i m i n a t o r and n a t o r was  s i g n a l a n d was  digital  to isolate  a  s i g n a l from the c o n t i n u o u s l y  20  nsec  t h e c e s s a t i o n o f e a c h p u l s e w i t h a sample w i d t h o f 0.3 The  at  counter.  after nsec.  oscilloscope,  to the height of the f o l l o w e d by an  The p u r p o s e  amplifier,  of the  t h e c o u n t e r from p u l s e s below a  discrimi-  certain  -45-  voltage;  i n t h i s manner p u l s e s o r i g i n a t i n g f r o m  sampling period  circuit  was e l i m i n a t e d .  o f t e n seconds  C o u n t s were r e c o r d e d o v e r a  and y i e l d e d  contained a s i g n a l . This s i g n a l  noise i n the  t h e number o f s a m p l e s  indicated  thea r r i v a l  which  o f one o r  more p h o t o - e l e c t r o n p u l s e s a t t i m e o f s a m p l i n g .  .2  Monochromator  The monochromator was experiment,  dispersion  i s approximately  were u s e d  t i v e pass in  band from  thef i f t h  5500 % t o 7500  1.25  width  ensured  that  the exit  .3  slit  A.  Appropriate  Corning  o r d e r a n d gave a n e f f e c To g u a r d  against  w i d t h was 1.75  mm f o r a l l m e a s u r e m e n t s .  errors  plane of the  mm a n d t h e e n t r a n c e The u n e q u a l  widths  s l i t was a l w a y s  encompassed  slit.  Spectral  Calibration  s p e c t r a l response  o f t h e system  u s i n g a G. E . 6v-9A t u n g s t e n s t r i p approximately  a t the p o s i t i o n  was m e a s u r e d  f i l a m e n t lamp p l a c e d  o c c u p i e d by t h e e l e c t r o n gun w i t h  f i l a m e n t f o c u s e d on t h e monochromater s l i t .  through  order and t h e  image i n t h e e x i t  t h e image o f t h e e n t r a n c e  The  the  for his  The r e c i p r o c a l  i nthef i f t h  p o s i t i o n i n g the s p e c t r a l l i n e  slit  lines/mm.  4  to isolate  monochromater, t h e e x i t  by  300  r e s o l v i n g power i s 300,000.  theoretical filters  b y v a n A n d e l /17/  l e n g t h E b e r t mount w i t h a 6"  a n d i s a 42" f o c a l  8" c o n c a v e g r a t i n g h a v i n g  by  built  t h e lamp was 5 amps a n d t h e t e m p e r a t u r e  The c u r r e n t o f t h e tungsten  .46.  was  c a l c u l a t e d by measuring  Hartmann a n d B r a u n  filament  t h e b r i g h t n e s s temperature w i t h a pyrometer  and then  calculating  the t r u e temperature  by t h e method g i v e n by R u t g e r s a n d de Vos  /27/.  The p y r o m e t e r  i n t u r n h a d b e e n c a l i b r a t e d a t two  tures,  1800°K  a n d 1340°K,  s t a n d a r d lamp, t y p e T-24  w i t h a G. E . t u n g s t e n r i b b o n  86-P-50.  The p y r o m e t e r  a g r e e w i t h i n one p e r c e n t o f t h e c a l i b r a t i o n U n f o r t u n a t e l y t h e s t a n d a r d lamp directly the  filament  was f o u n d t o  temperatures.  I t s e l f was t o o l a r g e t o b e u s e d  t o measure t h e r e s p o n s e w i t h o u t  serious modification of  equipment. Initially  used  t h e s t a n d a r d s o u r c e was t h e G. E„ "Sun Gun"  i n the preliminary  4.2.  Upon m e a s u r i n g  over t h e range dip  tempera-  the intensity  58O0X t o 6800°v i n  of approximately  w i t h a w i d t h o f 100 this which  intensity  °v.  known w h e t h e r t h i s further  steps,  i n section  o f t h e Sun Gun  i t was f o u n d t h a t occurred at  a  6000°i  The o p e r a t i n g v o l t a g e o f t h e lamp f o r 20v  dc a s o p p o s e d  to the rated  i n t h e p r e l i m i n a r y measurements.  120v  dc  I t i s not  d i p i s p r e s e n t a t t h e h i g h e r v o l t a g e a s no  i n v e s t i g a t i o n s were made.  also uncertain;  described  distribution  i n the d i s t r i b u t i o n  measurement was o n l y had been used  experiment  possibly  The c a u s e o f t h i s  dip i s  i t i s c a u s e d by t h e g a s ( i o d i n e )  contained  i n t h e envelope surrounding t h e tungsten filament f o r  purposes  of cleansing.  showed no s u c h d i p .  The s t r i p  filament  lamp f i n a l l y  used  4.3.2  E x p e r i m e n t a l Method  The t r a n s i t i o n are  divided  levels  into  c a l c u l a t e d by a b s o r p t i o n  f o u r groups c o r r e s p o n d i n g t o t h e f o u r  on which a l l t h e s p e c t r a l l i n e s  probabilities two  probabilities  terminate.  To r e l a t e t h e  b e t w e e n a n y two g r o u p s t h e r e l a t i v e  Intensity of  common u p p e r - l e v e l l i n e s must b e m e a s u r e d , o n e i n e a c h  group  ( s e e e q u a t i o n (2.14)).  f o u r groups line  T h e s i m p l e s t way t o r e l a t e a l l  i s t o c h o o s e one l i n e f r o m e a c h g r o u p w i t h e a c h  h a v i n g t h e same u p p e r In  this  desireabillty  level.  experiment  t h e c h o i c e o f l i n e s was g o v e r n e d b y  of a high signal-to-noise ratio  f o r the lines  measured as w e l l a s t h e n e c e s s i t y o f c h o o s i n g from a group a l i n e t h a t reasons the  had been measured i n a b s o r p t i o n .  i t was n o t p o s s i b l e  f o u r groups and  t o choose  one u p p e r  6678 ( s ^ a n d s ) ; 2  s^).  \\6217, 6383,  diagram i n d i c a t i n g The  3  first  line,  were  2  Three other l i n e s  and  6533.  from t h e p ^ l e v e l  self-consistancy  Fig.  notation  10  were  checks;  shows a p a r t i a l  they  term  the transitions.  intensities  measured one p a i r  of lines  6163, 6599 ( s and s ) ; 6334, 6506 ( s ^ and  m e a s u r e d t o g i v e two i n d e p e n d e n t were  common t o  They were X.X.6096,  (The l e v e l d e s i g n a t i o n s a r e i n t h e Paschen s e c t i o n 5.1).  particular  Forthese  level  instead three separate pairs  chosen t o l i n k t h e f o u r groups t o g e t h e r .  (see  lower  o f the three pairs  a t a time;  of lines  were  t h e monochromator was s e t o n t h e  and t h r e e t e n second c o u n t s were r e c o r d e d b e f o r e  p r o c e e d i n g on t o t h e next l i n e  of the pair.  T h i s was r e p e a t e d  -48-  •+4  -f<5  cc  2  X  •C  Fig.  S)  « IN  N  <  10  < < IT  Partial  <<  Term D i a g r a m o f Neon;  Measurement  ten  Intensity-  Transitions  t i m e s and t h e r a t i o o f sums o f t h e c o u n t s c a l c u l a t e d  m e a s u r e d r e l a t i v e i n t e n s i t y , t o be c o r r e c t e d response t o get the t r u e  relative Intensity.  r e p e a t e d t w i c e more f o r e a c h p a i r ; made on t h e p ^  This  procedure  s i m i l a r measurements  c o u n t s due t o s t r a y  and continuum  electron  f o r instrument was  were  lines.  Error noise,  as the  light  room l i g h t ,  photomultlplier  from t h e g l o w i n g cathode o f t h e  gun had t o be s u b t r a c t e d  from t h e neon c o u n t s by  o b s e r v i n g the counts at a time 5 microseconds a f t e r the e x c i t a t i o n pulse,  when t h e n e o n e x c i t a t i o n had  For  decayed.  c a l i b r a t i n g the s p e c t r a l response of t h e system,  an a n a l o g o u s p r o c e d u r e i s f o l l o w e d .  The s i g n a l due t o t h e t u n g s t e n  -49-  lamp was  s a m p l e d and c o u n t e d  over a t e n second p e r i o d at  each  o f t h e w a v e l e n g t h s f o r w h i c h n e o n measurements were made. light Fig.  a n d n o i s e c o u n t s were made by b l o c k i n g o f f t h e lamp. 11 shows t h e r e s p o n s e o f t h e s y s t e m  t h e t u n g s t e n lamp.  R^X.^jJig)  One o f t h e b a s i c is pile-up  error;  can occur  essentially  now  Stray  m  a  y  b  e  to the r a d i a t i o n  computed f r o m t h i s  systematic errors  with this particular  from  curve.  o f c o u n t i n g methods  counting apparatus  two t y p e s o f p i l e - u p  there  e r r o r and t h e y  will  be d e s c r i b e d . Pile-up  what  i s t h e o v e r l a p p i n g o f two p u l s e s .  happens i f t h e d i s c r i m i n a t o r l e v e l  signal  If individually  g r e a t e r than one-half but l e s s  nator l e v e l  no c o u n t  together they w i l l be no c o u n t ;  i s registered  register  t h a n one t i m e s t h e d l s c r i m i '  f o r separate a r r i v a l .  intensity  i s assumed p r o p o r t i o n a l  o f t h e two o v e r l a p p i n g p u l s e s w i l l  the apparent  separately  intensity  intensity.  i s s e t low, t h e a r r i v a l  again register  a s one  they s h o u l d g i v e a count  i s less  than the t r u e  count,  o f two, so  intensity.  I f the  i s s e t low enough, t h e number o f p u l s e s o f h e i g h t l e s s  the d i s c r i m i n a t o r l e v e l occurs  Added  to the  i s greater than the true  On t h e o t h e r hand, i f t h e d i s c r i m i n a t o r  although a r r i v i n g  t h e s e p u l s e s have a  a c o u n t o f one, w h e r e a s t h e r e s h o u l d  i f the intensity  count, the apparent  level  i s s e t h i g h and t h e  i s s a m p l e d a t a t i m e when two p u l s e s o v e r l a p a t t h e anode  o f t?ie p h o t o m u l t i p l i e r . height  Consider  infrequently.  apparent  count  i s small,  and t h e former p i l e - u p  In both cases the e r r o r  than  case  i n c r e a s e s as t h e  increases.  Thus f o r a l l measurements t h e d i s c r i m i n a t o r l e v e l  was  5 co-  Figure  11  Relative  Response of  Measuring  Circuit  Intensity-  -51-  kept  low  (4850  and  t h e count  10  seconds).  per  a b s o r p t i o n experiment lines  s m a l l compared t o t h e number o f The  neutral density  were u s e d  on t h e e s p e c i a l l y  t o keep t h e c o u n t b e l o w 250 The  presence of pile-up  when t h e t r a n s m i s s i o n o f one the  apparatus.  250  p e r 10  p e r 10  the  "bright"  seconds.  of the f i l t e r s  was  c o u n t was  apparent  measured  on  approximately  t h e t r a n s m i s s i o n a g r e e d t o w i t h i n 1% o f t h e  v a l u e a s m e a s u r e d on t h e a b s o r p t i o n a p p a r a t u s . hand a n upward d e v i a t i o n o f more t h a n 5% was unfiltered  from  a t h i g h c o u n t s was  When t h e u n f i l t e r e d  seconds  filters  samples  c o u n t was  a p p r o x i m a t e l y 700  p e r 10  On t h e o t h e r  o b s e r v e d when t h e seconds.  The  e s t i m a t e d a c c u r a c y o f t h e t r a n s m i s s i o n as measured w i t h t h e absorption apparatus the  i s about  counting apparatus  2%  is linear.  so a t 250  c o u n t s p e r 10  seconds  -52-  CHAPTER 5  RESULTS AND  DISCUSSION  For d i s c u s s i o n of the r e s u l t s ,  i t i s appropriate to  b e g i n w i t h a s h o r t d i s c u s s i o n o f the neon term spectra.  Following this,  sections,  one  and  pertaining  the other to the  concludes presents  explicitly  emission.  w i t h a combination final  s e c t i o n on t h e the theory.  results.  E r r o r s and  in  two  to the absorption final  o f t h e two  experiment  s e c t i o n of t h i s  previous  chapter  s e c t i o n s and  o f t h e r e s u l t s and. t h e v a l i d i t y  e s t i m a t i o n of the accuracy  of  of  the  discussed.  Neon S p e c t r u m  Thirty  spectral  lines  and  infra-red. region result  and  second  12  The  are presented  and  A g e n e r a l d i s c u s s i o n i s g i v e n i n each  significance  r e s u l t s are also  5.1  the r e s u l t s  scheme  excited  g i v e n i n Angstroms;  designation of the l e v e l s Paschen / 2 9 / n o t a t i o n ; here.  visible  between the  the f u l l  lines  in this  represent  experiment.  i s given i n both  the  first  2p-*3s and 2 p^3p.  t r a n s i t i o n s with the corresponding  on w h i c h measurements were t a k e n  used  neon i n t h e  transitions  s t a t e s o f t h e atom,  shows t h e a l l o w e d  lengths  from  e m i t t e d by  t h e LS /28/  latter notation w i l l  Fig. wave-  transitions The and  the  g e n e r a l l y be  -53-  LS Notation  Notation  Grooncl  Figure First  12  Neon Term  Stare  Diagram;  and S e c o n d E x c i t e d S t a t e  Configuration  5.2  Absorption - Circular  As was  Apertures  m e n t i o n e d i n s e c t i o n 3.2.2, t h e  a p e r t u r e method was  more a p p l i c a b l e e x p e r i m e n t a l l y f o r l i n e s  showing s m a l l a b s o r p t i o n . absorbing than  2  l i n e s were g e n e r a l l y l e s s  t h e o t h e r l i n e s by  a f a c t o r o f t h r e e o r more  were m e a s u r e d o n l y by  The  s  t h i s method.  on some o f t h e o t h e r g r o u p s o f  5.2.1  If both N of the absorbing  l  4  and  T  a  lines.  P i g . 13  the absorbing lengths.  R,  (2.3)  a s a f u n c t i o n o f R,  I t c a n be  over the c r o s s - s e c t i o n shows t h a t t h e t r a n s -  the r a d i u s of the a p e r t u r e s , i s  shows a t y p i c a l p l o t  gas  Transmission  are constant  column, e q u a t i o n  m i s s i o n T s h o u l d not v a r y as  and  Measurements were a l s o made  C r o s s - S e c t i o n a l V a r i a t i o n of  varied.  circular  of the t r a n s m i s s i o n of f o r the v a r i o u s  discharge  seen t h a t the shape of t h e s e c u r v e s  s i m i l a r f o r each l e n g t h , d e c r e a s i n g m o n o t o n i c a l l y  are  towards  the  centre of the tube w i t h a corresponding tendency to l e v e l o f f . The  curves  f o r t h e o t h e r s p e c t r a l l i n e s b e h a v e d i n t h e same  manner i n d i c a t i n g over  that conditions are d e f i n i t e l y  the c r o s s - s e c t i o n of t h e a b s o r b i n g column.  mission should  increase with R i f  increases with decreasing T but  roughly  a decrease  s p e a k i n g an i f k i! Q  constant  The  trans-  Whether i t  depends on t h e v a l u e o f k_  increase occurs  i s "small".  ever, t h a t the observed  decreases.  not  if k £ Q  There i s reason  and  i s "large"  a and  t o b e l i e v e how-  increase i n transmission i s  caused  14 tl  z o  co oo Z CO  |-K>  J  I  ,06H  7  Z  3  F I G 13  TRANSMISSION A S A FUNCTION OF R  6  w h o l l y by a decrease  5.2.2  in  5.^.1).  (see d i s c u s s i o n i n s e c t i o n  Curve P i t t i n g  2  2  For t h e process o f f i t t i n g the s i x v a l u e s of d ( R T ) / d ( R ) c o r r e s p o n d i n g t o the s i x a b s o r p t i o n l e n g t h s t o t h e t h e o r e t i c a l curves  (see s e c t i o n  3.2.1 and e q u a t i o n (2.9)), t h e s l o p e s were  c a l c u l a t e d as a f u n c t i o n o f R, as R was v a r i e d from t h e minimum t o t h e maximum diameter o f a p e r t u r e used, .5 mm.  i n steps o f  G e n e r a l l y some p o r t i o n o f t h e t h e o r e t i c a l curves c o u l d  be found which f i t t e d t h e s i x p o i n t s w e l l a l t h o u g h i n some cases the s i x p o i n t s showed s c a t t e r a t l a r g e R (5.5 the f i t was not as good.  t o 6.5 mm) and  F i g . 14 shows an example o f curve  f i t t i n g where t h e curves o f F i g . 3 a r e p a r t i a l l y redrawn and t h e e x p e r i m e n t a l l y determined a r e superimposed,  = 10 ma  a ) , b ) , and c) show f i t t i n g s t o t h e curves  c o r r e s p o n d i n g t o a = .5, fit  s l o p e s o f \6l64 f o r R = 4 mm, I  .7,  and .9 r e s p e c t i v e l y , w i t h the b e s t  b e i n g f o r a = .7 g i v i n g k  « .245 c m . - 1  Q  t a i n t i e s i n e s t i m a t i n g a and k  Q  G e n e r a l l y t h e uncer-  from the t h e o r e t i c a l  were no g r e a t e r than about 10% and 5% r e s p e c t i v e l y .  curves I t can be  seen from F i g . 3 t h a t t h e curves a r e c l o s e l y spaced f o r s m a l l values of k ! Q  , and f o r l a r g e k ^ Q  a t v a l u e s o f a ~ 1. In  these r e g i o n s a l e s s p r e c i s e v a l u e o f a i s determined. Curve f i t t i n g was a l s o attempted  u s i n g the data o f  T versus log( I ) at a p a r t i c u l a r aperture r a d i u s .  I t was found  t h a t a r e a s o n a b l y good f i t c o u l d be made but t h e v a l u e s o f a and k  Q  were much d i f f e r e n t from t h e v a l u e s determined  using  -58-  d(H  T)/d(R  ).  effectively  5.2.3  The  the  v a l u e s of f ^  from  equation  were  Strengths  relative  oscillator  (2.11).  In t h i s  c a l c u l a t e d and  t h i s way  same.  Relative Oscillator  The  calculated  strengths f  e  c a n be  l  computed  s e c t i o n these q u a n t i t i e s  i n s e c t i o n 5»6  are converted  r  to  are  transition  probabilities. 1-4  Tables  list  the  S g , s ^ , and  The  a b s o r p t i o n by  and  the experimental  well  s^ l i n e s  rel  t h e s ^ l i n e s was p o i n t s d i d not  so t h e s e q u a n t i t i e s  f  r  o  m  T  a  D  l  e  1  i  c o u l d not P i g . 15  g r a p h i c a l form.  n  maximum p o s s i b l e e r r o r s due curves; of  I n most c a s e s  curve  fitted  best;  a were t a k e n f r o m able. k  Q  to the  the best  I t was  determined  the d e v i a t i o n of f 10$  and  and  poor-fit  be  determined  e  ^ from  o f t e n much l e s s .  The  c u r v e s was  as  by  e r r o r bars  fitting  to the  a  90% curves  the  represent  theoretical  l e v e l and under t h e difficult  f o r w h i c h t h e f i t was f  p  the b e s t - f i t  same  to t e l l  values of k  e  l  f o r w h i c h t h e f i t was  The  I .  shows some o f t h e d a t a f o r  t h a t even c a l c u l a t i n g curves  r  a for  f i t the t h e o r e t i c a l  case the average  the curves  from  and  Q  g e n e r a l l y g r e a t e r than  Sometimes i t was  in this  found  k »  f i t o c c u r r e d a t t h e same v a l u e  a f o r l i n e s w i t h t h e same l o w e r  operating conditions.  »  r e l  as a f u n c t i o n o f R f o r v a r i o u s  c i r c u l a r a p e r t u r e method. f  the values of f  not  30$  using values definitely  c u r v e s was  and  and  Q  unreason-  n o t more  d e v i a t i o n o f a between t h e  h i g h as  which  indicates a  of poor, than  best-fit  slow  -59-  TABLE 1  CIRCULAR APERTURE DETERMINATION OF f  R (ma)  (mm)  6  rel  :  s  2  V^i)  2.0 2.5 3.0 3.5 4.0 4.5 5.0  5852\ 1.00  -  Average  10  1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0  1.00  2.0 2.5 3.0  1.00  Average  2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0  N  E  S  »  I =7ma  1.00  s  6599 1.32 1.30 1.29  66?8 2.23 2.22 2.22  1.26 1.19 1.10 1.25 1.10 1.10 1.09 1.13 1.10 1.10 1.16  2.13 2.06 1.92  1.28  2.18  2.14  2.15 2.17 2.17 2.19 2.11  2.04  1.12  2.10 1.97 2.11  1.19  2.06  1.18 1,18 1.18 1.18  4.0 4.5 12  I  1.14  Average  10  L  2.04 2.04  6717 1.34 1.31 1.31 1.27 1.23 1.17 1.10 1.25 1.22 1.24  1.22 1.20 1.19  1.18 1.14  1.20 1.21 1.18  1.19  1.17  2.05 2.05 2.05  1.17  1.18  2.05  1.18  1.2?  2.02  1.21 1.20 1.20 1.19 1.19  1.24 1.24  1.23 1.23 1.22 1.2.1 1.20  2.04  2.01 2.02  1.18 1.18  2.03 2.04  1.18  1.18  2.05 2.05 2.06  Average  1.22  2.04  1.18  Total  1.19  2.08  1.20  Average  1.17 1.16 1.13  6929 2.02 1.99 1.97 1.87 1.82  1.71 1.51 1.85 1.72 1.72 1.68 1.72 1.69 1.65 1.67 1.60 1.68 1.76 1.74 1.74 1.74 1.74 1.74 1.74 1.78 1.76 1.75 1.74 1.73 1.73 1.76 1.74 1.73 1.75 1.75  -60-  TABLE 2  CIRCULAR APERTURE DETERMINATION OP k , a : s Q  X  5852  a  (ma) R(mmrv 6  2.0 2.5 3.0 k.5 5.0  10  1.5 2.0 2.5 3.0  ?' 4.0 5  5.0 10  12  2.0 2.5 3.0 4.0 k.5 5.0 5.5 2.0 2.5 3.0 3.5 4.0 5.0 5.5 6.0  k (cm ) _ 1  0  2  LINES, I  6678  6599 a  k (cm ) _ 1  0  = 7 ma  a  k (cm ) _1  0  6929  6717 a  .020 .024 .025 .0230 .0235 .0198 .0175 .052 .050 .052 .050 .050 .050 .046 .040  0.9 1.3 1.5 1.55 I.85 1.85 2.0 I.05 1.1 1.25 1.35 1.5 1.7 1.9 2.0  .032 .031 .034 .0350 . 033 .0293 .0277 .067 .064 .064 .066 .064 .064 .062 .053  1.0 1.1 1.4 I.65 1.85 2.0 2.05  .0495 .050 .050 .0505 .051 .0465 .038  0.85 1.0 1.15 1.35 1.65 1.85 2.0  1.1 1.15 1.25 1.4 1.55 1.75 1.95 2.1  .113 .114 .113 .114 .116 .111 .108 .095  0.9 lvO 1.1 1.25 1.45 1.6 1.9 2.05  .043 .042 .046 .044 . 0405 .0385 .0305 .0235 .046 .047 .045 .046 .0435 .0405 .037 .0295 .0238  1.15 1.2 1.5 1.65 1.75 2.0 2.0 2.05  .050 .053 .049 .053 .0513 .0503  0.95 1.15 •1.2 1.5 1.7 2.0  .0865 .0855 .084 .084 .081 .075  0.95 1.1 1.2 1.4 1.55 1.75 2.0 2.1 2.5  .0645 .0635 .O63 .063 .061 .060 .052 .044 .025  0.95 1.05 1.2 1.4 1.6 1.9 2.1 2.4 2.2  .093 .100 .0975 .095 .096 .091 .0795 .064 .045  k (cm ) _ 1  o  a  k^cm ) - 1  a  .031 .032 .033 .0335 .034 .0275 .021 .071 .071 .070 .072 .074 .069 .068  0.9 1.1 1.3 1.55 1.9 1.9 1.9 1.0 1.1 1.2 1.4 1.6 1.8 2.1  .0525 .053 .0525 .0495 .04? .0415 .033 .103 .098 .098 .089 .096 .091 .O87 .088  1.05 1.2 1.35 1.5 1.7 1.9 2.0 1.0 1.05 1.15 1.3 1.^5 1.6 1.8 2.2  0.95 1.05 1.2 1.4 1.55 1.75  .054 .054 .0555 .054 .053 .0523  1.0 1.15 1.35 1.5 1.75 2.0  .073 .078 .0775 .076 .074 .0715 .062  0.9 1.1 1.35 1.4 1.6 1.85 2.05  0.8 1.0 1.15 1.3 1.5 1.7 I.85 2.0 2.0  .053 .060 .0595 .0595 .059 .053 .0485 .035 .0225  0.7 1.0 1.15 1.35 1.55 1.75 2.05 2.1 2.05  .085 .0865 .0895 .088 .083 .079 .071 .055 .039  0.8 0.95 1.15 1.3 1.5 1.7 1.9 2.0 2.05  -61-  TABLE 3  CIRCULAR APERTURE DETERMINATION OF f  X  a  rel  !  s  3  a  d s  4  L I N E S  R(mnO \ x  10  4,0 4.5 5.0 5.5 6.0 6.5  • •  6266  6533  1.22 1.24 1.20 1.14  1.73 1.71  1.00  1.20  v  10  6074  .714 • 733 .681  .675 .653  .652 .638  .678  Average  2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5  1.85 1.96  1.91  1.87 LINES  R(mm) \  2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5  s  6164  \ \ ( A )  2  ! ~ 7ma  2.08  Average  (ma)  »  LINES  ^\X(?)  (ma)  >  n  6074 .745 .744 .696 .678 .644  6096  6383  1.00  1.16 1.16 1.16  1.15  1.18  1.17  .626  .585 .546  1.16 1.16 1.20  .658  1.17 1.00  .74  .72 .72  .66 .66 .64 .65  Average  .68  T o t a l Average  .673  6507 1.69 1.65  1.71  1.68  1.70  1.74  1.69  1.67 1.69 1.69  7245 .596 .567 .542 .497 .487 .443  .430 .391 .494  1.28  i1  1.25  1.18 1.20 1.16 1.16 1.16 1.12 1.12 1.11  1.55 1.60 1.59 1.58 1.59 1.56 1.60  .47  1.17 1.17  1.58 1.64  .43  .46 .44 .43 .42 .40 .40 .465  1  1  ;  1  j  TABLE 4  CIRCULAR APERTURE DETERMINATIONS OF k , a : Q  I  s  and  LINES  = ? ma  LINES  a (ma)  10  MB) R(mm)  4.0 4.5 5.0 5.5 6.0 6.5  6266  6164 ^(cm  - 1  k (cm  )  0.245  0.280 0.290 0.210  0.7 1.0 1.2 1.2  10  2.0 2.5 3-0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5  )  0.700 0.575 0.390 0.350 0.275 0.235 s  6074 .0935 0.103 0.114 0.114 .0.106 0.111 0.093 0.075  - 1  o  u  6533 a  l.l  1.15 1.1 1.15 1.15 1.15  0  _ 1  )  0.270 0.240 0.220 P.195 0.150 0.116  a  k (cm o  - 1  )  a  lc (cm -1, o  K  o  (en  - 1  )  0.9 l.o 1.1 1.2 1.15 1.15  LINES  6333 O.I63 .0.135 0.140 0.7 0.143 0.9 0.182 0.151 1.1 0.193 0.151 1.2 0.170 0.170 0.137 1.3 0.148 0.121 1.4 0.106 1.5 ^ 0.133 0.084 1.5 0.098 O.O79. 0.0615 1.45 0.710 0.500 0.65 0.500 0.740 1.0 0.520 0.720 1.1 0.645 0.570 1.1 0.500 0.450 1.1 0.440 O.36O 1.1 0.430 0.300 1.1 0.245 1.1 0.315 0.205 1.1 0.230 0.230 0.135 1.15  0.110 0.110 0.098 0.098 0.083 0.06I 0.046  0.9 I.05 1.15 1.35 1.45 1.4 1.45  0.280 0.280 0.290 0.270 0.260 0.230 0.185 0.150 0.120  0.5 0.7 0.3 1.0 1.1 1.2 1.2 1.2 1.2  "724T  6507  6096  6074 0.45 0.75 0.95 1.15 1.25 1.5 1.55 1.6  k (cm  0.5 0.3 0.95 1.1 1.15 1.3 1.4 1.5 1.45 1.5 0.7 0.65 0.85 1.05 1.05 1.1 1.2 1.15 1.2 1.2  0.232 0.260 0.250 0.230 0.212 0.200 0.165 0.135 0.103  1.00 0.75 0.55 0.455 0.375 0.315  0.6 0.9 1.0 1.1 1.2 1.3 1.35 1.4 1.35  1.2 1.2 1.15 1.15 1.15 1.15  0.093 0.102 0.112 0.114 0.106 0.096 O.O76 0.055 0.039 0.240 0.250 0.260 0.245 0.220 0.205 0.165 0.130 0.103  2.o  f  -j  18-  'rel  6506A 1.6  1-2'-  7-o .8-  I | tJ^  6-  ~*  1  t  Pig.  15  f  .  I ...a  3  6  . I-  4  5  , as a F u n c t i o n of R  6  7  074^  -64.  dependence o f f It values  p  ^ with  c a n be  of a are  other series. slightly  e  a.  significantly The  2 and  seen upon comparing T a b l e s  pressure  higher than  higher f o r the  i n the  lines  2  5 mm  s o u r c e was  L a n g /30/  i n the absorber. of the S g l i n e s  pressure broadening  s  i f there  broadening  s  the  m e a s u r e d c o u l d be of  the values  5»3  lines  higher than  Absorption -  This allowed lines  a x i s o f t h e t u b e t o be S g l i n e s was  f i t to the k Tables  for  no  Q  of  I  definite  and  a  the  in section  5.^»  consequently  - a  curves.  5 and  6 list  I„. s  annulus  too  I t c a n be  s^,  absorption  s m a l l t o measure a c c u r a t e l y  the values s^,  The  and  of f  r e  ^»  s^ l i n e s  k ,  and  Q  r  e  l  with  the f i t t i n g  I  a  f o r various  s e e n t h a t t h e r e seems t o of f  the  or  I . g  of the  be The  points  ( i n t h e c i r c u l a r a p e r t u r e method) a r e g e n e r a l l y  a p p l i c a b l e here the  significance  used w i t h the  a c c u r a t e l y measured.  systematic v a r i a t i o n  curves  discussed  The  a  l e s s d e n s e r e g i o n s away f r o m  r e m a r k s made p r e v i o u s l y c o n c e r n i n g to  i s pressure  t h e t r a n s m i s s i o n o f t h e more  i n the  measurements made on t h e  values  be  than  Annul!  strongly absorbing  and  shown t h a t  effective  lines.  l a r g e r a b s o r p t i o n t u b e was  configuration.  the  source  f o r other  of a obtained w i l l  The  of  i n the  the  i s much more p r e v a l e n t  i t i s conceivable that 2  than  the  Hg w h i c h i s  has  the other l i n e s ; of the  4 that  also.  experimental value  I t was  observed  o f T was  less  that  than  i n some  trials,  the t h e o r e t i c a l  value  65  TABLE 5 f  \ X ( A ) I (ma)\  (ma)  s  8 10 10 10 X  a  7.6 7 7 7 I  2 4 6 8 8 10 10 J  a  (ma)  1 1 2 2 2 2 2 2 2  f i  7 7 7 7 7.6 7 7.6 MA) I (ma>^ s  7.6 8 7 9.2 9.2 6 7.0 6.0 5.0  2» 4  rel  6266  1.82 1.88 l 84 !  4  s  6096 .852 .860  .611  .869  5882 .347  n  d  s  5  L  I  N  E  S  6533 1.00  s  .592 .600  rel  a  1.83  6074  f  s  LINES  6164  f  s  :  re]  1.14 1.18  (ma>\  \  rel  1.19 1.21  \x(X)  (ma)  f  ANNULUS DETERMINATION OP  !  5  8  5945 .592  LINES  6305  6383 1.00  6507 1.44 1.44  1.41 1.41  .271 .265 .266 ,251  7245 .401  .402 .423 .448  1.43  .440  6334 1.00  6402  LINES  6143 1.43 1.38 1.40 1.40 1.42  6217 .244  2.79 2.71 2.60  2.52 2.59 2.60  7032 .988 1.01  TABLE.6 ANNULUS DETERMINATION OF k , o l Q  :  S g ,s  a  k  4  , and s  g  LINES  s. LINES 6164 I  I  a (ma)  (ma)  8 10 10 10  7.6 7 7 7  k  0  ( c m  _  1  )  a  s  .0187 .0164 .0176 .0177  .45 .65 .7 .55  7 7 7 7 7.6 7 7.6  1  .0293 .0261 .0289 .0276  a  .5 .65 .65 .5  k  0  ( c m  -  1  )  .0168 .0144 .0163 . 0156  a  .5 .65 .65 .5  k  ( c m  .0118 .0135  .85 .5  .0157 .0190  .7 .4  .0161  .65  . 0216  .55  .0064 .0090 .0073 .0096  -  1  )  (cm  )  a  k  (cm "'') -  cr  a  k  (cm  1  )  a  .0133 .0196 . 0199 .0244 .0343 '. 0277 .0386  6245  6507  6383  .5 1.0 .7 1.0  1  .8. LINES 4  6305  6096  6074 2 4 6 8 8 10 10  \Ccnf )  o  6533  6266  1.45 1.3 .75 .5 1.0 .7 1.0  .0195 .0288 .0296 .0425  1.45 1.3 .8 .85  .0060 .0095 .0099 .0129  1.4 1.4 .8 .6  .0518  1.05  .0135  .6  s.-LINES 5945  5882 1 1 2 2 2 2 2 2 2  7.6 8 7 9.2 • 9.2 6 7.0 6.0 5.0  .0205  1.35  .0356  0  6143 1.35  .0807  1.35  .0790 .102 .101 .104  1.15 1.35 1.3 1.3  6217  .0153  1.35  .0638 .0625 .059 .0755 .0734 .0755 .0700 .0726 .0735  7032  6402  6334 1.35 1.4 1.15 1.35 1.3 1.3 1.25 1.25 1.25  .163 .174 .165  1.3 1.35 1.2  .193 .190 .194  1.3 1.25 1.25  .077  1.45  .072  1.25  -67-  when i = 10  cm.  Since the other experimental points  well with the theoretical predictions due  to the effect  i n t h e tube  t h e d i s c r e p a n c y may b e  i n t h e d i s c h a r g e as i t "rounds t h e c o r n e r "  (see s e c t i o n  occurred,  5.4.2).  was m e a s u r e d f r o m  i n c l u s i o n o f t h e 10  cm p o i n t ;  When t h e a b o v e d i s c r e p a n c y  t h e curves w i t h and without the value of f  r  e  t h e s e two methods was s u b s t a n t i a l l y t h e same. culating fit,  f  r  e  i  annulus  no d i f f e r e n c e  curves  The  common t o T a b l e s 1 a n d 5» i n the values of f  r  e  calculated  f o r the presence  there i s  to the theoreti-  of only a single isotope,  o f t h e c u r v e s c o u l d be found w h i c h f i t t e d  Qualitatively  increasing k i. ; Q  fitting  this  t h e p o i n t s t o a curve  The f r a c t i o n a l  one-isotope and two-isotope  Q  fits  decrease  was  s h o u l d be s o ,  t e n d t o z e r o more q u i c k l y  "pushes" t h e experimental T v e r s u s l o g ( i ) p l o t e. s m a l l e r k . o  adequately.  t h e same, w h i l e k  i t c a n be s e e n t h a t  since the one-isotope curves  i.  that  obtained by t h e  l  t h e e x p e r i m e n t a l p o i n t s were f i t t e d  v a l u e s o f a were a p p r o x i m a t e l y  lower.  I t i s apparent  a n d t h e c i r c u l a r a p e r t u r e method. If  portions  i n cal-  c u r v e s w h i c h d e f i n i t e l y were n o t t h e b e s t  i n comparing l i n e s  essentially  ^ c a l c u l a t e d by Again  o f 5% a t most were o b s e r v e d .  variations  also,  cal  from  agreed  with  o f t h e same a t o the l e f t ,  o f k^ b e t w e e n t h e o  depends o n t h e a b s o r p t i o n o f  the  spectral line  and i s l a r g e r t h e higher the a b s o r p t i o n .  The  value of f  lines. less  Thus f  p  e  l  depends o n t h e k  r  e  l  f o r the one-isotope  t h a n t h e v a l u e computed f r o m  Q  v a l u e s from f i twill  two s p e c t r a l be g r e a t e r o r  t h e two-Isotope  curves  d e p e n d i n g on whether t h e a b s o r p t i o n o f t h e r e f e r e n c e l i n e i s  68. greater or l e s s in  f*  ^  w  a  s  n  than the other l i n e .  This  observed  difference  g r e a t e r t h a n a p p r o x i m a t e l y 5% and was  0  less for  low k . o  5.4  D i s c u s s i o n of R e s u l t s and  5.4.1  Fictitious  E r r o r s o f A b s o r p t i o n Method  Line-Shapes  o f t h e t h i n g s t o be n o t i c e d f r o m T a b l e s 2 and  One  4  Is the v a r i a t i o n of the v a l u e of a over the c r o s s - s e c t i o n of the a b s o r p t i o n tube. the r e l a t i v e  and a p p r o x i m a t e l y .6  t o 1.3  spectral lines  f o r the  temperature  s^  of the emitting of the tube.  a four-fold  i n the a b s o r b e r would y i e l d  1200°K a t t h e c e n t r e . d i d not observe t h i s absorption  was  lines; four i n  gas  Geissler cor-  Assuming,  b o t h t h e s o u r c e and t h e o u t e r r e g i o n s o f t h e  a b s o r b e r a r e a t room t e m p e r a t u r e , temperature  and  e m i t t e d by a h y d r o g e n - h e l i u m - f i l l e d  t o the w a l l  therefore that  mm  has m e a s u r e d t h e D o p p l e r w i d t h s  t u b e and c o n c l u d e d t h e t e m p e r a t u r e responded  6.5  to R =  c h a n g e s by a f a c t o r o f a b o u t  Bamberger /31/  this distance.  mm  experiment,  going from a p p r o x i m a t e l y 1 t o 2 f o r the S g  two,  apparently the temperature  of  R = 1.5  i n c r e a s e o f a from  g e n e r a l l y about lines  Under the c o n d i t i o n s o f t h i s  This  Increase i n  a temperature  seems h a r d l y p o s s i b l e .  of  Irwin  i n h i s l i n e - w i d t h measurements on a  /12/ similar  tube. E c k e r and  the temperature  Z o l l e r /32/  have c o n s i d e r e d t h e o r e t i c a l l y  variations across a c y l i n d r i c a l  positive  column  -69-  and  f o r t h e column u s e d  i n this  experiment,  a current  4 amps w o u l d b e r e q u i r e d t o g e t s u c h a v a r i a t i o n ; a constant temperature,  here.  predict with the  Granting that both the  a b s o r b e r a n d e m i t t e r s h o u l d have t e m p e r a t u r e s temperature,  they  equal t o the w a l l temperature,  operating conditions used  o f about  close  t o room  t h e v a l u e s o f a s h o u l d t h e n be a p p r o x i m a t e l y u n i t y ,  c o n t r a r y t o what was f o u n d  in fitting  the data to the theor-  e t i c a l curves.. The spectral  reason f o r these r e s u l t s  lines  do n o t have a p u r e  i s probably that the  Doppler p r o f i l e .  has m e a s u r e d t h e s p e c t r a l d i s t r i b u t i o n  o f t h e neon  a s a f u n c t i o n o f p r e s s u r e a n d showed t h a t o r d e r o f 1 mm It  Hg, D o p p l e r b r o a d e n i n g  i s e x p e c t e d , however, t h a t  /33/  Lang  X5852 l i n e  at pressures of the  i s t h e dominant p r o c e s s .  there w i l l  be some  deviation,  particularly  a t t h e edges o f t h e s p e c t r a l l i n e ,  due t o v a r i o u s  combinations  o f n a t u r a l b r o a d e n i n g , and c o l l i s i o n and S t a r k  b r o a d e n i n g , a s w e l l a s some s e l f - a b s o r p t i o n o f r a d i a t i o n the source. mentioned  Indeed,  absorption  s e l f - a b s o r p t i o n seems t o b e p r e s e n t , a s  i n s e c t i o n 4.2.  distribution  o u t " and a l a r g e p a r t  d e v i a t i o n s from a pure  most o f t h e c e n t r e o f t h e l i n e of the t o t a l  comes f r o m t h e n o n - D o p p l e r In s e c t i o n  Slight  i n t h e wings o f t h e l i n e c a n be s i g n i f i c a n t  i s large;  2.1.3  from  wings.  i s a comparable  Doppler when  i s "absorbed  amount o f t h e l i g h t  transmitted  (The i s o t o p e e f f e c t d i s c u s s e d process.)  A s o l u t i o n of t h i s problem  woultt b e t o m e a s u r e t h e  s p e c t r a l d i s t r i b u t i o n b y t h e s t a n d a r d methods s u c h a s a h i g h r e s o l u t i o n spectrograph o r Pabry-Perot  interferometer.  In  -70-  a c t u a l p r a c t i c e i t w o u l d be  a t i m e - c o n s u m i n g and  c e d u r e t h a t w o u l d have t o be each operating  condition.  u n d e r t a k e n on  Also  hand, t h e  sufficiently  h i g h t o a l l o w more a c c u r a t e Lang a p p a r e n t l y  i n the wings o f the  there  p o i n t s to the  ing having i n Tables  an  explanation  accuracy  match a t r a n s m i s s i o n  4,  That specific  and this  of the  good f i t o f  and  Q  curve  given  and  i n A p p e n d i x 5»  and  self-absorbed  a corresponding  a Voigt  ( i . e.  two  that  which  to those  considering  cited  two  a self-absorbed  Doppler plus  distributions  I t i s shown i n t h e  Doppler p r o f i l e s  curves  of a pure  can  Doppler  Because of the u n c e r t a i n t y p a r a m e t e r s p e r t a i n i n g to. t h e  quantitative  exper-  conclusions  Qualitatively;  they  can  be  be  and  the  gas  results  appendix that  Voigt  found which f i t the  profile. i n the  source  and  actual the  line-shapes  absorber,  no  drawn f r o m t h e s e c a l c u l a t i o n s .  show t h e p o s s i b i l i t y  non-Doppler line-shapes  and  .  natural)  Numerical c a l c u l a t i o n s f o r a s i n g l e - i s o t o p e  are  20%  f o r pure Doppler broaden-  c o u l d h a p p e n i s s e e n by  have b e e n p e r f o r m e d f o r t h e s e  transmission  the  c o u l d be  prevailing  examples o f n o n - D o p p l e r l i n e - s h a p e s s  distribution.  been  6.  Doppler d i s t r i b u t i o n ,  and  o f o n l y about  the  be  a n a l y s i s t h a n has  Doppler t h e o r e t i c a l curves  the parameters k 2,  for  o f t h e measurements w o u l d  i s non-Doppler broadening processes  approximately  e a c h l i n e and  line.  A-reasonable imental  has  pro-  i t i s d o u b t f u l whether, w i t h  equipment a t  done h e r e .  accuracy  tedious  "fictitious"  of  equivalence  between  Doppler line-shapes.  more d e t a i l e d c a l c u l a t i o n p e r t a i n i n g t o a s e l f - a b s o r b e d  Doppler  A  -71-  source that  was u n d e r t a k e n I n t h e a p p e n d i x /  f -|_ o b t a i n e d  from f i t t i n g  re  absorbed  source  i s not very  Doppler line-shape, d i f f e r markedly.  This  In t h e experiment  the value  of absorber is  and s o u r c e  the k  of f  p  using a  and a f o r t h e two  Q  e  indicate self-  on d e v i a t i o n s f r o m a p u r e  i s i n accordance with ^ was  profiles  observation,  generally  independent  i n the acceptance of the values  r e j e c t i n g the values  of k  and a ;  Q  with  Q  these  and a , f  not  e  l  variations.  discussed source  r  remained constant The r e s u l t s  i n s e c t i o n 4.2  of the i n t e n s i t y  show t h a t most l i n e s  The e f f e c t  Doppler d i s t r i b u t i o n more w e i g h t  should  f  p  the l e s s  on f  p  e  Because o f the u n c e r t a i n t y  emitted  by t h e  are definitely  the absorption  so t h a t  ^ f o r l i n e s which are l e a s t  i n the value  of k ,  values  Q  d e n s i t i e s o f t h e atoms i n t h e l o w e r s t a t e s a s a  f u n c t i o n of R c a l c u l a t e d from equation  (2.10) a r e i n d o u b t a n d  c o m p u t a t i o n s have n o t b e e n c a r r i e d o u t .  5.4.2  D i s c u s s i o n of E r r o r s  The e s t i m a t i o n o f e r r o r s i s u s u a l l y d i f f i c u l t s i t u a t i o n here  i s no e x c e p t i o n  0  l  measurements  absorbing.  of t h e r e l a t i v e  e  values  o f t h e d e v i a t i o n s from a non-  i s smaller  be p l a c e d  of  and g e n e r a l l y independent o f  h a v e some s e l f - a b s o r p t i o n s o t h a t t h e l i n e s  pure Doppler.  This  v a r i a t i o n of  c o n d i t i o n s and consequent v a r i a t i o n o f t h e " f i c t i t i o u s " of k  since  c u r r e n t , and method o f measurement.  t h e main j u s t i f i c a t i o n  while  transmissions  dependent  although  The r e s u l t s  The most l i k e l y  and t h e  and most  -72-  important and  .1  causes  of e r r o r  Stimulated  (2.2)  has  must be  is negligible.  c o r r e c t e d by m u l t i p l y i n g b y  and  Zemansky /19/0  g^ and  I r w i n /12/  weights.  d i s c h a r g e tube  he  found  e m i s s i o n was  measurement o f  X.5852  mm  (see f o r  and  upper  levels,  statistical  N^/^  Hg).  in a here At  and  I  =  correction f o r stimulated l i n e w h i c h amounted t o  .996.  =  compared t o t h e a c c u r a c y  of  the  Q  i n s e c t i o n 4.2,  L a d e n b u r g ' s /7/  the absence of s t i m u l a t e d emission  results  i n the G e i s s l e r  tube.  Accuracy  Throughout the course  of t h i s  intensity-measuring c i r c u i t  v a r y i n g the l i g h t  intensity  density  The  filters.  equation  k .  Transmission  of the  (2  (see  NjS^/Nj^gj.  s i m i l a r to that used  is negligible  As m e n t i o n e d indicate  of the lower  same p r e s s u r e  the largest  f o r the  This correction  Qj^ = 1 -  gj the corresponding  of dimensions  Q  i n the  the f a c t o r  has m e a s u r e d t h e r a t i o  c o n t a i n i n g neon at the ma,  If i t i s not, k  Nj a r e t h e atom d e n s i t i e s  respectively,  e r r o r s a r e made.  b e e n assumed t h a t s t i m u l a t e d e m i s s i o n  example, M i t c h e l l and and  a r e d i s c u s s e d below,  Emission  a b s o r p t i o n tubes  .2  experiment  e s t i m a t i o n s of the magnitude of the  It  15  in this  l i n e a r i t y b y more t h a n  output 2%  a  into was The  was  experiment checked  the  linearity  periodically  by  t h e monochromator u s i n g n e u t r a l never  found  to deviate  from  chart recorder could usually  be  -73-  r e a d t o b e t t e r t h a n 2% and for  t r a n s m i s s i o n s were m e a s u r e d t h r e e t i m e s  e a c h d i s c h a r g e l e n g t h and  the average  analysis.  E r r o r s h e r e s h o u l d be  .3  Pitting  Curve  and  taken f o r  random and  less  subsequent 2%.  t h a n about  Slopes  2  In  fitting  the experimental p o i n t s  to  the t h e o r e t i c a l  c u r v e s , i t was  of  the f i t t i n g  usually  uncertainty t i o n of f of  f  r  e  i  r  e  was  of f ^ .  p  e  l  e s t i m a t e and  g r e a t e r t h a n 5%.  points.  The  apparent  so t h a t  Q  maximum  for a single  error  calcula-  deviation  involved  in  ( s e e T a b l e 1) and  of the approximation to  accurate experimental  v a r i a t i o n of f  to c a l c u l a t i n g  Optical  The  depends oh t h e q u a l i t y  o r d e r p o l y n o m i a l assuming  .4  uncertainty  ) i n t h e c i r c u l a r a p e r t u r e method i s h a r d  a second  in part  t h a n 10%  the  )  2  d(R T ) / d ( R  wavelengths  found that  t h a n 5% o f k  less  o f T o r d(R T ) / d ( R  Over s e v e r a l measurements t h e s t a n d a r d  2  to  w o u l d be  s h o u l d be no  computing  less  2  r e  ] _ at large  the poor  the s l o p e s by  fitting  R f o r some  i s no  doubt  due  t h e p o l y n o m i a l method.  Alignment  When measurements were r e p e a t e d on a s e r i e s tral  lines aftera  day,  without  short  period  i t was  g e n e r a l l y agree w i t h i n  5%,  spec-  of time such as t h e o r d e r o f a  changing the alignment  source, or the o p t i c s ,  of  of the a b s o r p t i o n tube,  found that  the values of k  Q  would  whereas i f r e p e t i t i o n took p l a c e a f t e r  a p e r i o d o f a few weeks o r t h e equipment was  disturbed  and  realigned, of k .  there  I t can  Q  w o u l d be  be  a l a r g e r d e v i a t i o n between the  s e e n , however, t h a t  p o n d i n g t o t h e s e c a s e s do  not  deviate  manner, s y s t e m a t i c a l l y o r o t h e r w i s e , to alignment. should  be  generally  diminished the  Therefore  by  as  v a r i a t i o n of f  r  e  _  corres-  drastic a Independence  ^ due  n a t u r e and  r e 1  to  the  alignment  error  is  number o f m e a s u r e m e n t s , r e a l i g n i n g  End-Window R e f l e c t i o n s  F r i s h and  Bochkova / 3 V  o f a gaseous d i s c h a r g e parallel  emitted the  i n nearly  of f  i n d i c a t i n g an  of a s t a t i s t i c a l  i n c r e a s i n g the  values  o p t i c s b e t w e e n e a c h measurement.  .5  two  the  the  values  mirrors  absorbing  from the  gas.  by p l a c i n g the  and  r a d i a t i o n had  measured a b s o r p t i o n c o e f f i c i e n t s discharge  measuring the  light  undergone m u l t i p l e  Conceivably  s o u r c e c o u l d be  in this  tube between  output a f t e r  r e f l e c t i o n s through experiment  r e f l e c t e d b a c k and  the  w i t h e a c h p a s s and  an  previously.  If plane  a n a l y s i s as  t h e windows a r e  surfaces  c o n s i d e r e d as  of r e f l e c t i v i t y  c u l a r to the  axis  given  i n the  above r e f e r e n c e  given  by  T  given  of the  r , and  are  . S „ y ^ «  the  introduce  singly-reflecting positioned  tube, a procedure s i m i l a r to shows t h a t  radiation  f o r t h between  end-windows u n d e r g o i n g a b s o r p t i o n error i n the  the  the  perpendithat  transmission  j  j  is  ....5.D  -75-  For  glass, r =  approaches l i n e and  .04  .998  and  the f a c t o r  ( l - r ) / ( l - r e ~ 2  2  f o r high a b s o r p t i o n c l o s e to the  i s e f f e c t i v e l y u n i t y elsewhere.  multiple  .6  reflections  Uniform  The with  the  This  ensured  the case,  t h a t t h e v a r i o u s glow and anode a n d  c o l u m n , and  t u b e have b e e n assumed;  this positive  e l e c t r o n s and gradient.  e r r o r due  and  dark space  this  chosen (see F i g . 5 ) .  penetrate  absorption  column.  concentrations  of p o s i t i v e  a constant  low  however, and striations  s t a t i o n a r y o r move a l o n g  t h e column  column a p p e a r s u n i f o r m . striations  are  striations  Donahue and  only  as  glow a  ions  and  voltage-  dark  running  condi-  In a low-pressure  column i s g e n e r a l l y c o n s i d e r e d equal  into  column r e g i o n would  a s s u m p t i o n d e p e n d s on t h e  Generally the motion of these  these  to  regions  the l e n g t h of the  T h i s s i t u a t i o n i s notalways so,  be  to  process.  c e r t a i n c o n d i t i o n s a l t e r n a t e b r i g h t and  that  the  only the p o s i t i v e  i s c h a r a c t e r i z e d by  a p p e a r w h i c h may  the  perpendicular  cathode would not  o c c u r r i n g i n the p o s i t i v e  r e g i o n of constant  thus  centre of  c o n f i g u r a t i o n o f t h e a b s o r p t i o n t u b e was  Uniform c o n d i t i o n s along  discharge  )  Conditions  a s s o c i a t e d w i t h the absorbing  the  ^  e l e c t r o d e s l o c a t e d away f r o m t h e m a i n c o l u m n  the absorbing  tions  ^  is negligible.  Discharge  a s s o c i a t e d with the  be  not  k  E v e n i f t h e windows o f  t h e a c t u a l a b s o r p t i o n t u b e were p a r a l l e l and the a x i s , which i s probably  2  under  /35/»  i s so r a p i d t h a t  D i e k e /36Y  e x c e p t i o n a l l y absent  contend and  play  76  an  e s s e n t i a l p a r t i n t h e mechanism o f t h e glow d i s c h a r g e . /37/  Krebs that  found,  u s i n g neon i n a s i m i l a r tube  the s t r l a t i o n s  this  of the positive  period  of the photocell  of o s c i l l a t i o n  modulation period  o f no l e s s  or greater),  positive  limited  large s l i t  than  Because o f t h e r e l a t i v e l y  variations averaged  2mm) a  1.8 msec a n d a n i n t e n s i t y -  compared t o t h e a b s o r p t i o n t i m e  local  column would be  25$.  (approximately  the r e s o l u t i o n but y i e l d e d  of approximately  of the s t r i a t i o n s  seconds  column w i t h  confirmed the existence of running s t r i a t i o n s i n  a b s o r p t i o n tube. A r e l a t i v e l y  in front  here,  o n l y d i s a p p e a r e d a b o v e a c u r r e n t o f 2 amps.  Rudimentary examination a photocell  t o that used  short  («10  of conditions i n the  out i n any measurements.  One o t h e r v a r i a t i o n o f c o n d i t i o n s i n t h e p o s i t i v e c o l u m n was o b s e r v e d  when a p h o t o g r a p h  when t h e d i s c h a r g e had a n u n u s e d  o f t h e t u b e was  electrode situated  t h e two c o n d u c t i n g e l e c t r o d e s , a s l i g h t discharge  i n t o t h e unused side-arm  n o t i c e a b l e by eye, t h i s manifested of  intensity  Fig, be  i t s presence  between  of the  Although not  by a s l i g h t  decrease  w i t h a camera.  The e f f e c t  of this  would  absorption length, although  was  ignored.  E n d - E f f e c t s o f A b s o r p t i o n Column  So error  itself  Intensity decrease.  a shorter effective  in the analysis,  .7  took p l a c e .  a b o v e t h e s i d e - a r m when o b s e r v e d  16 shows t h i s  to yield  diffusion  taken;  f a r no m e n t i o n h a s b e e n made c o n c e r n i n g  I n t r o d u c e d by t h e r o u n d i n g  the  o f t h e d i s c h a r g e a t t h e ends.  -77-  (see F i g . 16).  f r o m F i g . 17  It i s evident  that  Incident  Arrows i n d i c a t e p o s i t i o n of s i d e - a r m s , segments n e a r ends o f d i s c h a r g e  Fig.  s u c h as the  CD  Photograph of  d i a m e t r i c a l l y opposite  absorbing to the  region that  length.  By  tend  two  through the the  details assumed at  constant  of these that  the  e a c h end, i n the  end  With these  are  total  discharge  the  than to  the  longer equal  e l e c t r o d e s , the  errors  i n opposite d i r e c t i o n s this  effect  absorption  of a l l the  rays  tube.  i n c i d e n t beam, two  effect  as  i s due  length  However u s i n g  the  a t t e m p t s have b e e n  ends have on  c a l c u l a t i o n s are  and  regions  This  of the  diagram  e r r o r f o r the  annular  end  absorption  centres  absorption  made t o c a l c u l a t e t h e  path  assuming an  shown i n t h e  l e a d t o an  For  The  s u c h a AB.  to c a n c e l each other.  l e n g t h may passing  rays  clamps).  CD p a s s e s t h r o u g h and  d i s t a n c e between the  f o r the and  rays  (opaque  Discharge  a r e more s t r o n g l y a b s o r b e d . i n t h e  more d e n s e end  is  16  are  rays  given  the  i n A p p e n d i x 6.  b e n d s t h r o u g h 90°  a first  transmission.  In a  approximation that k  It  circular and  a  are  region. s i m p l i f y i n g assumptions  the  results  of  the  F \ G . 17  END-EFFECTS  OF  DISCHARGE  calculations show that no correction for the ends is necessary. Consequently no correction was applied. The basic fault in this analysis is that k is not constant in the end zone. A better approximation i f the prof i l e of k across the diameter of the tube were known would be o Q  to assume this profile is preserved in "going around the corner" and perform a t r i p l e numerical Integration over the frequency, length, and angular position on the annulus to calculate the error. Because the form and magnitude of k is not well known and Q  because of the complexity of the calculations, no attempts were made in this direction. It is likely that for the less highly absorbing lines the end-effect  error is small and of course is highest for the  10 cm discharge length.  As mentioned previously the 10 cm  point sometimes did not seem to f i t very well in the curvef i t t i n g , although whether this point was included or not made l i t t l e difference in the value of f  r e l  determined.  As a result of the analysis, no corrections for endeffects for the method of circular apertures was applied either.  .8  Estimated Errors  The averaged values of the relative oscillator strength and a numerical estimate of the errors are given in Table 7. The values of the errors given represent the ratio of the standard deviation of f  p e l  to the value of f  r e l  ,  in percent.  These  hopefully account for contributions to random errors from such  80-  TABLE 7  f  r  e  l  AND ESTIMATED ERRORS  (The number i n p a r e n t h e s e s f o l l o w i n g t h e e r r o r i s t h e number o f measurements)  \d)  s  2  Lines  s  3  Lines  s  4  Lines  5852 6599 6678 671? 6929  Lines  1.00  Reference  1.19  5.5^,(4) 2.3^(4) 2.6#(4) 4.0^(4)  2.08  1.20 1.75 1.18  6074 6096 6304  .589  6383 6506 7245  1.85 1.00  2.3^(5) 1.5^(5) Reference  .861  2.9#(6) 0.9^(5)  .263 1-00  3.3% (*> Reference  1.42  1.6^(7) 6.1^(7)  .416  6217 633^  .347 10 %(1) .592 10 %{1) 1.41 1.4^(5) .244 10 %(1) 1.00 Reference  6402  2.64  3.7%(6)  7032  1.00  7.5^(2)  5945 6143 5  Estimated Error  6163 6266 6533  5882  s  rel  f  causes as alignment, and  curve  fitting,  transmission accuracy  a r e made f r o m a p u r e l y s t a t i s t i c a l  approach.  deviation a representing the e r r o r i s the best standard f  p  e  l  .  d e v i a t i o n of an i n f i n i t e  The s t a n d a r d  etc.  The s t a n d a r d  estimate  tothe  number o f measurements o f  deviation s calculated  f r o m t h e n measurements 2  of f  r  e  a c t u a l l y made i s r e l a t e d  l  ( )/( i-i))s*~ r  t o a by t h e r e l a t i o n  ( s e e f o r example, T o p p i n g  r  each s p e c t r a l l i n e  /38/).  The v a l u e  i s indicated i n brackets  a n d 7*5% r e s p e c t i v e l y were a s s i g n e d F o r most l i n e s  systematic  s m a l l and a r e not Included shapes could is  and incomplete  discussion i s given 5.5  the values of  to the error.  e r r o r s a r e b e l i e v e d t o be analysis.  systematic  By f a r t h e most h i g h l y a b s o r b i n g  the e r r o r estimate  of n f o r  Non-Doppler  line-  i s o t o p e s e p a r a t i o n ( s e e A p p e n d i x .1)  contribute a significant  high.  that  i n this  =  following the error.  F o r l i n e s w h i c h were m e a s u r e d o n l y o n c e o r t w i c e 10%  a  error i f absorption line  i s \6402 so  g i v e n h e r e may b e o p t i m i s t i c .  Futher  i n s e c t i o n 5«6.  Emission  5.5-1  Relative Transition  Probabilities  For t h e c a l c u l a t i o n o f r e l a t i v e ties  equations  A  (  H  transition  probabili-  (2.14) a n d ( 4 . 2 ) y i e l d  VvjA)  =  JARtfo^Jfa.Jt)  ...(5.2)  82  where .  8 gives  Table (5.2) and  for the  lines  each l i n e p a i r and  estimated  are  from the  5.5.2  the  error.  independent two  The  of  error analysis  e r r o r are  The l  2^  f  o  fractional This  r  a  c  last  W  a  standard  v  absorption  b e l o w and  involved e  l  e  n  S t h  error  of  i n m e a s u r e l n g R^  the  three sets  and  6533  F i g . 11  was  estimated at  .2  Emlssivity  e r r o r s "in  rather  t h a n by  6% t o  9$.  and  numerical the  main  given.  Temperature  £.U,T. )  as  (X. X. ) 1S  direct  was  of  a  n  d  2  P a i r were e s t i m a t e d f r o m  XA.6217, 6383,  curve of  of  It.  estimates  3% f o r R|  for  r e l  calculated  experiment;  and  c  A  three p a i r s  i s merely  amounted f r o m b e t w e e n 1%  f o r .R . c  The  n  equation  Error  errors e  in  columns l i s t s  i s more amenable t o  discussed  Intensity-Ratio  J  the  factors  Errors  sources of  ,  of  two  ^^(6383/6533)  so  here than i n the  c^l  final  O n l y two  estimation  R  the  the  values immediately preceeding  -Discussion  .1  v a l u e s of  the  measurements. k%  , and derived  to  from  measurement and  5$ the the  error  Error  g i v e n by  Larrabee  /26/  amd  de  Vos  /25/  TABLE 8  x /x n  X  2  •->.  1 2 ! X  INTENSITY MEASUREDSITT3  R E L A T I V E TRANSITION PROBABILITIES FROM  \  %  ( X  1» 2 X  }  R;u x ) lf  2  J(X ,T ) 1  t  A  r e l  (X ,X ) 1  2  J(X ,T ) 2  t  10.8  1.01  17.5 6.47  6.49  .535 .626  .974  1.00  1.63  2.32  .334  .591 .572  6217/6383  .974  1.00  .832  .241  5.6% 6.2%  6217/6533  .952  1.01  .711  .668  8.0%  1.02  6164/6599 6334/6506  .913 .934  6096/6678  6383/6533  .542  3.37  1.83 3.95  x  .802  2.77  k.5% 4.1$  8.9%  84-  are both approximately by  about  2.5$,  £i\j_,T )/£  i ti s estimated  (^2 t^ T  t  although t h e i r values  i  s  n  o  S  r  e  a  t  e  here that r  t h  the error i n the ratio  l%  an  The b r i g h t n e s s  e  t e m p e r a t u r e o f t h e t u n g s t e n lamp m e a s u r e d w i t h was  1768°K"14 'K 3  f o u n d t o be  was  c a l c u l a t e d t o be  using  1900°K  +  l6°  factor i s the  The t r u e temperature  T  t  K where t h e d i f f e r e n c e b e t w e e n  L a r r a b e e ' s o r de V o s * s v a l u e s  From t h i s  t h e pyrometer  where t h e u n c e r t a i n t y  d e v i a t i o n o f 10 measurements.  standard  differ  of £  4° K.  amounted t o o n l y  temperature and i t s u n c e r t a i n t y ,  theuncertainty i n  J U - p T j . ) / j ( X » T ) was l e s s t h a n 1% f o r a l l w a v e l e n g t h s u s e d . 2  .3  Pile-Up  t  Error  The 4.3.2 the  second type o f p i l e - u p  c a n be r o u g h l y  estimated  error discussed  i n section  I n t h e f o l l o w i n g way.  a v e r a g e number o f p h o t o - e l e c t r o n  pulses  arriving  nis at the  anode o f t h e p h o t o m u l t i p l i e r p e r s a m p l i n g p e r i o d , a n d h e n c e i s G a d s d e n /39/  proportional to the Intensity. time d i s t r i b u t i o n o f t h e a r r i v a l so  that  t h e p r o b a b i l i t y o f no p u l s e s  sampling period is  l-e" .  one  n  i se" . n  i sclosely  Poisson,  a r r i v i n g during the  The p r o a b i l i t y  o f one o r more  arriving  T h e a p p a r a t u s u s e d h e r e c o u n t s how manysamples  o r more p u l s e s .  4850  of pulses  h a s shown t h a t t h e  I f there  samples, then i t f o l l o w s  are  C counts f o r t h e normal  from above  that  a.o(5.3)  l - ~ = C/4850 n  e  This  equation  (and  therefore  may be s o l v e d  contain  e x a c t l y f o r n but f o r a low count  low n ) e q u a t i o n  (5*3)  becomes  approximtely  -85-  n ( l - n / 2 ) = C/4850  and  250  f o r the C =  mately pair,  2%,  the l e s s  b e l o w 250,  i s the e r r o r of the r a t i o s filters  the pile-up  t o do t h i s  e r r o r was  (.3  is invalid  at  is  .4  by  count  the v o l t a g e l e v e l  a pulse f a l l s  a Poisson  the sampling  w i t h i n °Q/2  width  However i f t h e w i d t h o f t h e p u l s e s  s e t by t h e d i s c r i m i n a t o r has a n a count  distribu-  individual photo-electron pulse  (approximately 5 nsec).  T h i s g i v e s an e f f e c t i v e the  of the counts;  e x p e c t e d t o have b e e n k e p t  f o r t h i s a n a l y s i s because  v a l u e ft, on a v e r a g e of  C/4850 i s a p p r o x i -  and t o keep t h e  be r a i s e d t h a t  n s e c ) i s s m a l l e r t h a n an  width  n =  1$. An o b j e c t i o n may  tion  i n assuming  The more e q u a l t h e c o u n t s a r e f o r e a c h w a v e l e n g t h  using the o p t i c a l  below  the e r r o r  average  i s r e g i s t e r e d whenever t h e c e n t r e o f e i t h e r edge o f t h e s a m p l i n g  s a m p l i n g w i d t h o f ft + w,  w i d t h o f t h e s a m p l i n g g a t e , and  the P o i s s o n  gate.  where w i s distribution  valid.  Radiation Trapping  One  f a c t which  the  emission i n t e n s i t i e s  the  lines.  has b e e n t a c i t l y i s the absence  T h i s demands t h a t  lower l e v e l  assumed i n m e a s u r i n g  of s e l f - a b s o r p t i o n  t h e number d e n s i t y o f atoms o f  o f t h e t r a n s i t i o n be  the  small.  C o n s i d e r a t i o n o f t h e e x c i t a t i o n and processes occurring  of  i n t h e gas a f t e r  de-excitation  s w i t c h i n g on t h e  electron  86-  beam c a n g i v e  a n u p p e r bound on t h e number d e n s i t i e s o f t h e  l o w e r l e v e l s o f t h e t r a n s i t i o n s i n t h e f o l l o w i n g way.  l e v e l s o f t h e 2p^3s  important processes which populate the four configuration  a r e e x c i t a t i o n o f atoms i n t h e g r o u n d s t a t e by  c o l l i s i o n with electrons upper l e v e l s .  i n t h e e l e c t r o n beam and d e c a y  emission of r a d i a t i o n , d i f f u s i o n to walls subsequent d e - e x c i t a t i o n , r i a t e frequency. four  bring  not  and a b s o r p t i o n  the  of the container  about t r a n s i t i o n s between t h e s e e x c i t e d the populations  among t h e f o u r  change t h e t o t a l p o p u l a t i o n  the populating  r a d i a t i o n n e e d n o t be c o n s i d e r e d e v e r y atom r a i s e d t o a n e x c i t e d  c a n be o b t a i n e d b y  The considering  disregarding  of t h e resonance  as a p o p u l a t i o n e n e r g y s t a t e by  process  since  self-absorption  t h e t r a n s i t i o n o f a t l e a s t one atom i n t h e r e v e r s e  direction,  and t h a t Por  density  This  l e v e l s b u t does  of the configuration.  Imprisonment  between  atoms c a n  states.  p r o c e s s e s m e n t i o n e d a b o v e and  de-populating processes.  requires  and  o f r a d i a t i o n of approp-  c o l l i s i o n s with neutral  u p p e r bound o n t h e number d e n s i t y only  accompanying  As w e l l , b e c a u s e t h e e n e r g y d i f f e r e n c e s  l e v e l s are small,  redistributes  from  The p r o c e s s e s w h i c h d e - p o p u l a t e t h e l e v e l s a r e  spontaneous t r a n s i t i o n s t o t h e ground s t a t e w i t h  the  The  atom w i l l  population  T  =N N Q e  0  been  by e l e c t r o n c o l l i s i o n  of the configuration  — d t  have a l r e a d y  "counted". the t o t a l  i s g o v e r n e d by t h e f o l l o w i n g  number equation  ...(5.4)  T  4 where NL = E N ,  I s t h e number d e n s i t y  of a l l four  l e v e l s , Q„ i s  8? the  total  c r o s s - s e c t i o n f o r e x c i t a t i o n t o any  the  configuration, N  g r o u n d s t a t e , and area  In the  and  Is the  other  f l u x of  populating  i n neon the  configuration. this  N  number d e n s i t y  The  only  into  mately  the  10  7  the  10"  that  .  According  cascading  to  contributes  magnitude s m a l l e r . higher total can  unit  higher  i s from the  f o r each of the  cm  .  F r i s h and  ten  2p-^3p  levels in  Revald  /40/  I f a l l t h e s e atoms  cascade  effective cross-section  lower c o n f i g u r a t i o n s  cm  from  by  t h i s method i s  Revald / 4 l / the  for  approxi-  configuration -17 2  c r o s s - s e c t i o n f o r d i r e c t e x c i t a t i o n i s a p p r o x i m a t e l y 10 so  In  2  2p^3s c o n f i g u r a t i o n t h e  populating  i s cascading  b e e n m e a s u r e d by  a l l approximately  the  o f atoms i n  d i r e c t cascading  cross-sections  c o n f i g u r a t i o n has  are  levels  e x c i t a t i o n e l c t r o n s per  process  -19 and  the  e l e c t r o n beam.  The levels  i s the  Q  of  at best  e f f e c t w h i c h i s one  Detailed values  configurations e f f e c t of  an  are  cascading  not  f o r the  of  for  the  i t i s probable that  e x c i t a t i o n time used  make a c o n t r i b u t i o n w h i c h  from d i r e c t e x c i t a t i o n .  order  of c r o s s - s e c t i o n s  known, b u t  'cm  the  here  i s comparable t o  that  Thus f o r r o u g h c a l c u l a t i o n s , e q u a t i o n  (5.4) i s v a l i d f o r e s t i m a t i n g p o p u l a t i o n d e n s i t i e s . From t h i s equation i t follows N « ^e^o^T* ^der experimental 17 -2 -1 8 3 1 ( 1  t  h  e  T  conditions N  0  «  used here, the  10 ^cm"-^, Q 1  yields  » 1 0 ~ ^ c m , and 1  T  N , p ( t ) £ 10  approximate values  cm~^  lower c o n f i g u r a t i o n .  2  the  N  » 10  'cm  e x c i t a t i o n time t =  f o r t h e maximum number d e n s i t y f o r each l e v e l w i l l  of  course  of  sec 200 the  be  smaller. For  Doppler l i n e s ,  the  e f f e c t of  self-absorption is  , nsec  88  g i v e n by t h e f a c t o r calculations  and  give k  S of equations from e q u a t i o n  Q  k P  of  5.6  Absolute T r a n s i t i o n  ition  (2.16).  for this  Probabilities  mentioned b e f o r e , by combining t h e r e l a t i v e  probabilities  complete  obtained.  between l i n e s  s e t of r e l a t i v e  h a v i n g t h e same l o w e r  transition probabilities  Here, o n l y t h r e e r e l a t i v e  needed t o t i e t h e f o u r l o w e r - l e v e l T h e r e were however, f i v e  theresults  mental to  error  arrive  placed  discussed  (emission) may b e  groups o f l i n e s  together.  i n d e p e n d e n t measurements made i n check.  I t was f o u n d  were c o n s i s t e n t w i t h i n t h e e s t i m a t e d  at thefinal  relative  The f i n a l  on t h e a b s o l u t e  recently  level  experi-  a n d s o a w e i g h t e d a v e r a g i n g method was employed  5.6.1).  section  trans-  emission p r o b a b i l i t i e s a r e  emission thus a l l o w i n g a s e l f - c o n s i s t e n c y that  value  i s negligible.  ( a b s o r p t i o n ) w i t h t h o s e h a v i n g t h e same u p p e r l e v e l a  Rough  as  i n A p p e n d i x 2 shows t h a t  the self-absorption  As  (2.2)  or  gun i s a p p r o x i m a t e l y 1 cm, k '^-^ 10"  as ^ f o rt h e electron  Reference t o the table  (2.15)  made i n t h i s  transition  p r o b a b i l i t i e s (see  set of r e l a t i v e p r o b a b i l i t i e s are  scale  u s i n g one l i f e t i m e  laboratory  measurement  and t h e a b s o l u t e v a l u e s a r e  a n d compared w i t h t h o s e o f o t h e r w o r k e r s I n s e c t i o n s  5.6.2 and 5.6.3.  -89  5.6.1  " M u l t i - P a t h " Method o f R e l a t i v e T r a n s i t i o n  With f i v e it  independent  i s p o s s i b l e t o o b t a i n up  lating  A  y e  ^  spectral  lines  The  involved  "routes" are best out  calcu-  P i g . 18 shows t h i s  The v e r t i c a l  arrows  s e e n when t h e  in a transition  l a b e l i n g t h e rows, and  marked a t t h e i n t e r s e c t i o n  the upper  array  levels  array with the  of the appropriate connect the  i n t h e e m i s s i o n measurement and hence  line-pairs  Indicate  the  I n t e r c o n n e c t i o n b e t w e e n t h e rows. To u t i l i z e  the  c o m p l e t e l y the i n f o r m a t i o n gained from  I n t e n s i t y measurements, t h e f o l l o w i n g method was  to c a l c u l a t e t o X.5852.  the e n t i r e  S t a r t i n g at the wavelength  a l o n g the arrows possible. row  without  may  relative  a l o n g t h e rows and  t o an a r b i t r a r i l y  a p a t h which  l e a v i n g t h e row  p a t h may  i n q u e s t i o n , one p r o c e e d s  Since the t r a n s i t i o n p r o b a b i l i t i e s  i n t h e row,  relative  vertically  o f F i g . 18 by a s many i n d e p e n d e n t p s t h s a s  are c a l c u l a t e d  line  adopted  set of t r a n s i t i o n p r o b a b i l i t i e s ,  t o \ 5 8 5 2 by m o v i n g h o r i z o n t a l l y  it  measurements  l i n e , w i t h X.5852 c h o s e n a s t h e  different  l a b e l i n g the columns.  rows a n d c o l u m n s .  intensity  i n d e p e n d e n t ways o f  investigated are layed  w i t h the lower l e v e l s  wavelengths  relative  to f i v e  f o r one p a r t i c u l a r  reference l i n e .  the  Probabilities  :  first  in a  particular  chosen  jumps t o more t h a n two i s not  independent.  spectral squares  Also  no  p a s s t h r o u g h t h e same s q u a r e more t h a n o n c e a l t h o u g h  "Jump" o v e r a p r e v i o u s l y u s e d s q u a r e .  parentheses f o l l o w i n g the wavelengths number o f I n d e p e n d e n t  The number i n  i n F i g . 18  paths f o r that wavelength.  indicates The  the  individual  s  z  6539(3) LIME  6678(3)  67/7(5)  t 6 533&)  6266(3)  63CV&)  6383(4  72+S@>  -  £382(4)  *9*5(+)  FIG.T8 T R A N S I T I O N A R R A Y F O R  62/7(4)  MULTI-PATH  6*02(4)  METHOD  7£XS2(4)  -91  relative used  transition probabilities  to c a l c u l a t e  average  of each step  the p r o b a b i l i t y  i s then c a l c u l a t e d  from  the t r a n s i t i o n probabilities,,  relative  these The  obtained along a p a r t i c u l a r path  9 lists  Table  i n t e r s e c t i o n o f a row of the r e l a t i v e the  these  and  weight  X5882 l i n e  row.  the a b s o r p t i o n and  example o f one  6096—*^6678—»-5852. is  10%  Table from while  5*6%, 9.  1.2%,  The  T a b l e s 1, s^ =  product 3,  (|pj^) The  The  5,  have b e e n  2.3$  f o r the  5882—*-6334 — 6 5 0 6 — » j  respectively,  A  r e l  j i s Wj =  .144  12.6%,  A^^  2  associated  ^  1/s ^ where s j i s t h e  d e v i a t i o n a s s o c i a t e d w i t h the path. computed u s i n g t h e  derived  (5882/5852) =  given the  step  as g i v e n i n  d e v i a t i o n of  f a c t o r t o be  and  calculated.  d e v i a t i o n a_ f o r each  gives a standard  weighting  the  f o r the wavelengths at  emission error analysis  standard  8 yield  and  estimated  of which the path i s  of the r e l a t i v e p r o b a b i l i t i e s  with a p a r t i c u l a r path  thus  the  independent, c a l c u l a t i o n  and  a  value  T h e s e d e v i a t i o n s have b e e n  f o r the p a t h  k 5%,  given to a  of  e r r o r s , where t h e number a t  transition probability  i s g i v e n here  weighted  values  i s d e r i v e d from  o n l y those which are r e q u i r e d here An  A  are  column i n d i c a t e s t h e s t a n d a r d d e v i a t i o n  head o f t h e c o l u m n and  o b t a i n e d from  t o X.5852.  independent  e r r o r s of the t r a n s i t i o n p r o b a b i l i t i e s composed.  i n a path  The w e i g h t e d  standard  average  is  formula  ( s e e f o r example, T o p p i n g  /38/).  The  standard  d e v i a t i o n of  the  5852 5852 5882 5945 6074 6096 6143 6163 6217 6266 6304 6334 6383 6402 6506 6533 6599. 6678 6717 6929 7032 7245  5882  5945  6074  6096  6143  6163  6217  6266  6304  10% 10%  6334  6383  6402  6506  2.5% 10% 10%  10%  6.2%  7.5% 2.9% 4.1% 5.5% 2.3% 2.6% 4.0%  3.3% 1.4%  10% 6.2% 10%  0.9%  3.7% 3.3%  1.2%  7.5% 2.3% 4.1%  8.0%  6929  5.5%  2.3%  2.6%  4.0%  7245  7.6% .  3.7% 5.6%  1.5%  7.5% 5.6% 1.6%  4.5% 10% 7.5%  8.9%  6.1%  1.6% 8.9%  5.7% 4.2% 1.8%  4.5% 4.2% 2.2% 10%  7032  4.5% 2.3% 8.0% 1.5%  10%  2.3% 10% •  6717  1.4% 2.3%  10%  6678  4.1% 1.2%  2.9% 0.9%  7.5%  10%  6599  10% 10%  2.5% 10%  6533  7.5%  7.6%  6.1%  TABLE 9 ESTIMATED ERRORS OF TRANSITION PROBABILITIES (EMISSION AND ABSORPTION)  5.7%  1.8% 3.7%  2.2% 3.7%  -93-  TABLE 10  RELATIVE AND ABSOLUTE NEON  PROBABILITIES AND OSCILLATOR  ^el 5852 5882 59^5 6074 6096 6143 6163 6217 6266 6304 633^ 6383 6402 6506 6533 6599 6678 6717 6929 7032 7245  . 10.0 1.44 1.44 8.54 2.50 3.17 1.90 .948 2.87 .691 2.11 4.33 3.91 3.68 1.43 3.17 3.20 3.01 2.50 2.88 1.39  STRENGTHS  f  xlO"' 6.58 .948 .948 5.62 1.64 2.09 1.25 .624 1.89 .455 1.39 2.85 2.57 2.42 .941 2.09 2.11 1.98 1.64 1.90 .915  TRANSITION  abs  ERROR  % .113 .0295 .0503 .104 .152 .118 .214 . 0216 .334 ; . 0449 .0832 .17^ .221 .256 .181 .136 .235 .13 * .197 .0845 .0720 2  1.6 13.0 13.0 10.7 7.0 11.3 7.6 13.0 7.5 12.4 11.2 8.4 11.7 9.1 8.0 6.0 3.9 5.3 7.3 12.6 12.5  94-  v a l u e s o f A^-^ and  i s u s e d a s a n e s t i m a t i o n o f t h e e r r o r o f A^^CA.)  i s computed by t h e f o r m u l a  The f i n a l determined  relative  i n t h i s manner  transition  are listed  tion of the absolute probabilities discussed  5.6.2  i n t h e next  Lifetime  X.  =  of l e v e l  1 i s connected t o t h e spontaneous  2  A  •••(5-7)  i k  l e v e l o f n e o n t h e r e a r e o n l y two a l l o w e d  downward t r a n s i t i o n s ,  time o f t h i s  i n the table i s  through the r e l a t i o n  I /  the  A n d e l /17/  also l i s t e d  The determina-  Measurement  transition probabilities  van  i n T a b l e 10.  and e r r o r s  section.  The l i f e t i m e  For  probabilities  X.5852  a n d X.5400. Recent  g i v e s t h e v a l u e o f 15.2 level.  The i n t e n s i t y  + .25  of  X5400  measurements b y nsec. f o r the l i f e -  was m e a s u r e d t o b e  -2 less  10  than  of the Intensity of  X5400  transition  t o an e r r o r o f l e s s  t h a n \%„  contribution of the amount  X.5852  A (5852) abs  was t a k e n t o be  (15.2  X  neglecting the  *  t o t h e l i f e t i m e would Consequently  10' f-  From t h i s a b s o l u t e v a l u e , t h e c o m p l e t e be computed a n d a r e shown i n T a b l e 10. possible  so t h a t  9  (6.58  ±  the value of  .11)  X  10  7  sec." .  s e t o f a b s o l u t e v a l u e s may Also included are the  e r r o r s a s s o c i a t e d w i t h them a n d t h e o s c i l l a t o r s t r e n g t h s .  1  -95-  TABLE 11  COMPARISON  OF ABSOLUTE TRANSITION  PROBABILITIES  x(i)  5852 5882 59^5 6074 6096 6143 6163 6217 6266 6304 633^ 6383 6402  6506 6533 6599 6678 6717 6929 7032 7245  THIS EXP'T  6.58 •948 .948 5.62 1.64  2.09 1.25 .624 1.89 .455 1.39 2.85 2.57 2.42 .941  2.09 2.11 1.98 1.64  1.90 .915  (XIO" ) s e c " 7  1  IRWIN  DOHERTY  FRIEDRICHS  LADENBURG  /12/  /10/  A l /  /7/  6.0 .96 .93 5.90  12.8 2.12 1.70 7.8 2.4  6.8 1.15 1.05 4.8 1.6 2.75 1.5 .61 2.2 .38 1.4 2.65 5.3 2.22 1.2 2.35 2.35 2.4 1.8 2.0 .72  3.51 .69 .61 3.0 .89 1.34 .78 .35 1.20 .27 .84 1.5 2.7 1.3 .7 1.2 1.1 1.1 .8 1.06 .42  1.5 .77 .4  3.25 2.44 1.46 3.84  .93 2.07 4.17 5.78 2.14  4.32 4,10 4.17 3.56 3.24 1.80  TABLE 12  \ 5852  5882 59^5 6074 6096 614-3 6163 6217 6266 6304 6334 . 6383 6402  6596 6533 6599 . 6678 6717 .6929 7032 7245  COMPARISON OF RELATIVE TRANSITION PROBABILITIES  THIS  IRWIN  /12/  EXP'T  10.0 1.44 1.44 8.54 2.50 3.17 1.90 .943  ( 1.6*) (13.0#) (13.0*) (10.7*) . ( 7.0*)  10.0 1.69 1.54 7.06  UP*) (15*) (15%) (10%)  (11.3*)  4.04  (10%) (20%)  .( 7.6%)  2.20  (15%)  (13.0*)  2.87 ( 7.5%) .691 (12.4*) 2.11 (11.2*) 4.33 ( 3.4*) 3.91 (11.7%) 3.63 ( 9.1*) 1.43 ( 8.0*) 3.17 ( 6.0*) 3.20 ( 3.9*0 3.01 ( 5.3*) 2.50 ( 7.3*) 2.88 (12.6*) 1.39 (12.5*)  2.35  .897 (15%) 3.24  (15%) .559 (10%)  2.06 3.68  (15%) (10%)  7.79 3.26 1.76 3.45 3.45 3.53 2.65 3.21 1.13  (25%) (10%) (15%) (10%)  DOHERTY  FRIEDRICHS  /10/(30*)  /ll/(20-30^) . /7/(20-30*)  10.0 1.97 1.74 8.55 2.54 3.82 2.22 .997  10.0 1.60  10.0 1.66  1.55 9.85  1.33 6.09 I.87  2.54 2.50 1.29  3.42  .769 2.39 4.27 7.98 3.70. 1.99 3.42  (10*0 (10*). (10*)  3.13 3.13  (15*) (10*)  3.02 1.20  2.28  LADENBURG  .668  1.91 1.14  3.00 .726 1.62 3.26 4.51 2.66 I.67  3.37 3.20 3.26  3.78 2.53  l.4l  -97-  5.6.3  C o m p a r i s o n and  For /10/, both  / l l / ,  comparison w i t h the  /12/  by  different  t h e a b s o l u t e and  here w i t h those as  g i v e n by  present  from the  c a n be  results  Friedrichs  a b s o l u t e b a s i s by  accuracy  adopting .85  of t h i s value  to  Because of  be  and  can  .21  extremely  in  evidence  of systematic  the present  are  of  the  does  Doherty This  to the  fixing  by  f = the  .5 f o r  f-sum r u l e .  t o be  In  o f \5852,  after  The  Doherty's  error.  h i g h a b s o r p t i o n , X.6402 seems  lines  t o m e a s u r e and  that his value  e r r o r s so t h a t t h e optimistic  and  there  those  i s somewhat  l a r g e d i f f e r e n c e seems t o  work i s t o o  \6k02,  on  e x p l a i n the d i s c r e p a n c i e s , while  o f t h e most d i f f i c u l t  Irwin c i t e s  those  error.  attributed  the value  considered  its  nevertheless this  presence  errors  s c a l e L a d e n b u r g and  l a r g e v a r i a n c e between t h e v a l u e measured h e r e  but  measured  date.  measurement o f t h e l i f e t i m e  a b s o l u t e v a l u e s must be  others.  list  Ladenburg p l a c e s h i s r e l a t i v e v a l u e s  c o m p u t i n g t h e bounds o f  one  The  than  work w i t h i n e x p e r i m e n t a l  of the a b s o l u t e s c a l e .  t o be  above.  shows g e n e r a l a g r e e m e n t a s  I n d i c a t e s t h a t t h e d i f f e r e n c e s may  Andel's  12  seen t h a t Ladenburg's a b s o l u t e v a l u e s  agree w i t h the present  from van  and  /7/,  are also included.  However on t h e r e l a t i v e  uncertainty  11  transition probabilities  references cited  Irwin, who.claims the b e s t  an  of other workers  h i g h e r whereas Doherty's a r e lower  work.  Probabilities  methods, T a b l e s  relative  the authors  It generally  D i s c u s s i o n of Absolute  indicate  e r r o r estimate  for this  line.  is a  of  the  high the given  - 89  The l i f e t i m e s absolute  transition  o f t h e 2p^3p l e v e l s  probabilities  of  data  probabilities, an  error  p^  level,  13 a n d i n c l u d e s  i n Table  computed b y I r w i n / 1 2 / a n d K l o s e  thelifetimes  less  computed  15$.  /15/.  Several  f r o m t h i s work do n o t c o n t a i n a l l t h e  b u t t h e ones m i s s i n g than  from  (5-7)•  by means o f e q u a t i o n  T h i s h a s b e e n done a n d i s c o n t a i n e d similar  may be computed  Again  a r e small and c o n t r i b u t e  agreement  f o r which the l i f e t i m e  i s good e x c e p t  f o r the  i s due o n l y t o t h e \6402  transition.  TABLE 13  COMPARISON OP UPPER-LEVEL LIFETIMES  LEVEL l  p  P2  3 P4 P  p  5  P6  7 *8 p  p  9  PlO  THIS  EXP'T  IRWIN / 1 2 /  (X10 )  KLOSE  9  /15/  15.2* 23.6*  14.7*  14.7  18.1  16.3  17.7*  20.7*  21.3  20.0  23 22  25.8**  20.1*  18.9  23.5 23.0*  20.3  22  23.2* 25.4  20.3  19  22.5  26.5* 37.7 35.3**  * Missing 1 transition ** M i s s i n g  2 transition  24.3  probability probabilities  sec.  -99-  CHAPTER 6  CONCLUSIONS  Relative  transition probabilities f o rtransitions  between t h e e x c i t e d  state  configurations  Ne I have b e e n s u c c e s s f u l l y m e a s u r e d b y a new method. ments were made on b o t h a v a r i a b l e d i s c h a r g e a b s o r b e r and a p u l s e d obtain  length  cylindrical  Measuredc glow  e l e c t r o n gun e m i t t e r t o  a complete s e t o f r e l a t i v e p r o b a b i l i t i e s . The  transmission  o f t h e glow d i s c h a r g e  varied  over the c r o s s - s e c t i o n  mainly  to a variation of the excited  m i s s i o n was compared w i t h t h a t Doppler-broadened was f o u n d . and  of  2p^3s a n d 2p^3p  o f t h e column;  absorber  this i s attributed  atom d e n s i t y .  The t r a n s -  w h i c h w o u l d be o b t a i n e d  s p e c t r a l l i n e s and a g e n e r a l l y  good  from comparison  The v a l u e s o f t h e p a r a m e t e r a were anomolous however  s u b s e q u e n t n u m e r i c a l c a l c u l a t i o n s showed t h e p o s s i b i l i t y o f  e q u i v a l e n c e between non-Doppler and " f i c t i t i o u s " shapes.  Doppler  line-  The r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s computed f r o m  method a r e v a l i d  although the accuracy  i s less with  a b s o r b i n g l i n e s due t o b o t h n o n - D o p p l e r l i n e - s h a p e s mations used t o account  highly and  f o r the presence of isotopes.  approxiExperi-  mental evidence e x i s t s f o r the presence of s e l f - a b s o r p t i o n i n the  G e i s s l e r tube Use  feasible  source.  of a pulsed  f o r measurement  advantage i s that  e l e c t r o n gun e m i t t e r of r e l a t i v e l i n e  self-absorption  has been  intensities.  i n the emitting  found The  neon i s  negligible. Finally  this  a l i f e t i m e measurement by v a n A n d e l / ! ? /  -100-  allowed absolute w e l l as  lifetimes  transition probabilities of the upper l e v e l s  t o be  of the  calculated  transitions.  as  -101-  APPENDIX 1.  ISOTOPE CORRECTION  Equation the  case  this  (2,9)  o f a gas c o n t a i n i n g two i s o t o p e s .  equation  i s contained  Consider occurring  Doppler-shaped w i t h primed  i n this  the case  i n the r a t i o spectral  2.1.3 f o r  was g i v e n i n s e c t i o n  appendix.  o f a gas h a v i n g  K(K-l). lines  The d e r i v a t i o n o f  I f both  then  two i s o t o p e s  t h e i s o t o p e s have  i n the n o t a t i o n o f Chapter  and unprimed q u a n t i t i e s  referring  2,  t o t h e two i s o t o p e s ; 1., T-  with  cjin  ZU = I > " ^ , X(*)=X* /  and with  CO  ->—  _  {.(O - LX)  where <S i s t h e c e n t r e f r e q u e n c y of  y  *) CA -  -CO  eX  ~r,  ? ^ o — — ^  separation of the spectral  r7~  lines  t h e two i s o t o p e s . The  energy  into  the absorber  per unit  time  i s thus  -102-  and  the energy t r a n s m i t t e d p e r u n i t  E =\  time i s  f ( I W + XVv)U  dWA  ...Ui.i)  I f t h e r a t i o 161 / A S ) ^ i s l a r g e enough, t h e two components may b e c o n s i d e r e d a s s e p a r a t e a n d e q u a t i o n  (Al.l)  becomes  so t h a t t h e t r a n s m i s s i o n i s  ( [ Pd^v) + X'<r*0)dv>]dA •'A-  'o  D i f f e r e n t i a t i o n with respect to the area f o r axially  symmetric  d(R^T)  yields  Sj*™*  =  The 1.  geometry  +  ...  f o l l o w i n g a s s u m p t i o n s a r e now  T h e r e i s ho p r e f e r e n t i a l  thermal  ( A i  .  2 )  made:  h e a t i n g between t h e  I s o t o p e s , so t h a t T = T', T „ = T i . a n d t h e r e f o r e a = a ' . ' . a a ' s s' r  2.  The p o p u l a t i o n s o f c o r r e s p o n d i n g  levels  of the Isotopes are  i n t h e r a t i o K and t h e t r a n s i t i o n p r o b a b i l i t i e s f o r corresponding t r a n s i t i o n s  are equal, o r less  stringently,  -103-  Prom t h e s e a s s u m p t i o n s , and t h e f a c t "k+'fr  4  - \ + Ot\o~ ) ^  =  ^  =  and  since  /  /H I  that  f  f  , i t c a n be s e e n  .  ^  that  b  .. ( A l . 3 )  ^Llf  Q  5^.  so  |  s  that  -  K  ... (A1.4)  equation (Al.2)  becomes:  7 T ^ o < 4 J U ) +aFft(bJU.*)]  =  [  F  ...(AI.5)  which i s i d e n t i c a l w i t h equation (2.9). A few comments a b o u t priate  here.  measurement  In t h i s  experiment  the assumptions  t h e t i m e s o f o b s e r v a t i o n and  a r e of the order of minutes.  of  the c o l l i s i o n  of  10^  are appro-  A rough  calculation  f r e q u e n c y between t h e i s o t o p e s g i v e s a v a l u e  c o l l i s i o n s p e r second.  With t h e energy t r a n s f e r  fraction  -104-  being  .5  brium  t o be e s t a b l i s h e d b e t w e e n t h e I s o t o p e s .  f o r e l a s t i c c o l l i s i o n s , ample t i m e o c c u r s f o r e q u i l i -  Half  2.  o f assumption  has been e x p e r i m e n t a l l y  verified  b y C o n n e r a n d B l o n d i /42/, a s w e l l a s L a n g /33/,  observed  f o r neon t h e r e l a t i o n  seems r e a s o n a b l e t h a t particularly  this  t h e lower The  errors  who  (Al.4).  g i v e n by e q u a t i o n  It  s h o u l d h o l d f o r a l l l e v e l s and  level  1,  Justifying  t h e assumption.  i n t r o d u c e d i n c o n s i d e r i n g t h e two D o p p l e r  lines  c o m p l e t e l y s e p a r a t e d c a n be e s t i m a t e d b y c o n s i d e r i n g t h e  ratio  o f t h e Doppler width t o the s p l i t t i n g .  M i s h i m a /kj/ found  have m e a s u r e d t h e i s o t o p e s p l i t t i n g o f n e o n , a n d  i t t o be b e t w e e n  Doppler widths similar  .02  a n d .035  o f t h e neon l i n e s  t o that used  room t e m p e r a t u r e ,  here, and found t h e widths  .017A.  line-width ratio  Knowing t h i s  ratio,  n u m e r i c a l l y as a f u n c t i o n o f k calculated digital  exactly.  measured t h e source  t o correspond t o  This gives an isotope  g r e a t e r than 1 t o a p p r o x i -  Q  e q u a t i o n ( A l . l ) may b e i n t e g r a t e d i  and a, and T ( o r d ( R R ) / d ( R ) ) 2  T h i s h a s b e e n done u s i n g a n IBM  computer and t h e e r r o r between e q u a t i o n s i s shown g r a p h i c a l l y  those l i n e s  doubt  I r w i n /12/  2.  mately  For  A*.  using a radiation  o r approximately  s e p a r a t i o n t o Doppler  (Al.5)  Nagaoka a n d  that  2  7Q40  ( A l . l ) and  i n F i g . A l as a f u n c t i o n o f k i . . Q  are highly absorbing, the value of k  i n e r r o r due t o t h i s  cause, p a r t i c u l a r l y  Q  i s no  f o r high absorber  c u r r e n t s a n d n e a r t h e a x i s o f t h e t u b e where a b s o r p t i o n i s greater.  T h i s ' c o u l d be one o f t h e r e a s o n s  f o r the poor  t h e c u r v e s t h a t was o b s e r v e d f o r some s t r o n g l i n e s  f i t to  ( s e e remarks  -106-  in section  5.2.3).  t h a n 3 and an X L  G e n e r a l l y most o f 1.5  assuming separated in determining f since  f  r  e  l  r e  than  5*.  ] _ c a n be c o n s i d e r a b l y l e s s  depends on t h e r a t i o  i nf  r  kl Q  of less  o f two k » s 0  The e r r o r than t h i s  however,  (see equation  (2.11))  comparable a b s o r p t i o n and v a l u e s of XL ,  i nthe values of k  make t h e e r r o r  had a  o r g r e a t e r making t h e e r r o r i n  c u r v e s t o be l e s s  F o r two l i n e s h a v i n g error  lines  e  Q  will  ^ less.  tend  i n t h e same d i r e c t i o n a n d  the  -107-  APPENDIX 2.  EVALUATION OF TRANSMISSION EQUATION  The equation  (2.8)  method o f c o m p u t i n g t h e r i g h t - h a n d i soutlined i nthis  Equation  (2.8)  (Al.5)  form o f e q u a t i o n s  and ( 2 . 3 ) :  k jH  with x =  (2.8)  , a =  Q  0.094,  appendix.  can be evaluated  i n t e g r a t i o n o f equation  side of  e i t h e r by n u m e r i c a l  o r by use o f t h e i n f i n i t e  a n d b =0.104.  For small x the  c o n v e r g e s r a p i d l y a n d t h e number o f t e r m s n e c e s s a r y evaluate  i t i s small.  recourse  t o numerical The  is  For large x the opposite integration  series  series  i n order t o  i s t r u e and  i s best.  problem i n c a l c u l a t i n g t h e s e r i e s f o r l a r g e x  t h a t t h e terms a r e n o t s m a l l u n t i l  n > x and e v a l u a t i o n  c o n s i s t s o f computing t h e d i f f e r e n c e between p a i r s o f l a r g e numbers.  With a f i n i t e  "word l e n g t h " s u c h a s i s p r e s e n t  computer, t r u n c a t i o n a n d r o u n d - o f f U s i n g a n IBM was  found  values  7040  digital  o f x necessary  call  on numerical The  critical.  computer w i t h d o u b l e p r e c i s i o n , i t  t h a t f o r t h e T ' s encountered,  i nthis  experiment, t h e  were l o w enough t o u s e t h i s  ever f o r t h e l a r g e r x used to  o f t h e t e r m s becomes  in a  i t probably  series.  How-  w o u l d have b e e n q u i c k e r  integration.  FORTRAN I V p r o g r a m i s g i v e n b e l o w .  The f i r s t  -108-  sum  i n equation  s e c o n d sum these  (A2.1) i s c a l l e d t h e m a j o r s e r i e s  the minor s e r i e s .  The  procedure  in  and  the  calculating  sums f o r a g i v e n x i s t o e v a l u a t e s u c c e s s i v e t e r m s  their absolute value ceases. error,  i s less  than  10  F o r s p e e d o f c o m p u t a t i o n and terms a r e  evaluated  , a f t e r which  computation  minimization of  from p r e c e e d i n g  terms,  until  round-off  thus:  X I t was x =  35,  found  that  the major s e r i e s  at which value  approximately  100.  becomes u n s t a b l e  t h e number o f t e r m s computed  A spot-check  u s i n g a Simpsons R u l e n u m e r i c a l agree to three s i g n i f i c a n t  o f t h e v a l u e s was I n t e g r a t i o n and  figures.  above was  carried  was  found  out to  IBFTC — 1 ~C C ^ 4  SUM D O U B L E P R E C I S I O N T » T E R M » R A T I 0 » R » A 2 * A I »X I » R 1 » X F , D S Q R T . X 1 » X 2 » T 2 » T 3 PTWE-N'S-rO N R A T I 0"( 5 0 0 ) , R ( 5 0 0 ) " READ(5»1)XI,XF,DELX,A»AF,AD»M1 FORMAT(6F8.4,14) X I =X ( I N I T I A L ) >XF = X ( F I N A L ) » D E L X = I INCREMENT I N X, D I T T O FOR A ? A F » AD WR T M1=.MAX. N O . O F T E R M S I N S E R I E S • DO 12 I 1 = 1 » N N WR I TE ( 6 »4 ) • FORMAT(1H1>7XJ3HSUM>6X»2H X,6X»5HALPHA) A I= A**2 R ( 1 ) - 1 . D0 + A 2 : RATIOt1)=1.D0/DSQRT(R{1)) M2 = M1 DO 6 I - 2 > M 2 A I= 1 R ( I ) =R( I - l ) +A2 R A T 1 0 ( I ) - D S Q R T ( R ( I - 1 ) /R ( I ) ) / A I  :  —  :  T> C C  7  C A L C U L A T I O N OF  MAJOR  SERIES  GO  175  X1=XI T=1.D0  N--i 3  C — C C ir7-5  30  TERM--RAT 1 0 ( 1 ) * X 1 IF(ABS(TERM).LT..0001) T-T + T E R M I F C N . G T . M 2 ) GO TO 189 N =N+1 Rl-RATI0(Psl)"Xl • TERM=-TERM*R1 GO TO 3 CALCULATION  OF  MINOR  X2=0.104XX1 T2=1.D0 N =l TERM- RATIO(1 ) « X 2 IF(ABS(TERM) .LT..0001) T2=T2+TERM ir(N.GT.M2) GO TO 1 0 0  TO  SERIES  GO  TO  170  :  —  ALPHA  170 180 183 189 184 18 2  N = N+1 R1 = RA TI 0 ( N ) * X 2 —T~E~R M — T E R M " RT: GO TO 30 T3=(T+.094*T2)/1.094 GO TO 18 WR I T E ( 6 »18 3) F O R M A T ( I X » 4 1 H N U M S E R OF TERMS GO TO 12 WR I T E ( 6 J 1 8 4 ) F O R M A T ( I X » 4 1 H N U M B E R OF TERMS GO TO i 2 W R I T E ( 6 > 2) T 3 ? X 1 ? A FORMAT(5X>3F8.3 i r i A i . O t i A M  1U  1U  X1=X1+DELX GO TO 7 1 u  TT.  i h l A . b t . A I - ;  A=A+AD GO TO 99 S I OP END  GU  1U  1<L  i !  I N MI NOR S E R I E S  TOO  LARGE)  i i  I N MAJOR S E R I E S  TOO  LARGE)  -109-  APPENDIX 3.  SELF-ABSORPTION CORRECTION  Self-absorption a gaseous s o u r c e . the  By  The c o r r e c t i o n  paragraphs  considering  c a n be shown t h a t  optically for  reduces the I n t e n s i t y  e m i t t e d by  f a c t o r S t o be a p p l i e d t o  measured i n t e n s i t y f o r Doppler-broadened l i n e s  in the following  it  FACTOR  Irwin  the t o t a l  i f stimulated  line  of r a d i a t i o n  i n t e n s i t y e m i t t e d by a n  $ c a n be r e p r e s e n t e d by ( s e e  /12/)  B J O - - ^  1 =  2.2).  the equation of t r a n s f e r  thick layer of length  example,  where,  (see s e c t i o n  i s derived  9  ^ ) ^  ...(A3.1)  emission i s n e g l i g i b l e  B = Substitution  of the simple  k( S> ) r e s u l t s i n t h e c o r r e c t i o n However when two i s o t o p e s in  Appendix  Doppler p r o f i l e f o r  f a c t o r g i v e n by e q u a t i o n  a r e p r e s e n t , k ( ~i> ) h a s t h e f o r m  1.  ,  -co'*  (2.15). given  -110-  n-o  Substituting f o r k from above i n t o variable  Q  then  value  yields  equation  values  (2.2) and B the integration  (2.16).  of S f o r s e v e r a l  of the isotope separation are given i n Table o f S i s d e f i n e d such  that  S = 1.0  when o n l y one i s o t o p e i s p r e s e n t ;  9.9:100, S = 1.099 well,  L  and changing  A t a b l e of numerical values  *  from e q u a t i o n  (A3.1),  equation  f r o m ~P t o co  1  the correction factor  calculated  with the values  values  of k $ Q  g i v e n by L a d e n b u r g a n d L e v y / 7 /  It f o r the  w h i c h a r e common t o b o t h .  The  computer program u s e d t o e v a l u a t e  (2.16) i s g i v e n b e l o w .  numerical  As  i s o t o p e has b e e n  (2.15) a n d h a s b e e n i n c l u d e d .  from equation  agrees  i n the r a t i o  thickness i s zero.  f o r a single  The  f o r no s e l f - a b s o r p t i o n  f o r two I s o t o p e s  when t h e o p t i c a l  A3.  To c a l c u l a t e  equation  the factor  i n t e g r a t i o n was r e s o r t e d t o .  The method o f i n t e g r a -  t i o n c h o s e n was Simpson's R u l e b e c a u s e o f i t s . s i m p l i c i t y , w e l l as t h e f a c t  that the accuracy  only to three s i g n i f i c a n t  figures.  n e e d e d was n o t h i g h  as  —  A f t e r c o m p u t a t i o n o f sS  n  ,  -111-  the that  s e r i e s was e v a l u a t e d used  isotope (and  i n a manner e n t i r e l y  analogous t  i n A p p e n d i x 2.  The s i n g l e  i n t h e program g i v e n  s e l f - a b s o r p t i o n f a c t o r was computed b y p u t t i n g  therefore  TABLE A3  a = b = 0)  i n t h e program.  SELF-ABSORPTION CORRECTION  FACTOR FOR A  ONE AND TWO ISOTOPE GAS S TWO ISOTOPES) XI =1.5 n =2.0  n-=1.0 0.0 .62  .04  .06  .08  .1 .2  '? .4  .5 .6 .7 .8 .9 1.0 1.2 1.4 1.6 1.8 2.0 2.4 2.8 3.2 3.6 4.0  •  1.099 1.091 1.083 1.075 1.068 1.060 1.023 .988 .956 .924 .895 .867 .840  .915 .791 .7^6 .705 .668 .635 .604 .550 .504  .466  .432 .403  K  1.099 1.091 1.084 1.077 1.069 1.062 1.02? .994 .962 .933 .904 .877 .852 .827 .804  .761 .721 .685 .653 .622 .569 .524 .485 .451 .422  1.099 1.092 1.084 1.077 1.070 1.063 1.030 .998 .967 .938 .911 .884 .860 .836 .813 .771 .733 .698 .666 .636 .584 .540  .502 .469  .440  (ONE  s ISOTOPE)  1.000 .993 .986 .979 .972 .966 .933 .902 .873  .845 .818  .793 .769 .7^7 .725 .685  .648  '  .615 .584 .556 .507 .466  .430 .399 . 372  SIBFTC  10  ISOABS R E A L OMEGA »OMEGAF DOUBLE P R E C I S I O N S U M » T E R M > R A T I 0»A I»DSQRT»S D I M E N S I O N R A T I O ( 1 0 0 ) »S( 1 0 0 ) R E A D ( 5 » 1 0 ) X,XF>DX,OMEGA,DOMEGA »OMEGAF FORMAT(6F8 . 1 ) I F ( X F . G T . 3 5 . )STOP • I F ( X F . L E . 3 5 . )N = 120 IF(XF.LT.20.)N=60 I F U F . L T . 1 0 . )N = 35 IF(XF.LT.5.0)N=20 I F ( X F . L T . 1 . 3)N=10 N l = 20 N2=40 N3 = 20 B = 2. 5 A= 2. 5 RT=SQRT(1.1) HK=.099 HK1 = RT#H,<  •  XI =X  23 11 C c c  7 c c  WR 1 I E ( 6 »11 ) »5HOMEGA) FORMAT ( 1 H I >7X? 1HS » 1 I X » 4-HK0#L »»8HNO.TERMS,5X 3X •  COMPUTE S ( J ) Jl =l DO 50 J = J 1 >N I N T E G R A T I O N FROM - I N F . TO BN1=N1 H=l./(BN1*B) SUME = 0 . SUMO=0. L=l K= l N l 1 = N1-1 DO 1 0 0 1 = 1 , N 11 AI= I  103  •  Y=AI*H Y=1. / Y Y2=Y*Y  -B  102  101 100  c c  204  201 203 202 200  B R AK = ( E X P ( - Y 2 ) + H K 1 * E X P ( - 1 . 1 * ( (Y +OMEGA)**2) ) ) F 1 = Y 2 * ( (BR A K ) * # J ) I F ( L . E Q . 2 ) GO TO 101 IF(K.EO.l)SUMO=SUMO+Fl IF(K.EQ.O)SUME=SUME+F1• I F ( I . E Q . N l 1 )G0 TO 102 GO TO 1 0 0 Y = l ,/B L=2 GO TO 103 FF1=F1 K=l-K SUM1 =( 1 . 33 3 3 3 * S U M O + . 6 6 6 6 7 * S U M E + .33 3 3 3 * F F l ) * H INTEGRATION FROM -B TO A BN2=N2 H=(A+B)/BN2 L= 1 K=0 SUME=0. SUMO=0. DO 2 0 0 I = 1 » N 2 AI = I-1 W = -B + AI-«-H VI2 =W-«-W BR AK = ( E X P ( - W 2 ) + H K 1 * E X P ( - 1 . 1 * ( ( W - O M E G A ) * * 2 ) ) ) F2=BRAK*#J I F ( I . E Q . 1 ) G O TO 20 1 I F ( L . E Q . 2 ) G O TO 2 0 2 I F ( K . E O . l ) S U M O = SUMO + F 2 I F ( K . E Q « 0 ) S U M E = SUME + F2 I F ( I.EO.N2 )GO TO 2 0 3 GO TO 2 0 0 FI2=F2 GO TO 2 0 0 W=A L=2 GO TO 2 0 4 FF2=F2 K = 1-K SUM2=( 1 .33 3 3 3 * S U M O + . 6 6 6 6 7 * S U M E + . 3 3 3 3 3 * ( F F 2 + F I 2) )*H  c  303  302  301 300 50 C C C 18  55  8  2  INTEGRATION FROM A TO I N F . BN3=N3 H=1./(A*BN3) SUME=0. SUMO=0. L=l K=l N31=N3-1 DO 3 0 0 .1 = 1 >N31 AI =I Y=AI*H Y=l./Y Y2=Y*Y , BRAK= ( E X P (--Y2 ) +HK1*EXP (-1 . 1* ( ( Y-OMEGA ) **2 ) ) ) F3=Y2*((BRAK)**J) 1 F ( L . E Q . 2 ) G O 10 3 0 1 I F ( K . E O . l ) S U M O = SUMO+F3 IF(K.EQ.0)SUME=SUME+F3 1 h I I.EQ.N3 1 )GO 10 302 GO TO 3 0 0 Y= A L=2 GO TO 3 0 3 FF3=F3 K=l-K SUM3 = ( 1 . 3 3 3 3 3*SUM0+.66667*SUME+. 3 3 3 3 3 * F F 3 ) * H S(J)=SUM1+SUM2+SUM3 S ( J ) NOW  ; 1 '  1  ! 1  j {  1  ] I  ;  i  COMPUTED  J2=J1+1 DO 55 I=J2»N Al = I RATIO(I)=(S(I)/S(I-l))/Al I F ( J 1 . GE • 2 ) G 0 TO 8 TERM = -S (,2 ) * X / 2 . SUM=S(1) J3=J2+1 DO 2 I = J 3 > N I F ( A B b ( I t K M ) . L I . l . D - 4 ) G 0 TO 3 SUM=SUM+TERM TERM=-TERM*RATIO(I)*X  ,  3 6  5 4  16 17  19  IF(I-N)5»6»6 J1=N+1 N=N+10 GO TO 7 SUM=SUM/1.77245 W R I T E ( 6 » 4 )SUM »X » I »OME GA FORMAT(5X»F7.4»5X,F5.3,5X,I 3,5X,F4.1) X-X+DX I F ( X - X F ) 16 » 16 »17 Jl =l GO TO 18 X = XI OMEGA=OMEGA+DOMEGA I F ( O M E G A - O M E G A F ) 2 3 >23?19 STOP END  '  j i i  | 1  1 j  I  ! ;  -112-  APPENDIX 4.  R E L A T I V E INTENSITY MEASUREMENT OP SPECTRAL LINES  The t h e o r y equation  of spectral lines Consider  slit  derives  pass-band  If  (sees e c t i o n 4.1).  intensity.  slit  a wavelength region  The  i s then t r i a n g u l a r o r t r a p e z i o d a l , sizes of exit  and e n t r a n c e  slit.  t h e monochromator i s s e t on w a v e l e n g t h x  the width o f t h e e x i t  A \^  where D(.X ) i s t h e l i n e a r M  i s denoted by W , xt  M  and  t h e n i t encompasses  g i v e n by  dispersion.  w h i c h t h e image o f t h e e n t r a n c e  where M(x)  of relative  the case i n which the i l l u m i n a t i o n covers  depending on t h e r e l a t i v e  is  appendix  o f a monochromator and i s o f u n i f o r m  transmission  the  i n this  (4.1) f o r t h e q u a n t i t a t i v e measurement  Intensities  the  developed  slit  The c o r r e s p o n d i n g covers,  Ax  n t  ,  i s given by  i s the l a t e r a l m a g n i f i c a t i o n o f t h e instrument  exit plane  and  i s the width of t h e entrance ^ A^N^SO  assumed h e r e t h a t  slit.  the transmission  i d e a l monochromator i s t r a p e z o i d a l o f w i d t h ^ X  x  t  region  •  in It  of an This i s  shown i n F i g . A4,.a. t(x,Xjj) i s t h e t r a n s m i s s i o n  o f t h e monochromator and  r e a c h e s a maximum, T ( X ) i n t h e r e g i o n M  .  _ A * ^  z  t  - A K t  ^  X  ^  >\  2.  Z  The d e t e c t o r  +  output  current  b a n d o f w a v e l e n g t h s dX, c e n t r e d  due t o r a d i a t i o n i n a s m a l l  at X i s  -113-  6i  = J T l t ^ A  M  )  where <TL i s t h e s o l i d a n g l e s u b t e n d e d monochromator and i n p u t  lens,  S(\)  d e t e c t o r , and I(X) i s t h e i n t e n s i t y unit  wavelength  interval  ...(A4.1)  S(*)1M6?\  a t t h e s o u r c e by t h e  i s the s e n s i t i v i t y per unit  of the  s o l i d angle per  of the source.  t  ••tew,)  /  \.  1  >M  1  z.  Pig.  A4,I  Pass-Band o f Monochromator  I n t e g r a t i n g over a l l wavelengths response,  yields  the t o t a l  thus:  X i t S X d A  L = j df 2.  ...(A4.2)  ;  -114I.  For a s p e c t r a l  i  where t h e s u b s c r i p t two  X-^, x  lines  2  indicates  o f t h e same  _ p / >. v  UK)  A X ^  variable  x'  must be =  line  radiation.  Tfro  n  Therefore f o r  £  source, the v a r i a t i o n  a  and w a v e l e n g t h  S(*,)T (?\ .)  taken i n t o account.  (X-X )/A'X'^  2 : t  line-width  N  For a continuous over  of w i d t h <S/N«A>\  line  d  M  o f I and  Introducing a  writing a Taylor series  S  new expansion  ~2 for  I and  S about  Now  X'(o)  x'  =  0  ^fC(0-36o)J/|  and  terms i n the expansion a r e r e t a i n e d ,  with  s - X0)/x^o)  ,  i f only the f i r s t then  <r = S6)/3tf>)  two  X  -115-  and  t h e t r a n s m i s s i o n i s g i v e n by  (see P i g .  \ - ex.  v  A^.b)  J  7  l -  o-  where  a  = »-  Equation  n  t  (A^.2) t h e n becomes  K M= [^[»+i(6-Odo--0-'o>-2:*U-0^-0]5  with  and a, 81 , and T  are functions of  Therefore  but  — ****  A  A  ^ '  ]  i f two  X.  wavelengths  X-p  X  2  =  where D i s t h e l i n e a r  dispersion.  The  ratio  are  compared,  -116-  is  then  i d e n t i c a l with equation  (4.1).  -117-  APPENDIX 5.  CURVE-PITTING OP NON-DOPPLER SPECTRAL DISTRIBUTION TO DOPPLER SPECTRAL DISTRIBUTION  Attempts of pure  Doppler-broadened  Doppler s p e c t r a l  1.  a r e made h e r e t o e q u a t e  lines,  intensity  length  J(_ iinn wwh hich e (see Appendix 3 ) .  t o two t y p e s o f n o n -  as d i s c u s s e d i n s e c t i o n  Self-Absorbed Doppler  The  spectral lines  thetransmissions  5.4.1.  Distribution  d i s t r i b u t i o n o f a gaseous  source of  s e l f - a b s o r p t i o n t a k e s p l a c e i s g i v e n by  6  1(9} - B d - ^ ^ which,  f o r k(9  4  )  ) g i v e n b y a D o p p l e r d i s t r i b u t i o n a n d k j l &~ 1 Q  reduces t o t h e form g i v e n i n Chapter For a uniform, mono-isotopic gas w i t h a p u r e  -  2. e m i t t e r and a b s o r b e r  Doppler a b s o r p t i o n c o e f f i c i e n t ,  mission T i s actually  T  ...(45.1)  g i v e n by  \ (i - E*P c -Jk (^h)) B  E x P( - A . (SO A )  d v>  the trans-  -118-  = 2  2  O-o  (->)  y"^  (Tv -r1) \ m\ J/0-+I + ^ d i 1  Ante  ...(A5.2)  where y = k „ i _ a n d x = k OG  6  ,0 , a n d t h e s u b s c r i p t s e a n d a OS.  Q.  refer  i  to e m i t t e r and absorber, r e s p e c t i v e l y . The  question  i s r a i s e d , c a n t h i s be e q u a t e d t o a  D o p p l e r t r a n s m i s s i o n w i t h no s e l f - a b s o r p t i o n ? i . e. f o r the  s i xabsorption lengths  and  a* s u c h t h a t  T  s ^  5  ^ ° 0  l  a  a  i ,, i s t h e r e some v a l u e  = Vz<'<*0^ =//-->  where x, = k ,/ . a n d x' = k» „ i oa a^ oa  T ' C Z \ =  as  given  i n equation An a t t e m p t  numerically k»  rt  and  #  T  ...(A5.4)  (2.3). h a s b e e n made t o s o l v e e q u a t i o n computer;  (A5.3)  values of  ( s e e s e c t i o n s 3.2.1  3.2.2) were u s e d t o compute T* (xj^, a ' ) . oa  ?  ^^K^  a n d a* d e t e r m i n e d e x p e r i m e n t a l l y  as k  ...(A5.3)  -  , and a^'  i n t h e IBM 7040 d i g i t a l  was e v a l u a t e d  o f x*  T s  (y»  was i n c r e a s e d i n s t e p s u s i n g , •  x  i»  a  assumed  )  -119values of the parameters y and a u n t i l the root-mean-square deviation between T* and T for the six absorption lengths was s  a minimum. Some examples of T and T' for two wavelengths are g  shown in Table A5..1. error is possible;  It can be seen that a f i t with a low rms the error is better than some of the experi-  mental f i t s to the theoretical curves in determining k ' a'.  Another point to be noticed is that k  o a  and  substantially  Q a  differs from k £ when a 4 a* indicating a large uncertainty &  in approximating the 'fictitious* k»  to k  Ocx  .  Further compu-  Oct  tations were carried out on the two lines in Table A5.1; f  r e l  as k  since  is proportional to k ( r e l ) , this latter ratio was computed Qa  Q  e  i  e  was varied, for a = .9 and 1.0 , and compared: with the  measured value of .0285/.0193 = 1.48.  The results of these  computations are shown in Table A 5 . 2 .  The value of  X.6383 was increased in steps of .01.  l&^JL^  for  The corresponding value  for X6505 was assigned by assuming k f r e l ) = k' (rel). Exact values of k _ i ^ for the Geissler tube are not oe e known although from measurements of k made by Irwin /12/ koe ^ i ' e could be of the order of .3 for some of the strongly , absorbing lines; as Well, in the present calculations the Q  determined value of k is uncertain to 5 units in the last oa figure.  Both these facts do not allow any quantitative conclu-  sions to be made from the above tables, but the variation of k ( r e l ) appears to be much less than that of "absolute" k Qa  as a function of k„ i . oe e  Q a  TABLE A5.1 a*  oa  (cm )  6506  .0285  i  k oe  -1  1.3  ABSORPTION LENGTH (CM).  e  .05  T  T  6383  .0193  1.3  SELF-ABSORBED DOPPLER LINE-SHAPE F I T  .05  i  s  T» T  s  10  15  20  25  35  .844 .845  .778 .780  .891 .886  .842  .719 .722 .797 .792  .666 .668 .755 .750.  .575 .575 .679 .673  TABLE A5.-3 k»  cc  1  oa  1  .0285  1.3  .01 T  v  a  oa  ,  45  -1  RMS ERROR  (cm  .501 .0230 .497 .614 .0157 .605  1.0  .003  1.0  .006  VOIGT.LINE-SHAPE F I T ABSORPTION LENGTH (CM)  a  (cm" ) 6506  .838  k  k  a  oa  10  15  20  25  35  .844  .778  .719  .666  .575  .501 . 0238  .854  • 783  .723  .681  .575  .497  45  (cm ) -1  RMS ERROR  1.0  .004  •121-  TABLE A5.2  CALCULATION OF k  ' ( r e l ) FOR SELF-  oa ABSORBED DOPPLER LINE-SHAPES k^cnT )  a'  .0193  1.3 1.3  1  x (i) 2  6383 6506  .0285  ( o^e k  .9 •9 .9  .9 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0  o2  y •1.48  k (cm )  Vcnf )  _1  1  0  .OI52  .0148  .0152 .0150  .0295  .0220 .0220  . .0443  .0218  .04  .0149  .0591  .01 .02 .03  .0161 .0160  . 0140  .0216 .0234 .0232 .0230 . 0230 .0228 .0226  .0295 .0443 .0591 .0738 .0886 .1034  .08  .0159 .0159 .0157 .0156 .0154 . 0154  .09  .0153  .1329  .05 .06 .07  ol  1  .01 .02 .03  .04  / k  6506'  .6383 a  k  .1181  .0224  .0222 .0220  ! V  k  o l  1.45 1.45 1.45 1.45 1.45 1.45 1.45 1.45 1.45 1.45 1.45 1.44 1.44  -122-  The and  compose T a b l e s  u s i n g the the T*  2.  computer program used t o e v a l u a t e A5.1  and  A5.2  i s g i v e n below.  FUNCTION TFALS s u b p r o g r a m , w h i l e  FUNCTION TTRUE s u b p r o g r a m a s k =  T  f o r minimum rms  g  Voigt  T_  T.»  D o p p l e r and  i s computed  line-broadening  processes  Voigt  profile  are  spectral line  shape i s  ( s e e f o r example, M i t c h e l l and  /19/)  Cu -  and  - -  v  (A5 5)  J&iSL  i s the n a t u r a l h a l f - w i d t h of the o t h e r parameters a r e as out  that  distribution, Gaussian or  and  as  spectral line,  defined previously.  this  distribution  most  individual  It should  i s p e r h a p s a more  and be  "real"  broadening processes  are  Lorentzian.  For source  until  a combination  AM = Jjo. r * /  pointed  from  error.  v  the  i s computed  i s v a r i e d f o r some a  Q &  n a t u r a l broadening, the  the  Zemansky  where  (A5.3)  Distribution  When t h e  g i v e n by  equation  the  case of n e g l i g i b l e  a line-shape  ponding transmission  g i v e n by  self-absorption in  equation  becomes, a g a i n  (A5«5)»  f o r uniform  the  and  the corres-  mono-  of  -123  isotoplc  e m i t t e r and  absorber  T^C-X^OL) )  VOI6Tc'tO G-)  a  and  i s d e f i n e d from e q u a t i o n  x i s d e f i n e d as Again,  can t h i s  This equation equation  (A5»3)  (A5.5) a s  k(-i>)/k  Q  before„  m i s s i o n f o r some v a l u e s  to  dco  J  where' VOIGT( OJ , )  ..-.(A5.-6)  be  equated to a pure Doppler  o f k'-and a*? o  has  for k  1.  been e v a l u a t e d  e.  trans-  can  i n a manner e q u i v a l e n t  u s i n g a n assumed v a l u e  o f a and  a,  OQ,  t o see whether a s o l u t i o n does e x i s t ; results solution a'5  of t h i s  computation.  A5.3  I t i s seen t h a t an  i s possible for a k and : oa  e x c e s s i v e computing time  t i o n of l i t t l e  Table  the  approximate  a much d i f f e r e n t  as w e l l as  value precluded  shows  t h a n k* and o  the g a i n i n g of  f u r t h e r computational  informa-  investiga-  tion,, The  program u s e d t o e v a l u a t e e q u a t i o n  g i v e n b e l o w and previous  is similar  section.  integration  TKAA c a l c u l a t e s T  i n form t o the program In  FUNCTION TPKA e v a l u a t e s T*,  r a t h e r t h a n by .  The  (A5.7) i s a l s o  the  infinite  VOIGT i n t e g r a l  FUNCTION VOIGT f r o m a p r o g r a m w r i t t e n by  series,  but  by  and  Is e v a l u a t e d Young  the  /4V.  numerical  FUNCTION in  IBFTC  c 1  c  7 77  10  6 8 12 Li )I0  15 b  5 11  FALST1 REAL K P 0 , L , K P 0 L , K 0 L E , K 0 , K O I , K 0 L , K 0 F , K 0 M I N D I M E N S I O N L<6) »TP(-6) » T ( 6 ) , E ( 6 ) DATA L / 1 0 . > 15 . , 20 ., 25 . , 3 5 . ,45 . R EAD ( 5,1) K P 0 , A L F A P K P C A L F A P = F I C T I T I O U S V A L U E S OF K AND ALPHA FORMAT(2F6.3) K0=KP0/5.5 READC 5 , 1 ) K O L E , A L F A K O L E =K*L FOR E M I T T I N G SOURCE, A L F A = OTRUE'? ALPHA K0F =10.*K0 K O I = KO DK = KO DO 7 1=1,6 KPOL = KPO*L( I ) TP(I)=TFALS(KPOL,ALFAP) WRITE(6 ,5)KOLE,ALFA FORMAT(1X//1X,7H(K0L)E=,F7.4,3X,5HALFA=,F5.2) J= 1 E2 = 0. DO 10 1=1,6 K0L=K0*L(I) T(I)=TTRUE(KOLE,KPL,ALFA) E < I ) =T( I ) - T P ( I ) E2=E2+E(I)*E(I) ERMS = S Q R T ( E 2 / 6 . ) W R I T E ( 6 ,8 ) ( T ( I ) , I = 1 ,6) , KO,ERMS FORMAT(1X///1X,22HMEASURED TRANSMISSIONS , 5X,6F9.3) WRI TE ( 6 ,6 ) ( TP ( I ) , 1 = 1 ,6 ) FORMAT( I X , 2 2 H S E L F - A B S T R A N S M I S S I O N S , 5 X , 6 F 9 . 3 / 1 X , 3 H K 0 = , F 9 . 4 , 5 X , 5 H E R 1MS= ,3X , F6 . 3 ) I F ( J . EQ. 1 ) GO TO 15 I F ( E R M S . G E . E M I N ) GO TO 11 EM I N= ERMS K0MIN=K0 GO TO 11 EM IN = ERMS KOMIN = K0 J=2 K0=K0+DK I F ( K O . L E . K O F j G O TO 9 I F ( KOMIN.EQ.KOF ) GO TO 20  •  16 jOl . 'TT Zl A  j | \  i  I  '  J  j"  I F ( K O M I N . E Q . K O I ) G 0 N U - K U rll  IN  TO  20  1  UN  K 0 I = K 0 K0.F = K O M I N + DK  j  DK = D K / 5 •  !  I F ( D K . L E . 1 . E - 4 ) S T 0 P G O 2 0 2  T O  77  W R I T E ( 6 J 2 1 ) 1  F O R M A T ( 1 X / 1 X , 2 2 H E N D - P T .  M I N I  M U M , B E W A R E )  S T O P E N D  .  6  3  FUNCTION T F A L S t X l . A L F A ) D O U B L E P R E C I S I O N T , T E R M > R A T I 0 > R , A 2 > A I »RI >DSQRT D I M E N S I O N R A T I O ('100) » R ( 1 0 0 ) IF(Xl.GT.10.)Ml=100 I F ( X 1 . L E . 1 0 . )M1 = 3 5 IF(X1.LE.6.5)M1=25 IF(X1.LE.4.5)M1=20 I F ( X 1 . L E . 3 . ) M l = 15 IF(X1.LE.1.)M1=10 I F ( X 1 . L E . . 2 ) M1 = 5 A 2 = ALFA-"-ALFA R(1)=1.D0+A2 RATIO(1)=1.D0/DSQRT(R(1)) DO 6 I = 2 > M 1 A I= I R ( I ) =R( I - l ) +A2 R A T I O ( I ) = D S Q R T ( R ( I -1 ) / R ( I ) ) / A I T=l.DO N =l T E R M = - R A T I O ( 1 ) X1 Rl=RATIO(1)*X1 I F ( A B S ( T E R M ) . L T . . 0 0 0 1 ) G O TO 1 7 T = T-f T E R M N=N+1 R 1 =R AT I 0 ( N ) -x-Xl TERM = - T E R M » R 1 GO TO 3  I  1 1  1  17  TFALS=T RETURN END  i  I  •  1 i  i i ! I  9 8  2' 3  12 J i |:o 9  8  |7 3 S |4  3  1  FUNCTION T TRUE(X ? Y ? ALFA) REAL NUM I F ( X . G T . 1 .5)MMAX=2 5 IF(X.LE.1.5)MMAX=10 I F ( Y . G T . 1 0 . >MAX=100 I F ( Y . L E . 1 0 . )MAX = 3 5 NMAX=50 DEN0M=SUM1(X,MMAX) S U M = SUM 2 < Y i A L F A ? 0 ? M A X ) T E R M = - S U M 2 ( Y , A L F A , 1 , MAX ) -*X /2 . DO 2 N = 2 » N M A X I F ( A B S ( T E R M ) . L T . 1 . E - 4 ) G 0 TO 3 AN=N+1 SUM=SUM+TERM TERM=-TERM*SUM2 ( Y , A L F A >N,MAX)*X/AN NUM=SUM TTRUE=NUM/DENOM RETURN END  FUNCTION SUMKX.MMAX) DIMENSION R(50) .RATIO(50) R ( 1) =2• RATIO! 1 )= ( 1 ./R(1) )**1.5 DO 1 I = 2 » M M A X Al =I R ( I ) =R( I - l ) + 1 . R A T I 0 ( I ) = ( R ( I - 1 ) / R ( I ) )-"--"-1. 5 / A I SUM1=1. TERM=-RATIO(1)*X DO 2 I = 2 » M M A X IF(AB S(TERM).LT.1.Z-4) R1TURN  !  1 !  2  1 5  2 3  SUM1=SUM1+TERM TERM=-TERM*RAT10(I)*X END  FUNCTION SUM2(X,ALFA>M*MAX) DOUBLE P R E C I S I O N TERM*RAT I 0 > R » A 2 » D S Q R T » A I>AM,DABS D I M E N S I O N R( 1 0 0 ) » R A T 1 0 ( 1 0 0 ) A 2 =AL F A * A L FA AM=M R(1)=AM+1.D0+A2 RAT 10( 1 )=1.D0/DSQRT(R( 1 ) ) DO 1 I = 2 » M A X AI=I R(I)=R(I-l)+A2 R A T I O ( I ) = D S G R T ( R ( I - 1 )7 R ( I ) ) / A I SUM2=1.D0 T ER: i = - R A T I 0 ( 1 ) * X DO 2 1 = 2 * M A X IF(DABS(TERM).LT.1.D-4)GO TO 3 SUM2=SUM2+TERM TERM=-TERM*RATIO(I)*X RETURN END  SIdFTC  C 1 C  I  FALST6 REAL KPO,L,KPOL,KOLE,KO,KOI,KOL,KOF,KOMIN DIMFNSION L ( 6 ) , T P ( 6 ) , T ( 6 ) , F ( 6 )  i  DATA  I  L/10.  1  , 15. , 2 0 . , 2 5 . ,35. , 4 5 .  R E A D ( 5 » 1 ) !<P0 , A L F A P KPO,ALFAP = FICTITIOUS FORMAT(2F6.3) READ(5,1)ALFA,A ALFA = @TRUE@ A L P H A , A  VALUES  OF  K  AND  i l  ALPHA  ! =  (NATURAL  TO  DOPPLER  L I NE-WIDTH  R A T 1 0 ) ---SORT ( A L O G ( 2 ) )  K0=KP0/5.5 K0F=10.*K0  i •i  K0I=K0 DK = K 0 DO 7 1=1,6 7 77 3 9  WRITE(6 » 3 ) A , A L F A FORMAT(1X//1X,17HLINE J=l E2 = 0 . DO 1 0 1=1,6 K0L=K0*L(  10  6 8  12 1 5  110  i WIDTH  RAT I 0 = , F 6 . 3 , 3 X , 5 H A L F A = , F 5 . 2 )  i i  I )  I  T(I)=TKAA(K0L,ALFA,A) E ( I )= T ( I ) - T P ( I ) E2=E2+E(I)*E(I) ERMS=SQRT(E2/6.) WR I TE (6 , 6 ) (TP ( I ) , I =1 , 6) FORMAT( 1X///1X,22HMEASURED T R A N S M I S S I ON S , 5 X , 6 C ° . 3 ) W R I T E ( 6 , 8 ) ( T ( I ) ,1 = 1 , 6 ) ,KO » ERMS F O R M A T ( I X , 2 2 H DOPPLER T R A N S M I S S I O N S , 5 X , 6 F 9 . 3 / l X , 3 H K 0 = , F 9 . 4 , 5 X , 5 H E R 1MS=,3X , F 6 . 3 ) IF(U.EQ.1)GO  Ji  1 i  KP0L=KP0*L(I) TP(I)=TPKA(KPOL,ALFAP)  TO  IF(ERMS.GE.EMIN) EM I N = E R M S K0MIN=K0 GO TO 11 EMIN=ERMS  15 GO  TO  11  KOMIN=K0 1 1  J =2 K0=K0+DK I F ( K 0 . L E . K 0 F ) G O  TO  IF(KOMIN.EQ.KOF)GO  9 TO  20  I?  IF(KOMIN.EQ.K0I)GO  TO  20  £  KO=KOMIN-DK KO I = K 0  17  9 L % 8 6 0l# 11  K0F=K0MIN+DK DK=DK/5. I F ( D K . L E . 1 . E - 4 ) S T 0 P GO TO 77 20 2 1  WRITE(6,21) FORMAT ( 1 X / 1 X » 2 2 H E N D - P T . STOP • ' END  FUNCTION N=10  M I N I MUM » 3EWARF. )  TPKA(X,Y)  A l =2 . AN = N H = A1/AN SUME=0. SUMO=0.  T 12 11 |io  9 8 |7 6  74 75 4  L = l K =0 DO 2 I = 1 » N A I =I -1 W= A I* H WA=W*Y W2=W*W WA2=WA*WA E=EXP(-WA2 E2=EXP(-W2) F = E 2 * E X P ( - X * E) I F ( I . E Q . 1 ) G O TO I F ( L . E Q . 2 ) G O TO I F ( K . E Q . O ) G O TO SUMO=SUMO+F GO TO 7 5 SUME=SUME+F I F ( I . E Q . N ) G O TO GO TO 2 F I =F  0  s  4 5 74  • •  •  6  5 2  GO TO W = A1 1 =2  2  GO  3  TO  !  1 '  I  •  i  F F =F . K=l-< SUM1=(1.33 333*SUMO+.666 67*SUME+.3  1 -  3333*(FI+FF) ) *H  H = 1 . / (. A 1 * A N ) SUME=0. SUMO=0. L=l K =l • N1=N-1 DO 1 0 I = 1 » N1 A I = I W=A I*H W=l./W 13-  '  76 77 1 2  I  1 1 10  12 11 9  8  i I  W2=W*W WA=W*Y  1  WA2=WA*WA E=EXP(-WA2) E2 = E X P ( - W 2 )  1  F=E2*EXP(-X*E)*W2 IF( 1 . F Q . 2 ) G O TO 11 I F ( K . - E Q . O ) GO TO'76 SUMO=SUMO+F GO TO 77 SUME=SUME+F I F ( I . E Q . N l ) GO T O 12 GO TO 10 W = AI 1 =2 GO TO . FF=F  '  . •'  1 i j 1 i •  ••  13  K=l-K SUM2=( 1 . 33 33 3 * S U M O + . 6 66 6 7 * S U M E + . 333 3 3 * F F ) * H SUM=SUM1+SUM2 ' • • TPKA=2.*SUM/1.77245 RETURN END  |7  • •  •  i I FUNCTION  7  i  T KAA(X » Y > Z )  N = 10  I  Al =2 .  j  AA=Y*Z AN = N H=Al/AN  I i i  SUME=0. SUMO=0. L = l K =0 DO  3  2  I = 1 » N  i  A I = I - l • W=AI*H WA=W*Y  i  W2=W*W WA2=WA*WA V =V O I G T ( W A » AA) VV =V O I G T ( W » Z ) F=VV*EXP(-X*V) I F ( I . E Q . 1 ) G O TO I F ( L . E Q . 2 ) G O TO I F ( K . E Q . 0 ) G O TO SUMO=SUMO+F 74  I F ( I . E Q . N ) G O GO TO 2  4  FI=F GO TO  6  W = A1 L =2 GO TO FF = F  2  -  GO TO 75 SUME=SUME+F  75  5  i 4 5 74  TO  6  2  3  K=l-K S U M 1 = ( 1 . 3 3 3 3 3 - - S U M O + . 6 6 6 6 7 - - - S U M E + . 3 3 3 3 3 - " - ( F I'+FF ) ) * H H =l o / ( A 1 * A N ) SUME=0. SUMO = 0 . L=l K=l  •  N1=N-1 DO 10  13  11  10  v  '2 _±L |10 9 8 |7 6  5  W= 1 . / W  \ ,  ;  \  33333*FF ) *H  FUNCTION VQIGT(XIN,YIN) DIMENSION A ( 4 2 ) » H H ( 1 0 ) » XX ( 1 0 ) D I M E N S I O N R A ( 3 2 ) » C A ( 3 2 ) » . R 5 ( 3 2 ) , C a ( 3 2 ) , 8 ( 4 4 ) , A K ( 5 ) . , AM ( 5 ) , DY ( 4 ) D A T A H H ( 1 ) , H H ( 2 ) , X X ( 1) , X X ( 2 ) , A / 0 . 8 0 4 9 1 4 0 9 E - 0 0 , 0 . 8 1 3 1 2 3 3 5 E - 0 1 , 0 . 5 7 4 164762 , 1 .65068012 , 0 . , 0 . 19999999E 0 » 0 . , - 0 . 1 8 4 E 0 , 0 . , 0 . 1 5 58 3999 , 0 . , - 0 70 8 1 5 9 E - 1 , 0 . , - 0 . 5 8 5 1 4 1 2 4 E - 1 , 0 . , 0 . 3 6 2 1 5 7 3 E - l , 0 . , - 0 . , 0 . 1 1 1 9 6 0 H E - 1 , 0 . , - 0 . 5 6 2 3 1 8 9 6 E - 2 , 0 . , 0 . 2 6 4 8 7 6 3 4 E - 2 > 0 . 0 . , 0 . 4 8 9 9 5 1 9 9 E - 3 , 0 . , - 0 . 1 9 3 3 6 3 0 S F - 3 , 0 . , 0 . 7 2 2 8 7 7 4 5 E - 4 - 4 , 0 . , 0 . 8 6 6 2 0 7 3 6 E - 5 , 0 . , - 0 . 2 7 8 7 6 3 7 9 E - 5 , 0 . , 0 . 8 5 6 6 8 7 3  6 6 E - 6 , 0 . , - 0 . 2 5 1 8 4 3 3 7 E - 6 , 0 . , 0 . 7 0 9 3 6 0 22 F - 7  9 L 8  !6  :  SUM2 = ( 1 . 3 3 3 3 3 » S U M O + . 6 6 6 6 7 * S U M E + . SUM=SUM1+SUM2 TKAA=SUM/.8862 RETURN END  2 . 1 2 1 6 6 4 , 0 . , 0 . 8 7 3 2 0 8 4 9 7 6 5 E - 1 , 0 . 4 , - 0 . 1 1 7 3 2 6 7 E - 2 , 5 , 0 . , - 0 . 2 5 6 5 5 5 1 2 E  _J  '  K=l-K  •  |  |  F=VV*EXP(-X*V)*W2 IF. ( L . E Q . 2 1GQ TO 1 1 IF(K.EQ.O)GO TO 76 SUMO=SUMO+F GO TO 7 7 SUME=SUME+F IF(I.EQ.N1)GO TO 12 GO TO 1 0 W=AI L =2 GO TO 1 3 F F= F  12  . T  W=AI*H W2 = W * W WA=W*Y WA2=WA*WA V =VOIGT (WA,AA) VV=VOIGT(W,Z)  76 77  iy  1=1,Nl  ;  [»l JZI-  401  »  X =X I N  £  Y =Y I N  »  t'i  -  200  X2=X*X Y2=Y*Y I F ( X - 7 . ) I F ( Y - 1 . )  203  RA ( 1 )=0 .  s  -  9 200,201,201 202,202,203  L  8 6 01 11  CA(1)=0. RB( 1 ) = 1 . CB(1)=0.  -  »  Zl  RA(2)=X CA(2)=Y R B ( 2 ) = . 5 - X2 + Y2  t  1  C B ( 2 ) = - 2 . *X#Y CB1=CB(2) CA1=0. UV1=0. DO 2 5 0 J=2,31 JMINUS=J-l JPLUS=J+l FLOATJ=JMINUS R B 1 = 2 . - : ; - F L O A T J + R B ( 2.)  250 251  R A l =- F L O A T J * ( 2 . - » - F L O A T J - l o ) / 2 . R A ( J P L U S ) = R B 1 * R A ( J ) - C B 1 * C A ( J ) + RA1 * R A ( J M I N U S ) - C A 1 * C A ( J M I N U S ) CA(JPLUS)=RB1*CA(J)+C31*RA(J)+RA1*CA(JMINUS)+CA1*RA( JMINUS) RB ( J P L U S ) = R B 1 * R B ( J ) - C 3 1 * C S ( J ) + R A 1 * R S ( J M I NUS ) - C A 1 * C 3 ( J M I NUS ) C B ( J P L U S ) = R 3 1 * C ° ( J ) + C 3 1 * R 3 ( J ) + R A 1 * C ? ( JMI NUS)+CA1*RB ( JMINUS) UV=(CA(JPLUS)*R3(JPLUS)-RA(JPLUS)*CB (J P L U S ) ) / ( P B ( J P L U S ) * R 3 ( J P L U S ) + 1CB(JPLUS)*CB(JPLUS)) IF( A . B S ( U V - U V l ) - l . E - 7 ) 251, 250 * 250 UV1=UV VOIGT=UV/l.772454  202  RETURN I F ( X - 2 . )  301  ARNT=1.  301,301*302  12  MAX=12.+5.*X2 KMAX=MAX-1  (10  DO  6  303  K=0,KMAX  AJ=MAX-K  9 8 7  303  ARNT=ARNT#(-2.*X2)/(2.*AJ+1.)+1. U=-2 .*X-"-ARNT GO TO 3 0 4  "  s  4 3  i I j  I jS ji  Ii  |« .  ;  J  302 305  I B B J  F ( X - 4 . 5 ) (43)=0. (44)=0. =42  DO 307  306  307  305,306,306  1  K=l,42  1  1  3 ( J ) = o 4 * X * E ( J +1 ) - 8 ( J + 2 ) + M J ) J=J-1 U=B(3)-B(1) GO TO 3 0 4 A RNT = 1 .  !  MAX=2.+40./X AMAX =MAX DO 3 0 8 K = l , M A X 308 304  . | . : I  A R N T = A R N T * ( 2 . * A M A X - i . ) / ( 2 . * X 2 ) +1 . A MA X = A MA X - 1. U=-ARNT/X  i 1  ;  V=1.772454*EXP(-X2) H =. 02  \ ; 1  JM=Y/H 311 310  IF(JM) H =Y  3 1 0 , 3 1 1 , 3 1 0  •  3 18  DY(1)=0. DY ( 2 ) - - - ; / 2 . DY(3)=DY(2)  •  • '  313  "I ! i !  '  i  ,4  UU=U+.5*AK( J) VV =V + • 5 * A M ( J ) ' AK ( J + l ) = 2 . - ( YY-x-UU+X-VV ) * H  3 14  !  •  DY(4)=H AK(1)=0. AM( 1 )=0 . DO 3 1 3 J = i YY=Z+DY(J)  i !  .  '  z=o. L=O  3 12  .1  A M ( J + l ) = - 2 . * ( l . + X * U U - Y Y * V V ) * H I F ( J - 3 ) 3 1 3 , 3 1 4 , 3 1 3 A K ( 4 ) =2 . - » - A K ( 4 ) AM(4)=2.*AM(4) CONTINUE Z=Z + H L=L+ 1 U = U + . 1 6 6 6 6 6 7-"- ( A K ( 2 ) + 2 . * A K ( 3 ) + A K ( 4 ) + A K ( 5 ) )  1  : 1  •  ,  V=V+.1666667*(AM(2)+AM(3 )+AM(3)+AM(4)+AM(5)) IF(JM) 3 15 317  315,320*315  320  I F(L-JM) 313,317*220 AJM=JM H=Y-AJM*H GO TO 312 VOIGT=V/1.772454  201  RETURN F1=0.  330  DO 3 3 0 J = l , 2 F l = F l +Hri(J)/(Y2+(X-XX 1 ) VOIGT=Y*Fl/3.1415927 RETURN END  ( J ) ) -» ( X - X X ( J ) ) ) + H H ( J ) / ( Y 2 + ( X + X X ( J )  ) *(X +XX(J ) )  -124-  APPENDIX 6.  END CORRECTION ATTEMPTS  An i n v e s t i g a t i o n i s u n d e r t a k e n  here i n t o t h e e f f e c t s  t h e ends o f t h e a b s o r b i n g column have on t h e t r a n s m i s s i o n (see s e c t i o n 5 o 4 . 2 . 7 ) . The geometry o f t h e ends o f t h e d i s c h a r g e a r e drawn i n P i g . A6.1.  The c y l i n d r i c a l d i s c h a r g e has a n o u t e r r a d i u s  R and bends c i r c u l a r l y a t t h e ends t h r o u g h 90° w i t h a n i n n e r and o u t e r r a d i u s o f c u r v a t u r e D and D + 2R r e s p e c t i v e l y . assumed k  It is  and n a r e c o n s t a n t i n t h e ends o f t h e d i s c h a r g e .  A  o  •  Consider a s i n g l e r a y of l i g h t which leaves t h e s t r a i g h t p o r t i o n o f t h e d i s c h a r g e a t p o s i t i o n r,© a n n u l u s o f r a d i u s r ( r = 1.07 cm).  i n the cross-section of the I t emerges f r o m t h e c u r v e d  p o r t i o n of the discharge a t point B a f t e r t r a v e r s i n g a distance <^t( & ) on p l a n e A. <?C may be computed from t h e geometry on t h e end as, a f u n c t i o n o f 9 Jt  Q  . The t o t a l d i s t a n c e t r a v e l l e d i s JL  Q  + 2oC  being the length of the s t r a i g h t p o r t i o n of the discharge*  L e t £,(.9)  be d i v i d e d i n t o two segments, z and A z ( 6 5 ) , where  z i s independent o f 9 .  T h e r e f o r e f o r each p a r a l l e l r a y o f  l i g h t t h e i n t e n s i t y out o f t h e d i s c h a r g e i s where L = Jt^ + 2z, and t h e t r a n s m i s s i o n i s t h e n o 7  T =  ..(A6.1)  -126-  If the bottom of the annulus the  electrodes) i s symmetrically  (see  F i g . A6.2)  holds,  equation -?  T  and  ( i , e.  blocked  the  s i d e toward  o f f at an a n g l e  the u s u a l assumption of Doppler  &. M  line-shapes  (A6.1) becomes,  \  '  '  = ...(A6.2)  where  Z\r^  =  —  J £A^y"cl ©  and cm  H )  n  t f  Q  L )  O  Fig.  A6.2  Annulus w i t h  P o r t i o n Blocked  Off  -127'  That P tends to zero rapidly as m increases can be seen m  for k « l , where the presence of the term k^ ensures the rapid Q  decrease; k  Q  on the other hand the same tendency is present as  increases because although the k^ factor is then not so  small, the Integral (or sum) P i s . m  At any rate it seems  advantageous to try to choose conditions so that the f i r s t correction term (T^ is small or zero by making  £"~z as small  as possible. The f i r s t case which was tried was to choose L equal to the distance between the centres of the electrodes, i . e. z = D + R and calculate ^ on the computer such that £ ^ - 0 . The results of this calculation are shown in Table A6.1 using some experimentally determined values of k  Q  and a for the case  in which the end-effects should be the greatest, which corresponds to L = 10 cm.  It was found that A J < 0 for O == B ^TT  which  means the effective absorption length for the f i r s t order correction is less than the distance between the electrodes for any O , although | A/^| value -.08 cm.  is a minimum at & =TTwhere A £ has the  Also included in this table are the succeeding  terms (T ) of equation (A6.2) up to m = 4. It can be seen that m  even for the highest value of k , the correction necessary is Q  not greater than .003. For absorption lengths greater than 10 cm the correction terms rapidly decrease. that k  Q  Table 6 shows  attains this highest value only for X.6402,  Because the  value of k is uncertain due to its "fictitious "quality Q  (see  section 5.^.1), as well as the unjustified but simplifying assumption of constant conditions in the ends, it is apparent  128-  \  TABLE A6.1 END-CORRECT I ON ATTEMPT #1: 0-1T , L • 10 cm . ^ = .©an on"  cm l 2 3 k  193  e  .019  -.003  .001 .002 .0001 «10" «10~  5  «10~  7  .04, -.006 .004 ,009 . —4 .0006 wlO"1 «»10  -.005  .03  .001 .0005 6 «10"' « - 1 0 "  .82  -1  "Ton  "Tim  -.16 2.26 «•»16  CAW  wIO"  7  6  4  6  TABLE A6.2 END-CORRECTION ATTEMPT #2.  = 1.99 cm,  R + D = 2.03 cm, L =* 10 cm Tm k =.082 m  m 1  (-2) ^7m! m  k =i.0217 Q  0  2  2.26  3 k  -.35 .63  Q  0  0 .001 «-10' «10~  7  6  «10"  6  Q  0  - .002 «-10"  k =.193  5  .00Q  -4  «-10 * «10~ 4  -129-  that these corrections cannot be quantitatively applied.  It  is likely however, that those spectral lines Table 6 indicates as having a small value of k  Q  do not need end-effect corrections;  this cannot be said of lines like \6402 quite so definitely. The second correction attempt sought an effective absorption length for a fixed value of 0 was chosen as TT .  , which in this case  Again T^ was to be as small as possible so  a value of z was looked for such that A z = 0. equality to occur, z has the value 1.99 cm.  For this  D + R for the absorp-  tion tube (see Fig. A6.1) is 2.03 cm so the effective absorption length is essentially equal to the distance between the electrodes.  This of course follows from the f i r s t correction  attempt i f S^TT d the general comments given concerning that a n  attempt are generally applicable here also. of the correction series  The f i r s t four terms  are given in Table A6.2.  The three computer programs used to compute F and m  A^™  are given below;  the f i r s t two were used in the f i r s t  end-correction attempt, and the f i r s t and the third in the second attempt.  The only remarks necessary concerning these  programs is that the presence of two isotopes was taken into account, and that numerical integrations were done using Simpson*s Rule.  1  SIBFTC NDC0R1 1 FORMAT(314) 2 FORMAT(2F10.3) 76 F O R M A T ( I X > F6.4> 2X » F 6 . 2 * 2X >F4.0 » 2X F 6 o 4 9 2 X , 3 14) D0U3LE PRECISION T ? T E R DIMENSION RATI0(100)»R(100)sEK(5C ) s A ( 5 0 ) R E A D ( 5 J 1 ) N » M1 J M 2 C N=NO. OF C A R D S M 1 = M A X . N 0 . OF T E R M S , M 2 = 0 R D E R OF CORRECTION R E A D ( 5 9 2 ) ( E K ( I ) , A ( I ) 9 I = 1 ,N) C EK( I ) = K ( 0 ) 9 A( I ) =ALPHA 25 DO 70 I = 1 9 N EL=10. Jl =l A2=A(I)**2 AM2=M2 RR=1.+AM2*A2 RA=1./SORT(RR) R(1)=RR+A2 RAT 10( 1 ) = 5 Q R T ( R R / R ( 1 ) ) . DO 6 K=2,Ml AK = K R(K)=R(K-l)+A2 6 RAT 10 ( K ) = SGRT ( R ( !<- 1 ) /R ( X ) ) / A X C MAJOR S E R I E S 624 EKM2 = EK ( I ) *-"-M2 T = E K M 2 -»-R A E K L = EK ( I ) -"-EL EKL1=-EKL*RATI0(1) TERM=T-x-Ei<Ll M= 2 28 I F ( ABS ( TERM ) . LT . .0.001') GO TO 17 T=T+TERM I F ( M . G E . M l ) GO TO 17 E<L2=EKL*RATI0(M) TERM =-TERM-*Ei<L2 M = M+1 GO TO 28 17 M3=M C MINOR S E R I E S  |  ?  M  5  EK 2  = ( . 1 0 4 - - - E X ( I ) )>#y.2  T 1=EKM2 R A EKL= . 104-x-EK ( I  1  EKL1=-EKL*RATI0(1) TERM=T1*EKL1 M=2 128  :  i  53  IF(ABS(TERM).LT..0001) GO T O 1 1 7 T1=T1+TERM I F ( M . 6 E . M 1 ) GO T O 1 1 7 E K L 2 =E K L - " - R A T l O ( M ) T E RM= - TE RM E KL 2 M = M+1 GO TO 1 2 8 T=(T + T l ) / l . 0 9 4 W R I T E ( 6 , 7 5 ) El< ( I ) , A ( I ) , Z L , T , M 3 GO T O ( 5 0 , 5 0 , 5 0 , 5 3 , 5 3 , 7 0 ) , J 1 EL =EL + 5 • J1=J1+1 GO TO 6 2 4 EL=EL+10.  70  J1=J1+1 GO TO ' 6 2 4 C O N T I N'JE  117  50  60 61 62 63  GO TO M2 = 2 GO TO M2=3 GO TO M2 = 4 GO TO STOP END  i  ' 1 i 1 !  1  I  !  i i i  (60 , 61 , 6 2 , 6 3 ) ,M2  !  25  ! 25  i i  25  i  i !  i $ I BFTC C C 1  c  NDCOR2 TO C O M P U T E READ(5 , 1)N N = 0RDER OF FORMAT(12) THETA=3.14159 M =50 M=DIVISION R=1.27  MOMENTS  CF  DELTA  L  FOR  END  CORRECTIONS  OF  ABS TUBE  I  1  MOMENT  !  i OF  INTEGRA TION  I MTERVAL  ; !  £  1  s  ' 9  D= .  76  RR =  1 . 0 7  i * L  : 8  RD = R + D  ', 6  R2 = R * R RR2 = R R * R R  ! U  Oil  AM = M D O  1 zi J =l ,  8  5 0  H = T H E T A / A M  SU|ViE = 0 . SUMO=0. K =  0  DO  I=1,M  2  A I = I-1 X=AI*H 6  RM=RD+S3RT(R2-RR2*(SIN(X)**2) ) E L =SQRT ( R M * R M - ( RD+RR*COS( X) ) * * 2 ) DEL=EL-RD F=DEL**N I F ( I . E Q . 1 )  GO  TO  3  I F ( L . E Q . 2 )  GO  TO  4  I F ( K . E Q . l )  SUMO=SUMO+F  IF(K.'EQ.O)  SUME =SUME+F  I F ( I . E Q . M )  GO  GO 3  5  TO  5  2  F I = F G O  I  TO  2  T O  X = T H E-T A  L=_2 ?  G O  T O  Vr  4  F F = F  12  2  K=l-K  6  Ji  S U M = 1 . 3 3 3 3 * S U M O + .  II 0  S U M =  9  A N G L E  3  W R I T E < 6 > . 7 )  2  = T H E T A *  17  7  F O R M A T  6  8  T H E T A  5  »4  S T O P  cND  6 6 6 6 7 * S U M E + .  . * S U M * H / T H E T A 1 8 0  . 7 3 . 1 4 1  S U M> ANG  5 9  L E  ( I X , E 1 4 . 7 » 4 X , F 6 . 2 )  = T ; - I ' E T A - 3 .  1 4 1 5 9 / 5 0 .  3 3 3 3 3 *  ( F I + F F )  61  M  M  ID  0  _  0"w _  n  —I  0> A  0)  c: c:II  I—'  II  II  II  1 "Tl —1  ro i—• A •  C)  "11 O  "Tl O  r~  II  IV>  o  0* 10  C >.»)  1—1 t — i 1—1 i—i "Tl Tl Tl Tl Tl  CD T| O —  n  o t-j  ui  rv)  O  • M £3 0  ,  1.0  o + U l CJN 3 ON  rn m r~  o i~ ll  o  o  o  1—'  o  e  rv)  I—  6 -i II  Co Co  c. - c  *  1  2  I  N  ~  D  II  o  CD O  ru  A  A)  A3  II  (NJ  A3  II  rv>  O  ro I  1  —  o  4>  A3  II  *  A3  A3  XI  A)  a II  n  A3  O  A3  A3  II  II  II  -J  Ul  II  o  A3  (-". -J»  +  •  o  o  ON  ro  - J  2  o  A3  m >  o — Ul  2  o n o A3  A3  —1  A3  XI  i  O  AJ IV)  -p-  10  C/l  + +  -.1  O O  x  A ;  ;n o  <IN  A)  n  - i rn o n Ul  II  A A r~ - H m M co n > • O • e r o x i >— rn rn r n rn M r n A 3 + I o O a o * r~ —i co  cn Co Co Q o cz C O  :t co  T I  T)  2  m + 0  o  rv>  10  '. 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