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Polarization of electron impact light from helium Whitteker, James Howard 1967

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The University of B r i t i s h Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of JAMES WHITTEKER B-.Sc. Carle ton University, 1962 FRIDAY, OCTOBER 6, 1967, AT 3:30 P.M. ROOM 301, HENNINGS BUILDING  COMMITTEE IN CHARGE Chairman:  B. N. Moyls  F.W. Dalby B. Ahlborn C E . Brion  M. McMillan H. Gush C.A. McDowell  External Examiner: Prof„ Robert Krotkov University of Massachusetts Amherst Massachusetts  Research Supervisor: F.W. Dalby  POLARIZATION OF ELECTRON IMPACT LIGHT FROM HELIUM  ABSTRACT  The  p o l a r i z a t i o n of l i g h t from helium atoms  excited by the impact of low energy electrons has been 3 3 ° measured for the spectral lines 2 P - 2 S (10,829 A) and  3 3 ° 3 P - 2 S (3889 A). An electron beam carrying a  current of 1 0 y U A was directed  into helium gas at a  -3 pressure of 4 x 10  torr or l e s s .  measured as a function  P o l a r i z a t i o n was  of electron energy i n a range  from the e x c i t a t i o n threshold (approximately 23 electron 3 3 volts) to 50 e.v.  For the 2 P - 2 S l i n e , this work  represents the f i r s t reported measurement of this type. There i s special interest i n the value of p o l a r i z a t i o n near the e x c i t a t i o n threshold.  The theo-  r e t i c a l threshold p o l a r i z a t i o n for both lines studied in this thesis i s 36.6%.  In the experiment of this 3 thesis, the observed p o l a r i z a t i o n of the 2 P l i n e r i s e s to 21% near threshold, and by means of a curve f i t t i n g procedure may be extrapolated to 32 * 67„. 3  The p o l a r i -  3  zation of the 3 P - 2 S l i n e r i s e s to 117» and may be extrapolated to 15 1 3%.  GRADUATE STUDIES  F i e l d of Study:  Atomic Physics  Elementary Quantum Mechanics Waves Electromagnetic Theory Nuclear Physics Plasma" Physics Spectroscopy  Wo  Opechowski J.C. Savage  GiM. Volkoff J.B. Warren L„ de Sobrino A.M. Crooker  Special R e l a t i v i t y Theory  H. Schmidt  Molecular Spectroscopy  F.W. Dalby  Advanced Spectroscopy Advanced Quantum Mechanics  A.J. Barnard H. Schmidt  \ .  AWARDS 1958-61  International Nickel Co. Scholarship  1962-65  National Research Council Scholarship  1966  UBC Graduate Fellowship  1967  National Research Council Postdoctorate Fellowship  POLARIZATION OF ELECTRON IMPACT LIGHT FROM HELIUM  by JAMES HOWARD WHITTEKER B.Sc,  Carleton  University,  1962  t  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in  the Department of PHYSICS  We  accept  required  this  thesis  as c o n f o r m i n g t o t h e  standard  THE UNIVERSITY OF B R I T I S H COLUMBIA October,  1967  In p r e s e n t i n g  for  thesis  an a d v a n c e d d e g r e e a t  that  the  Study.  Library  shall  I further  thesis  for  Department  or  this  scholarly  or  publication  without  of  of  P  make  Q f . f r  it  that  freely  £  ?  of  British  available  permission  for  of  for  this  thesis  for  permission.  s, cs  / Of { 7  Columbia  It  financial  is  the  requirements  Columbia,  I  reference  and  extensive  p u r p o s e s may be g r a n t e d b y t h e  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada Date  fulfilment  the U n i v e r s i t y  b y h.i>s r e p r e s e n t a t i v e s .  my w r i t t e n  Department  agree  in p a r t i a l  copying of  this  Head o f my  understood  gain  agree  shall  that  not  be  copying  allowed  ABSTRACT  The p o l a r i z a t i o n of l i g h t from helium atoms e x c i t e d by the impact of low energy electrons has been measured f o r the spectral lines 2 P - 2 S 3  (10,829  3  A) and 3 P - 2 S 3  3  (3889  e l e c t r o n beam c a r r y i n g a current of lOyuA was d i r e c t e d helium gas at a pressure of 4 x 10  t o r r or l e s s .  A). An  into Polarization  was measured as a f u n c t i o n of e l e c t r o n energy i n a range from the e x c i t a t i o n threshold (approximately 23 e l e c t r o n v o l t s ) to 3  3  50 e.v. For the 2~T - 2 S l i n e , t h i s work represents the f i r s t reported measurement of t h i s type. There i s s p e c i a l i n t e r e s t i n the value of p o l a r i z a t i o n near the e x c i t a t i o n threshold.  The t h e o r e t i c a l threshold  p o l a r i z a t i o n f o r both l i n e s studied i n t h i s t h e s i s i s  36.6$.  In the experiment of t h i s t h e s i s , the observed p o l a r i z a t i o n of the 2 P l i n e r i s e s to 21$ near threshold, and by means of J  a curve f i t t i n g procedure may be extrapolated to 32 3  1  6 $ . The  '9  p o l a r i z a t i o n of the 3 P - 2^S l i n e r i s e s to 11$ and may be extrapolated to 15 i 3^,  TABLE OF  CONTENTS  CHAPTER I.  PAGE INTRODUCTION  . . . . . . . . . .  References II.  and F o o t n o t e s f o r C h a p t e r I  . . .  THEORY  9 11  2.1  Introduction.  . . . . . . .  11  2.2  The C o l l i s i o n  Process  14  2.3  The R a d i a t i o n  Process  17  2.4  Threshold  2.5  2 P Polarization Calculations  24  2.6  Depolarization  25  2.7  P o l a r i z a t i o n as a F u n c t i o n  2.8  I n t e n s i t y as a F u n c t i o n  2.9  The E f f e c t on  Polarization  21  due t o a M a g n e t i c F i e l d . o f Angle  of Angle.  o f E l e c t r o n Beam  . .  . . .  and F o o t n o t e s f o r C h a p t e r  EXPERIMENTAL DETAILS  26 27  Dispersion  Polarization  References III.  1  28 II.  . . . . .  . .  29  .  30  3.1  Vacuum S y s t e m  30  3.2  Helium Source  3.3  E l e c t r o n Gun - D e s i g n and O p e r a t i o n  3.4  E l e c t r o n Gun - C o n s t r u c t i o n  39  3.5  E l e c t r o n Gun Mount  43  3.6  Collision  45  3.7  Optics  47  3.8  Photomultipliers  50  3.9  Photomultiplier  Chamber  Cooling  .  34  . .  36  53  iv CHAPTER III.  PAGE 3 - 1 0 S i g n a l Processing  5 3  3 . 1 1 P o l a r o i d Turner  6 0  References and Footnotes f o r Chapter I I I . . . IV.  6 3 64  EXPERIMENTAL RESULTS 4.1  Data  64  4.2  Energy Scale  7 6  4.3  Experimental Sources of Error  7 8 85  References and Footnotes f o r Chapter IV. . . . V.  DISCUSSION OF RESULTS AND CONCLUSIONS. . . . .  8 6  5.1  P o l a r i z a t i o n Structure  8 6  5.2  Threshold P o l a r i z a t i o n  8 6  5.3  E x c i t a t i o n Curves  8 8  5.4  Conclusions  8 9  5.5  Suggestion f o r Further Work  9 0  References and Footnotes f o r Chapter V . . . . APPENDIX I I I A.  Properties of an E l e c t r o n Beam. . . .  APPENDIX I I I B.  The P o t e n t i a l i n a Region  9 1 9 2  E l e c t r o s t a t i c a l l y Shielded by Grids APPENDIX I I I C. APPENDIX IV A.  S i g n a l Processing Theory  1 0 0  P o l a r i z a t i o n of Light due to  O p t i c a l Elements APPENDIX V A.  9 5  P o l a r i z a t i o n Model  1 0 3 •  1 0 5  LIST OF TABLES TABLE I. II.  PAGE T h e o r e t i c a l Threshold P o l a r i z a t i o n s . . . . „ . Comparison of C o l l i s i o n and Spin-Orbit I n t e r a c t i o n Times .  III.  22  23  Threshold P o l a r i z a t i o n s and Other Parameters Found by Curve F i t t i n g  8 8  LIST OF FIGURES FIGURE  PAGE  1.  Expected and Observed P o l a r i z a t i o n Curves. . . .  4  2.  Energy Level Diagram f o r Helium  7  3.  E x c i t a t i o n and Emission.  12  4.  Vacuum System. .  31  5.  Arrangement of Apparatus . . . . .  33  6.  Ion Gauge C a l i b r a t i o n f o r Helium  35  7.  E l e c t r o n Gun  8.  E l e c t r o n Gun Mount, Cutaway View  9.  "Vapour Degreasing" Method of Cleaning Vacuum  . . . . . . . .  44  46  Parts •10.  37  Evidence of P o t e n t i a l Minimum  45  11.  Focusing Properties of O p t i c a l System  49  12.  O p t i c a l Transmission of Interference  Filter. . .  51  13.  O p t i c a l Transmission of Interference  Filter. . .  52  14.  P h o t o m u l t i p l i e r Cooling  54  15.  Electronics:  Block Diagram  55  16.  E l e c t r o n Gun Cathode Supply  57  17.  Microammeter f o r E l e c t r o n Beam  58  18.  Device Used to Rotate P o l a r o i d  6l  19.  E l e c t r o s t a t i c Shield  95  20.  E l e c t r o s t a t i c Shield .  96  21.  P o t e n t i a l Inside S h i e l d  97  22.  RC F i l t e r of Phase S e n s i t i v e Detector  100  vii FIGURE  PAGE  2 3 - 2 6 . • P o l a r i z a t i o n Data f o r 3889A Line 27-33.  P o l a r i z a t i o n Data f o r 1 0 , 8 2 9 A Line  34.  P o l a r i z a t i o n as a Function of Pressure . . .  35-  P o l a r i z a t i o n as a Function of O p t i c a l Aperture  36.  65-68 69-75  77  79  P o l a r i z a t i o n and E x c i t a t i o n Curves f o r the 3 S - 2 P (7065A) Line . . . . . . . . . 3  3  8l  37.  I n t e n s i t y Model.  105  38.  Mathematical Model of P o l a r i z a t i o n  108  ACKNOWLEDGEMENTS I wish t o thank Professor F. W. Dalby f o r suggesting the problem and f o r s u p e r v i s i n g the research. I wish a l s o to thank my wife f o r her valuable assistance i n the preparation of t h i s thesis. This work was supported by The N a t i o n a l Research Council of Canada.  CHAPTER I INTRODUCTION Atomic l i n e r a d i a t i o n e x c i t e d by e l e c t r o n  impact w i l l , i n  general, be p o l a r i z e d r e l a t i v e to an axis p a r a l l e l to the e l e c t r o n beam.  A simple way to v i s u a l i z e the e f f e c t i s to think of the atom  as a c o l l e c t i o n of charged p a r t i c l e s connected by springs.  I f this  atom i s h i t d i r e c t l y by a p r o j e c t i l e t r a v e l l i n g i n the z d i r e c t i o n , the atom w i l l tend to v i b r a t e  i n modes i n which the displacements  of the e l e c t r i c charges are along the z a x i s . radiated,  The l i g h t that i s  then, w i l l be p o l a r i z e d to some extent along the z a x i s .  I t turns out that the p o l a r i z a t i o n observed i s , i n f a c t , u s u a l l y p o s i t i v e with respect to the z a x i s , as one would expect from the d e s c r i p t i o n j u s t given, although a m i n o r i t y of s p e c t r a l l i n e s show negative p o l a r i z a t i o n . When we wish to speak q u a n t i t a t i v e l y of the p o l a r i z a t i o n , we use the f o l l o w i n g d e f i n i t i o n for the degree of p o l a r i z a t i o n P. I f in i s the i n t e n s i t y of l i g h t with i t s e l e c t r i c vector i n the d i r e c t i o n of the e l e c t r o n beam, and i f I  x  i s the i n t e n s i t y of  l i g h t with i t s e l e c t r i c vector i n the d i r e c t i o n perpendicular to the e l e c t r o n beam, we have P - I" - I I" - I  x  x  I  2  I t i s u s u a l l y understood that the l i g h t i s viewed from a d i r e c t i o n perpendicular to the e l e c t r o n beam. I t i s very d i f f i c u l t to make d e t a i l e d p r e d i c t i o n s of the p o l a r i z a t i o n of l i g h t due to e l e c t r o n impact.  For a given  s p e c t r a l l i n e , the p o l a r i z a t i o n depends i n general on the d e t a i l s of the c o l l i s i o n process, and i s therefore d i f f i c u l t to c a l c u l a t e . Even though the laws governing electron-atom c o l l i s i o n s at nonr e l a t i v i s t i c energies are completely known, the c a l c u l a t i o n of low energy s c a t t e r i n g and e x c i t a t i o n cross sections at low energies i s extremely complex.  By low energies i s meant energies l e s s than a  few hundred e l e c t r o n v o l t s , i n the region where the Born approximation does not apply.  In f a c t , even though there has been  i n t e n s i v e work on electron-atom s c a t t e r i n g i n the past few years the only type of electron-atom s c a t t e r i n g that can be c a l c u l a t e d a c c u r a t e l y i s electron-hydrogen e l a s t i c scattering,"'" and to a 2  l e s s e r extent, electron-hydrogen i n e l a s t i c s c a t t e r i n g .  For other  cases, one can make approximations, such as the d i s t o r t e d wave approximation, that are somewhat b e t t e r at low energies than the Born approximation, but which cannot r e a l l y be expected to produce d e t a i l e d , accurate cross sections."'"  This i m p l i e s that they  also cannot be expected to produce d e t a i l e d , accurate p o l a r i z a t i o n curves. In s p i t e of these d i f f i c u l t i e s , i t i s p o s s i b l e to make a unique p r e d i c t i o n f o r the p o l a r i z a t i o n of a given l i n e very close to the e x c i t a t i o n t h r e s h o l d f o r that l i n e .  This p r e d i c t i o n  I  3  depends only on angular momentum c o n s i d e r a t i o n s , as w i l l be seen i n Chapter I I . The p o l a r i z a t i o n p r e d i c t e d at threshold i s the maximum p o s s i b l e f o r that s p e c t r a l  line.  Measurements of the p o l a r i z a t i o n of l i g h t due to e l e c t r o n impact were made f o r a number of atoms by s e v e r a l workers during the years 1925 to 1935-  During the same period a number of  measurements were made of a r e l a t e d phenomenon, the p o l a r i z a t i o n of l i g h t due to the absorbtion of resonance r a d i a t i o n . e l e c t r o n impact experiments,  Of the  the only ones that involved a  d e t a i l e d study of the p o l a r i z a t i o n as a f u n c t i o n of the energy of the e l e c t r o n s were those by Skinner and Appleyard.  They studied  several l i n e s i n the mercury spectrum, and measured the p o l a r i z a t i o n of l i g h t due to e l e c t r o n s ranging i n energy from 0 . 5 or 1 e.v. above threshold to about 200 e.v.  Typically their  curves  have the general appearance of the one shown i n Figure 1(B). With decreasing e l e c t r o n energy, the p o l a r i z a t i o n r i s e s i n magnitude to a maximum which occurs a few v o l t s above threshold. Then as threshold i s approached more c l o s e l y , the p o l a r i z a t i o n drops toward zero.  This l a s t e f f e c t i s one that i s contrary to  t h e o r e t i c a l expectations, which i n d i c a t e a curve of the form shown i n Figure 1(A). In the past few years, there has been a r e v i v a l of I n t e r e s t i n the subject due to the use of p o l a r i z a t i o n measurements as a means of d e t e c t i n g microwave t r a n s i t i o n s .  Most of the recent  measurements, however, have not been concerned with p o l a r i z a t i o n  4  I as a t o o l f o r other experiments, but have been done w i t h a view to understanding the phenomena i n v o l v e d . the measurements described i n t h i s t h e s i s .  This i s true also of In the past few  years there have been p o l a r i z a t i o n measurements on atomic hydrogen, helium I I , l i t h i u m , sodium, and mercury.^  0  100 e.v.  100 e.v.  F i g . 1.  Expected  (A) and observed  (B) p o l a r i z a t i o n curves.  The r e s u l t s of these experiments may be described b r i e f l y as f o l l o w s : H:  Measurements i n d i c a t e that the p o l a r i z a t i o n remains  f i n i t e near t h r e s h o l d , but do not allow a comparison of the threshold value w i t h theory.  This i s because the Balmer ex. data  involve three unresolved l i n e s w i t h unknown i n t e n s i t y r a t i o s , and because the Lyman <x. r e s u l t s are very imprecise.  He:  The p o l a r i z a t i o n of most of the l i n e s v a r i e s  r a p i d l y near threshold.  Curves of the form of Pigure 1(B) are  common i n the work before 19&3, but do not appear i n r e s u l t s published since then, and i t appears that the e f f e c t i s a property of the experimental method rather than a property of electron-helium c o l l i s i o n s . Nevertheless, except i n the case 8 of some of the most recent work,  the p o l a r i z a t i o n has not been  observed to come close to the t h e o r e t i c a l value at t h r e s h o l d . In the case of the exception j u s t mentioned, the p o l a r i z a t i o n i s observed to r i s e to the t h r e s h o l d value from a minimum that i s very close to t h r e s h o l d . He I I : The p o l a r i z a t i o n of one l i n e has been shown to increase monotonically w i t h decreasing e l e c t r o n energy, but comparison w i t h theory i s impossible. L i ^ , L i ' , Na ^: 7  2  The p o l a r i z a t i o n s of the resonance  l i n e s have been found to r i s e monotonically w i t h decreasing e l e c t r o n energy (as i n curve A) and to approach the p r e d i c t e d value at t h r e s h o l d , e x a c t l y as one would expect.  In f a c t  these measurements are good enough to check the p r e v i o u s l y published values of hyperfine s t r u c t u r e and n a t u r a l l i n e width.  However, there i s a l i t h i u m l i n e f o r which the p o l a r -  i z a t i o n decreases close to threshold. Hg:  The p o l a r i z a t i o n of the D l i n e s i s f i n i t e near  threshold, but the observations involve two unresolved l i n e s with an unknown i n t e n s i t y r a t i o .  These r e s u l t s i n d i c a t e ,  6  I however, that the e a r l i e r r e s u l t s of Skinner and Appleyard were wrong near threshold, probably as a r e s u l t of the  low  l i g h t i n t e n s i t i e s involved. The  question to be answered then, i s that of  behavior of the p o l a r i z a t i o n curves near threshold.  the This i s  where theory gives a d e f i n i t e answer, and t h i s i s also where measurements are d i f f i c u l t because i n t e n s i t i e s are low.  The  experimental work described i n t h i s t h e s i s pursues that question f o r two l i n e s i n the helium spectrum. The Figure 2.  energy l e v e l diagram f o r helium i s shown i n The  l i n e s connecting d i f f e r e n t energy l e v e l s  represent s p e c t r a l l i n e s or m u l t i p l e t s f o r which the p o l a r i z a t i o n due  to e l e c t r o n impact has been measured.  Double  l i n e s i n d i c a t e those f o r which data appear i n t h i s t h e s i s . The numbers at the top of the columns i n d i c a t e the t h e o r e t i c a l threshold p o l a r i z a t i o n s from l i n e s ( i n the case of s i n g l e t l e v e l s ) or m u l t i p l e t s ( i n the case of t r i p l e t l e v e l s ) o r i g i nating i n these columns.  These numbers apply to L -*• L - 1  t r a n s i t i o n s i n the case of upper P and D s t a t e s , and L-* L + 1 t r a n s i t i o n s i n the case of upper S s t a t e s . i  1  The lines.  l a r g e s t p o l a r i z a t i o n s have been observed with  The P- *S l i n e s are predicted 1  D- i  J  to have the l a r g e s t polar-  i z a t i o n s , but the observed p o l a r i z a t i o n s are not high, probably because, except at very low pressures, some of the l i g h t i s due to e x c i t a t i o n by trapped resonance r a d i a t i o n .  The  3 P-2  S  -19- e.v.  Figi 2. Energy Level Diagram for Helium. The ground state, which is not shown, is a 's state and is at zero electron volts.  8  I (3889A)  t r a n s i t i o n i s the only one f o r which the p o l a r i z a t i o n  d i d not, u n t i l r e c e n t l y , appear to approach zero near threshold. The primary concern of t h i s thesis i s the p o l a r i z a t i o n of the 2 P - 2 S 3  is  3  (10,829A)  m u l t i p l e t of helium.  This m u l t i p l e t  of p a r t i c u l a r i n t e r e s t because i t o r i g i n a t e s from a low  l y i n g l e v e l that i s comparatively w e l l separated from neighbouring l e v e l s , and because some t h e o r e t i c a l work has been done on i t . U n t i l now, no o p t i c a l measurements of p o l a r i z a t i o n have been reported f o r t h i s m u l t i p l e t , although the alignment of the 2 ^ s l e v e l r e s u l t i n g from the 23p_2^S t r a n s i t i o n has been measured by an atomic beam method.9 The 3 P - 2 S 3  thesis.  3  (3889A)  m u l t i p l e t i s also studied  i n this  I n t h i s case, the work i s not new, although the  s t a t i s t i c a l accuracy i s somewhat higher than i n previous measurements.  Because other workers have studied  this  m u l t i p l e t , the r e s u l t s presented here also serve as a t e s t of the experimental method.  I  9  References and Footnotes f o r Chapter I 1.  A b r i e f and l u c i d account of the state of low energy electron-atom s c a t t e r i n g theory as of 1964 i s given by E. Gerjuoy i n Physics Today _l8, 24 (May 1965) .  2.  P. G. Burke, H. M. Schey, K. Smith, Phys. Rev. 129,  3-  References f o r t h i s e a r l y work are given by I. C. P e r c i v a l and M. J . Seaton, P h i l . Trans. Ser.  1258 (1963).  A 251, 113 (1958).  4.  An account of t h i s work i s given i n A.C.G. M i t c h e l l and M. W. Zemansky, Resonance R a d i a t i o n and E x c i t e d Atoms (Cambridge U n i v e r s i t y Press, London, 1961).  5-  H.W.B. Skinner and E.T.S. Appleyard, Proc. Roy. Soc. (London) Ser. A 117, 224 (1927).  6.  For example, W. E. Lamb and T. H. Maiman, Phys. Rev.  7.  References f o r recent p o l a r i z a t i o n measurements are l i s t e d below with respect to the atomic species studied.  105, 573 (1957)•  H: -  H. Kleinpoppen, H. Kruger, and R. Ulmer, Physics L e t t e r s 2, 78 (1962). W. L. F i t e and R. T. Brackmann, Phys. Rev. 112,  1151 (1958).  He:  R. H. McFarland and E. A. S o l t y s i k , Phys. Rev.  127, 2090 (1962).  D. W. 0. Heddle and C. B. Lucas, Proc. Roy. Soc. (London) Ser. A 271, 129 (1963). R. H. Hughes, R. B. Kay, L. D. Weaver, Phys. Rev.  129, 1630 (1963).  (8).  R. H. McFarland, Phys. Rev. L e t t e r s  10, 397 (1963).  (8).  D.W.O. Heddle and R.G.W. Keesing, Proc. Roy. Soc. (London) Ser. A 2_5_8, 124 (1967) . E. A. S o l t y s i k , A. Y. Fournier and R. L. Gray, Phys. Rev. 153, 152 (1967).  R. H. McFarland, Phys. Rev. 15_6, 55 (1967). L i , L I , Ha ; H. Hafner and H. Kleinpoppen, Z e l t . Phys. 198, 315 (1967). 6  Hg:  7  23  H. G. Heideman, Physics L e t t e r s 13, 309 (1964).  H. K. Holt and R. Krotkov, Phys. Rev. 144, 8 ? (1966).  CHAPTER I I THEORY 2.1  Introduction The theory of the p o l a r i z a t i o n of l i g h t from atoms due  to e l e c t r o n impact has been reviewed and developed by P e r c i v a l and Seaton.  They derive expressions f o r p o l a r i z a t i o n i n terms  of the r e l a t i v e cross sections f o r e x c i t a t i o n to the various M L s t a t e s , where M momentum.  L  i s the Z component of o r b i t a l angular  They do not attempt to c a l c u l a t e the cross  sections themselves.  Such a c a l c u l a t i o n involves a l l the  d e t a i l s of the c o l l i s i o n process and at best can be done only approximately.  However, at t h r e s h o l d , one can p r e d i c t the  p o l a r i z a t i o n without a d e t a i l e d knowledge of the c o l l i s i o n process.  This w i l l be discussed l a t e r .  The theory  developed  by P e r c i v a l and Seaton i s r e s t r i c t e d to atoms which can be described i n terms of LS c o u p l i n g , and which have zero o r b i t a l angular momentum i n t h e i r ground s t a t e s , and i t i s also r e s t r i c t e d to dipole r a d i a t i o n . general.  Otherwise  i t i s quite  The e f f e c t of hyperfine s t r u c t u r e i s c a l c u l a t e d ,  i n c l u d i n g the case i n which the hyperfine separation i s comparable w i t h the n a t u r a l l i n e width.  (This i s of i n t e r e s t  i n the case of atomic hydrogen.) In the f o l l o w i n g pages I s h a l l o u t l i n e the theory that i s a p p l i c a b l e t o helium.  Hyperfine s t r u c t u r e w i l l  II  12  therefore be ignored.  The theory presented here w i l l f o l l o w  P e r c i v a l and Seaton quite c l o s e l y i n d i s c u s s i n g the c o l l i s i o n process, but w i l l depart from them to some extent i n d i s c u s s i n g the r a d i a t i o n process.  P e r c i v a l and Seaton use  the tensor operator methods developed by Racah, while the theory presented here w i l l use the more pedestrian methods described by Condon and Shortley. The emission of r a d i a t i o n due to e l e c t r o n impact i s considered to take place i n two d i s t i n c t (i)  steps:  the c o l l i s i o n process, i n which the atom i s  e x c i t e d from the i n i t i a l ( u s u a l l y ground) state to an excited  stateand  (ii)  the r a d i a t i o n process, i n which the atom drops to  state /f , with the emission of a photon.  Fig.  3.  (See Figure 3)  E x c i t a t i o n and Emission.  13  II  These two processes take place on quite d i f f e r e n t time scales.  The c o l l i s i o n process takes a time presumably of the  -14  order of 10  sec. (the t r a n s i t time of the s c a t t e r e d  e l e c t r o n at 0.1 v o l t s ) or l e s s ( f o r higher e n e r g i e s ) . The r a d i a t i o n time i s much longer, 10"^ in this thesis.  sec. f o r the l i n e s studied  There i s another time i n t e r v a l of importance,  namely the time r e q u i r e d to t r a n s f e r angular momentum from the o r b i t a l state of an atom to i t s s p i n s t a t e , and vice versa. As an estimate of t h i s s p i n - o r b i t i n t e r a c t i o n time, we take the inverse of the f i n e structure t r a n s i t i o n angular frequency, i . e . l/2nf.  The shortest i n t e r a c t i o n time found  i n t h i s way f o r helium i s 10~H 2 P state.  sec., which occurs i n the  Thus, to a good approximation, we can consider  t h a t , f o r the d u r a t i o n of the c o l l i s i o n process, the s p i n and o r b i t a l angular momenta are uncoupled.  On s i m i l a r  grounds, we may a s s e r t . t h a t there i s no s p i n - o r b i t i n t e r a c t i o n between the atom and the i n c i d e n t e l e c t r o n s . For the reasons given above, we can assume that s p i n and o r b i t a l angular momenta are separately conserved during the c o l l i s i o n , and that s p i n coordinates are not involved i n the c o l l i s i o n process.  Since s p i n i s l e f t out of the  p i c t u r e during the c o l l i s i o n , the r e l e v a n t q u a n t i t i e s i n a d e s c r i p t i o n of the c o l l i s i o n process are the cross sections f o r e x c i t a t i o n to the various o r b i t a l angular  14  II These s t a t e s we l a b e l by t h e i r M L v a l u e s ,  momentum s t a t e s .  s e c t i o n s by Q M . .  and we denote the c r o s s  In order to d e s c r i b e  the r a d i a t i o n p r o c e s s , however,  we must d e s c r i b e  the e x c i t e d s t a t e s o f the atom i n the L S  coupled scheme.  We r e q u i r e , t h e r e f o r e ,  the  e x c i t a t i o n cross  the  cross  sections  sections Q M  l  a r e l a t i o n between  i n the L S coupled scheme and  i n the uncoupled scheme.  This i s  what i s done i n the next s e c t i o n . 2.2  Collision The  distance  Process  wave f u n c t i o n of the s c a t t e r e d e l e c t r o n a t a l a r g e  r from the s c a t t e r i n g centre  has the form e ^ " fp ( k ) , 1  1  where fp ( k ) i s c a l l e d the s c a t t e r i n g amplitude, and i s a f u n c t i o n o f the d i r e c t i o n ( k ) .  The s u b s c r i p t i n d i c a t e s the  s t a t e i n t o which the atom i s e x c i t e d .  The cross  section f o r  s c a t t e r i n g i n t o a s o l i d angle d u about d i r e c t i o n ( k ) i s proportional  to jf^s ( k ) | ^dw, and the t o t a l cross  excitation into state/S  section f o r  i s p r o p o r t i o n a l to ° | f ^ ( k ) | dw.  Now  the r e l a t i o n s h i p between the s c a t t e r i n g amplitudes i n the /s=SUMj scheme and the/3  where t h e . C follows  that  M  s  M  L  M  j  =SLM ML S  are v e c t o r  scheme i s  coupling  coefficients. It  15  II  (2)  We can eliminate the mixed terms i n t h i s expression byapplying our assumption that spin and o r b i t a l angular momenta are separately conserved during the These conditions  collision.  are: M  L  + mi = 0  M  s  + m  s  = M  s  (3)  -  CO  m  g  where m' r e f e r s to the i n c i d e n t e l e c t r o n and m to the scattered e l e c t r o n .  In the f o l l o w i n g d i s c u s s i o n l e t t e r s with  a s i n g l e prime r e f e r to the i n i t i a l l e v e l ; unprimed l e t t e r s r e f e r to the e x c i t e d l e v e l ; and l e t t e r s with a double prime r e f e r to the l e v e l a f t e r r a d i a t i o n has taken place. to Figure  3-  Refer  The r i g h t hand side of (3) i s zero because i n  the i n i t i a l s t a t e , M =0 by assumption. L  We have  ra -0 t  because  we define the z axis to be d i r e c t e d p a r a l l e l to the d i r e c t i o n of t r a v e l of the i n c i d e n t e l e c t r o n . I f we expand the s c a t t e r i n g amplitude i n t o s p h e r i c a l harmonics i n the f o l l o w i n g  way,  (5) we f i n d , by applying the conservation  vanishes unless M =Mg, M =M°. s  L  conditions,  that  16  II  Hence  Therefore the cross s e c t i o n i s given by Q^LTMj  ^^fc^n^J  Now by our previous  QsLn M 5  assumption,  ( 7 )  L  Q5L,M H 3  i s l  independent of  M , so we w r i t e s  Q M  Q s L M  =  U  f  t  M  (8)  L  Furthermore, because of the a x i a l symmetry of the system, Q ^ i s independent of the s i g n of M . u  That i s , there i s  nothing i n the system to favour l e f t or r i g h t hand r o t a t i o n s . Hence we w r i t e Q M  L  =  (9)  Q | M J  This leaves us with  QsLTM^^^^n^J  ysVr  Q | M J  (10)  which i s the r e l a t i o n s h i p we set out to f i n d . We s h a l l a l s o require the r e l a t i v e p r o b a b i l i t i e s of e x c i t i n g the various f i n e s t r u c t u r e l e v e l s . We have  But M hj s  ' ' ' J s  L  2L+\  (12)  This f o l l o w s from the symmetry p r o p e r t i e s of the vector coupling c o e f f i c i e n t s .  Therefore  II  Q  17  7  =  £L±A C  U  (aL+i)(as+-i)  "  . (13)  L  where we define As we might expect then, the cross s e c t i o n f o r e x c i t i n g a given f i n e s t r u c t u r e l e v e l i s simply p r o p o r t i o n a l to the s t a t i s t i c a l weight of that l e v e l . 2.3  The R a d i a t i o n Process Our next task i s to f i n d the p o l a r i z a t i o n of the  r a d i a t i o n that i s due to each JMj —• j'Mj t r a n s i t i o n .  After  t h a t , we sum over Mj and Mj to o b t a i n the p o l a r i z a t i o n of each s p e c t r a l l i n e .  F i n a l l y , we sum over J and' j" to obtain  the p o l a r i z a t i o n of the m u l t i p l e t , which i s the q u a n t i t y that i s measured. The degree of p o l a r i z a t i o n i s defined as T  11  - T-'-  We now put t h i s i n t o a form that i s more convenient f o r calculations.  Ix-I -I y  X  l  Define  Iz-T.\. '  1 - 1 * . +  !?+ I  z  Then we obtain p _ 2>Iz. - I The p o l a r i z a t i o n , then, i s determined by the r e l a t i v e values of I  z  and I , and t h i s i s what we now c a l c u l a t e .  The emission  rate A ^ f o r l i g h t of a given p o l a r i z a t i o n /i i n the t r a n s i t i o n  18  II «  //  JMj —* J Mj i s p r o p o r t i o n a l to the moment.  square of the t r a n s i t i o n  That i s , we have  A (J ^ j - - * J " n j ) = K K I • 1-1P/4 i J " f l j ' > |  '.  %  (16)  where P i s the dipole moment operator  p, = +  1Z K i s a constant c h a r a c t e r i s t i c of the m u l t i p l e t . The  Mj, MJ' dependence of (16) ;  i s given by Condon and Shortley,  The Theory of Atomic Spectra, (which w i l l be r e f e r r e d to as TAS) equations 9^11•  Bearing i n mind the required q u a n t i t i e s  i n (15), and n o t i c i n g that t h i s i s a convenient point at which to sum over Mj,.we obtain A° (j M ->J ") - Y\ j ( J M T I P \S" M .> 1 * T  0  flfJM ->rWKI  ICTMTIP/<|J-"M">I = %  T  M«r  where the ( j j P j j )  '  "'  K  kvT  p j  J  n  " ) * i% (j", 7  J )  7  x  (ir j  ;/  are the reduced matrix elements of TAS 9^11,  and the — ( J , J ) are the r e s u l t of summing the MjMj dependent part of the matrix elements  oveTycc.  They are  Z ( j , J + l ) = ( j + l ) ( a J + 3)  ZZ (J, J ) •= J (J + i) Z(J,T-|)= J U J - I ) Equations (17)  give the r a t e of emission  (!8) (TA5  1*5)  i n the (J —»j')  line  from one atom i n the state JMj. The rate of e x c i t a t i o n of  II  19  atoms to the state JMj i s p r o p o r t i o n a l to the e x c i t a t i o n cross s e c t i o n to that s t a t e , which i s  Q J M = E (Cr-\-ji, n) —' S  L  \ - % .  J  T  Q  i ^l  (io)  M  The r a t e of r a d i a t i o n i s p r o p o r t i o n a l to the q u a n t i t i e s n W j r  A ° ( J M J  b  -  » J " )  A ( 5 L J M  A ( S L Ti  0  V)  T  )  ^feA^J  is+r  QiMj|<  J M  j|R»l " j)r J  n  A(j^->P)  where A(SLJMj) i s the t o t a l emission rate from the state SLJMj. Next, to f i n d the rates of emission i n the s p e c t r a l l i n e J — > J , we sum (19) over Mj to obtain  1(J-J')-K-  <^f^y  £  L  Qi«.il<J!Pi^>r -  where we have used (12) and (13).  < ' ") J J  (20)  K has been replaced by K°  i n order to accommodate such q u a n t i t i e s as atom density and e l e c t r o n beam current, and A(SLJMj) which i s independent of J and M  s  (TAS 13% ) . Equations (20) enable us to derive expressions  f o r the  p o l a r i z a t i o n of l i g h t i n a given s p e c t r a l l i n e by use of  20  II (15).  equation which  We  require  i n TAS  easy,  unity,  and we  triplet we  The  = L, J* = i f .  I n the  case  then  sum  results  For upper  S states  P  =  p _  of helium  p  After  o v e r J and z" .  3  calculations  appear  i n the  (L=0)  L = 0)  lines  or  multiplets (oo\  ^  o  2 —> L = 1)  o  lines  or  '  numerical tables and  -S m u l t i p l e t s  Seaton,  o f the  Tables 1  ( t h e ones s t u d i e d  15 (Qo - Q 1 )  j  multiplets  a  and  in Percival  _  dependence  G (Q Q +- Q i - A Q z l h Q +h,Q,-i-h .0x  These f o r m u l a e  P  / 7  This  (S(Qo — Q h Q + h, Q ,  o  3  summing  (21)  (L= _  because  0  0  F o r D —* P  to  11 8.  of these  ( L = 1—»  P —> S  is  reduce  i s e v e n more work t o do,  must  g i v e n i n TAS  form:  \  the procedure  o f the whole m u l t i p l e t .  o v e r M j , we  following  of  lines,  done u s i n g t h e e x p r e s s i o n s f o r the J and J  <J ;P| J*;,  given  the v e c t o r c o u p l i n g c o e f f i c i e n t s  singlet  however, t h e r e  (20)  0  the v e c t o r c o u p l i n g c o e f f i c i e n t s  want t h e p o l a r i z a t i o n  c a n be  For  of helium  have J  lines,  equations  of  since  and  ( j M j | P jJ"Mj)  76.  p.  In the case quite  9 11  i s g i v e n i n TAS  tabulated  t h e M j dependence o f  and  coefficients 2.  in- the  I n the  K  2 1  are  case  t h e s i s ) we  have 1 oh\  . 21  II 2.4  Threshold P o l a r i z a t i o n In general, the cross sections  Qj | M t  are d i f f i c u l t to  c a l c u l a t e , but one can assert that as the energy of the i n c i d e n t electrons i s reduced to approach the threshold value, Qi/Qo  approaches zero.  threshold i s completely  I f t h i s i s so, the p o l a r i z a t i o n near determined and i s 15/41 = 36.6$ i n  the case of -P- -3 m u l t i p l e t s . a s s e r t i o n i s as f o l l o w s .  The j u s t i f i c a t i o n f o r t h i s  The i n i t i a l state of the e l e c t r o n -  atom system has i t s z component of o r b i t a l angular momentum equal to zero, and therefore t h i s must be true of the f i n a l state a l s o , under our previous i.e.  M  L  assumptions.  + m, = 0  (3)  I f the energy of the scattered e l e c t r o n i s s u f f i c i e n t l y s m a l l , the scattered e l e c t r o n must be i n an S s t a t e , because otherwise i t s impact parameter would be impossibly l a r g e . so, then we have m  £  Q,, /Q  0  I f this i s  = 0 , and therefore M L = 0 a l s o .  Therefore  approaches zero. The p r e d i c t e d threshold p o l a r i z a t i o n s f o r s e v e r a l types  of t r a n s i t i o n s i n helium are shown i n Table I . In view of the f a c t that measurements have i n s e v e r a l cases f a i l e d to show a p o l a r i z a t i o n near threshold as high as p r e d i c t e d , i t i s worthwhile considering where the assumptions leading to the p r e d i c t i o n s may be vulnerable. b i l i t i e s come to mind.  Two p o s s i -  II TABLE I THEORETICAL THRESHOLD POLARIZATIONS S p e c t r a l Line  Threshold P o l a r i z a t i o n  S - 'p  0$  P - 'S  100$  1  1  'D - 'P P -  50$  1  Multiplet 3  S - P  0%  3  3p - S  36.6$  3  •a B  J  (i)  3  -  P  31.7$  The range i n energies over which e l e c t r o n s are  scattered i n pure S waves may be smaller than the energy width of the e l e c t r o n beam. o  The radius of an e x c i t e d Helium  .  .  atom i s 5 or 10 A, (depending on the s t a t e ) .  The impact  parameter of a 0.1 e.v. e l e c t r o n i s o A, so the threshold p r e d i c t i o n i s not dependable f o r energies much l a r g e r than this.  An e l e c t r o n beam from a thermionic  cathode has, at  best, an energy r e s o l u t i o n of about 0.2 v o l t s .  It is in  f a c t with t h i s c o n s i d e r a t i o n i n mind that the 2 P state was chosen f o r study.  A helium atom i n an n=2 state i s smaller  than one i n an n=3 or higher  state.  II  23  (ii)  The f a c t o r by which the s p i n - o r b i t time i s  l a r g e r than the c o l l i s i o n time i s not overwhelmingly l a r g e , and requires c l o s e r examination.  The numbers given i n  Table I I are very rough, but they provide some idea of the s i z e of the q u a n t i t i e s involved.  The c o l l i s i o n time i s  c a l c u l a t e d f o r the l a r g e s t e l e c t r o n energy f o r which the scattered e l e c t r o n should be predominantly i n an S s t a t e , and i s compared w i t h the s p i n - o r b i t i n t e r a c t i o n time.  TABLE I I COMPARISON OF COLLISION AND SPIN-ORBIT INTERACTION TIMES Symbol Atomic Radius Energy f o r Impact Parameter - R and -  1.  3 P  2P 3  3  o  R  5A  E  0.15  a  12A e.v.  Velocity Corresponding to E v  2.3x10^  Frequency of 1 - 0 f.s. Transition • f  2.8x10  Spin-Orbit Interaction Time 1/2 nf  6x10  C o l l i s i o n Time R/v ~Cc  2.2xl0"  Ratio  3xl0  T-is/z,  cm./sec.  10  -12  3  0.03  e.v.  1.0x10^ 8.1x10  sec. 1 5  sec.  9  T 1  2x10  1.2xl0 2xl0  3  cm./sec H  z  sec.  _ l i |  sec  24  II The value R i s estimated from a p l o t of e l e c t r o n density i n the hydrogen atom.  E and v are simply taken from the Bohr  formula. The r a t i o of s p i n - o r b i t time to c o l l i s i o n time seems to be large enough to allow the f i g u r e s i n the table to be adjusted by as much as a f a c t o r of 10 perhaps, and s t i l l leave the assumption i n t a c t that s p i n coordinates are not i n v o l v e d i n the c o l l i s i o n process.  N o t i c e , however, that e s p e c i a l l y  f o r the 3~T l e v e l , i t i s p o s s i b l e that the t h r e s h o l d p o l a r i z a t i o n holds up to only very small energies above t h r e s h o l d . 2.5  3  2 P Polarization Calculations Massey and Moiseiwitch have done a d i s t o r t e d wave 3  c a l c u l a t i o n of e x c i t a t i o n cross sections to the 2 P l e v e l of helium. They make p r e d i c t i o n s f o r the p o l a r i z a t i o n of l i g h t 3  3  i n the 2 P - 2^S l i n e . I n order to compare these p r e d i c t i o n s w i t h experimental p o l a r i z a t i o n s , i t i s necessary 2  3  3  toconvert them to p o l a r i z a t i o n s of the 2 P - 2 S m u l t i p l e t . F o r t u n a t e l y , there i s a one to one between P and  Q i / Q ,  0  5  correspondence  and t h i s i s e a s i l y done.  The con-  v e r s i o n formula i s c-(  hz+h/)  h, hf -  "  H, u:  G-(h.»h.) h» h,' — h, h/  / v  ,7  ( a 5 )  II  25  where P i s the m u l t i p l e t p o l a r i z a t i o n and P polarization.  /  Is the l i n e  The values obtained are p l o t t e d along with  the experimental data i n Figure 28. 2.6  D e p o l a r i z a t i o n due to a Magnetic F i e l d The p o l a r i z a t i o n of l i g h t from an atom depends on the  r e l a t i v e populations of the magnetic states of the e x c i t e d level.  A magnetic f i e l d d i r e c t e d at r i g h t angles to the  quantization axis w i l l tend to mix the magnetic s t a t e s , and i f t h i s magnetic f i e l d has a component i n the d i r e c t i o n of observation,  the p o l a r i z a t i o n i s decreased.  This d e p o l a r i -  z a t i o n i s known as the Hanle e f f e c t and i s described by M i t c h e l l and Zemansky.  I f the d i r e c t i o n s of observation  and of the magnetic f i e l d are the same, the reduction i n p o l a r i z a t i o n i s given by (26)  where H i s the magnetic f i e l d and X i s the r a d i a t i v e l i f e t i m e of the e x c i t e d s t a t e .  For the l i n e s studied i n t h i s t h e s i s  we have P "Po  I -r- ( a-9 H )  where H i s measured i n gauss.  x  26  II I f we want the d e p o l a r i z a t i o n  to be l e s s than 1%, say,  we must reduce any transverse magnetic f i e l d to less than 3.5 x 10  -2  gauss.  •2.7 P o l a r i z a t i o n as a Function of Angle In the theory of the p o l a r i z a t i o n of l i g h t due to e l e c t r o n impact on atoms, we assumed that the observer looks from a d i r e c t i o n at r i g h t angles to the e l e c t r o n beam. But i n p r a c t i c e , the observer looks at a cone of l i g h t rays.  In  t h i s •section we f i n d how the p o l a r i z a t i o n v a r i e s with the angle of observation.We consider the l i g h t r a d i a t i o n to o r i g i n a t e from three mutually perpendicular dipole antennae.  The z axis  antenna radiates with i n t e n s i t y I" i n a d i r e c t i o n perpendicular to i t s a x i s , and the x and y antennae each r a d i a t e with i n t e n s i t y I t h e i r axes.  x  i n d i r e c t i o n s perpendicular to  The r a d i a t i o n i n t e n s i t y from a r a d i a t i n g 2  dipole v a r i e s as s i n 0, where 0 i s measured from the dipole axis .  I f we look at the l i g h t at an a n g l e d from the  perpendicular to the e l e c t r o n beam, the p o l a r i z a t i o n we see i s  I " 4- I -- ( I s  1 1  Msin "^ 1  II  27 (27)  I - P(o)^ I f oc i s s m a l l ,  The  t h i s becomes  t o t a l e f f e c t on the observed p o l a r i z a t i o n i s found by-  aver aging over the d i r e c t i o n s 2.8  Intensity Not  of o b s e r v a t i o n .  as a F u n c t i o n o f Angle  only the p o l a r i z a t i o n , b u t a l s o the i n t e n s i t y of  l i g h t v a r i e s w i t h the angle of o b s e r v a t i o n .  I f 9 i s the  angle from the z a x i s , the i n t e n s i t y i s g i v e n by 1(9)  - I"+  1(G)  - 1 (%)(l  l  x  - (I -  1 1  -!^)  cos  a  G-  P c o s * &)  (28)  (We have used the same model as i n the p r e v i o u s The  section.)  total intensity i s  (29) The  importance of t h i s r e l a t i o n s h i p  measure c o l l i s i o n cross s e c t i o n s  i s that  i n order to  by measuring l i g h t  i n t e n s i t i e s i n a d i r e c t i o n p e r p e n d i c u l a r t o the e l e c t r o n beam, one must know the p o l a r i z a t i o n o f the l i g h t .  28  II 2.9  E f f e c t of D i s p e r s i o n of E l e c t r o n Beam on P o l a r i z a t i o n I f the axis of p o l a r i z a t i o n i s rotated by angle Q, the  new p o l a r i z a t i o n i s P' =  sln^e-  I " cos^6+ I1  I" I  =  +• I  I slh &-I u  v  x  c o ^ 9-  x  4- X  P (i - a s \ n  ^  %  (30)  Por small angles, t h i s becomes P' =  The  P ( i - a ^ )  .  t o t a l e f f e c t on the observed p o l a r i z a t i o n i s obtained by  averaging over the v e l o c i t y d i r e c t i o n s i n the elec6ron beam.  II  29 References and Footnotes f o r Chapter I I  1.  I . C. P e r c i v a l and M. J . Seaton, P h i l . Trans. Ser.  A 251, 113 (1958).  2.  E. U. Condon and G. H. S h o r t l e y , The Theory of Atomic Spectra, (Cambridge U n i v e r s i t y Press, London, 1963)  3.  H.S.W. Massey and B. L. M o i s e i w i t c h , Proc. Roy. Soc. (London) Ser. A 258, i h j (i960).  4.  A.C.G. M i t c h e l l and M, ¥. Zemansky, Resonance R a d i a t i o n and E x c i t e d Atoms (Cambridge U n i v e r s i t y Press, London, 1961).  CHAPTER I I I EXPERIMENTAL DETAILS 3.1 Vacuum System The vacuum system i s shown i n Figure 4.  The various  parts are demountable, being j o i n e d by nuts and b o l t s and sealed with neoprene "0" r i n g s .  I t i s a conventional system,  f o r the most p a r t , and i t i s p o s s i b l e to obtain pressures as -7 low as 2 x 10  t o r r with I t .  The main pump i s an o i l d i f f u s i o n pump ( B a l z e r s , D i f f . 170) with a speed of 90 l i t r e s / s e c o n d with the b a f f l e i n place.  The d i f f u s i o n pump i s backed by a mechandial pump  (Welch 1402) with a pumping speed of 100 l i t r e s / m i n u t e . I n s e r i e s with the d i f f u s i o n pump i s a water cooled b a f f l e which reduces o i l backstreaming, and a l i q u i d nitrogen t r a p . The trap was f i t t e d with a copper c o l l a r that was kept c o l d by thermal conduction through a copper rod from the inner part of the trap.  The purpose of t h i s c o l l a r was to discourage  o i l creep along the warm outside w a l l s of the trap.  When  low energy e l e c t r o n beams are being used i t i s important to keep o i l out of the vacuum system, because o i l can be deposited as an i n s u l a t i n g layer which w i l l charge up to large p o t e n t i a l s . When the vacuum pumps were operating, the trap was always kept c o l d .  A f i l l i n g of l i q u i d nitrogen  Cold Trap  Cold Collar  Valve Liquid Nitrogen  Z3  Water Cooled Baffle  Collision Region  i  , Helium Leak Hinpe--Q  Valve  Needle Valve  Charcoal Trap,  1  Diffusion Pump  —  Mechanical Pump 10 cm.  F i g . 4. Vacuum S y s t e m . The c o m p o n e n t s are d r a w n t o s c a l e , b u t t h e vacuum c o n n e c t i o n s are s c h e m a t i c o n l y .  32  Ill l a s t e d f o r about 16 hours.  Normally the trap was f i l l e d  twice d a i l y . The next component upstream from the l i q u i d n i t r o g e n trap i s a p l a t e v a l v e .  I t was u s e f u l during the p r e l i m i n a r y  stages of the experimental work when the vacuum chamber had to be opened o f t e n . working.  I t was not used once the experiment was  However, the poxts i n the valve housing were used.  One pasrt was used f o r rough pumping, and another was used f o r e l e c t r i c a l wires.  The e l e c t r i c a l connections i n t o the vacuum  were made through glass i n s u l a t e d feed-through components that were soldered to a brass p l a t e . The vacuum chamber was made from a piene of i n d u s t r i a l pyrex p i p e , w i t h 4 inches nominal i n s i d e diameter.  I t was  b o l t e d to a brass flange and sealed with an "0" r i n g .  The  chamber could be supported from below and removed whenever i t was necessary to change anything i n s i d e .  The e l e c t r o n gun  mount s l i d e s i n t o the vacuum chamber and the end w a l l of the mount d i v i d e s the chamber i n t o two s e c t i o n s .  One s e c t i o n  contains the e l e c t r o n gun, and the other i s the c o l l i s i o n region.  (See Figure 5) The hole connecting the two sections has a con-  ductance of 0.6 l i t r e s / s e c . f o r helium.  The pumping speed  f o r helium at the p o s i t i o n of the vacuum chamber i s estimated to have been 60 l i t r e s / s e c .  Hence when helium was  admitted to the c o l l i s i o n r e g i o n , the pressure r a t i o between  ELECTRON GUN  TUNGSTEN 1OTE5H  ELECTRO COLLECTOR  PYREX VACUUM CHAMBER WALL  POLAROID  5CM INTEFER EN€E~ FILTER  PHOTO MULTIPLIER Eig. 5.  Arrangement o f Apparatus  CYLINDRICAL TENS  34  Ill the  c o l l i s i o n region  gun  was a p p r o x i m a t e l y  of  the c o l l i s i o n  and t h e s e c t i o n c o n t a i n i n g  100/1.  B a k i n g a t 120°  B e c a u s e t h e pumping  r e g i o n was s m a l l ,  chamber h a d t o be b a k e d  the e l e c t r o n  i n order  that part  to achieve  speed out  o f t h e vacuum low p r e s s u r e s .  C f o r a day o r two was s u f f i c i e n t  t o allow the  _7 pressure  'to go down t o 5 x 10  ionization the  gauge.  ionization against  The c a l i b r a t i o n  a Bayard-Alpert  This  type  gauge was c a l i b r a t e d  good enough f o r t h i s threshold,  impurity  99-5$  pure.  6.  light  T h i s was e v i d e n t l y n o t  s i n c e near the e x c i t a t i o n  was a t l e a s t  The h e l i u m was t h e r e f o r e  i t through a l i q u i d n i t r o g e n  proved  i s shown i n F i g u r e  I t i s s a i d by the s u p p l i e r  experiment,  the impurity  helium l i g h t .  passing  curve  Source  ( L i q u i d A i r Co.) t o be  by  torr.  (Veeco R G - 7 5 P ) •  Tank h e l i u m was u s e d .  This  or i f  a McLeod gauge when t h e p o l a r i z a t i o n e x p e r i m e n t s  Helium  the  longer,  f o r a number o f weeks, t h e  were m e a s u r e d w i t h  gauge  were f i n i s h e d . 3.2  running  w o u l d go down t o 2 x 10  Pressures  as measured b y an  I f t h e b a k i n g was c o n t i n u e d  pumps were l e f t  pressure  torr,  t o be an e f f e c t i v e  l e v e l was v e r y  small,  cooled  as i n t e n s e  as  p u r i f i e d by charcoal  trap.  enough p r o c e d u r e  that the  and was p r o b a b l y  determined  t h e c l e a n l i n e s s o f t h e vacuum  system.  35  Fig« 6« Ion Gauge Calibration for Helium. The ion gauge readings correspond to a factory calibration for dry nitrogen.  Ill  36  The helium from the tank was admitted by means of a needle valve through the charcoal trap i n t o a r e s e r v o i r region with a volume of roughly one l i t r e where i t was l e f t at a constant pressure of up to 0.5 atmospheres during a run of s e v e r a l hours.  The helium passed from the r e s e r v o i r i n t o the  c o l l i s i o n region through a very f i n e glass c a p i l l i a r y leak, made by drawing out a piece of c a p i l l i a r y tubing i n a flame. A pressure of 0.5 atmospheres i n the r e s e r v o i r gave r i s e to a pressure of about 4 m i l l i t o r r i n the c o l l i s i o n r e g i o n . 3.3  E l e c t r o n Gun - Design and Operation The e l e c t r o n gun i s shown i n Eigure J.  according to a design by Simpson and Kuyatt."*"  I t was made In this  experiment the requirement i s f o r an e l e c t r o n gun that w i l l produce a s t a b l e , w e l l defined e l e c t r o n beam at low energy, and with as high a current as p o s s i b l e .  At low energies,  the current d e n s i t y i s l i m i t e d by the d i s p e r s i v e e f f e c t of space charge.  An example of the magnitude of t h i s e f f e c t  which i s relevant to the e l e c t r o n gun that was used i s the following.  A 25 v o l t , 10/cA, e l e c t r o n beam with a diameter  of 2 mm. w i l l , i n a length of 4 cm. be dispersed to an extent that the e l e c t r o n s at the edge of the beam w i l l be moving at an angle of 0.05 radians from the beam a x i s . (The d e r i v a t i o n of t h i s quantity i s given i n Appendix IIIA.)  Ill  38  I t w i l l be seen l a t e r that the observed behaviour of the e l e c t r o n beam at i t s best i s consistent with t h i s p i c t u r e . Because of the space charge e f f e c t , there i s a d e f i n i t e upper l i m i t to the amount of current that can be forced through a 2  given space at a given energy by e l e c t r o s t a t i c focusing.  The  e l e c t r o n beam can be confined magnetically, but the author considers a magnetic f i e l d o b j e c t i o n a b l e , because i n a p o l a r i z a t i o n experiment i t i s the d i r e c t i o n of the e l e c t r o n ' s v e l o c i t y that i s important rather than the e l e c t r o n ' s p o s i t i o n . A magnetic f i e l d confines the p o s i t i o n of the e l e c t r o n s , but allows the electrons to move i n a s p i r a l motion w i t h a v e l o c i t y component perpendicular  to the e l e c t r o n beam.  The design of the e l e c t r o n gun used here i s intended to put the maximum p o s s i b l e current i n t o a beam of given dimensions.  I t does t h i s by f i r s t a c c e l e r a t i n g the e l e c t r o n s  to 10 times t h e i r f i n a l energy i n order to draw s u f f i c i e n t current from the outside, and then d e c e l e r a t i n g them and p r o j e c t i n g them i n t o the e l e c t r o n beam at the proper  angles.  Voltages were applied to the p l a t e s of the e l e c t r o n gun as i n d i c a t e d i n the f i g u r e . l e f t at a constant  The g r i d potentiometer Had  s e t t i n g such that the p o t e n t i a l d i f f e r e n c e  between the cathode and g r i d was 8$ of the cathode p o t e n t i a l . The anode p o t e n t i a l was adjusted as necessary to be 10 times the magnitude of the cathode p o t e n t i a l .  (It really  should  have been 9 times, but the change made very l i t t l e d i f f e r e n c e  39  Ill i n the beam shape.)  To the cathode was applied a square wave  p o t e n t i a l at a frequency of 500 H . z  The l i g h t from the e l e c t r o n  beam was chopped i n t h i s way, as w i l l be explained  later.  The p o t e n t i a l a p p l i e d to the cathode determines the e l e c t r o n energy since the c o l l i s i o n chamber i s at ground p o t e n t i a l . At 25 v o l t s , the e l e c t r o n gun d e l i v e r e d from 5 to 10/sA,  depending on the c o n d i t i o n of the cathode.  The e l e c t r o n  beam, which i n the presence of helium could be seen w i t h dark adapted eyes, was 2 mm.  i n diameter where i t emerged from the  gun, and spread to a diameter of 4 mm. c o l l e c t o r which was 4 cm. away.  at the e l e c t r o n  A f t e r the gun had been i n  service f o r s e v e r a l weeks, the beam would spread to 1 cm. at the c o l l e c t o r .  Removing the gun and cleaning i t with  t r i c h l o r o e t h y l e n e vapour r e s t o r e d the o r i g i n a l beam shape. 3.4  E l e c t r o n Gun - Construction The e l e c t r o n gun was made from a k i t supplied by  Nuclide General Corporation.  I t c o n s i s t s of s t a i n l e s s  s t e e l p l a t e s and ceramic spacers connected by ceramic rods. Before t h i s k i t was obtained, the author spent a large amount of time i n f r u i t l e s s attempts to make an e l e c t r o n gun.  These attempts w i l l not be described here, but a few  comments may be i n order. The main point i s that the number of materials that can be used at elevated temperatures i n a vacuum i s severely  4o  Ill restricted.  T h i s i s p a r t i c u l a r l y true o f i n s u l a t i n g m a t e r i a l s .  Ceramics and g l a s s are about the o n l y m a t e r i a l s used.  As f o r metals, brass  high vapour pressure s o l d e r should  that can be  cannot be used, because o f the  of z i n c .  Ordinary  e l e c t r i c a l soft  not be used, even below i t s m e l t i n g  point,  because when i t becomes warm, i t sprays the vacuum chamber with m e t a l l i c vapour.  A ceramic m a t e r i a l t h a t promised to be very  u s e f u l i s Sauereisen Insa-Lute cement. forms a hard, s t r o n g ,  c e r a m i c - l i k e body.  When i t i s d r y , i t Unfortunately, ^after  o  being  heated to o n l y 120 C i n a vacuum f o r a few days i t d r i e s  out, and crumbles to powder under the s l i g h t e s t s t r e s s . The  c h i e f d i f f i c u l t y i n making e l e c t r o n guns, then,  i s the i,ack o f a s u i t a b l e i n s u l a t i n g m a t e r i a l thaft can be worked e a s i l y and p r e c i s e l y .  T h i s i s important, because  the metal p a r t s must be a l i g n e d p r e c i s e l y by i n s u l a t i n g pieces  that are small and d i f f i c u l t  to make.  A suitable  m a t e r i a l that has r e c e n t l y become a v a i l a b l e Is Boron N i t r i d e , a v a i l a b l e from The Carborundum Co., Latrobe, Pa., U.S.A. There appear to be three p o s s i b l e approaches to making e l e c t r o n guns f o r experimental work. make p r e c i s e  insulating parts.  T h i s i s what has been done  at the f a c t o r y i n the e l e c t r o n gun k i t . 3 a suggestion  by Krotkov  One i s t o  As an a l t e r n a t i v e ,  was to use s y n t h e t i c  b a l l s as p r e c i s i o n i n s u l a t i n g spacers.  sapphire  A second approach  41  Ill i s to a l i g n the metal parts p r e c i s e l y on some sort of j i g , and f i x them i n place with a p l a s t i c i n s u l a t i n g m a t e r i a l .  This i s what i s done i n the commercial manufacture of e l e c t r o n guns, i n which the p l a s t i c m a t e r i a l i s g l a s s . requires s p e c i a l equipment.  But this,  A t h i r d approach i s to use ready-  made e l e c t r o n guns, from t e l e v i s i o n tubes f o r instance.  This  i s a good approach, of course, only i f one can f i n d a gun 4 s u i t a b l e f o r the experiment.  Heddle and Keesing  used a low  energy e l e c t r o n gun from a magnetron tube, which, however required a magnetic f i e l d to operate. The k i t solves the problem of making the e l e c t r o n gun, but one s t i l l has to decide what k i n d of cathode to use and how to attach i t .  To s t a r t w i t h , the e l e c t r o n gun used  i n t h i s experiment requires a planar cathode, and f o r the best energy r e s o l u t i o n , and l e a s t thermal l i g h t , the cathode should operate at a low temperature. oxide cathodes.  These were t r i e d .  they are short l i v e d i n p r a c t i c e .  These c r i t e r i a suggest The disadvantage i s that  They poison e a s i l y , and  should be kept under continuous high vacuum.  They can be  taken out of the vacuum, put back, and r e a c t i v a t e d i f care i s taken to keep them dry, but t h e i r emission i s s u b s t a n t i a l l y reduced, and the procedure can be repeated at most two or three times.  They also tend to make the gun a b i t d i r t y ,  since the binder evaporates during a c t i v a t i o n and s e t t l e s on other parts of the gun.  42  Ill D i s p e n s e r cathodes were f i n a l l y used.  They r u n a t a  o  somewhat h i g h e r temperature,  (1100  o  n  C as opposed t o oOO  .  C.)  b u t they r e c o v e r a f t e r p o i s o n i n g , and they s u r v i v e b e i n g t a k e n t o atmospheric p r e s s u r e q u i t e w e l l .  They can even be  left  under rough vacuum f o r a w h i l e w i t h o u t r e q u i r i n g r e a c t i v a t i o n . Only t h r e e d i s p e n s e r cathodes were used i n a l l . The cathodes were mounted t o a s t a i n l e s s s t e e l p l a t e by means of t h r e e t u n g s t e n w i r e s 0.01" long.  i n diameter and 1 cm.  The w i r e s were spot welded w i t h t a n t a l u m f o i l b e i n g  used as f l u x .  (The m a n u f a c t u r e r s  recommend t h a t o n l y  r e f r a c t o r y metals be u s e d a t the cathode a v o i d p o i s o n i n g t h e cathode.)  temperature  to  S h o r t e r , t h i c k e r w i r e s were  t r i e d , b u t i t was f o u n d t h a t t h e g r e a t e r heat n e c e s s i t a t e d h e a t e r temperatures  loss  h i g h enough t o b u r n o u t  h e a t e r f i l a m e n t s a f t e r a few hours o f o p e r a t i o n .  W i t h the  arrangement j u s t d e s c r i b e d , however, h e a t e r s o u t l a s t e d the cathodes.  The h e a t e r was spot welded ( w i t h t a n t a l u m  foil)  t o t u n g s t e n w i r e s which were s u p p o r t e d by a g l a s s s t r u c t u r e . (See F i g u r e  7.)  The e l e c t r i c a l l e a d s were bare n i c k e l w i r e s spot welded t o t h e s t a i n l e s s s t e e l p l a t e s o f the e l e c t r o n gun. These w i r e s were spot welded a t the o t h e r end t o p l u g c o n n e c t o r s made from one i n c h f i n i s h i n g n a i l s cemented i n t o p i e c e s of ceramic t u b i n g .  On the o t h e r s i d e o f the  Ill  43  connectors, w i t h i n the valve housing which was always c o o l , enamelled copper wire was used. The cathodes were a c t i v a t e d at 1150  o  C brightness o  temperature and operated at approximately 1000 C brightness temperature.  I n order to f i n d the r e l a t i o n s h i p between  temperature and heater current, the cathode was heated i n a vacuum, without the remainder of the e l e c t r o n gun, and i t s temperature was measured with an o p t i c a l pyrometer. 3.5  E l e c t r o n Gun Mount This i s shown i n Figure 8.  ceramic rods.  The e l e c t r o n gun r e s t s on  The r e s t of the mount i s made of copper.  The  end of the e l e c t r o n gun i s attached with screws to the w a l l separating the c o l l i s i o n region from the r e s t of the vacuum chamber.  The whole mount was made to s l i d e i n and out of the  vacuum chamber, and to make a f a i r l y .close f i t with i t .  The  idea was to make the hole that the electrons passed through the only important passageway f o r helium between the two regions of the vacuum chamber.  The f i t between the e l e c t r o n  gun and the vacuum chamber was close enough that baking at a o  temperature a great deal higher than 120 C would have been r i s k y because of the expansion of the copper. The whole assembly of e l e c t r o n gun and mount, except f o r the cathode, was cleaned with t r i c h l o r o e t h y l e n e vapour,  45  as shown i n Figure 9, j u s t before p u t t i n g i t under vacuum. 3.6  C o l l i s i o n Chamber Everything i n the c o l l i s i o n chamber except o p t i c a l  parts was coated with c o l l o i d a l graphite to reduce surface 5  •  6  charging-^ and r e f l e c t i o n s of l i g h t and electrons . A g r i d of f i n e tungsten mesh 2 cm. i n diameter concentric with the e l e c t r o n beam was used to s h i e l d the e l e c t r o n beam from surface charges on the viewing.window. That such surface charging was very important was shown by the f o l l o w i n g observation when the s h i e l d was not present.  I f one looked at the e l e c t r o n beam (with helium i n  the c o l l i s i o n r e g i o n ) , what was seen depended on the energy of the e l e c t r o n s .  Up to 24 v o l t s , nothing was seen.  Then as  the energy was increased, the beam would become v i s i b l e a t both ends, and lengthen from each end towards the middle and unite when the e l e c t r o n energy was approximately  30 v o l t s .  (See Figure 1 0 . ) D  •====>  Cl  24-  v o l t s  c = Z ]  c=:zi:::__:iZZZ) 3 0  vo  it  s  F i g . 1 0 . Evidence of P o t e n t i a l Minimum.  46  9. "Vapour Degreasing" Method of Cleaning Vaouum Parts.  tig*  Ill  47  This e f f e c t i s i n t e r p r e t e d gradient along the beam.  as being due to a p o t e n t i a l The p o t e n t i a l was 6 v o l t s  lower  at the centre of the c o l l i s i o n region than at the ends. I n order to remedy t h i s , ' an e l e c t r o s t a t i c s h i e l d made of wires spaced at 3 nmu i n t e r v a l s was placed around the beam. However i t was not e n t i r e l y e f f e c t i v e .  The tungsten mesh  f i n a l l y used has a wire spacing of 0 . 8 mm. and i t e l i m i n a t e d the e f f e c t .  The e l e c t r o s t a t i c p o t e n t i a l  calculations  necessary to determine how f i n e a mesh i s needed are given i n Appendix I I I B . The e l e c t r o n  c o l l e c t o r i s a copper cup f i l l e d w i t h  f i n s i n order to reduce e l e c t r o n  reflections.  The vacuum chamber, except f o r the viewing window, was surrounded by two layers of magnetic (Conetic AA, P e r f e c t i o n  Mica Co.).  shielding  The transverse  magnetic f i e l d at the p o s i t i o n of the e l e c t r o n beam was measured to be 0 . 0 1 gauss.  The l o n g i t u d i n a l f i e l d was of  the same order of magnitude. 3.7  Optics Because the l i g h t i n t e n s i t y i n t h i s experiment i s  small, i t i s important to c o l l e c t as much of the l i g h t as possible, within certain limitations.  One l i m i t a t i o n i s  the p o l a r i z a t i o n of l i g h t changes w i t h the angle of observation (equation 2 7 ) . Therefore we cannot c o l l e c t  48  Ill l i g h t over a large angle oc .  However we may c o l l e c t  from as large an angle 0 as we l i k e .  light  Another l i m i t a t i o n i s  imposed by the s i z e of the l i g h t detector, which i s effectively  about 1 cm. i n diameter i n t h i s experiment.  The o p t i c a l system used i s shown i n Figure 11. The l i g h t from the e x c i t e d helium Is focused on the photocathode, i n the plane of the e l e c t r o n beam by a c y l i n d r i c a l l e n s , and i n the perpendicular plane by an e l l i p t i c a l aluminum m i r r o r . The f o c a l r a t i o of the mirror i s approximately f/0.5 and that of the lens f/5.  Thus l i g h t was c o l l e c t e d from a  s o l i d angle of approximately 4$ of 4rr , .and from an area of approximately 1 cm. (along the beam) by 2 mm.  The image  s i z e of t h i s part of the e l e c t r o n beam i s 1 cm. x 1 cm. Thus i n one plane, l i g h t i s c o l l e c t e d from a large angle and small object, and i n the other plane l i g h t i s c o l l e c t e d from a small object and a large angle. The mirror was cut from a s o l i d piece of aluminum with a m i l l i n g machine with i t s head t i l t e d at the proper angle to form the desired e l l i p s e . "Brasso" and " S i l v o " .  I t was p o l i s h e d with  I t was found that s o l i d aluminum  i s not an i d e a l m a t e r i a l f o r making mirrors because i t i s somewhat porous. I t should be noted that the i n t e n s i t y received from an o p t i c a l  of l i g h t  system l i k e the one j u s t  described  i s quite s e n s i t i v e to changes i n the s i z e and shape of the  49  SIDE  Top  Fig. 11.  VIEW  View  Focusing Properties of Optical System.c  ill  50  e l e c t r o n beam.  Therefore e x c i t a t i o n curves obtained w i t h i t  cannot be r e l i e d upon to be accurate.  However, t o t a l  i n t e n s i t y changes should not a f f e c t the accuracy of the p o l a r i z a t i o n measurements. The s p e c t r a l l i n e s were i s o l a t e d w i t h i n t e r f e r e n c e f i l t e r s , and analysed f o r p o l a r i z a t i o n by a sheet of p o l a r o i d o  which turned 90  at a u t o m a t i c a l l y timed i n t e r v a l s .  Type  HNP'B p o l a r o i d was used f o r the 3889A l i n e and type HR f o r the 1 0 , 8 2 9 A l i n e .  Transmission curves f o r the i n t e r f e r e n c e  f i l t e r s are shown i n Figure 12 and Figure 1 3 . 3.8  Photomultipliers For measurements on the 3889 A l i n e , an E.M.I. 6 2 5 6 s  p h o t o m u l t i p l i e r was used.  I t had a dark cureent of about  130 counts/sec. at room temperature and about 5 counts/sec. at 260°K.  I t was u s u a l l y not necessary to c o o l i t .  The 7  6256s was operated at 1500 v o l t s and had a gain of 2 . 5  x 10 .  For measurements•on the 10,829A l i n e , a P h i l l i p s CVP 150 p h o t o m u l t i p l i e r s e l e c t e d f o r r e l a t i v e l y high •infrared response was used.  I t s quantum e f f i c i e n c y at  1 0 , o 2 9 A was approximately o x 10  . I t was cooled to 135 K  where i t had a dark current of 10 counts/sec.  The CVP 150 5  was operated at 1420 v o l t s and had a gain of 6 . 5 x 10 .  32003400  3600  3800  400d  4200  Wavelength A Fig. 1 2 . Optical Transmission of Interference F i l t e r  52  o  Ill 3.9  53  Photo-multiplier  Cooling  The housing msed to c o o l the CVP 150 p h o t o m u l t i p l i e r i s shown i n Figure 1 4 .  L i q u i d nitrogen i s b o i l e d o f f , and  the r e s u l t i n g c o l d , dry n i t r o g e n i s passed around the photomultiplier.  A thermister attached  to the p h o t o m u l t i p l i e r  was used to measure i t s temperature.  The c o o l i n g device was  supplied by Spex, but had to be modified  somewhat.  A brass  sleeve was added to improve the c o l d nitrogen flow and to help provide e l e c t r o s t a t i c s h i e l d i n g . on the i n s i d e .  I n s u l a t i o n was added  F i n a l l y , i n order to prevent the p o l a r o i d  turner from g e t t i n g c o l d i t was necessary to warm i t by passing hot water through a c o i l i n thermal contact with i t ( c o i l not shown i n diagram).  The device f i n a l l y operated  s a t i s f a c t o r a l l y down to 135°K, as measured by the thermister. 3.10  Signal  Processing  A block diagram of the e l e c t r o n i c s i s shown i n Figure 15. described  The functions of the various components are i n the f o l l o w i n g s e c t i o n s .  E l e c t r o n gun C o n t r o l .  The e l e c t r o n gun c o n t r o l  supplies the various p o t e n t i a l s to the e l e c t r o n gun and measures the various currents.  I n order to separate the  l i g h t due to the e l e c t r o n beam from s t r a y l i g h t , the  Foam Plastic ((k\l Bakelite Aluminum  rs-Tr  Wire Spacer Optical Filter Quartz Evacuated Cell Polaroid'  OTTTT  i ( ( ; i ( i (/i i i Resistor Chain  Photomultiplier  q i .i i i i i i i i i i t i i i i i b5 / / / / ATF^  o  »  o o o  oo  o °  5  v  PM Cables  &  • oo  c  Gas Outlet Heat Exchanger  10 cm.  F i g . 14. P h o t o m u l t i p l i e r Cooling. The p h o t o m u l t i p l i e r was wrapped i n aluminum f o i l whioh was connected at cathode p o t e n t i a l through the wire spaoer.  Pre Amplifier  Lock - in  Amplifier  Analog to Digital Converter  Photomultiplier Switch Polaroid  Control  F—H  Turner Electron Gun Control Electron  Gun  Fig. 15. Electronics? Block Diagram  Scaler  Scaler  Ill  56  e l e c t r o n beam was  chopped.  The usual way  to do t h i s i s  simply to turn the beam on and o f f at some frequency, but i n t h i s experiment i t was The beam was  done i n a s l i g h t l y more subtle  way.  always on, but the energy given to the e l e c t r o n s  a l t e r n a t e d between the working values, and a value one or v o l t s below the e x c i t a t i o n threshold.  This was  two  done to  minimize the amount of background l i g h t coherent w i t h the s i g n a l when measurements were made close to threshold. chopping was  done, then, by applying a square wave p o t e n t i a l  to the cathode. Figure  The  The c i r c u i t used to do t h i s i s shown i n  16. Also shown i s the way  was measured.  I t was  i n which the applied p o t e n t i a l  compared to the p o t e n t i a l along a  p r e c i s i o n (0.1$ l i n e a r i t y ) potentiometer, which was turn c a l i b r a t e d with a mercury b a t t e r y as  in  standard.  The method of chopping made a s p e c i a l c i r c u i t necessary f o r measuring the e l e c t r o n beam current.  I t was  necessary to measure the current during the "on" part of the cycle.  This c i r c u i t i s also shown i n Figure  17.  The e l e c t r o n gun c o n t r o l - a l s o supplies the l o c k - i n a m p l i f i e r w i t h a reference s i g n a l derived from the same o s c i l l a t o r that d r i v e s the cathode supply. Preamplifier. with a 100K  The p h o t o m u l t i p l i e r output was  loaded  r e s i s t o r and fed i n t o a broadband p r e a m p l i f i e r .  57  -V.  -Va  10 Turn P r e c i s i o n Potentiometer  rig. 16. Eleotron Gun Cathode Supply„ Potentials -Vo and -V* are supplied alternately to the cathode at a frequency of 500 Hz. Vo and V*. are independently adjustable from 0 to 50 volts. The greater of Vi and V is measured with the peak rectifier and potentiometer circuits. a  58  Fig. 17. Mioroammeter for Electron Beam. 1$ acouraoy resistors are used. Peak ourrent i s measured.  Ill  59 _5  This arrangement had a time constant of 10  seconds.  The  p r e a m p l i f i e r (Micronoise, Denro Labs) has a gain v a r i a b l e between 10 and 5 0 . Lock-in a m p l i f i e r .  The l o c k - i n a m p l i f i e r c o n s i s t s of  a tuned a m p l i f i e r and a phase s e n s i t i v e detector.  The phase  s e n s i t i v e detector responds only to that part of the s i g n a l that i s coherent w i t h , and i n phase with the reference  signal.  The l o c k - i n a m p l i f i e r used i n t h i s experiment i s a model J B - 4 , Princeton Applied Research. l i n e a r i t y of 1%.  I t has a gain of 9000 and a  The output i s a D.C.  which i s 5 v o l t s at f u l l s c a l e .  d i f f e r e n t i a l voltage  In t h i s experiment, i t was  used with a one second time constant.. Analog to d i g i t a l converter.  I t was found that  longer i n t e r g r a t i o n times were r e q u i r e d than were convenient to provide with RC c i r c u i t s , so d i g i t a l was used.  averaging  The anagog to d i g i t a l converter i s 'a device  constructed from o p e r a t i o n a l a m p l i f i e r s that puts out pulses at a rate p r e c i s e l y p r o p o r t i o n a l to the p o t e n t i a l d i f f e r e n c e applied to i t s input. 10 .)  ( L i n e a r i t y i s 3 parts i n  Five v o l t s gives r i s e to 100 pulses per second.  Thus  the number of pulses r e g i s t e r e d over a given time i n t e r v a l i s a measure of the average output of the l o c k - i n a m p l i f i e r .  60  Ill Switch c o n t r o l .  The switch c o n t r o l determines both  the p o s i t i o n of the p o l a r o i d and the flow of s i g n a l pulses. The sequence of operations, repeated every 20 seconds, i s as f o l l o w s . To s t a r t w i t h , the pulses are f l o w i n g to one scaler.  Then, at a s i g n a l from the timer, the pulses are  switched o f f , and the p o l a r o i d turns 90°•  S i x seconds  l a t e r (the time r e q u i r e d f o r t r a n s i e n t s i g n a l s to die away) the pulses are switched on again, t h i s time going to the other scaler.  I n t h i s way, a r b i t r a r i l y long i n t e g r a t i o n times can  be achieved, and slow d r i f t s i n the t o t a l l i g h t i n t e n s i t y do not a f f e c t the r e s u l t . up to 20 minutes were used.  I n p r a c t i c e , i n t e g r a t i o n times The switch c o n t r o l was made up  of m u l t i v i b r a t o r c i r c u i t s with long time constants, and electro-mechanical r e l a y s .  The timer was a free running  m u l t i v i b r a t o r that completed a cycle every time the p o l a r o i d turned.  Thus there was no p o s s i b i l i t y of a  b i a s i n the lengths of time given to the " p a r a l l e l ! s i g n a l 1  and the "perpendicular" s i g n a l .  When a constant voltage  (a dry c e l l ) was placed across the input terminals of the analog to d i g i t a l converter, the s c a l e r readings were found to be equal to w i t h i n a few parts i n 10 . 3.11  P o l a r o i d Turner This i s shown i n Figure l 8 .  small wheel with a f r i c t i o n d r i v e .  I t i s turned by a The small wheel i s  61  Fig. 18. Device Used to Rotate Polaroid.  Ill driven by a f l e x i b l e cable that i s r o t a t e d by a r e v e r s i b l e e l e c t r i c motor.  The motor i s turned on only during the  time that the p o l a r o i d i s moving.  63  Ill  References and Footnotes f o r Chapter I I I 1.  J . A. Simpson and C. E. Kuyatt, Rev. S c i . I n s t r . 34, 265  (1963).  2.  J . R. P i e r c e , Theory and Design of E l e c t r o n Beams (Van Nostrand, New York, 1 9 5 4 ) .  3.  R. Krotkov, P r i v a t e Communication.  4.  D.W.O. Heddle and R.G.W. Keesing, Proc. Roy. Soc. (London) Ser. A 25_8, 124 (1967) .  5.  E. Lindholm, Rev. S c i . I n s t r . 3 1 , 210 ( i 9 6 0 ) .  6.  P. Marmet and L. Kerwin, Can. J . Phys. 3 8 ,  787,  i960.  CHAPTER IV EXPERIMENTAL RESULTS 4.1 'Data The p o l a r i z a t i o n of l i g h t as a f u n c t i o n of a p p l i e d p o t e n t i a l i s shown i n Figures 23 to 33• Each of the eleven f i g u r e s represents data taken on one day. The e r r o r bars represent r.m.s. s t a t i s t i c a l e r r o r s only.  These were  determined from estimates of photelectron pulse r a t e s . c o r r e c t i o n s have been a p p l i e d to the data.  No  The v e r t i c a l  dashed l i n e s at the bottom of some of the graphs i n d i c a t e " o f f " voltages used.  (See s e c t i o n 3.10)  The t h e o r e t i c a l  curve i n Figure 28 i s derived from values given by Massey and Moiseiwitch"*" as the r e s u l t of a d i s t o r t e d wave c a l c u l a t i o n '(see s e c t i o n 2 . 5 ) .  The curves drawn through  the p o l a r i z a t i o n data near t h r e s h o l d are taken from the threshold p o l a r i z a t i o n model which w i l l be discussed l a t e r , and have been f i t t e d to the data. The " e x c i t a t i o n " data are simply p l o t s of I" - l d i v i d e d by the e l e c t r o n beam current.  x  They are p l o t t e d i n  order to give some idea of the l i g h t i n t e n s i t y , and because they are of some i n t r i n s i c i n t e r e s t .  The e x c i t a t i o n scale  i s a r b i t r a r y and i s not shown on the graphs.  Among the  i — i — i — r  24 22 3 P-2 S 3  20  3  3889 A  18 -3  16  torr  2x10  1 yd  14  A  12 10}  0  o  8|  +J  m N  1 o  Q.  61  Polarization f Excitation  •-  41  2  0 -2  24  Fig. 23.  28  J-  L  32 36 40 lied Potential (volts)  44  66  36343 P--2*S 3  3230  3 889 A  —  28262422 20 §  torr  4x10  18  _ g 16 c  10 8 6  0  ©  •o  Polarization  {  Excitation  •  4  " * ^A  J  1-1  2 J  24 Fig.  24.  L  28  J  1  32  l  I  36  1  Potential  40  44 (volts)  48  3 P-2 S 3  20  S  3889 A  18  -3  2x10  torr  16 1412 5? 10 g  8 h  -H  03  M S-  6h  ro O  4h 2h 0 -2k  Polarization, f • Til + T4.  Excitation  Figo  25,  23  24  25  26 (volts)  • •*  27  A  t  I  l  1  1  j  1"  |  "j-  T  0  J  3 P-2 S 3  3  3889 A 4 x10  -3  torr  o  —  0  14  •  12 0. \>  10 5  s  c  .2 +-> n» Z  \  8 —'  '  \ e  6  0  e  \> X  4  •  —  0  O  °  o  o  o  —  OJ e  £  2 0 _  Polarization 4 Excitation  °  —  e  i  Fig. 26.  1  24  1  25 Applied  i  I  ,  26 Potential  I  27 (volts)  .  I  28  t  I  I  I-  I  24  I  1  •  •  1  I  1  I  1  2 P-2 S 3  22  •  20  3  10.829A 0  0 0  18  a  16  14  o  o o  o  O -,  2  o  o  ~  0  0  0  C  o  •  10 nj  •  N  Z O °-  8  Polarization $  •  Excitation  •  6  4  ^  8  A  e •  2 —  •  0  •  •  • •  «  a  *  "~*  I  ! i  . •  i _  i  !  20 Fig. 87.  1 1  24  1""  !  28 Applied  I  I  32 Potential  I  I  1  36 (volts)  1 40  I  44  T—i  r  2 P-2 S 3  3  10,829 A  24 22  c  o  20 18 16  m o  CL  ! <y» O  14  o  8  12 L10  Polarization 4  8  Excitation  6  •  Theoretical Polarization  4 2 J  24 F i g . 28,  L  28  32 Applied  I I 36 40 Potential  I  44 (volts)  48  o  T  2*P10 829  2*S A  20 18 16 •  14 0  12!  o o  io|  r o £  8|  N  Polarization >  61  Excitation  4 2 0  Fig. 29.  22  23 Applied  24 Potential  25 (volts)  • Ji±Ji • MA  J  24 2 P-  2*S  S  22  10,829 A*  20 18 16 14 12 10 8 :' e\  Polarization  :  Excitation  A  •  2 0|  21  Fig. 30,  22  23 Applied  24 Potential  25 (volts)  26  27  71  24 2 P-2 S S  22  3  10,8 29 A  20 18 16 14 12 10 8 6 4  Polarization  $  Excitation  • >tA  2 0  20  Fig. 31.  21  i  22 Applied  23 Potential  1  24 (volts)  25  26  7»  1  i  24 22 2 P3  20  2S 3  10,829 A  18 .tcr  14 12  I  101  H3  M  O  Qi O  Polarization 4 -  6|  1"  Excitation  MA  • P-  2  o  20 Fig. 32.  21  22 Applied  23 Potential  i  24 (volts)  25  26  7ff  24 22 2 P-2 S 10,829A J  ,S  0  20 18 16 14 12 10  •s\  Polarization { Excitation  6  •  4 2 ' 0|  L 21  Fig.33.  i  22  23 24 . 25 Applied P o t e n t i a l ( v o l t s )  26  27  76  IV  graphs that show the whole energy range only Figures 24 and 28 show the c o r r e c t e x c i t a t i o n curve.  For the other graphs,  the apparent e l e c t r o n beam current i s an average of the " o f f " and "on" c u r r e n t s .  The e x c i t a t i o n data are expected to be  l e s s accurate than the p o l a r i z a t i o n data.  This i s because  slow d r i f t s i n s i g n a l i n t e n s i t y , and v a r i a t i o n s i n the s i z e of the e l e c t r o n beam a f f e c t the i n t e n s i t y data but not the p o l a r i z a t i o n data.  The e x c i t a t i o n data are not considered  to be accurate enough to j u s t i f y p o l a r i z a t i o n c o r r e c t i o n s i n order to o b t a i n r e l a t i v e cross s e c t i o n s . The helium pressure and e l e c t r o n beam current are i n d i c a t e d on the graphs of the 3889A l i n e p o l a r i z a t i o n .  For  the 10,829A data the experimental c o n d i t i o n s are a l l _ -3  approximately as f o l l o w s :  4 x 10  t o r r , 7/^A near t h r e s h o l d  and higher currents at higher energies.  The v a r i a t i o n of  p o l a r i z a t i o n w i t h pressure i s shown i n Figure 3 ^ . 4.2  Energy Scale The " a p p l i e d p o t e n t i a l " i s the p o t e n t i a l d i f f e r e n c e  a p p l i e d between the cathode and the s c a t t e r i n g chamber, which was at ground p o t e n t i a l .  The thresholds f o r  e x c i t a t i o n are taken to be the values obtained by e x t r a p o l a t i n g the steepest p a r t s of the i n t e n s i t y curves. d i f f e r e n c e s between these apparent thresholds and the  The  T  X*  10,829  A  —  5-  X?  3889  .  A  o  1  I  I  1  "2  3  4  HELIUM PRESSURECmiHitdrr)  Fig. 34. Polarization as a Function of Pressure  -si  78  IV 3  spectroscopic  3  values are, f o r the 2^P, 3 Pj 3 S l i n e s  r e s p e c t i v e l y 1.95 volts.  3  v o l t s , 1.8 v o l t s , 1.9 v o l t s , or 1.9*0.1  (Some of the curves do not show t h i s agreement.  were taken before the voltage applied to the cathode properly c a l i b r a t e d . )  The threshold energies obtained  These  was from  f i t t i n g curves to the p o l a r i z a t i o n data tend to be a b i t higher than the ones j u s t given, but not by more than about 0.2 volts. 4.3  Experimental Sources of Error P o l a r i z a t i o n due to o p t i c a l elements.  There were no  elements i n the o p t i c a l system capable of p o l a r i z i n g p a r a x i a l l i g h t rays, but f o r the h i g h l y convergent l i g h t that was  used,  the m i r r o r , the curved glass w a l l sBf the vacuum chamber, the c y l i n d r i c a l l e n s , and the i n t e r f e r e n c e f i l t e r can a l l e f f e c t the p o l a r i z a t i o n . The c o n t r i b u t i o n to the p o l a r i z a t i o n due to the glass w a l l and the lens can be c a l c u l a t e d , and -0.5%  and - 0 . 4 $ r e s p e c t i v e l y .  (See Appendix IVA)  The  are effects  of the mirror and f i l t e r can be l a r g e r and were found by varying the aperture at the p o s i t i o n of the l e n s . o  In the case of the 3889A l i n e , the p o l a r i z a t i o n as a f u n c t i o n of aperture v a r i e d over a range of 2 or 3% (depending on the e l e c t r o n energy) i n a way to i n t e r p r e t .  (See Pigure 3 5 . )  that i s d i f f i c u l t  At e l e c t r o n energies  I  I  8 _ •'Spherical lens at f/10 7  I  8  0  8  o  0  6  I  79  0 —  3889 A  0 0 o  5  o  Mirror o —  °  °  0  o  3889 A  c o o °  Lens  N  o o  CL  0 0 _  O  0  11  °  o  10 829  • 10  A  Mirror 11  o O  10 ~  0  10 829 A  0  Lens  I  2 3 A p e r t u r e (cm.)  I  Fig. 35. Polarization as a Function of Optical Aperture.  8o  iv  s u f f i c i e n t l y low that the 3889A l i n e was  the only one  within  the bandpass of the f i l t e r that could be e x c i t e d , i t was  found  that the p o l a r i z a t i o n at f / 1 0 agreed with the f u l l aperture value, while the value obtained with a s p h e r i c a l lens at was  1%  higher.  The  3889A p o l a r i z a t i o n must be  f/10  considered  u n c e r t a i n to at l e a s t ±% on t h i s account. In the case of the 1 0 , 8 2 9 A l i n e , these problems were o  e v i d e n t l y absent, 'since the observed p o l a r i z a t i o n  was  independent of aperture to b e t t e r than Yfo (see Figure 35) • As a f u r t h e r check on the p o l a r i z i n g e f f e c t of 3  o p t i c s , the p o l a r i z a t i o n of the 3 S-2 measured.  °  P (7065A) l i n e  was  This l i n e o r i g i n a t e s from an upper S s t a t e ,  and should have zero p o l a r i z a t i o n s i n Figure 36. The  3  the  The  The  r e s u l t s are shown  observed p o l a r i z a t i o n i s about  -O.hfo.  r i s e i n p o l a r i z a t i o n s t a r t i n g at 25 v o l t s occurs at  the threshold  of the 3 D - 2 P (6678A) l i n e , f o r which the 1  1  transmission of the interference  f i l t e r is 0.1  times that  of the 7065A l i n e . V a r i a t i o n of p o l a r i z a t i o n with angle.  The  cone of  l i g h t c o l l e c t e d from the e x c i t e d helium extends to  0.1  radians on e i t h e r side of the d i r e c t i o n perpendicular to the e l e c t r o n beam.  For the p o l a r i z a t i o n s that were  12 EXCITATION  10  8  2 2  6 <*  <  o  POLARIZATION  4 i  O 0.  5  -21 1  24  26  25 AR P LI ED  27  ROT ENTI AL  28  (volts)  Fig. 36. Polarization and Excitation Curves for the 3 S-2 P (7065 A) Line 3  3  co  X  UJ  IV  82  observed, t h i s angular e f f e c t reduces the p o l a r i z a t i o n by 0.1%  (for P - 20%) at most, which i s e n t i r e l y n e g l i g i b l e .  (Refer to s e c t i o n 2.7.) D i s p e r s i o n of e l e c t r o n beam.  When the e l e c t r o n beam  was at i t s worst, the h a l f angle of the e l e c t r o n cone was 0.13  radians.  This r e s u l t s i n a p o l a r i z a t i o n of 20% being  reduced by 0.2%, which again i s n e g l i g i b l e .  (Refer to  s e c t i o n 2.9.) Coherent background.  The coherent background  c o n s i s t s of any unwanted s i g n a l that i s coherent w i t h the chopping- of the e l e c t r o n beam. to measure d i r e c t l y .  This s i g n a l was too small  I n order to estimate the e f f e c t of the  coherent background s i g n a l , i t s magnitude was changed by a f a c t o r of perhaps 2 or 3 .  This was done by changing the  " o f f " p o t e n t i a l applied to the e l e c t r o n beam by 1 or 2 v o l t s when the "on" p o t e n t i a l was near threshold.  At the lowest 0  s i g n a l l e v e l s , the p o l a r i z a t i o n of the  10,829A  l i n e seemed  to change by an amount comparable with the s t a t i s t i c a l e r r o r . This t e s t was not done f o r the 3889A l i n e , although d i f f e r e n t " o f f " p o t e n t i a l s were used f o r d i f f e r e n t runs. d i f f e r e n t runs, the plateau of p o l a r i z a t i o n near i s reproducible,  For the threshold  but the way i n which the p o l a r i z a t i o n f a l l s  IV  83  o f f below threshold i s not.  I t i s assumed that t h i s f a l l i n  p o t e n t i a l below threshold i s due to the background s i g n a l . Incoherent background.  In observations of the 3889A  l i n e , the incoherent background consisted of dark current and unmodulated l i g h t from impurity gases. -7 l i g h t at 5 x 10  t o r r was 50 counts/sec.  The background ( i . e . 50 photo-  electrons/sec.). In observations of the 1 0 , 8 2 9 A l i n e , the dominant background was l i g h t from the hot cathode which amounted to 800 to 1000  counts/sec.  These known background l e v e l s together with shot noise were used to determine the s i z e of the e r r o r bars. For comparison, the weakest s i g n a l i n the p o l a r i z a t i o n curve i s equivalent to 40 Unwanted o p t i c a l wavelengths.  infrared  counts/sec. The i n t e r f e r e n c e  f i l t e r s have bandpasses wide enough to transmit l i g h t from other helium l i n e s .  (See Figures 12 and 13-)  Near  threshold, however, none of these l i n e s are e x c i t e d . 3889A Filter: i s 140A.  The width of the transmission curve  Several unwanted helium l i n e s are transmitted by  t h i s f i l t e r , which have thresholds of 0.7 v o l t s or more above the 3 8 8 9 A threshold.  The r e l a t i v e i n t e n s i t i e s of  these l i n e s transmitted by the f i l t e r were measured with a  IV  84  monochrometer.  The f r a c t i o n of the l i g h t that was due to  these l i n e s was found to be approximately 10$ at 30 v o l t s and 20$ at 45 v o l t s . the  4 D-2 P 1  1  (3964A)  10,829A  The increase i s due almost e n t i r e l y to line.  Filter:  The width of the transmission curve  at h a l f maximum i s 125A. The only i n t e r f e r i n g l i n e s are weak ones among states' of high p r i n c i p a l quantum number.  They  begin at 3 v o l t s above the 2^p t h r e s h o l d and together contribute perhaps 1$ of the l i g h t . Cascading. from higher l e v e l s .  Some of the l i g h t r e s u l t s from cascading Again, t h i s does not occur near threshold. 2  Cascading i n helium has been discussed by G a b r i e l and Heddle. Electronics.  The a m p l i f i e r s  and other components  together are l i n e a r to w i t h i n about 1 $ .  IV  85  References and Footnotes f o r Chapter IV 1.  H.S.W. Massey and B. L. Moiseiwi ch, Proc. Roy. Soc. (London) Ser. A 2 5 8 , 147 ( I 9 6 0 ) .  2.  A. H. G a h r i e l and D.W.O. Heddle, Proc. Roy. Soc. (London) Ser. A 2 5 8 , 124 ( I 9 6 0 ) .  CHAPTER V DISCUSSION OF RESULTS AND CONCLUSIONS 5.1  P o l a r i z a t i o n Structure In the 2 p _ 2 S p o l a r i z a t i o n curve (Figures 2 8 , 2 9 , 3 0 ) , 3  3  there appears a bump at 1 . 2 v o l t s above threshold. i s quite reproducible and the u n c e r t a i n t y ' i n  The bump  i t s peak r e l a t i v e  to the apparent threshold i s perhaps - 0 . 2 v o l t s .  It is  tempting to i d e n t i f y t h i s structure with the resonance i n forward i n e l a s t i c e l e c t r o n s c a t t e r i n g at 1 . 6 above threshold observed by Chamberlain."'" However, because of the 0.'l_4 v o l t discrepancy i n energy and the f a c t that the structure  does  not appear as an increase i n the. p a r a l l e l e x c i t a t i o n function,  the r e l a t i o n s h i p between the bump and the resonance  i s unclear.  An experiment with better energy r e s o l u t i o n would  help. 5.2  Threshold P o l a r i z a t i o n 3  3  In the case of the 2-T-2 S l i n e p a r t i c u l a r l y , the structure  of the p o l a r i z a t i o n curve" near threshold i s b u r i e d  under the broad energy d i s t r i b u t i o n of the e l e c t r o n beam. What follows  i s an attempt to estimate the threshold p o l a r i -  z a t i o n by u s i n g a model of the e l e c t r o n energy d i s t r i b u t i o n and the p o l a r i z a t i o n and i n t e n s i t y curves.  We assume that:  V  87 (i)  The i n t e n s i t y I has the form I=kx where x i s  e l e c t r o n energy i n e l e c t r o n v o l t s r e l a t i v e to the threshold energy. (ii)  The true p o l a r i z a t i o n P near threshold i s given  by P = P o (1-yx) where P o i s threshold p o l a r i z a t i o n . (iii)  The energy d i s t r i b u t i o n of the e l e c t r o n beam  having mean energy x  i s of the form exp ,-lx-Xol/cr.  0  Assumption ( i i i ) i s c o r r e c t at l e a s t f o r the high energy edge of the energy d i s t r i b u t i o n , since the apparent e x c i t a t i o n curve below threshold i s exponential.  The  r e s u l t i n g apparent p o l a r i z a t i o n Pa(x) i s then given by Pa(x)/Po  = 1-2^0-  P^(x)/P  = l-2y<r - 4jcrR(x/o-)  c  • x * 0 x ^ 0  where R(t)  =• ( l - t + ^ t - e x p . ( - t ) ) / ( e x p . (-t)+2t) 2  The d e r i v a t i o n of t h i s expression, and a graph of Po.(x) are given i n Appendix VA. parameters cr and y .  There are two adjustable  cr was determined by f i t t i n g  exponential curves to the e x c i t a t i o n functions below threshold,  y was determined by f i t t i n g -R(x/o~) curves  to the p o l a r i z a t i o n curves near threshold. . The r e s u l t s are shown i n Table I I I . The threshold p o l a r i z a t i o n s obtained i n t h i s way are 32 ^6$ f o r the 2~ P12- S l i n e and )  3 3 1 5 3 $ f o r the 3 P-2 S l i n e . ±  :>  The e r r o r l i m i t s are somewhat  88  V a r b i t r a r y , since they depend on the model, the accuracy of which i s d i f f i c u l t to judge.  However, i t can be s a i d that  the data are consistent w i t h the p r e d i c t e d threshold p o l a r i z a t i o n f o r the 23p_2 S l i n e but not f o r the 3 P - 2 S l i n e . 3  3  3  TABLE I I I THRESHOLD POLARIZATION AND OTHER PARAMETERS POUND BY CURVE FITTING Transition 3 3 3 P - 2 S J  M°)  (*)  o~ ( v o l t s )  J  J  Po(*)  10.0  0.20  0.80  15.0  11.4  0.16  O.78  15.4  0.79  15.2  average 3 3 2 P - 2 S  Hvolts)  20.8  0.17  1.13  33.5  19.0  0.20  0.5  24*  21.0  0.15  1.07  32.0  20.3  0.15  1.13  31.0  average  1.11  theoretical  0.27**  - 31-8 36.6  *Not included i n the average **Massey and  5.3  Moiseiwitch  E x c i t a t i o n Curves I t was mentioned before that the measured e x c i t a t i o n  functions cannot be r e l i e d upon to be accurate because the  .  89  V  o p t i c a l system i s s e n s i t i v e to changes i n the shape of the e l e c t r o n beam.  o  Nevertheless, the 3889A e x c i t a t i o n curve  seems to e x h i b i t more or l e s s the same features as those 2 3 4 measured by other workers. ' ' I t • i s expected, then, 0  that the same i s true of the 10,829A e x c i t a t i o n curve. I n p a r t i c u l a r , . i t appears to f l a t t e n out s l i g h t l y at about one v o l t above t h r e s h o l d i n the same way as the cross  section  curve estimated by Holt and Krotkov. 5.4  Conclusions This t h e s i s has reported the f i r s t measurement of 3  3  the p o l a r i z a t i o n due to e l e c t r o n impact of the 2 P-2 S multiplet  i n helium.  The shape of the p o l a r i z a t i o n curve  i s s i m i l a r to that p r e d i c t e d by the d i s t o r t e d wave c a l c u l a t i o n of Massey and M o i s e i w i t c h , but the observed p o l a r i z a t i o n d i f f e r s from the t h e o r e t i c a l one i n d e t a i l and 3  i n magnitude.  Some structure  3  i n the 2 P-2 S p o l a r i z a t i o n J  curve provides a l i k e l y connection between p o l a r i z a t i o n measurements and e l e c t r o n s c a t t e r i n g measurements. This t h e s i s has also reported a measurement of tone 3  3  p o l a r i z a t i o n of the 3 P-2 S m u l t i p l e t with better  than  u s u a l s t a t i s t i c a l accuracy near threshold. In answer to the question of whether the p o l a r i z a t i o n approaches the t h e o r e t i c a l value at t h r e s h o l d , i t can be 3  3  said that the p o l a r i z a t i o n of the 2 P-2 S m u l t i p l e t does,  v  90  w i t h i n the u n c e r t a i n t i e s of the experiment, and that the 3  3  p o l a r i z a t i o n of the 3 P-2 S m u l t i p l e t does not, a t l e a s t not on an energy scale comparable with the energy r e s o l u t i o n of the e l e c t r o n beam. 5.5  Suggestion f o r Further Work The  importance of t h i s type of experiment l i e s i n  f i n d i n g p o l a r i z a t i o n values near threshold, and the obvious l i m i t a t i o n of the work reported i n t h i s t h e s i s i s the lack of e l e c t r o n energy r e s o l u t i o n . obtained  However, the energy r e s o l u t i o n  i n the present work i s close to the l i m i t imposed  by the cathode temperature.  I suggest t h e r e f o r e , that the  next step f o r anyone wishing to pursue t h i s l i n e of i n v e s t i g a t i o n would be to b u i l d an e l e c t r o n energy s e l e c t o r of the type c u r r e n t l y becoming popular i n e l e c t r o n s c a t t e r i n g experiments.^  The use of such a device e n t a i l s  a severe reduction i n e l e c t r o n beam current, and therefore i n l i g h t i n t e n s i t y . However, i n the experiment of t h i s t h e s i s there was more l i g h t than necessary at the wavelength 3889A, and i t should be p o s s i b l e to trade some of t h i s f o r b e t t e r energy r e s o l u t i o n .  V  91  References and Footnotes f o r Chapter V 46  1.  G. E. Chamberlain, Phys. Rev.  2.  C. Smit, H.G.M. Heidman, J . A. Smit, Physica 2 9 , 245  155,  (1967).  (1963).  3.  A. H. G a b r i e l and D.W.O. Heddle, Proc. Roy. Soc. (London) Ser. A 2 5 8 , 124 ( i 9 6 0 ) .  4.  I . P. Zapesochnyi and 0 . B. Shpenik, Soviet Phys. JETP (English Transl.) _23, 592 (1966) .  5.  H. K. Holt and R. Krotkov, Phys. Rev. 144,  6.  J . A. Simpson, Rev. S c i . I n s t r .  82  (1966).  35,  1698  (1964).  92  APPENDIX I I I A Properties of an E l e c t r o n Beam In t h i s s e c t i o n , we c a l c u l a t e the e f f e c t of the space charge w i t h i n the e l e c t r o n beam on two p r o p e r t i e s of the e l e c t r o n beam that are important i n p o l a r i z a t i o n s t u d i e s . These p r o p e r t i e s are the energy d i s t r i b u t i o n of the electrons and the r a d i a l d i s p e r s i o n of the e l e c t r o n beam. (i)  P o t e n t i a l D i s t r i b u t i o n i n the Cross Section of an E l e c t r o n Beam We assume the e l e c t r o n beam to be a uniform  c i r c u l a r c y l i n d e r , and we assume the current to be evenly d i s t r i b u t e d w i t h i n that c y l i n d e r . coordinates  (z,r,0).  We use c y l i n d r i c a l  The r a d i a l e l e c t r i c f i e l d w i t h i n  the e l e c t r o n beam i s given by  where R i s the radius of the e l e c t r o n beam.  I n terms of  the e l e c t r o n current I , we have  where Ve i s the energy of the e l e c t r o n s .  Hence  and the* p o t e n t i a l r e l a t i v e to the centre of the e l e c t r o n beam i s  Numerically,  U[r)  this i s  l. 5 a x 10  =  ^  —  where I i s m e a s u r e d in/<A and V i s m e a s u r e d i n v o l t s . give  an example r e l e v a n t  to the experiment  this  t h e s i s , we p u t V=25 v o l t s , I - 1 0 j u A .  p o t e n t i a l v a r i a t i o n from the centre  We  To  described i n find  that the  t o t h e edge o f t h e beam  _o  is  3 x 1 0  volts.  This  i s e n t i r e l y n e g l i g i b l e because the  energy v a r i a t i o n o f the e l e c t r o n s for  other  (ii)  than  D i s p e r s i o n o f E l e c t r o n Beam due t o Space we have j u s t  seen, the r a d i a l  Charge  electric  f i e l d at  edge o f t h e beam i s g i v e n b y I  7 3 V V-m The  radial  a For  this  reasons.  As the  i s much g r e a t e r  E  £ R  3. TT  0  a c c e l e r a t i o n i s then given by (R)  -  ^  1  &TT  i  0  JJy  R  s m a l l d i s p e r s i o n s , the r a d i a l v e l o c i t y r  ^  <q--rrt V 0  where -£ i s t h e l e n g t h tudinal velocity.  ft  o f t h e beam and ./v i s t h e l o n g i -  Then the angle  assuming the d i s p e r s i o n i s small)  r\ _ jy>__r  becomes  i  of dispersion i s given by  1  J- _  (still  F o r o u r e x a m p l e o f V=25 v o l t s , I-10/{A, we h a v e  6  = 1.2 2 X ! 0 "  3  4-  T h e n i f t h e beam i s 4 cm. l o n g a n d 0.1  cm. i n r a d i u s , we  have 0 -  0, 0  5  The i n c r e a s e  i n r a d i u s o f t h e beam i s g i v e n b y  When t h e e l e c t r o n beam was o n i t s b e s t b e h a v i o u r , approximately observed.  the increase  i n r a d i u s t h a t was  this i s  actually  95 APPENDIX I I I B The P o t e n t i a l i n a Region E l e c t r o s t a t i c a l l y Shielded by Grids We are i n t e r e s t e d i n knowing how c l o s e l y we must space the g r i d s i n order to s h i e l d the e l e c t r o n beam from s t r a y electric fields.  We use a simple two dimensional model of  the s i t u a t i o n i n which an array of i n f i n i t e p a r a l l e l wire separated by distance a i s used to s h i e l d a space from a uniform e l e c t r i c f i e l d .  -I-  -f  ±  + 'Eo  a  F i g . 19.  Electrostatic Shield  The assumption i s made that the radius r of the g r i d e  wires i s small compared to a. A l l of the g r i d wires are grounded and have p o t e n t i a l V =  0.  The average surface charge i n the plane c o n t a i n i n g the grids i s f. e , a  0  so the charge per u n i t length on the wires i s  96 Consider the e l e c t r i c f i e l d beneath one of the wires (along the dotted l i n e ) .  r£ ^  S^l.  =  &7l  to  =  The f i e l d due to that wire i s  £ °  -  _Qr..  a TT  V"  v  %  And the corresponding p o t e n t i a l i s  a  1  r  T l  o  n = i  20.  Fig.  E l e c t r o s t a t i c Shield.  The f i e l d due to the remaining wires i s En  =  ? :  >i = i  -  ~  4  4  —  1  —  r  air  v +  € o  -•2- j . y-,->  ^—  .^in ©-  ^  n  n  %  The p o t e n t i a l i s V.  ^ =  5 IT Ayv  ri-o."  vi - 1  TT  f  i  rv=a.  -t-  -----  n-3  97  ( r i s s m a l l and i s taken as zero) 0  The f i e l d due to the .upper p l a t e  (the plane  charge  d i s t r i b u t i o n somewhere above the g r i d s ) i s x and the p o t e n t i a l i s Then the r e s u l t a n t p o t e n t i a l along the d o t t e d l i n e i s  V = v, + V, + V, - ^  3, TV  1  \JU -- +• -#sn-T\ - TLT_ [ r ^ (X 0  Introduce the dimensionless v a r i a b l e  x  r  /o.  Then  V -  4- iUx, X  3. TT  +  x6rv TT — TT X  where +  ("  X  n =i + X  where  JLt  J_  N  U s i n g t h i s method of f i n d i n g I w e V shown i n F i g u r e 21.  We  a r r i v e a t the values of  see t h a t we are e s s e n t i a l l y i n a  f i e l d f r e e r e g i o n beyond one g r i d spacing from the g r i d . At r>a, then, we have air  I  r  J  a  o r , w i t h r e g a r d to the diameter of the w i r e , 2v , 0  5TT  JyYV  3. r  .15 Q  we have  98  1 9  V ? oL 11  !.0  2.0  xFig.  2 1 . P o t e n t i a l Inside S h i e l d .  The p r a c t i c a l r e s u l t s of these c a l c u l a t i o n s are the following. (a)  I n order to be free of p e r i o d i c v a r i a t i o n s i n  p o t e n t i a l due to the f i e l d that leaks through the spaces between the g r i d s , we must make the g r i d spacing smaller than the distance between the g r i d and the e l e c t r o n beam. (b)  Provided we abide by ( a ) , the p o t e n t i a l i n the  shielded region i s approximately  A V = ^ y r ' , since the  factor  \JLYL y^r  cases.  I n the present experiment, we are concerned with  a  c  — I.15 i s of order u n i t y i n p r a c t i c a l  f i e l d s of the order of 6 v o l t s i n 2 cm., or 0 . 3 v o l t s per mm.  The g r i d spacing f i n a l l y used i s 0 . 8 mm. so  AV** —  x  0  ' - = 0.04 v o l t s .  5 TT  The f a c t that the s h i e l d that  was used i s a mesh rather than an array of wires i n only  one d i r e c t i o n should improve the s h i e l d i n g somewhat.  We see  then, that the s h i e l d i n g used was j u s t about what was needed, and s h i e l d i n g that was very much poorer would have made a s i g n i f i c a n t c o n t r i b u t i o n to the e l e c t r o n energy spread.  APPENDIX I I I C S i g n a l Processing Theory Transient Signals i n the Output of the Lock-in A m p l i f i e r The output s i g n a l of the phase s e n s i t i v e detector i s smoothed by a double s e c t i o n f i l t e r which i s shown schematically below. -— Voi + o-oe  AM  / V  Follower  For  22.  V  p.  C  Fig.  e  \/\/V-  /  -  c  RC F i l t e r of Phase S e n s i t i v e Detector.  p o l a r i z a t i o n experiments, a time constant of  RC = 1 sec. was used.  The response of such a f i l t e r to a  step f u n c t i o n input voltage of the form e ( i n ) = e  0  (a  constant) f o r time t < 0, e ( i n ) - 0 f o r t >0 i s given by  e  o  \  RC  I f we put RC = 1 sec., then i f we wait f o r 6 s e c , e/e  0  = 0.018.  The average s i g n a l during the next 14  seconds (during which time we are observing another s i g n a l ) i s given by e/e  0  (ave.) - 0.002.  That i s , the t r a n s i e n t  101 signal size  c a u s e s an  comparable  error to  e)  statistical  =  of  the  M" - -f  P -  the  co  N"  +  N  error  run  the  and  by  The  i s ./N+N . b  J \ +  b  N b N  j  N  N /N  error  in  i s independent  b  and'we r e f e r  to  count  r.m.s.  counts  r.m.s. s t a t i s t i c a l  .  the of  i t as  the  f.  by  YN + N U  Thus we  N"- N  X  X  ±  that  was  the  used  error  to  calculate  the  counting rate  s i g n a l was  The  was  the  r.m.s.  numbers N, The  lock-in  and  corresamplifier-  f o u n d by  m e a s u r e d b o t h by  counting.  have  z  bars.  of  can  /iVHNf  photoelectrons.  magnitude  we  -f  N"*^  x  the  pulse  s m a l l enough t h a t  denominator.  number o f  and  i n w h i c h the  method  i n t e n s i t y we  X  i n the  formula  signal  +• N N  i s assumed t o be  p o n d e n c y between' t h e output  as  1  r e p r e s e n t e d by  refer  i s small  a  - (N^ t f /N)  1  errors  the  i s given  N " - N- - t f  i s the  i s then  f a c t o r V±.+  N" + N This  light  ( t o t a l number o f  observation,  polarization  ignore  (which i s of  which  background p u l s e s .  b  i n the  The  polarization  The  N^  N  find  polarization.  P  and  error  N e x t we  The  a b o u t 0.2$,  o b s e r v a t i o n of  f r a c t i o n a l error  direction  signal,  errors .  i n an  signal pulses  The  next  Errors  Suppose N  of  c  compared, w i t h o t h e r  Statistical  i n the  the  doing usual  a  102 Lower L i m i t on U s e f u l S i g n a l Strength The analog to d i g i t a l converter responds to p o s i t i v e s i g n a l s only.  This f a c t places a lower l i m i t on the s i g n a l  strength that can be used, because a s u f f i c i e n t l y weak s i g n a l w i l l be noisy enough that the phase s e n s i t i v e detector output w i l l be negative f o r part of the time.  A lower l i m i t on the  s i g n a l strength implies an upper l i m i t on u s e f u l i n t e g r a t i o n times. We now make an estimate of t h i s upper l i m i t under the assumption that we require r.m.s. e r r o r s of 1% or l e s s .  The  output voltage x of the phase s e n s i t i v e detector v a r i e s with time, and presumably the amount of time spent at each value of x i s given by a gaussion where x  0  distribution  i s the average s i g n a l l e v e l .  negative 1% of the time i f we choose x  The s i g n a l w i l l be Q  = 2.3cr .  Now  the  e f f e c t i v e i n t e g r a t i o n time of the double s e c t i o n f i l t e r i s approximately  2 seconds.  I f we integrate the output  s i g n a l from t h i s f i l t e r over time T, the s t a t i s t i c a l u n c e r t a i n t y i s reduced by a f a c t o r  J2/T  .  I f we  now  i n s i s t that t h i s u n c e r t a i n t y be 1$, we require that 72/T  cr - 0.01  x  0  = 0.01  x 2.3 cr  from which we f i n d that T = 4000 seconds.  In p r a c t i c e ,  i n t e g r a t i o n times of about 2000 seconds.were the longest used.  103  APPENDIX IV A P o l a r i z a t i o n of L i g h t due to O p t i c a l Elements P o l a r i z a t i o n of L i g h t due to Passage through a Glass  Surface  Assume that a ray of l i g h t has an angle of incidence to the normal of a glass surface of 0 , and an angle of r e f r a c t i o n of 0'.  The amplitudes of the e l e c t r i c f i e l d s of  the transmitted l i g h t are given 'by E  EJL  o s\ i -$')  s I n" ( ) " c  P  =  3 sin  '  0  cos  0  (Jenkins and White, Fundamentals of Optics) where the primes r e f e r to r e f r a c t e d l i g h t and where Ep'^and E '^ are the e l e c t r i c f i e l d components r e s p e c t i v e l y p a r a l l e l (  s  t o , and perpendicular to the plane of incidence. We assume the i n c i d e n t l i g h t to be unpolarized; i . e . Ep = E$  .  Then the p o l a r i z a t i o n with respect to the  plane of incidence of the r e f r a c t e d l i g h t i s given by Ep  z  +  El  I t i s now  2 -  ^in^  (tf  -  0')  a s t r a i g h t f o r w a r d matter to c a l c u l a t e the  e f f e c t on p o l a r i z a t i o n of glass o p t i c a l elements, e s p e c i a l l y i f the angles 0 and 0  1  are small.  I t i s necessary to  average over a l l the angles 0 contained i n the cone of light.  104 P o l a r i z a t i o n of Light due to R e f l e c t i o n from a Metal Surface The s i t u a t i o n here i s somewhat more d i f f i c u l t than i n the l a s t s e c t i o n .  The p o l a r i z a t i o n depends on the r e f r a c t i v e  index and c o n d u c t i v i t y  of the metal i n a complicated way.  However, f o r a very good r e f l e c t o r the e f f e c t s cannot he large.  An aluminum surface r e f l e c t s about 90$ of blue l i g h t  and i s somewhat better  i n the i n f r a r e d .  I n general, l i g h t  p o l a r i z e d perpendicular to the plane of incidence i s reflected preferentially.  This means that i n the p o l a r i -  z a t i o n experiment, any p o l a r i z a t i o n due to the mirror i s negative.  :  105  APPENDIX V A P o l a r i z a t i o n Model Consider f i r s t the i n t e n s i t y of l i g h t as a f u n c t i o n of the nominal e l e c t r o n energy.  We assume that the e x c i t a t i o n  cross s e c t i o n has the form  -P  (IL)  =  kx  (x.> o) (x^ 0) x  - 0  and that the energy d i s t r i b u t i o n of the e l e c t r o n i s a (iL'-x)  =  -—  £  - IT'-  ^  ^  'nowhere x i s the nominal e l e c t r o n energy r e l a t i v e to the a v  e x c i t a t i o n energy, and k and cr are constants.  P i g . 37.  I n t e n s i t y Model.  Then the i n t e n s i t y of l i g h t i s given by Upon performing the i n t e g r a t i o n , we obtain I (x) -  ^ -  e  + kx  ( x * O)  IX I  2  '  106 Thus, below threshold, the i n t e n s i t y f u n c t i o n i s exponential i n energy, and s u f f i c i e n t l y f a r above threshold the i n t e n s i t y follows the e x c i t a t i o n cross section  correctly.  In order to f i n d apparent p o l a r i z a t i o n functions, must know how to add p o l a r i z a t i o n s .  That i s , i f i n a source  of l i g h t there are two components with i n t e n s i t i e s I and p o l a r i z a t i o n s P, and P  z  we  (  and I ^ ,  ( r e f e r r e d to the same a x i s ) , the  resultant polarization i s P _  Pi  II  I.  + +  Iz  U •  This may be shown e a s i l y from the d e f i n i t i o n ' of p o l a r i z a t i o n . I t follows then, that i f the p o l a r i z a t i o n f u n c t i o n i s P(x), the apparent p o l a r i z a t i o n f u n c t i o n P (x) i s given by 0L  $ U')q Cx'-X) dx' The denominator i s simply I ( x ) , which we have j u s t  calculated,  In order to c a l c u l a t e the numerator, we assume the p o l a r i z a t i o n f u n c t i o n to be P (x)  =  Po ( 1 - X t.)  X  *  0  The f i n a l r e s u l t i s given by Po. U)/pc  Po. ( x ) / p where  = i 0  =  1-0  R(x A)  X ^ O  107  One  apparent feature of t h i s r e s u l t i s that the  apparent p o l a r i z a t i o n i s constant below threshold.  This  feature i s common to a l l such p o l a r i z a t i o n models i n which an exponential e l e c t r o n energy d i s t r i b u t i o n i s assumed. The reason f o r t h i s i s c l e a r i f i t i s r e c a l l e d that the shape of the f u n c t i o n exp.(x'-x), considered as a f u n c t i o n of x', i s independent of the value of x. Another feature of t h i s p a r t i c u l a r model i s that the apparent p o l a r i z a t i o n Po_(x) approaches the "true" p o l a r i z a t i o n P(x) f o r large x, but more slowly than might be supposed.  P*. W  Por x >> cr, we have  « Pn (i - * x - a Graphs of the various functions are shown i n  Figure 3 8 . A convenient feature of the f u n c t i o n Po_(x) i s the way i n which the dependence ontfand the dependence on a- are separated i n the product 4!fcr R(x/cr ) . This means that only one 4tfc> R(x/cr ) curve has to be c a l c u l a t e d ; the others are obtained by m u l t i p l y i n g the coordinates by appropriate factors. The parameters cr and H are found from the data i n the f o l l o w i n g way; Exponential curves are made up on transparent sheets, and f i t t e d to the i n t e n s i t y data i n order to determine cr . Then 4ftcr R(x/cr) curves are made  108  x (Electron F i g . 38.  Volts)  Mathematical Model of P o l a r i z a t i o n  109  up, f o r s e v e r a l values of cr^f, and. f i t t e d to the  polarization  data i n order to determine f . I t was found necessary to make up only two sets of 4fcrR (x/cr ) curves, one f o r cr = 0.15 v o l t s , and one f o r o~ = 0 . 2 0  volts.  

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