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The hyperfine structure of mercury extracted from neutron irradiated gold Bedford, Ronald Ernest 1953

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THE HYPERFINE STRUCTURE OF MERCURY EXTRACTED FROM NEUTRON IRRADIATED GOLD  *T  RONALD ERNEST BEDFORD A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n the Department oi" Phys i c s.  We accept t h i s t h e s i s as conforming to the standard required from candidates f o r the degree o f MASTER OF ARTS.  Members of the Department'of Physics.  THE UNIVERSITY OF BRITISH COLUMBIA September, 1953,  (ii)  Abstract.  The neutron  h y p e r f i n e s t r u c t u r e of mercury e x t r a c t e d from irradiated  of a Pabry-Perot  gold has been i n v e s t i g a t e d w i t h the 3.*d  etalon.  The theory and design of the  i n t e r f e r o m e t e r are d i s c u s s e d i n d e t a i l . of s i x t e e n l i n e s i n the spectrum  The wavelengths  of H g ^ ® , and the hyper1  f i n e s t r u c t u r e of many l i n e s i n the spectrum  o f Hgl99  have been e v a l u a t e d and compared w i t h former  determinations,  The  r a t i o of H g ^ 1  to  H g ® ^ produced 1  d u r i n g the neutron  bombardment of g o l d has been determined  from  intensity  measurements of the h y p e r f i n e s t r u c t u r e p a t t e r n s . result yields the neutron  The  a value of (1.78± 0.10) X 10* barns f o r  capture cross s e c t i o n of Au  .  (iii) Acknowledgments. I t g i v e s me  pleasure  t o express my  thanks to Dr.  Crooker f o r h i s s u p e r v i s i o n of t h i s p r o j e c t and  for his  innumerable v a l u a b l e  suggestions.  Mr.  c o n s t r u c t i o n of the e t a l o n , to  W.  Maier f o r the  A. F r a s e r f o r the Mr. am  I am  a l s o indebted  to Mr.  c o n s t r u c t i o n of the s t e p s e c t o r , and  J . Lees f o r a i d i n the p r e p a r a t i o n indebted  A.M.  of the source.  to I  to the N a t i o n a l Research C o u n c i l of Canada f o r  the award of a Bursary and t h i s p r o j e c t was  carried  Summer Supplement under which  out.  (iv) TABLE OP CONTENTS  Abstract Achnowledgments Chapter: I:  Introduction  I I : The Theory of the Fa'bry-Perot I n t e r f e r o m e t e r 1.  The Theory  2.  The Fringe' Half-Width  3.  The R e s o l v i n g power of the E t a l o n  4.  The I n t e r o r d e r S e p a r a t i o n  of the I n t e r f e r e n c e F r i n g e s  5» Reduction o f Observations 6 .  The Rectangular A r r a y of Tolansky  7-. The E t a l o n Thickness III:General 1.  Theory  Multiplet Structure  2 . Hyperfine Structure :»  (a) Isotope E f f e c t  ;  (b) Nuclear Spin . 3.  The Spectrum of Mercury  4«The D i s i n t e g r a t i o n IV:  The  Equations  Apparatus  1.  The C o n s t r u c t i o n of the E t a l o n  2.  The Adjustment  3.The 4.  The  of the E t a l o n  Source Spectrograph  5. The Step S e c t o r 6 .  The Microphotonieter  (v)  V:  The Experimental 1. The  Procedure  37  P r e p a r a t i o n of the Source  37  2. The Photography of the I n t e r f e r e n c e Patterns 3. The Determination  38  of Wavelengths  39  4. The Measurement of the Mercury R a t i o VI: The Experimental R e s u l t s 1. The  43  C a l c u l a t i o n of Absolute Wavelengths 43  2.  The H y p e r f i n e S t r u c t u r e Separations  3.  The Neutron Capture  Cross S e c t i o n of Au 1 9 8  Appendix I:  Method of F o c u s s i n g a Prism Spectrograph  Appendix I I :  Bibliography  45 46  48  Method of F o c u s s i n g a Microphotometer  Appendix I I I :  40  Hyperfine S t r u c t u r e of H g  1 9 8  54 55 57  (vi) Illustrations: 1.  A decay scheme f o r Aul98.  To f o l l o w page 1  2.  A decay scheme f o r Au-^9  To f o l l o w page 1  3.  The p r i n c i p l e  #  of the e t a l o n .  4. Dependence of i n t e n s i t y d i s t r i b u t i o n upon R on R.  5.  Dependence of I  6.  The r e c t a n g u l a r  7.  Energy l e v e l diagram showing the h f s . of the Hg l i n e A = rw/ A  array  page 5 To f o l l o w page 8 To f o l l o w page 8 page 14  To f o l l o w page 22  8.  Schematic drawing of the h f s . Of l i n e X - ryt/ %  To f o l l o w page 22  9.  Pabry-Perot E t a l o n  To f o l l o w page 27  10.  C i r c u i t diagram of r . f . oscillator  To f o l l o w page 31  11.  Mercury d i s t i l l a t i o n apparatus  To f o l l o w page 37  12.  R e g u l a t i o n of p l a t e  tilt  page 50  (vii) page Tables: 1.  C a l c u l a t e d order of I n t e r f e r e n c e  43  2.  Wavelengths of H g  44  3.  Rectangular a r r a y f o r X •*  4.  Hyperfine s t r u c t u r e o f Hg-*- (observed)  5.  V a r i a t i o n of n w i t h  6.  E v a l u a t i o n of B, Cauchy's d i s p e r s i o n constant  51  Agreement'of c a l c u l a t e d focus w i t h a c t u a l focus  53  H y p e r f i n e S t r u c t u r e of H g l " (calculated)  56  7. 8.  1 9 8  9o-?7  ^  99  A  45 45 51  Plates: I  Fabry-Perot  p a t t e r n of Hg l i n e  5461 angstroms  5-9  II  Fabry-Perot  p a t t e r n of Hg l i n e 4077 angstroms  6©  III IV  Fabry-Perot p a t t e r n o f Hg l i n e  3341 angstroms 0 6 1  Fabry-Perot  3125 angstroms  p a t t e r n of Hg l i n e  6'2  CHAPTER I : The  INTRODUCTION.  transmutation  of gold by neutron i r r a d i a t i o n has  a source of growing i n t e r e s t during the past decade. n a t u r a l s t a t e g o l d c o n s i s t s of but that of atomic weight 197. was  subjected  captured  E a r l y workers found that when  ^  /ft  JJ  _  to H g ^ .  determined as 2.69 79  represent  e  equations:  / 9 »  _  to +~/? ) of the a s s o c i a t e d beta decay has  scheme f o r the  \pj may  1  The  ^  79  days.  Au  198  The most recent and  s a t i s f a c t o r i l y been complete decay  has been proposed by S c h i f f and  i s depicted i n Figure I t now  1  isotope.  1 9  these r e a c t i o n s by the f o l l o w i n g  (1) and  Au ^  to a f l u x of slow neutrons the s t a b l e nucleus  a neutron to form the r a d i o a c t i v e A u ^  half l i f e  In i t s  a s i n g l e s t a b l e i s o t o p e , namely  l a t t e r then decayed by beta emission  The  been  Metzger  1.  appears that the r e a c t i o n s of eqations  (1.1)  may  allow a seemingly u n r e l a t e d l i n e of endeavour to be brought to a successful conclusion. f o r a q u a n t i t y to serve  For years  p h y s i c i s t s have been  as the u l t i m a t e  standard  inadequacy of the I n t e r n a t i o n a l Prototype nized.  In 1889  Michelson  standard  of l e n g t h .  Metre was  early  recog-  of l e n g t h .  be used as  However, when they observed  r a d i a t i o n w i t h t h e i r i n t e r f e r o m e t e r , they found i t to be the most complex i n nature. cadmium was  The  and Morley s t a t e d that the wavelength of  the intense green l i n e of mercury would probably ultimate  searching  On  this one  of  the other hand the r e d l i g h t  of  more n e a r l y homogeneous.  taken to set up the l a t t e r as a  the  Consequently steps were  standard.  N a t u r a l mercury c o n s i s t s of seven s t a b l e i s o t o p e s of mass  1 0  Au  Ci  o  l j o  290 1381  X/"  )70  kev .0156  i9%  iguro 1: A decay scheme f o r a o A u ^  199  80  .070 mev.  9 8  i!gl99  •osi\ Tr>n<A •mat/.  igure 2: A decay scheme f o r 7QAU199.  2. numbers 196  (0.15%), 198  (13.2$), 202  (29.6%),  (10.1$), 199  204  (6.7%),  (17.0^), 200  (23.3$), 201  The r e s u l t i n g i n v o l v e d  hyper-  f i n e s t r u c t u r e p a t t e r n s account f o r the complexity of the lines.  W.F.  Meggers '(2) was  among the f i r s t  observed  to suggest that i f  one of the even i s o t o p e s c o u l d be separated from the r e s t i n s u f f i c i e n t q u a n t i t i e s to make d i s c h a r g e tubes, the r e s u l t i n g green l i n e would be an e x c e e d i n g l y monochromatic r a d i a t i o n of high i n t e n s i t y .  He has f u r t h e r proposed that t h i s green  should supersede  the red l i n e of cadmium as the u l t i m a t e standard  of  length.  I t would seem that the method of equations  line  (1.1)  i s a simple and convenient means of a r r i v i n g at t h i s d e s i r e d result. The Hg  initially  prepared i n t h i s manner was  s p e c t r o s c o p i c a l l y pure, but the y i e l d was manufacture  of lamps.  insufficient  F o l l o w i n g World War  found to be f o r the  I I more e f f e c t i v e  neutron sources were a v a i l a b l e and lamps of .several types were constructed. 10^  L a t e r workers, u s i n g neutron f l u x e s as high as  neutrons per c m . ^ s e c , d i s c o v e r e d the presence of Hg- -" 1  i n minute and v a r y i n g quantities, and a s c r i b e d i t . to the presence of  platinum as an i m p u r i t y i n the g o l d  inum r e s u l t i n g i n Hg- -").  T h i s was  1  (neutron i r r a d i a t e d  plat-  a f a l s e c o n j e c t u r e however.  198 I f Au were to possess an extremely high neutron capture cross s e c t i o n , then the f o l l o w i n g r e a c t i o n s would occur: 79  /  f  t  -r  0  —>  ^  7?  a~ -^  #/"  /99  79  For  /  ?  f  *~  #  *y*-  l a r g e neutron f l u x e s the q u a n t i t y of H g  1 9 9  produced  in this  manner would become a p p r e c i a b l e . Hence d u r i n g the neutron i r r a d i a t i o n a branching process takes p l a c e , the amount of Hg  199  produced being dependent on the  f l u x and the Au  cross s e c t i o n .  r a d i a t i o n from A u " 1  i s shown i n F i g u r e  The h a l f l i f e  i s known to be 3.3 days.  The decay scheme  2.  We see then that an accurate capture  cross s e c t i o n of A u  1 9  ®  determination  to c o r r e c t l y i n t e r p r e t  the r e a c t i o n s i n v o l v e d i n g o l d t r a n s m u t a t i o n . i n t e n s i t i e s of the 0.159MeV J'-ray of A u 1 9 R  they were able to estimate  isotopes were produced.  4  the r a t i o i n which the two  "barns (1 barn  s  an estimate  10" cm. ). 24  l a t e r paper (5) H i l l mentions that t h i s value suggests 1.6 X 10^ barns to be more  By comparing the  and the 411KeV y-ray  1 9 9  This i n turn allowed  cross s e c t i o n as 3.5 X 1 0  of the neutron  is a problem of some importance.  H i l l and M i h e l i c h (4) were among the f i r s t  of A u  of the beta  2  appropriate.  the s e t t i n g up of a Fabry-Perot  able f o r h i g h r e s o l u t i o n i n t e r f e r o m e t r y . the i n t e n s i t y of a s p e c t r a l l i n e  of t h i s  etalon s u i t - .  I t i s w e l l known t h a t  i s d i r e c t l y p r o p o r t i o n a l to the  amount of the isotope g i v i n g the r a d i a t i o n . the h y p e r f i n e  In a  ha too h i g h , and  I t i s proposed here to combine a determination cross s e c t i o n w i t h  of the  Hence i f we r e s o l v e  s t r u c t u r e patterns due t o the mercury e x t r a c t e d  from neutron i r r a d i a t e d g o l d , and measure the r e l a t i v e  intensities  of the components due to each i s o t o p e , we o b t a i n the r a t i o i n which the two isotopes were produced.  T h i s i n t u r n allows the  c a l c u l a t i o n of the d e s i r e d cross s e c t i o n . The and  succeeding  chapters  w i l l d e a l f u l l y w i t h the theory  c o n s t r u c t i o n of the I n t e r f e r o m e t e r ,  the p a r t i c u l a r problem at hand.  and i t s a p p l i c a t i o n t o  4. CHAPTER I I : The yet one  Fa'bry-Perot  THE  THEORY OP THE  i n t e r f e r o m e t e r i s one  of the most elegant  c o n s i s t s e s s e n t i a l l y of two f l a t s separated  FABRY-PERQT INTERFEROMETER. of the s i m p l e s t  of a l l o p t i c a l instruments. plane-parallel partially  by a narrow a i r space.  and  It  reflecting  L i g h t i n c i d e n t on one  of  the p l a t e s s u f f e r s m u l t i p l e r e f l e c t i o n s i n p a s s i n g through the instrument,  and  the r e s u l t i n g emergent beams i n t e r f e r e  construc-  t i v e l y and d e s t r u c t i v e l y to produce a s e r i e s of c i r c u l a r f r i n g e s . The  sharpness of the f r i n g e s i n c r e a s e s r a p i d l y w i t h i n c r e a s i n g  r e f l e c t i v i t y of the p l a t e s . allows  Measurement of the f r i n g e diameters  the c a l c u l a t i o n of wavelengths.  With a s u i t a b l e choice  of p l a t e s e p a r a t i o n an extremely h i g h r e s o l v i n g power i s a t t a i n able . The gap  i n t e r f e r o m e t e r may  be such that the width of the a i r  i s a d j u s t a b l e by motion of one  or both p l a t e s , or more commonly  the p l a t e s are f i x e d and no change of s e p a r a t i o n The  l a t t e r type  i s c a l l e d the e t a l o n .  is possible.  The most common metals  used to gain high r e f l e c t i n g power are s i l v e r and  aluminum,  the l a t t e r e s p e c i a l l y i n the u r t t r a - v i o l e t r e g i o n .  The  ment i s u s e f u l w i t h i n the t r a n s m i s s i o n range of quartz  instru(approx-  imately 2 0 0 0 to 2 0 , 0 0 0 angstroms). The  theory of the instrument  l e l s that of K.W. S e c t i o n 1: Consider  Meissner The  given here most n e a r l y p a r a l -  (6).  Theory of the  Interference Fringes.  the txvo p l a t e s of the e t a l o n with  s u r f a c e s S, and  Sg a d i s t a n c e t a p a r t , and  reflecting  suppose a monochromatic  plane wave i s i n c i d e n t on S. as i n d i c a t e d i n F i g u r e  3.  F i g u r e 3 : The p r i n c i p l e of the e t a l o n . Each time the r a y s t r i k e s e i t h e r S, or S 2 i t i s p a r t i a l l y  ref-  l e c t e d and p a r t i a l l y t r a n s m i t t e d . . We w i l l n e g l e c t here the raysr e t u r n i n g to the f i r s t medium. successive  The path d i f f e r e n c e between  t r a n s m i t t e d beams i s the same.  d i f f e r e n c e l e t the angle  To evaluate  this  of i n c i d e n c e be •©• and take the r e f r a c t i v e  index  of a i r to be u n i t y .  Then LM i s p a r a l l e l t o the o r i g i n a l  ray.  The path d i f f e r e n c e between rays 1 and 2 , d, i s given by  s i n c e the waves a t M and Q are i n phase. From the f i g u r e we see that  If X  be the wavelength of the I n c i d e n t l i g h t  the phase d i f f e r e n c e  between r a y s , denoted by p, i s given by  Equation  (2.2)  does not account f o r the p o s s i b i l i t y of a phase  change due to r e f l e c t i o n at the metal f i l m s .  This e f f e c t i s  g e n e r a l l y small however ( 6 ) and w i l l be n e g l e c t e d By equation phase d i f f e r e n c e .  (2.2)  the angle  here.  of i n c i d e n c e Q determines the  The aggregate of a l l rays i n c i d e n t at 0 w i l l  form a c i r c u l a r r i n g of phase p on l e a v i n g the e t a l o n .  Since  in an extended source a l l angles of incidence are present, there is a continuous change of phase across the resulting pattern. If p i s such as to give constructive interference we get bright c i r c l e s ; f o r destructive interference we get dark c i r c l e s . We w i l l now develop a quantitative expression for the intensity d i s t r i b u t i o n i n the interference pattern. The incident wave, i f taken to be of unit amplitude may be represented by the real part of JL and T i s the time.  , where zrr i s the frequency of the l i g h t I f R and T are the fractions of the  incident l i g h t reflected and transmitted respectively by each f i l m , then the i n t e n s i t i e s of successive emergent trains are T , R T , ... R2(k-1) 2 ( 2  2  2  T  f o r  t h Q  l 3 t )  2nd, ... k th t r a i n s ) .  The corresponding amplitudes are then T, RT, R T^.--,Since between 2  each of these there i s an increase in phase angle of p, the emergent waves may be represented by the r e a l parts of Te RTe  , ... R  ^Te  .  ,  The sum of these p a r t i a l  vibrations w i l l y i e l d the resulting v i b r a t i o n .  If there i s an  i n f i n i t e number of these emergent t r a i n s , as i s the case i n practice for r e l a t i v e l y large diameter plates and small separat i o n , then the resultant wave of amplitude A is given by rl~*  -  Tie  <?  £  (Note, however, the discussion on page This becomes: ...  and hence  st<+> t  ^  Jl  7  .)  7.  The  observable i n t e n s i t y I i s equal to AA , where A i s the complex  conjugate  of A.  Therefore  , jzl  and. by s u b s t i t u t i n g  Equation beam i n c i d e n t  cos p =/- 2.  *  ^  >  (2.4) holds f o r an i d e a l case. a t angle &, a s h i f t  decrease  This r e s u l t s  for a  of Zt tan & across the p l a t e  occurs a f t e r each r e f l e c t i o n and u l t i m a t e l y are l o s t .  Actually,  i n a broadening  some o f the beams  of the f r i n g e s  i n i n t e n s i t y i n the outer r i n g s .  and a  To take the e f f e c t  i n t o account each term i n the preceding summation should be multiplied  by a c o r r e c t i o n  now be f i n i t e .  f a c t o r , and the number of terms w i l l  Such a c a l c u l a t i o n  e t a l o n by Geiger  has been made f o r a square  ( 1 5 ) , and h i s r e s u l t s  show that  f o r small  plate  s e p a r a t i o n s and r e f l e c t i v i t y of 80$ the e f f e c t i s n e g l i g i b l e . Prom equation  which occurs f o r of equation  (2.4) we get f o r the maximum i n t e n s i t y  T T  -^f" =•  = o, j •••) . y  (2.2) t h i s leads t o  Using the value of p  X ~  For values of ©'satisfying  (2.6) a b r i g h t  tis- i s c a l l e d the order of  interference.  Q fringe  (l-O  results.  The minimum i n t e n s i t y i s given by which occurs f o r fy^ =•  a dark f r i n g e  results.  intensity varies equation  (2.4).  +1 )n  =»,/...)•  Therefore i f 0- s a t i s f i e s  Along a diameter of the p a t t e r n the  between these two extremes a c c o r d i n g t o  8.  Rewriting  and  equation  (2.4)  thus:  denoting by P the q a n t i t y  V^/h-a)  >,'  1  we  get  Note then that the sharpness of the f r i n g e s and  the r a t i o ^ o f  maxima to minima are determined by F, the " c o e f f i c i e n t P i n turn depends s o l e l y upon R, The  f r i n g e sharpness increases  dicated i n Figure  °£ Imin i -  3  4. m  as a f u n c t i o n of R.  n  (R+T)- 1 and  i d e a l case  cident l i g h t  intensity.  I ax  x  e  The  does not r e s u l t .  S e c t i o n 2:  The  From equation so p d e c r e a s e s .  n  p r a c t i c e because of  considered a trans-  s i n c e i t has  a large  absorption  (7).  Half-Width.  (2.2), as & i n c r e a s e s , cos & decreases,  Hence the order  of the  ab-  I t i s f o r t h i s reason t h a t s i l v e r i s  Fringe  and  of i n t e r f e r e n c e i s g r e a t e s t  at  pattern.  d e f i n e the h a l f width of a f r i n g e as the width at h a l f  the maximum i n t e n s i t y .  Suppose we  consider  1 at t h i s p o i n t , i . e . , '£ i s the value We  i  of R so that too low  c o e f f i c i e n t throughout t h i s r e g i o n  We  s  i s the same as the i n -  e q u a n t i t y A must always be  seldom used i n the u l t r a v i o l e t  centre  3  1^^  m  i n determining a f e a s i b l e value  the  value  by the metal f i l m , i . e . , R+T*A= 1 where A i s the  sorption c o e f f i c i e n t .  mission  The  given as a percentage of I^ax*  In the  absorption  coefficient.  r a p i d l y witto. i n c r e a s i n g R i n -  5 i s a p l o t of 1 ^  Figure  the. r e f l e c t i o n  of f i n e s s e " .  get from equations  [2.$,) and  J1  .  A.  =  (2.9)  the phase d i f f e r e n c e  of p v/hen I  =  « Imax*  fraction  Figure  of order  4; Dependence o f i n t e n s i t y upon R , ( 7 ) . .  distribution  Figure 5: Dependence of I  m i n  on R (7)«  9.  V» - *  At the maximum  Hence  giving  y  =  2  _  x*^v  T  n  .  , and so, f o r % we may  write  (^-zr + * J ^  ^  .?  J  V  T h e o r e t i c a l l y equation  0?- ^ /  (2.12) allows  the determination  R, the r e f l e c t i o n c o e f f i c i e n t of the p l a t e s .  Remembering  of that  the phase d i f f e r e n c e between maxima i s Z TT we may measure x and c a l c u l a t e R.  In p r a c t i c e the method i s l i k e l y to be u n r e l i a b l e  because of f r i n g e broadening clue to temperature change, and other  causes. S e c t i o n 3:  The R e s o l v i n g  Power of the E t a l o n .  The r e s o l v i n g power of any spectrograph i s d e f i n e d by  1  -  where  2) X  (  _  i  V AV  -  A\  s  '  the s m a l l e s t  (wave number) that can be r e s o l v e d .  change i n wavelength  Prom equation  (2.6),  since  cos & i s approximately u n i t y f o r the e t a l o n , M  A  = F  d e f i n e s a v a r i a b l e order M. D i f f e r e n t i a t i n g , ,  and  since  then Following  1  _ A  M  _-  Valasek  M_  ^ TT ^ /  Z  7  R  •  (8) i t i s concluded that two maxima are j u s t  r e s o l v a b l e when they cross a t 1= 0.405 l  m a x  «  the phase d i f f e r e n c e at t h i s p o i n t , equations  I f (j^ TT ty)  is  (2.5) and (2.9) give  10.  7  7 The  0.36?  C/-*) '  1 ~*  change i n phase d i f f e r e n c e "between the two j u s t  maxima i s  2 A*  resolved  , and so the r e s o l v i n g power becomes  *• -  /^/*  Since M i s p r o p o r t i o n a l to t the r e s o l v i n g power i n c r e a s e s  with  i n c r e a s i n g s e p a r a t i o n of the p l a t e s . We may note here t h a t i n p r a c t i c e an estimate ing  of the r e s o l v -  power i s given by  where n i s the number of e q u i v a l e n t beams forming the i n t e r f e r ence p a t t e r n . Section 4 :  The I n t e r o r d e r  Suppose two wavelengths  Separation.  X/  a n (  give r i s e to i t s own r i n g system. coinci-de, and as  IX * ~ <^/)  + /)  due to  X z  <A? rQ a  present.  Each w i l l  I f X, = ^ , t h e two systems  i n c r e a s e s the systems  u n t i l the r i n g of order m due t o order  i  .  diverge  X c o i n c i d e s w i t h the r i n g of t  This value  of \X ~ K  X/I = &X i s  c a l l e d the i n t e r o r d e r s e p a r a t i o n . If m  0  be the order of i n t e r f e r e n c e at the centre  of the  p a t t e r n where Q- o° then X=  Differentiating, ^ *  c  X ~  ~~~zz—  -—  ' .  (neglecting the s i g n ) .  .  11. This l a s t For  will  be t r u e a t o r n e a r t h e c e n t r e  t h e i n t e r o r d e r s e p a r a t i o n 2Sfm = 1 s o t h a t  • ^  AXIn terms  o f wave number  Section  5:  ,  Observations.  that  ^ a t the centre  X-  (i.O  0  2*  o f the p a t t e r n  X These g i v e  of  u.»>  y  v=  Reduction  We have s e e n  and  -  2  A  •  the r e l a t i o n  6 and  since & i s i n general  /~ The  =  by a l e n s  th fringe  (/-  0  T  J •  (p.H)  Again, ind  So  where  '""•Jl  D  u  the o r d e r  I s some p o s i t i v e then  ~  becomes o (/~  diameter o f the  =  g^*. )  ( ^  a t the centre fraction  e  £. .  a n d so t h e c e n t r e  i.e:  Substituting  ^  -  0  ,  >  of the k t h r i n g .  *v. '= ">»«•/ /• £  (k-1) o r d e r s ,  orders,  this  i s the order  Rearranging,  fringe,  l e n g t h f , the l i n e a r  - /*~* •  f o r s m a l l &,  In g e n e r a l  and i f b r o u g h t t o  i s determined by  %  by  s m a l l we may a p p r o x i m a t e b y  of focal  D  hut  ^  t  i n t e r f e r e n c e r i n g s a r e formed at i n f i n i t y  a focus k  o f the system.  0  - sr^^)  U./7)  .  o f the p a t t e r n I f m,  i s not i n t e g r a l ,  i s the order  The f i r s t exceeds  ring  exceeds the k t h  t h e k t h by • •  i n equation  (2.17),  o f the f i r s t  (£#k-l)  S i m i l a r l y we c o u l d g e t  S o l v i n g between t h e s e ^ t w o e q u a t i o n s  Note h e r e jacent By  t h a t t h e d i f f e r e n c e s between t h e s q u a r e s  diameters  averaging  i s c o n s t a n t , and i s i n f a c t  these  Plence a l e a s t  Such a c a l c u l a t i o n results Let  of t h e i r  only the f i r s t  squares  and l a s t  be b r i e f l y  fringes are  (9) and the  s e t down.  the constant d i f f e r e n c e  " v = %~  denoted  by N.*^- Then e q u a t i o n  0  (2.18) g i v e s  etc.  A a. + a. /  Applying  t h e method o f l e a s t  a and b a r e :  where  =^  ^  squares  the normal equations i n  /•  ^  When s o l v e d f o r a a n d b e t h e above e q u a t i o n s  i s not  of € i s necessary.  has been made b y R o l t a n d B a r r e l l  p  be  o f "S b u t t h i s  determination  investigations w i l l  of ad-  g i v e n by  d i f f e r e n c e s we g e t a v a l u e  a c c u r a t e .since i n a c t u a l i t y utilized.  f o r 6,  lead to  13. and  find for 6  f i n a l l y we  7J-  6-  *  e  the  S  -  ^  £  Section 6 :  The  Rectangular A r r a y of Tolansky.  S. Tolansky  (7)  has  d e v i s e d an extremely u s e f u l method f o r '  c a l c u l a t i o n of s m a l l wavelength d i f f e r e n c e s (such as a r i s e  i n hyperfine  s t r u c t u r e ) from measurements of the f r i n g e diameter®.  Suppose two wavelengths being  }>., and  / l ^ a r e present,  X,  components of a s i n g l e l i n e as i n h y p e r f i n e  Then f o r  X,  ,  * and  A  similarly for  =  i t - * * ,  by only about one  of the  structure.  p a r t i n 50,000 and  then  0 j L t  6  6  >  order of 50,000 they d i f f e r so we  are the f r a c t i o n a l p a r t s f o r  and  X *  Xa$?  a n d a r e  I f £, and  ^  4  * - />;  Since both  an<  '  >  -  X/  and^respectively  '  ^  Subtracting:  w r i t e N-^Ng^N.  ;  M  =  may  4  *.  >  x  ^ Since  ^  then  u  =  °= Z * V ,  - v , =  - ^o'J/j.  0  y  Prom equations is a  (2.20) and  y  (2.21) i t f o l l o w s that  D  x+/  -  P  J k t /  constant. Prom these  array.  Let  p r o p e r t i e s we  may  c o n s t r u c t the  rectangular  components of the p a t t e r n he a, b, c, ....  and  ~  sr*  14. the corresponding  diameters be D^ ,  D  a  i s shown i n F i g u r e  ^  e  a  r  r  a  v  6. RIN6-  NUHteM  3  2  /  V  N  N  a.  iv  /2  Jr  0*4.  A/2  DyJ.  3  ti  A/13  Nix  F i g u r e 6:  3V  The r e c t a n g u l a r a r r a y ( 7 ) .  In the f i g u r e a l l values averaged.  k c ' '**  of  should be the same and are  A l l < r y ^ i n a h o r i z o n t a l row should be e q u a l .  The  wave number s e p a r a t i o n between i n d i v i d u a l components i s given by v  Section 7 : The  ~  v  +  *  1 2 % '  The E t a l o n  (.*•>*>  Thickness.  order of i n t e r f e r e n c e of the f r i n g e s i n the p a t t e r n , and  the t h i c k n e s s of the e t a l o n , may be determined f a i r l y  readily  by the method of exact f r a c t i o n s , as d e s c r i b e d by Candler (10). The  two p r e - r e q u i s i t e s are t h a t the wavelength of the l i g h t be  known, and that the t h i c k n e s s be known w i t h i n the accuracy micrometer measurement.  The method allows  of a  the determination  of  the width of the a i r gap to b e t t e r than one part i n 1 0 . 8  The  f r a c t i o n a l parts f o r three or f o u r known l i n e s of the  spectrum are f i r s t  c a l c u l a t e d by the method of S e c t i o n 5.  Suppose the e t a l o n t h i c k n e s s by micrometer measurement i s t-j_. Then the approximate order of i n t e r f e r e n c e f o r the centre of the pattern due to  X, i s ~  The be  exact  A,  f r a c t i o n S , i s known so that the p r e c i s e order must  ( / w , / ^ ^  x ,  where X i s an i n t e g e r .  wavelengths are known, i . e .  2  -  Since the r a t i o s of the —  ;  etc.,  15. then f o r each o f the above p o s s i b l e orders the orders of the other l i n e s may be c a l c u l a t e d .  F o r only one of these  will  the values of the f r a c t i o n a l p a r t s agree w i t h the measured v a l u e s , and so the p r e c i s e order i s o b t a i n e d .  The value of  X above may be made s m a l l by a p p r o p r i a t e choice of the l i n e s . The  e t a l o n t h i c k n e s s i s then e v a l u a t e d from the r e l a t i o n  sm» X =  •  Using t h i s c a l c u l a t e d value of t , we may go  back and improve the p r e c i s i o n i n the wavelength values t o b e t t e r than  0.0005 angstroms.  Correspondingly  the absolute  wavelengths of any l i n e s of the spectrum may be obtained from measurements of t h e i r f r a c t i o n a l p a r t s .  In Chapter VI the  method i s used to e v a l u a t e some wavelengths i n the spectrum of Hg  1 9 8  .  16. CHAPTER I I I : Section  1:  It-has structure ween t h e on  one  GENERAL THEORY Multiplet  long  of  since  Structure  been  established  s p e c t r a l l i n e s i s c a u s e d by  emission  electrons.  a n o t h e r due  both to  l a r momenta.  Associated  resultant and  ^  only  case  of  one  intrinsic  not  orient  values  Note t h a t  and  a spin.angular  electron  spectra  themselves  of the  f o r j' >  according  spin,  j  to the  orbital  j  •  and  = (J**)/  jt=  tively,  o,  For  (s m e a n i n g 1=  side the  the  closed  orbital  of  are  , a  quantization  J.  set  of  discrete • the  values  respectively  >  —*  s but  standard  3,y,-->  quantum number  angu-  combine t o f o r m  quantum m e c h a n i c s  _>  hence the  Conforming to which  I s an  > '••  r e s u l t s of  the  orbital  (  same 1 and  e n e r g y , and  and  a r b i t r a r y d i r e c t i o n , hut  t o t a l moments a r e  —*  erent  forces  momentum v e c t o r ^  Because  i n any  bet-  strong  and  these  17(177)  Atoms w i t h t h e  exert  spins  in certain discrete directions, giving a  possible  multiplet  interactions  w i t h each such e l e c t r o n  a n g u l a r momentum v e c t o r  may  the  gross  their electrostatic repulsion  a n g u l a r momentum v e c t o r J, f o r the  the  These e l e c t r o n s  m a g n e t i c moments r e s u l t i n g f r o m  and  that  d i f f e r e n t j have s l i g h t l y  splitting  of  spectroscopic  the  o must n o t  he  levels arises.  nomenclature  c a l l e d s,p,d,f,g  diff-  ...  states  c o n f u s e d w i t h the  states  for  respecspin  s.)  case  o f atoms w i t h two  shells,  an  a n g u l a r momentum o f  ~j£  and  the  an  atom as  or more v a l e n c e i s associated a whole  i s the  electrons  with each, resultant  outand of  the o r b i t a l s and s p i n s of e a c h e l e c t r o n . I t i s p o s s i b l e to form t h i s r e s u l t a n t i n many d i f f e r e n t w a y s . Since Russell-Saunders  17. or  (LS) coupling presents  coupling of h y p e r f i n e  some c l o s e a n a l o g i e s w i t h the  s t r u c t u r e , we  (JI)  s h a l l d i s c u s s only i t here.  Under t h i s scheme the c o u p l i n g of the e l e c t r o n spins predominates and  i s too strong to be much i n f l u e n c e d by the  momenta.  Hence the y*^ of the i e l e c t r o n s may  -»  -»  which i n turn couples  very s i m i l a r to the preceding values  be combined to  ~*  —>  L  angular  S i m i l a r l y the U^- form  form a r e s u l t a n t S, the s p i n of the atom. a resultant  orbital  with  case of one  —>  S  to produce -J"  electron.  Again,  of J are l i m i t e d to j=  where now  U + s),  b  i  [L+  J  . . .  S-/),  U-Sl  • • •  As b e f o r e , L = 0 , 1, 2 , ... are termed S. P. D.  ... s t a t e s .  An e l e c t r o n i n a p a r t i c u l a r s t a t e c h a r a c t e r i z e d by values  of L, S, J may  not r e l e a s e energy and  other s t a t e without e x c e p t i o n .  ±'>  a  ( J  o-fr  J  .  type of  coupling,  rule for dipole r a d i a t i o n .  i s a s p e c i a l r e s t r i c t i o n i n (LS)  In general too only those t r a n s i t i o n s occur e l e c t r o n a l t e r s i t s value i n d i c a t i n g t h a t the  0  f o r which:  (L--0-^>o).  This i s the Laporte S - o  =  i s true f o r any  A L = ± / j O  (c)  any  Only those are allowed  o  This i s q u i t e g e n e r a l and (b)  pass over t o  A number of s e l e c t i o n r u l e s  govern the p o s s i b l e t r a n s i t i o n s . ()  the  of 1.  coupling  Rule  coupling.  f o r which a s i n g l e  (c) i s sometimes v i o l a t e d ,  i s not pure Russell-Saunders.  example of t h i s i s the mercury resonance l i n e of wavelength angstroms, which i s due Here  to the t r a n s i t i o n  *>» ~  6  -°-  An 2536 r  *  2) The  value  (Z$ + 1) i s c a l l e d the m u l t i p l i c i t y of the term  gives the number of p o s s i b l e values  and  of J providedZ >JT i n which case  i t a l s o g i v e s then the number of components i n the term  splitting.  18. —>•  t h e e n e r g y W(j s)o£  Consider Z. •  This  where A  i s given  the i n t e r v a l  model and the s t a n d a r d  I f now  we  consider  immediately  This  etc.),  interval  components  gives  this  rule,  becomes  i s p r o p o r t i o n a l to the h i g h e r o r qa an turn w e i g h t . o f  The d e g e n e r a c y i s t h e n  Section  2:  types  Structure.  of h y p e r f i n e  structure  in line  s p e c t r a a n d we  a level  i s (2J+1) describ-  (2J+1) a n d may  (Zeeman  Hyperfine  between  J value.  eigen-functions  removed by a p p l y i n g a m a g n e t i c f i e l d  hfs) occur  find  that the s p l i t t i n g  t h e number o f i n d e p e n d e n t  i n g the s t a t e .  Two  the v e c t o r  s t a t e s L, S, J a n d L, S, J - l we  The s t a t i s t i c a l and  .Using  that  i s t h e Lande  adjacent  factor.  s u b s t i t u t i o n s o f quantum m e c h a n i c s  by S ( S + l ) ,  2  between 5 a n d  by  is called  (replacing S  the'coupling  J  be  effect).  (hereafter abbreviated  shall  consider  these i n  turn. (a)  Isotope  The e f f e c t is  first  with  nucleus  of adding  considered.  rip  i 0  with  one o r two n e u t r o n s t o a  In o u r p a r t i c u l a r  an admixture  has a s p i n o f •§• u n i t  m u c l e a r magnetons, hfs.  Effect.  of  ID"/  case  we *  nucleus  are d e a l i n g ^  E  letter  and a m a g n e t i c moment o f /0.504  and t h e r e f o r e d i s p l a y s regular m a g n e t i c  One m e a s u r e s an I s o t o p e  shift  by m e a s u r i n g t h e d i s p l a c e -  19. ment of the  centre of g r a v i t y of t h i s h f s . l i n e  r e l a t i v e to the s i n g l e l i n e a r i s i n g f r o m ^ / Z ^ s h i f t due  t o the a d d i t i o n of two  neutrons,  pattern •  The  isotope  such as i s observed  between the n a t u r a l l y o c c u r r i n g even-even mercury i s o t o p e s Hg" *^, H g ^ , Hg^S 1  2 (  spacing one  r e s u l t s , as i n g e n e r a l , i n a r e g u l a r  i n the l i n e s due  t o these  isotopes.  observes t h a t the a d d i t i o n of but  i n .less than effect cases  a h a l f the s h i f t due  one  to two  Also i n general,  neutron neutrons.  i s r e f e r r e d to as "odd-even s t a g g e r i n g . " the  isotope s h i f t  results This  In  i n c r e a s e s i r r e g u l a r l y , and  special this  has  been r e l a t e d to s h e l l model s t r u c t u r e . In d e s c r i b i n g the observed i s o t o p e s h i f t s emphasize that the two  one  must  term systems are q u i t e d i s t i n c t ,  f u r t h e r t h a t i t i s a matter of d e f i n i t i o n whether one (a) the  same r e l a t i v e term values  s t a t e s , or whether equal to zero two  (b) one  s e t s the  (uses a b s o l u t e  schemes (a) and  d i f f e r e n t ways.  to the two  term v a l u e s ) .  (b) d e s c r i b e the  It i s apparently  assigns  corresponding ionization  —  ground  limits  Obviously  the  same p h y s i c a l f a c t i n  qinlte p o i n t l e s s to  say  that the h e a v i e r i s o t o p e i s s h i f t e d up unless  one. f i r s t makes  c l e a r which convention  compilation  due  i s b e i n g used.  In the  to B r i x (used here i n subsequent c a l c u l a t i o n s ) scheme  (a) i s u s e d . The  i s o t o p e e f f e c t a r i s e s from a m u l t i p l i c i t y  of which the  c h i e f kno?m  volume e f f e c t , considered The  ones are  (1) mass e f f e c t ,  (3) p o l a r i z a t i o n e f f e c t .  These are  of causes (2) briefly  i n turn.  c o r r e c t i o n , a p p r o p r i a t e f o r the two  body problem,  20. w i t h n u c l e i of mass M and M>0M i s w e l l known, and enlarges the term system of the h e a v i e r nucleus by the f a c t o r (1+-^) • As w e l l as t h i s "wobbling nucleus" "specific effect" first (16) f o r l i t h u l m . is  effect  there i s a f u r t h e r  c a l c u l a t e d by Hughes and E c k a r t  A d e t a i l e d p e r t u r b a t i o n method c a l c u l a t i o n  necessary. The  isotope  volume e f f e c t a r i s e s from the f a c t that the h e a v i e r i s generally larger.  In the case of p e n e t r a t i n g  e l e c t r o n s t h i s w i l l i n c r e a s e the o v e r l a p between and  nuclear  e l e c t r o n i c wave f u n c t i o n s i n the h e a v i e r nucleus,  reduce the b i n d i n g energy o f the terms a r i s i n g from ing electrons  (17).  and so penetrat-  T h i s phenomenon has been e x p l o t e d by  Kopferman i n c o n f i r m i n g  some p r e d i c t i o n s of the n u c l e a r  s h e l l model ( 1 8 ) . . The e f f e c t of p o l a r i z a t i o n has a l s o been t r e a t e d by Breit  (19), but the e f f e c t s o f nuclear mass and volume are  so dependent on n u c l e a r and e l e c t r o n i c d e t a i l s that no v e r i f i c a t i o n has been w e l l enough made to say whether i t i s measurable. (b)  Nuclear Spin;.  Just as f o r the e l e c t r o n s we assume that the nucleus of an atom has an i n t r i n s i c angular momentum o r s p i n w i t h which i s a s s o c i a t e d a magnetic moment.  This n u c l e a r magnetic  moment i n t e r a c t s w i t h the magnetic moment due t o J" to give a f u r t h e r s p l i t t i n g of the energy l e v e l s .  Since  the magnetic  moment v a r i e s i n v e r s e l y as the mass the n u c l e a r magnetic moment i s much s m a l l e r than that due t o the e l e c t r o n s , g i v i n g a much s m a l l e r , or h y p e r f i n e ,  splitting.  An exception t o  21. this is  general  of  the  moments  and  same  are  The  of  the  "3, t h e  and  (F=0-*0 i s V^zvj  where  now  the  hfs. is  may of  first  /I /  =  as  the  hoth (20).  before to  the  for  a  (nucleus  which 2iF*£l,0  coupling  - *l<r+0 -  is  factor.  The  the  a n d may  be  7  /  by  {*  splitting  higher  quite  given  2(2+/)  ~J  to  form  atom  approximation,  proportional  L  (JfI),(J+I-l),  occur  r ftf"J  interval  since  combine of  values  energy a  I  momentum  transitions The  Just  J and  the  splitting  (Bohr magnetons)  Russell-Saunders coupling holds  value  F  rigorously  in  cases. intensities  multiplet rule  are  which  lines  of  final  (2Fy-l)  states  a  the  that  is  The  3: now  go  prominent  interested  here  a n d 199  in  number  possible  values  then  !-=• 0 F may  for  the  the  or  which  on t o  lines only  ?  of  the F are  the  the  the  In  mercury  the  two  isotopes  same  detail  all  the  initial weight  has  governed  a  of  spin  b y F= the  one  the  spectrum.  0.  all  are  weights nuclei  Since  (J*I), value  hfs.  We  atomic  accordance with  only  of  sum  Mercury.  the  acquire  hyper-  respectively.  of  former  a  statistical  state of  to  investigate  In  of  intensities  belong to  final  Spectrum  components  Burger-Ornstein-Dorgelo  sum o f  respectively.  even mass  various  proportional  initial  We s h a l l more  the  hypermultiplet  state  of  of  governed by  Section  198  take  to  components  The  the  F may  the  structures,  b y 7.  s o now  angular  TF  1  A is  since  J ,  total  those  denoted  to  between  most  /f 2  p o s i t r o n i u m where  multiplet  is  forbidden).  =  reduced  only  in  same m a g n i t u d e  form  electrons).  fj-lj,  as  spin  S combined to  plus  of  occurs  order  nuclear  resultant  or  rule  the [J-lJ,  F«J.  Hence  of  S)  .  22. there i s no s p l i t t i n g of the Hg-'-  98  terms.  The second isotope  has a n u c l e a r s p i n o f |r and so by a s i m i l a r nreasoning are two p o s s i b l e values o f F, namely F=J£-§-. the H g  there  Consequently  terms w i t h J=0 are s i n g l e , and a l l other terms are  1 9 9  doublets.  F o r some of the l i n e s there i s a s h i f t  of the H g  component r e l a t i v e t o the centre of g r a v i t y o f the H g ^ s t r u c t u r e because of the isotope Consider  1 9 8  9 9  effect.  the s p e c i f i c example of the well-known green  l i n e of v/avelength 5461 angstroms, which i s due t o a t r a n s i t i o n  3 from a  3 S, t o a  P  0 a  state.  q u e s t i o n B r i x and Kopferman +718.5 and +303.6 cm. '  For the p a r t i c u l a r terms i n (13) give as i n t e r v a l f a c t o r s  r e s p e c t i v e l y f o r the H g ^  9 9  isotope.  Furthermore the i s o t o p e s h i f t s are 0.004 cm."" f o r t h e S , 7  ?  y  3 term and 0 f o r the  P  o  a  term.  Using  t h i s data we may c a l -  c u l a t e the a c t u a l s p l i t t i n g t o be observed, energy l e v e l diagram of F i g u r e 7.  i n d i c a t e d i n the  The t r a n s i t i o n s  allowed  by the s e l e c t i o n r u l e s are shown. 'When t h i s l i n e i s vie?/ed w i t h a spectrograph  i t s appear -  ance w i l l be as d e p i c t e d i n F i g u r e 8. The  s t r u c t u r e s o f a l l other l i n e s i n the spectrum may in  be found^an analagous manner. 32 l i n e s  This has been done f o r some  c o v e r i n g the wavelength r e g i o n from 2536 to 6716  angstroms, and these are t a b u l a t e d i n Appendix I I I . a l l cases  In  the i n t e r v a l f a c t o r s and isotope s h i f t s are those  of B r i x and Kopferman ( 1 3 ) . S e c t i o n 4: According  The D i s i n t e g r a t i o n E q u a t i o n s . to the well-know  theory of r a d i o a c t i v e decay  the number of atoms N e x i s t i n g a f t e r time t i s given by  TV  1  0  9  rig- - - ^ 1  1  3  ;s7s  S,  /„  + 4 -  - 7It.f  7  o  'igure 7: Energy l e v e l diagram showing Hg l i n e 5461  the h f s . of the  199 199  198 1 \ 1  1W  199  1  9  1  "*  KID"  -ZS9.6  s \+S9.J  + 818-S  o »  V  Figure  0:  Schematic drawing of the h f s . of the  l i n e  5461  A.  23.  . where Ne and X ing The of  tf*  /Vo  i s the  number o f atoms p r e s e n t a t t i m e  i s the decay  per u n i t  half-life T  constant or f r a c t i o n  ~  we  the  L the  case  JU. ~  an  is called  imaginary  such that reaction  ing In  ,  (j.rj  o f t r a n s m u t a t i o n by p a r t i c l e  The  entity  "cross Section."  bombardment  may  measure  chosen  I t g i v e s the  passes  our p a r t i c u l a r  nucleus  i t does n o t . . I t s v a l u e  i s measured i n " b a r n s " c a s e we  area  t h r o u g h i t the  the r e a c t i o n and upon t h e e n e r g y and  of the /o  (1 b a r n =  are d e a l i n g w i t h the  bombard).  "neutron  c r o s s s e c t i o n " , w h i c h measures the p r o b a b i l i t y  a target nucleus w i l l  the  for this  c i r c u l a r d i s c a s s o c i a t e d w i t h each  takes p l a c e ; otherwise  particle,  capture  the  is  .  ^  i f the b o m b a r d i n g p a r t i c l e  depends upon  decay-  to decay.and  J  amount o f m a t e r i a l t r a n s f o r m e d .  of  time  require some q u a n t i t y by means o f w h i c h we  purpose  o f atoms  time r e q u i r e d f o r o n e - h a l f  the a c t i v e m a t e r i a l p r e s e n t a t any  For  t=o,  time.  i s d e f i n e d as  g i v e n by  9)  (s.  J *  capture a neutron  from  the  that  incoming  flux. C o n s i d e r then of  slow  neutrons.  product elements,  a q u a n t i t y of TiFe w i s h t o c a l c u l a t e  t.  The  flux  the amounts o f t h e  as r e p r e s e n t e d by e q u a t i o n s  ( 1 . 2 ) , p r e s e n t a f t e r a time be  subjected to a  following  (1.1)  and  notation w i l l  adopted: cr^ = n e u t r o n A j \  =  decay  capture cross  section  constant  number of atoms p r e s e n t a t time  t where  i=$,g,S,4»:.  i  24. for the elements A u Note that X  o  cr  1 9 7  -  x  , Au  X  =  3  , Aul99, H g  1 9 8  X  V  "  , Hg  1 9 9  respectively,  *  - <T - <7~j, ^ 0  effectively .  3  Let the neutron flux he F.  1 9 8  Then we may write <r.s  Equation  fro  (3.6) expresses the fact that the increase i n the  number of atoms of Au  ' per unit time i s the product of the  probability an atom w i l l capture a meutron, the number of neutrons, and the number of atoms.  M - v . n r dt  S i m i l a r l y we may write  (* 7J  - X,AJ,  = y, 07 f  - X x A/3.  (S-fJ  d^L = X, A/,  (V J  This i s a set of r e a d i l y soluble l i n e a r d i f f e r e n t i a l  equations.  o  At time t=o, N equation  0  « N  say, while % =  Q  o (i=l,2,3,4).  Hence  (3.6) gives immediately -  Mo  -  *^  je  M  0  (?//J  Rewrite (3.7) thus:  ^  An integrating factor i s  JI  . Multiplying by  this factor and rearranging, ^  / * ( * • ' +  y  )  [A,*  rCep-njJJ-  which leads to  Analagou3ly, equations A ,  f-ofk'cr,  (3.8), (3.9), and (3.10) give:  n-nxt  -CXiJhfU  ^7  /,  . i  -  N V  £  X  F  X  r /  '  (  r  '  ^  2  f  « \  —  1  ,  /  f  r  f  ,  /  -CI,**  )]  ^  r  )  - ( \ + * i r ) \ ( • *  {[A,  ~ A, *• /=(*7-i)  5  —f  J  - //  t  The e v a l u a t i o n o f i r , i s t o be made by measuring the r a t i o ;  -i  of the amounts of H g  no  X i ?  199  ° and Hg  produced.  Immediately  a f t e r a c t i v a t i o n f o r a time t the r a t i o A u - ^ ^ A u the r a t i o H g  1 9 9  : Hg  equations above.  1 9 8  1 9 8  , or  , may be found from the a p p r o p r i a t e  I f these measurements are not made immed-  i a t e l y a f t e r e x t r a c t i o n from the f l u x , the r a t i o s w i l l due  change  to the d i f f e r e n t decay r a t e s of Au-*- and Au- - . The 98  f i n a l r e s u l t becomes very  1  99  unwieldy.  Consider an a l t e r n a t i v e and much more convenient  form.  We are d e a l i n g e s s e n t i a l l y w i t h a branching process which may be w r i t t e n s y m b o l i c a l l y as f o l l o w s :  I  i  u  U  (s. n)  iff  198  The  two competing processes  i n the r a t i o  ~X7  *^ t  1 9  f o r Au D r a n  t r a n s f o r m a t i o n occur  °hing ratio."  I f now the  r a t i o Hg- - : Hg^" be measured at such a time t h a t a l l a c t i v i t y has ceased, then the r e s u l t i s p r e c i s e l y 1  99  98  Jfi'" since a l l A u  1 9 9  formed decays to Hg- - . 1  99  The values o f A/  and P being a c c u r a t e l y known, we may c a l c u l a t e measured r a t i o o f the mercury Isotopes.  v, , from the  26. CHAPTER IV:  THE APPARATUS.  S e c t i o n 1:  The C o n s t r u c t i o n of the E t a l o n .  Fabry-Perot  I n t e r f e r o m e t e r s are g e n e r a l l y designed  with  e i t h e r a constant plate s e p a r a t i o n o r a v a r i a b l e gap, the two types being e q u a l l y common.  The l a t t e r has the obvious ad-  vantage of ease In the adjustment of i n t e r o r d e r s e p a r a t i o n and r e s o l v i n g power; the former has the advantage of s t a b i l i t y a prime requisite f o r l o n g exposures.  The e t a l o n c o n s t r u c t e d  here has a constant p l a t e s e p a r a t i o n , but the d e s i g n i s such t h a t the spacer may be removed and another  of d i f f e r e n t  l e n g t h s u b s t i t u t e d w i t h comparative  Hence the c h i e f  ease.  advantage of the second type i s not completely The housing  lost.  f o r the e t a l o n Is a t h i c k - w a l l e d brass  c y l i n d e r of i n n e r diameter  7cm. and l e n g t h 12 cm. w i t h three  p r o j e c t i n g studs p l a c e d symmetrically around one end. This c a s t i n g i s hinged  to a t h i c k brass p l a t e a t one end, the  other r e s t i n g on the p o i n t of a screw which turns i n t o the same p l a t e .  The e t a l o n t i l t may then be r e a d i l y a d j u s t e d .  The 7 cm. diameter silica,  p l a t e s are made one of quartz and one of  g i v i n g the maximum p o s s i b l e range of t r a n s m i s s i o n .  They are 1 cm. i n diameter the housing.  and are made t o f i t s e c u r e l y i n t o  In order t o a v o i d the p r o d u c t i o n of f a l s e  interference effects  (7) t h e i r plane faces make .angles o f  15 minutes w i t h each other, g i v i n g them a s l i g h t l y p r i s m a t i c shape.  One face of e i t h e r p l a t e i s o p t i c a l l y  flat.  Important f a c t o r s to be considered i n the design of an etalon are:  —  27.  1.  l e n g t h and m a t e r i a l o f s p a c e r .  2.  means o f a d j u s t i n g p a r a l l e l i s m  3.  focussing  4.  lens  reflectivity  of p l a t e s .  Considering the f i r s t spacers  were  separations etalon  of these,  chosen a f t e r a s t u d y t o be e x p e c t e d  t o make t h r e e  the lengths  o f the c a l c u l a t e d h f s .  the i n t e r o r d e r s e p a r a t i o n .  spacers  of lengths  respectively.  To g u a r d a g a i n s t  due t o changes  o f temperature and pressure  exposures they  effect  causing  were made o f i n v a r .  brass in  (this  0 . 8 cm. t h i c k ,  ring  inner diameter.  pins,  equal  of the  i n m e r c u r y was made, s i n c e t h e  thickness determines  was d e c i d e d  of p l a t e s .  1, 1.4, a n d 3 cm .  the expansion  Each separator  of the spacer  during  a broadening  consisted of a  7 cm. i n o u t e r d i a m e t e r ,  o f , a micrometer  e x a c t l y , thus  a n d a p i v o t on t h e s p a c e r  guaranteeing  reproducible  p i v o t was so p l a c e d t h a t t h e p i n s positions  as the studs  A fine plates housing  studs.  outer  rest  on t h e c a s t i n g  by t h r e e  steel  thin  brass  fitted  positions.  t h e same  accurately  The  relative  9 ) .  parallel  s p r i n g s mounted on t h e use the manipula-  r a p i d , and s e n s i t i v e .  on a v e r y  ring  (see F i g u r e  F o r an e t a l o n i n f r e q u e n t  t i o n must be s i m p l e , springs  occupied  adjustment f o r producing  i s provided  In a d d i t i o n  t o t h e a x i s o f t h e c y l i n d e r was c u t i n t h e  bottom o f the housing, this  a n d 5 cm.  Three e q u a l l y spaced p r o j e c t i n g i n v a r  i n l e n g t h w i t h i n the a c c u r a c y  parallel  long  of the f r i n g e s )  measurement, were mounted s e c u r e l y i n t h e r i n g . a groove  It  ring  p l a t e , as i n d i c a t e d i n F i g u r e  The heads o f t h e  placed against the  f).  The,pressure  exerted  28.  by  e a c h i s c o n t r o l l e d by  i n Brass loosen  one  screw i n each f o r m  surfaces.  the 5  springs  The  are  s p r i n g s are  p l a t e s , one  design  s w i n g them a s i d e .  The  bits  i n place  gives  with  spherical  by  the  effective  a  cylindrical  f u r t h e r end  of  p l a t e diameters  of  cm.  of the  5,  f r i n g e s formed i n the  focal  length  o f the  we  focal  know t h a t plane  objective.  fluorite  focal  end  length  i s mounted i n t h e  plates.  separated plates.  by  l e n s has  o n l y a few  an  see  the  centimetres  The  desire  of 3.2  from the  o f the  and  cm.  aperture  each  reflected of  f i n i t e : number will  cm.  is  regardless  1,  beams, m e n t i o n e d i n C h a p t e r I I , S e c t i o n  52  opposite  cm. 5  with  large  of  housing  aperture  effect  diameters  directly  achromat  t h i s arrangement  same e f f e c t i v e  of i n c i d e n c e  we  o f the  aperture  I t i s hoped t h a t by  beam w i l l angle  The  the  vary  Since  diameter rings a H i l g e r quartz  the  fastened  only  inner plate rests f i r m l y against  This  so  need  small steel  r e t a i n e r which i s held  housing.  and  Prom C h a p t e r I I , S e c t i o n  the  The  forms t h a t , t o remove t h e  heads o f t h e  brass  a screw.  thereby  the of be  minimized. The  plate r e f l e c t i v i t y  determines  and  the  r e s o l v i n g power.  can  not  be u s e d however b e c a u s e  intensity. important is  L o s s e s due and  must be  p e r h a p s the most  disadvantages.  Too  of the  It tarnishes  sharpness  coefficient  corresponding  loss i n  i n the m e t a l f i l m  t o a minimum.  efficient  fringe  high a r e f l e c t i o n  to a b s o r p t i o n kept  the  Although  m a t e r i a l i t has qi i t e r a p i d l y on  two  are  silver serious  exposure  to  29. the  a t m o s p h e r e , and  i t has  a l a r g e a b s o r p t i o n band i n t h e  near u l t r a - v i o l e t .  Consequently,  more s u i t a b l e .  d e p o s i t i o n o f t h e aluminum on t h e p l a t e s  was that ing  performed  by  a standard  evaporation  Tolansky  (7) o r S t r o n g  d e s c r i b e d by coefficient  reflection was  The  was  The  2:  The  Adjustment  used  removed an  extended  focussed f o r i n f i n i t y  to the  This  inclination  o f the e t a l o n .  by  By m o v i n g the  p a t t e r n appeared  Yiredge a n g l e out  removed,  the  towards  taken  o u t , and  polished against a f l a t  e t a l o n was procedure  a fraction  through  reassembled was  viewed w i t h  eye  This  and  the  continued u n t i l  to  of a wavelength of the  contin"open  indicated'  plates,  The  eye  pin i n  the a p p r o p r i a t e  observations  the  The  front  s u r f a c e of crocus  the  any  t o be  either  the  normal  across  each spacer  long.  objec-  before  the b a s e o f the wedge.  w h i c h p i n s were t o o spacer  placed  e x i s t e d between t h e  t h e n moved a c r o s s d i a m e t e r s t o determine  centre.  the  W i t h the  o f t h e r i n g s were f o u n d  the  (7)  between  looking in a direction  o r t o " c l o s e i n " t o the  opening  was  interference fringes  plates.  the diameters  a slight  carefully The  the  changing,i.e.,  out" from  pattern  and  f a c e s o f the  diameter, uously  of e q u a l  mercury source  eye  was  reflect-  I I , Section.2  i n order to gain accurate p a r a l l e l i s m  instrument,  turn  The  as  of t h e E t a l o n .  fringes  the  was  such  0.805 by a m u l t i p l e  method o f C h a p t e r  a l u m i n i z e d f a c e s o f the f l a t s  that  (14).  as  also applied.  A method i n v o l v i n g  tive  chosen  procedure  m e a s u r e d a c c u r a t e l y as  procedure.  Section  was  aluminum was  plate pegs  cloth.  repeated.  t h r e e p i n s were w i t h i n  same l e n g t h , i n d i c a t e d  by  30.  less  t h a n one f r i n g e  ing  fine  the  p r e s s u r e s e x e r t e d by the s p r i n g s It  and  adjustment  opening a c r o s s any d i a m e t e r . was t h e n e a s i l y  i s t o be n o t e d  that  remain-  o u t "by c h a n g i n g  supplied  f o r that  purpose.  t h e p r o c e d u r e may become t e d i o u s  r e q u i r e s much p a t i e n c e —  p o l i s h i n g b e i n g an e a r l y  carried  The  the reward  success.  Other  of great care i n points worth  mention-  ing a r e : (a)  In the l a t e r used  (b)  c a r e must  the pins are kept  be t a k e n flat  them and t h e m e t a l f i l m (c)  Bon Ami on g l a s s was  i n p l a c e o f c r o c u s c l o t h as b e i n g l e s s  Exceeding of  stages of p o l i s h i n g  t o ensure  so t h a t  abrasive.  that  optical  the s u r f a c e s  c o n t a c t between  i s obtained.  The p i n s s h o u l d be p o l i s h e d a t b o t h  ends and n o t on  j u s t one. (d)  By p l a c i n g to  t h e eye a t some d i s t a n c e f r o m t h e i n s t r u m e n t  vie?/ t h e f r i n g e s  increased  since  the  o f view.  to  field  variations  Section  3:  the s e n s i t i v i t y  the centre of the p a t t e r n  tube. the In  s i m p l i c i t y and convenience o f  procedures  greatly  measurements.  and s t a b i l i t y a r e f u r t h e r a d v a n t a g e s discharge lends i t s e l f  n e c e s s a r y t o reduce  a d d i t i o n , t h e comparative  source  d i s c h a r g e , such a  f o r the h i g h r e s o l u t i o n  The e l e c t r o d e l e s s  cooling  sensitive  The S o u r c e .  chosen  High i n t e n s i t y  fills  i n t h i c k n e s s o f the a i r gap.  high frequency external electrode  s o u r c e was  then  The c e n t r e i s p a r t i c u l a r l y  Because o f t h e extreme the  o f t h e method i s  influenced  ease  line  o f the  readily to breadth.  of p r e p a r a t i o n of such a  the choice.  A description  o f the  31 preparation  l a given  In C h a p t e r V,  A d e t a i l e d d i s c u s s i o n o f the discharge survey at  i s given  will  less  oscillating  atoms. tube  within the  The  here.  A  tube  so  electric  field  or  clamping  connecting  p r a c t i c e was  two  these  adopted  i n the  case,  ring.  The  o s c i l l a t o r u s e d t o e x c i t e the  ically  the  same as  is  its circuit driven The  in  by  length.  Two  by  a quartz  a t e i t h e r end  the  (21),  mercury discharges on  the  and  tube  ends  or  discharge  of The  10.  copper  i s bas-  Harnwell  (24),  The  and  was  were 5/8  oscillator  sealed  8  Inches  inches  in  4 inches  T h i s n a r r o w p o r t i o n was t o the  was  enclosed bulbous  0  tape.  Westfall  have I n v e s t i g a t e d  the  electrodes  e l e c t r o d e s ; the middle  rubber s e a l i n g  dependent  made o f v y c o r  j a c k e t w h i c h was  and  coll.  i n a brass  G-.P.  gas  supply.  inches  water  Meggers and  power  t o the  the  in Figure  was  Inches i n d i a m e t e r .  ends w i t h  is  voltage  by  itself  diameter to receive 3/8  described  d i a g r a m i s shown  a high  source  enclosed  and  energy  ends o f t h e  of f i n e  and  tube  t o e x c i t e the  electrodes  consisting  that  in close  either inserting  t o the  vapour  oscillations.  high frequency  in this  copper c o i l  or  i s placed  i s s e t up  by  hrief  c o n t a i n i n g gas  enough e l e c t r o n v e l o c i t i e s  coll,  electrodeless  only a  c a r r y i n g high frequency  i s generally obtained  the  ( 7 ) , and  c o u p l i n g between t h e  t u b e and  latter  Tolansky  1.  a c t i o n o f the  m i l l i m e t r e s pressure  to a c o i l  produces g r e a t  the  given  t h a n a few  proximity An  he  by  Section  (25)  and  thoroughly  J a c o b s e n and the  have f o u n d t h a t  frequency  o f the  a c t i o n of the  life  exciting  Harrison similar o f the  tube  oscillation,  -WVWF—i  + Ci 1 0 0 f % 1 0 , 0 0  A-- ammeter V - - voltmeter  811  Figure 10:  C i r c u i t diagram of  r,foscillator  32. increasing with time,  increasing frequency.  v a r y i n g from  driven gases  into  the w a l l s o f the  are present  with a gas-air  Section In the Perot  30 t o 300  the  A f t e r a p e r i o d of  hours,  the mercury i s a p p a r e n t l y  tube.  P r o v i d i n g no  s o u r c e may  be  r e j u v e n a t e d by  4:  The  Spectrograph.  t h e o r y of the r i n g  systems produced  i n t e r f e r o m e t e r ( C h a p t e r I I ) we waves.  In the  dealt  fringe  resolution  p a t t e r n and  of t h i s  by  wholly  investigation  composed o f a g r e a t number o f w a v e l e n g t h s e a c h own  heating  torch.  monochromatic l i g h t  its  adsorbed  the with  of  light  line  gives  these are a l l superimposed.  complex s t r u c t u r e  i s performed  by  the  etalon with a spectrograph of smaller r e s o l v i n g  but  sufficient  systems.  dispersion  For t h i s  was  used.  and  has  3A/mm. a t The relative  a Hilger E - l quartz  T h i s i n s t r u m e n t makes use  o f the  The crossing  power  fringe  spectrograph  L i t t r o w mounting,  12A/mm. a t 5 0 0 0 A  of approximately  and  2500A. external parallel  beam method o f m o u n t i n g t h e e t a l o n  t o the s p e c t r o g r a p h was  at  the f o c u s  in  the  is  t h e n f o c u s s e d on the  of the  to separate the v a r i o u s  purpose  a dispersion  Fabry-  o f a q a a r t z l e n s and  parallel  the  The  slit  o f the  objective.  of h i g h q u a l i t y ,  m o u n t i n g requires t h e use  but  has  i s placed  The  fringe  system-  s p e c t r o g r a p h by means The  the  collimating  lens  o b j e c t i v e must.  of an e x t e n d e d but  source  interferometer placed  beam e m e r g i n g t h e r e f r o m .  quartz f l u o r i t e  need not be  used.  source w i t h  intensity  distribution,  the a d v a n t a g e  available  light  i s employed  fringes.  Since  t h e whole a p e r t u r e o f t h e  that  The uniform  a l l the  i n the u s e f u l p r o d u c t i o n o f etalon. i s used  33. the m i r r o r  c o a t i n g must be extremely uniform, and the a d j u s t -  ment to p a r a l l e l i s m r e q u i r e s e s p e c i a l  care.  Note at t h i s p o i n t that s i n c e the L i t t r o w type graph has u n i t m a g n i f i c a t i o n , the  the quartz  s i z e of the r i n g system obtained  plate. slit  spectro-  o b j e c t i v e determines  on the photographic  F o r the photography of the i n t e r f e r e n c e patterns the  of the spectrograph i s opened to. a width of about 1 S e c t i o n 5:  The Step  mm.  Sector.  For a l l photometric work employing the photographic p l a t e . t h e r e must be provided  on the p l a t e a s e r i e s of  c a l i b r a t i o n marks of known r e l a t i v e i n t e n s i t y .  The measured  d e n s i t y of these marks then permits the c o n s t r u c t i o n of the H u r t e r and D r i f f i e l d to the exposure.  c h a r a c t e r i s t i c curve r e l a t i n g the d e n s i t y  The c a l i b r a t i o n i n t h i s  case was performed  by the use of a r o t a t i n g step s e c t o r p l a c e d in  f r o n t of the s p e c t r o g r a p h s l i t .  an opaque d i s c from wftich steps are removed. passing  immediately  The s e c t o r c o n s i s t s of  of angles x, y, z, ...  When i t i s r o t a t e d the t o t a l l i g h t i n t e n s i t y  i s reduced In the r a t i o s j  it)  p a r t i c u l a r sector  contained  > JTJ , s<Z > ••• •  s i x steps  This  of angles 1.785, 3.685,  13.384, 38.484, 149.685, and 360.000 degrees r e s p e c t i v e l y giving relative 83.857, 201.681.  i n t e n s i t i e s o f 1, 2.064, 7.498, 21.560, The r a d i u s of the l a r g e s t step was  Inches, and each step was cut to a depth of 2.5 mm. s e c t o r was  2.5 The  counterbalanced and mounted on the s h a f t of a  l/50 horsepower motor which gave a speed of 1725 r e v o l u t i o n s per minute. Two  independent determinations of the angles of the  34. s t e p s were made.  In t h e f i r s t  the t a b l e  of a rotating  removed.  The  radial  prism  the  table  Secondly,  c u t s were v i e w e d  allowed  the  comparator  the  t h e known r a d i i agreed  is  that  chief the  ation.  speeds  the  The  carried  originally  (22)  that  designed  this  by t h e  photographic  The  to a galvanometer  galvanometer  kodabromide paper As  used  here  rotating  and may  from  methods  sector  have a illumin-  critical  sane,  and  accurate results  h f s . o f the  in light  plate.  The  beam o f l i g h t  w h i c h a beam o f l i g h t The  two  for are  obtained.  mercury  microphotometer.  i n s t r u m e n t wses a vacuum  mitted  path of a f i x e d  of the  a i d of a M o l l  t o measure the v a r i a t i o n s  carried  Hilger  Microphotometer.  out w i t h the  d r i v i n g mechanism.  rotation  angles.  there i s a  are the  here  couple  the  the  same amount o f c o n t i n u o u s  i n t e n s i t y measurements i n the  l i n e s was As  from  of t h e  i s intermittent  o f the m a g n i t u d e u s e d  The  of the  results  o f the u s e  been shown  6:  and  were m e a s u r e d w i t h a  The  above w h i c h t h e e f f e c t s  Section  prism  0.5%»  than  illumination  I t has  frequency  steps.  criticism  different- effect  angle  w i t h the  on  c o r r e s p o n d i n g a n g l e s were c a l c u l a t e d  o f the  to better  The  of each  mounted  p e r p e n d i c u l a r l y from  microscope,  t h e measurement  chords  and  s e c t o r was  spectrometer,  above by means o f a t r a v e l l i n g of  the  on w h i c h  is reflected are  plate  the  trans-  i s moved a c r o s s  by means o f an  c u r r e n t s from  deflections  intensity  thermo-  automatic  thermoelement  i s mounted a m i r r o r to a photographic  t h e r e f o r e t r a c e d out  w h i c h i s wound on a r o t a t i n g t h e r e c o r d i n g mechanism was  are from  strip. on  the  drum. discarded in  35. favour  o f an  detector  automatic  currents  anr.n a p p r o p r i a t e  are  recording transmitted  amplifying  important  a d v a n t a g e s , not  The  o f the  trace  being is  more  of  the  least  recorder  This  through  arrangement  of which i s  p a t t e r n may  he  type  has  convenience.  v i e w e d as  n e c e s s i t y of developing  a c t i o n of t h i s  The  of r e c o r d e r  i t is  the  paper  is in  general  satisfactory. A  was  The  the  to  system.  the  intensity  r e p r o d u c e d , and  removed.  Brown p o t e n t i o m e t e r .  second v a r i a t i o n ,  the the  use  30  falling  ecu a l l y  p e r m i n u t e was beam.  In the  couple,  on  placed later  originally  f o u n d t o be the  great  chiefly advantage  absence  of  constant  on  over long drift  o f the  two  of  the  other  i . e . , the periods o f the  examination  revolutions  the  proper  of  thermo-  lead sulphide  While  not  as  fast  cu I t e s a t i s f a c t o r y .  the  chopper  installed.  d e t e c t o r s , the  c e l l was  the  The  the chief  the  chopper.  almost  clear plate trace time.  as  showed i t t o be  by  both detectors  reproducibility  between t h e  two.  was  was  i n t r o d u c t i o n of  v i b r a t i o n s of the hand was  cell  W i t h the  fairly  The  complete remained  thermocouple  clear plate trace occurred,  reproducibility  the  p r o j e c t i n g lamp  of experiment  the  place that  A motor d r i v e n  u n a v a i l a b l e , was  c a u s e d by  "drift,"  considerable prolonged  path  in  requires  r o t a t e d a t 1800  i n the  stages  detector  Such a c e l l  chopped.  t h e r m o e l e m e n t was use  i n i t i a l l y through n e c e s s i t y ,  infra-red  t h e more s e n s i t i v e .  drawback t o the noise,  i t be  spaced holes  C o m p a r i n g the  cell,  sulphide  vacuum t h e r m o - e l e n i e n t .  radiation with  of a leqd  introduced  linear.  e x c e l l e n t , as was  although The the  3 6  A convenient method for focussing the microphotometer is outlined in Appendix I I .  37  CHAPTER V:  THE EXPERIMENTAL PROCEDURE.  Section  The P r e p a r a t i o n  The  1:  samples  from the Atomic  of gold Energy  They h a d b e e n e x p o s e d pile,  a different  each sample. on t h i n or  mercury  in The  v a l u e o f the neutron f l u x  vacuo.  formed  was  consisting  during the neutron  The v y c o r tube  a graded  seal  apparatus  3).  heated furnace.  i s shown i n F i g u r e 1 1 . i n a f u r n a c e as  and t r a p D.  A temperature  The t u b i n g  flamed with a t o r c h to drive introduced  times, t h i s  flushing  molecules.  With  into  The  system  i n t o an  elec-  o f 4 5 0 ° C was m a i n -  outside  time t h e  t h e f u r n a c e was  o f f a l l adsorbed gases.  Helium  t h e s y s t e m a n d pumped out a fe?/  aiding  i n carrying  o u t a n y t r a p p e d gas  t h e h e l i u m p r e s s u r e maintained t o p r e v e n t  e n t r a n c e o f a i r , t h e t i p B was b r o k e n into  earlier  The column A i s a t t a c h e d by means  of s i x hours, during which  s y s t e m was e v a c u a t e d .  temperature  C i s the source d e s c r i b e d  to the pyrex t u b i n g  tained f o r a period  inserted  o f a dozen  the g o l d , and  t h o r o u g h l y c l e a n e d and t h e tube A i n s e r t e d  was t h e n  wound  irradiation i s  throughout  l o n g v y c o r t u b e , A, may be i n s e r t e d  trically  the  sample  strips  o f f by p r o l o n g e d h e a t i n g a t a h i g h  (Chapter I V ) , S e c t i o n of  Ontario.  pieces.  The d i s t i l l a t i o n  desired.  were o b t a i n e d  b e i n g used f o r  i s i n the form of f i n e  as a volume d i s t r i b u t i o n  was d i s t i l l e d  the mercury  t o n e u t r o n bombardment i n t h e a t o m i c  aluminum w i r e s , e a c h  The present  containing  Commission a t C h a l k R i v e r ,  The g o l d  more o f s u c h  of the Source.  o f f , the gold  t h e v y c o r column, a n d t h e o p e n i n g s e a l e d o f f .  t o pump  r  vycor T  i  to pyrex  D trap  source  'igure 11:  Mercury d i s t i l l a t i o n  apparatus.  helium  38.  The  t r a p D and t h e s o u r c e  pumping was to  continued u n t i l  a few microns,.  the h e l i u m  The g o l d was k e p t  f o r several hours,  450°C  C were immersed In l i q u i d p r e s s u r e was  the system  a n d -the e s c a p i n g m e r c u r y  were a g a i n f l a m e d  to d r i v e  t h e s o u r c e ; a n y t r a p p e d w a t e r v a p o u r was s o u r c e was  sealed o f f .  mercury a s l i g h t Very  little  source  t r o u b l e was  a stable  Section The  2:  source  discharge of high  vapour  a l l mercury  Into  d r i v e n o f f ; and t h e t o the  t o s e r v e as a  encountered  of  The u p p e r p a r t s  I t contained i n addition  pressure of helium  reduced  a t a temperature  c o n d e n s e d on t h e c o l d w a l l s o f t h e s o u r c e . of  a i r , and  carrier.  i n p r o d u c i n g w i t h the  intensity.  The P h o t o g r a p h y o f t h e I n t e r f e r e n c e P a t t e r n s and e t a l o n were mounted as d e s c r i b e d i n Chapte  IV, S e c t i o n 4, w i t h a q a a r t z l e n s o f 5 cm. a p e r t u r e a n d 20 focal that of  l e n g t h b e i n g used the apparatus  was  as t h e c o l l i m a t o r . aligned  correctly  the s p e c t r o g r a p h the mercury  incandescent from made.  on t h e o p t i c a l  s o u r c e was  b u l b , and the r a d i a t i o n  the prism end.  In o r d e r t o  The c o r r e c t  from  by a r a p i d  convenient  ensure axis  r e p l a c e d by an the s l i t  adjustment  was  The a c t u a l . f o c u s s i n g o f t h e s p e c t r o g r a p h  performed  cm.  viewed  then  easily  itself  was  method d e s c r i b e d In A p p e n d i x  I. Suitable trial  plates.  determination  slit  The f i n a l  depending  of  1mm.  photograph  and e x p o s u r e plates  taken  r e q u i r e d exposure.times  minutes, about  widths  on t h e l i n e  was u s e d .  times  were f o u n d  f o r the  On e a c h  p l a t e were an  of the mercury spectrum  photometric  v a r y i n g from  t o be e x a m i n e d .  using  2 t o 10  A slit  width  interference  and a c a l i b r a t i o n  exposure  39.  with  the step  sector.  F o r the l a t t e r  t h e e t a l o n was  and  t h e s e c t o r mounted I m m e d i a t e l y b e f o r e  for  each p l a t e a c h a r a c t e r i s t i c  w h i c h was the  subject  fringe For  ring  so  across  centre that  was  taken  obtained  o f d e v e l o p m e n t as  I n some c a s e s  at the centre was  t h a t the  the  In  visible.  of i n t e n s i t y r a t i o s ,  i n wavelength determinations.  t h e maxima as one p r o c e e d s  On a number  be  sharpness  out from the c e n t r e .  I n Kodak f o r m u l a D-19 3:  The  f r i n g e s could  p l a t e s u s e d were Eastman Type I I - F  Section  slit  While, e i t h e r  on e a c h p l a t e , and b e c a u s e o f i n c r e a s i n g  developed  of the  others  s e t a t one end o f t h e  a r r a n g e m e n t was u s e d b e c a u s e more  All  slit  the centre  of the s l i t ;  one h a l f o f e a c h r i n g was  served  to ensure  on t h e s l i t ,  s u i t a b l e f o r t h e measurement  obtained of  a diameter.  o f the p a t t e r n  the former  latter  care  c o r r e c t l y centred  placed  only  t y p e was only  t o t h e same c o n d i t i o n s  every exposure  p a t t e r n was the  c o u l d be  Thus  pattern.  s y s t e m was  running  curve  the s l i t .  removed  and f i x e d  The D e t e r m i n a t i o n  ( 3 ) , a n d were  i n Kodak  F-5.  of Wavelengths.  of s u i t a b l e plates  the f r i n g e d i a m e t e r s  o f s e v e r a l l i n e s were m e a s u r e d f o r a l l components o f t h e h f s . patterns.  F o r most l i n e s  containing  j j g l 9 9 components were v i s i b l e . with to  a H i l g e r comparator,  parts  5, a n d t h e wave number  Chapter I I , Section  6.  The measurements were made  and the r e s u l t i n g v a l u e s  c a l c u l a t e the f r a c t i o n a l  Section  s t r u c t u r e some o f t h e  used  by'method o f C h a p t e r I I ,  separations  by t h e method o f  40 S e c t i o n 4:  The  Measurement of the Mercury  r a t i o H g - ' - " : H g " i n the sample was  The  determined  1  measuring the r e l a t i v e i n t e n s i t i e s of the hgs. due  to each i s o t o p e .  of the  The  Ratio. by  components  c r i t e r i a determining which l i n e s  spectrum are most s u i t a b l e f o r the purpose a r e :  (a)  the l i n e must be of high i n t e n s i t y .  (b)  the H g " 1  must give r i s e to a simple h f s . w i t h  p r e f e r a b l y no more than three  components. 199  (c)  at l e a s t one  component of the Hg  must f a l l midway between the the f r i n g e (d)  intense Hg  orders  in  pattern.  no other  Condition  structure 198  l i n e may  overlap  the  chosen  line.  (a) i s necessary because of the low  trans1 Q9  mission  of the e t a l o n and  components; c o n d i t i o n s  the low  (b) and  i n t e n s i t y of the  (c) c o n s i d e r a b l y  the a c t u a l measurements; c o n d i t i o n of two  or more l i n e  The  simplify  (d) prevents  intermingling  patterns.  e t a l o n spacer of l e n g t h 1 cm.  used e x c l u s i v e l y , and  according  an i n t e r o r d e r s e p a r a t i o n  (0.97720155cm.) was  to equation  of 0.514  cm."^.  (2.15) i t gives  Prom the h f s . to  be expected  (Appendix I I I ) the l i n e s of wavelengths  4077, 3341,  and  for  the  3125  angstroms were chosen as most  i n t e n s i t y measurements.  apparently  Hg  We  might note that  s u i t a b l e s t r u c t u r e s as that of the l i n e  be r u l e d out by c o n d i t i o n  5461, appropriate such 3654A must  (d) above.  I d e a l l y , the exposures would be taken so as to have the d e n s i t i e s of these l i n e s f a l l of the  c h a r a c t e r i s t i c curve.  on the s t r a i g h t l i n e  In p r a c t i c e the  portion  intensity ratio  41. between t h e H g densities care  1  of both could  however, t h i s  attained. and  and H g "  1 9 8  In  condition  evaluating  the true  i s inherent  intensity  In the f i r s t  ratio  place,  decreasing  i n the instrument  order  itself  of i n t e r f e r e n c e . a n d may be compen-  i s drawn t h r o u g h t h e p e a k s o f s u c c e s s i v e  averages d e v i a t i o n s  line  with  The c o n s t r u c t i o n  due t o l o c a l  and s e n s i t i v i t y . these  l/60 inches.  the i n t e n s i t y o f  curve  component.  With  a number o f f a c t o r s  f o r b y t h e method s u g g e s t e d b y T o l a n s k y  graininess  line.  the microphotometer  sated  each separate  that the  c o u l d be as n e a r l y as p o s s i b l e  were t r a c e d w i t h  maxima d e c r e a s e s w i t h  This  on t h e s t r a i g h t  o f t h e maxima m e a s u r e d t o w i t h i n  must be c o n s i d e r e d . the  not f a l l  The p a t t e r n s  the heights  components was so g r e a t  (7).  A  smooth  maxima f o r  simultaneously  fluctuations i n plate  The i n t e r s e c t i o n s o f a n y v e r t i c a l  curves gives  the r e l a t i v e  heights  of the  peaks. S e c o n d l y , t h e i n t e n s i t y between o r d e r s pattern The  contributes  converse  of this  to the density  l i n e s were so chosen t h a t  nearly  on t h e H g  reflection  1 9 8  equation  (2.10).  m e a s u r e d Hg  minima.  coefficient  peak, t h e i n t e n s i t y  v  Finally,  To e l i m i n a t e  m  n  value  the*Hg  o f the H g was t h e n  1 9 8  was  1 9 8  the e f f e c t , very  t h e measured v a l u e  and the measured h e i g h t  of I j _  This  since  1  Using  1 9 8  component.  1  t h e H g " maxima f e l l  o f the  of the H g  1 9 8  c a l c u l a t e d from  subtracted  from the  intensity. to obtain  the d e s i r e d r a t i o ,  H g " maxima m e a s u r e d r e p r e s e n t 1  of the H g "  n e e d n o t be c o n s i d e r e d  components a r e so much more d e n s e . the  of the H g  recall  that the  the c o n t r i b u t i o n of only  42. 199 one component o f t h e Hg structure. The i n t e n s i t y r a t i o s among t h e s e v a r i o u s components a r e c a l c u l a t e d on the b a s i s o f the  i n t e n s i t y sum  strict  (Jl) coupling.  must be  increased  These t h r e e the  true  r u l e of  by  Hence the m e a s u r e d H g the  appropriate  c o r r e c t i o n s having  intensity ratio  of the  199 in  fact  this  the  Chapter I I I , S e c t i o n  ratio  Hg  intensity  been a p p l i e d we  obtain  h f s . components, w h i c h i s  198 : Hg  .  slightly  of t h e s e  then determined  of A u  according  1 9 8  assuming  factor.  Several  q u a n t i t y were made f r o m e a c h o f the  number o f p l a t e s w i t h  1 9 9  2  the  varying  neutron  to equation  determinations four  exposures.  capture  (3.17).  l i n e s , on  cross  The  of a mean  section  43. CHAPTER VI: Section 1:  THE EXPERIMENTAL RESULTS. The Calculation of Absolute Wavelengths. 198  For as many of the Hg  lines as possible the correct  values of the f r a c t i o n a l parts were calculated by a least squares application as outlined i n Chapter I I , Section 5. Using these values and Meggers' wavelengths ( I V ) , the order of interference and etalon thickness were determined.  The  l i n e 3341 A was chosen to calculate the approximate order, and the exact orders were found f o r 15 other lines by the method of exact f r a c t i o n s .  The wavelengths of these 15  lines were then calculated r e l a t i v e to Meggers' value of 3341.4814 A.  The results of these investigations are set  down i n Tables 1 and 2. The. unambiguity  of the method of exact fractions f o r  determing the order of interference i s depicted i n Table 1. The measured fractions f o r each l i n e are shown i n column 2, and the calculated orders i n column 3.  The coincidence of  observed and calculated fractions i s obvious. Table 1: Calculated order of interference. Order of Interference Observed Wavelength (A) fraction 3341.4814 0.121 58,489.121 0.486 62,527.493 3125.6700 0.068 62,410.068 3131.5510 62,404.269 3131.8420 0.261 0.997 53,369.991 3650.1567 3654.8393 0.399 53,474.392 0.173 53,351.168 3663.2808 53,297.753 0.752 4046.5715 4077.8379 0.433 47,927.435 44,842.857 4358.3376 0.855 0.999 35,789.991 5460.7532 0.169 33,874.162 5769.5984 5790.6626 0.941 33,750.941  44. o f sm..  Using the value "»* o X We able  3.2  S  f o r the l i n e  3341 A t h e e q u a t i o n  g i v e s f o r t the value  g e t here  a striking  example  t=0.9772015c; cm.  of the accuracy  obtain-  i n measurement o f l e n g t h when t h e measurement i s p e r -  formed u s i n g a monochromatic w a v e l e n g t h o f l i g h t as s t a n d a r d . The measured m  0  X  o f 15  wavelengths fractions ~  .  Burns and Adams Table  2:  5790.6625 5769.5972 5460.7519 4358.3377 4077.8380 4046.5716 3663.2808 3654.8393 3650.1566 3341.4814 3131.8424 3131.5510 3125.6706 3021.4997 2967.2842 2536.5068  Table  In  the c a l c u l a t i o n s line  i n Table  (27) a r e a l s o  of Hg  1 9 8  (angstroms)  Meggers a n d K e s s l e r  B u r n s and Adams  5790.6626 5769.5984 5460.7532 4358.3376 4077.8379 4046.4715 3663.2808 3654.8393 3650.1567 3341.4814 3131.8420 3131.5510 3125.6700 3021.4997 2967.2833 2536.5064  5790.6626 5769.5984 5460.7532 4358.3372 4077.8379 4046.5712 3663.2808 3654.8392 3650.1564 3341.4814 3131.8423 3131.5513 3125.6698 3021.4996 2967.2832 2536.5063 •  2 are r e l a t i v e here  t o the green  i n columns 2 asnd 3  line  s t a n d a r d because  5460.7532  i t was n o t t h o u g h t  as s t a n d a r d b e c a u s e o n l y t h r e e  Consequently  2, where f o r  listed.  measured f o r i t , r e d u c i n g t h e a c c u r a c y part.  the equation  o b t a i n e d by Meggers and K e s s l e r (28),  t h a t the wavelengths  of  this  o f t , from  These a r e f o u n d  Wavelengths  Bedford  We must n o t e  were c a l c u l a t e d , u s i n g t h e  and the value  comparison the values and  lines  Meggers' v a l u e  7 or 8 fringes  angstroms.  a d v i s a b l e t o use  fringes  c o u l d be  In the f r a c t i o n a l  o f 3341.4814 was t a k e n as  c o u l d be m e a s u r e d f o r i t .  45. Section  2:  For those visible,  The H y p e r f i n e lines  the f r i n g e  Structure Separations.  i n which the H g "  s t r u c t u r e was  1  diameters  were m e a s u r e d and t h e wave  number s e p a r a t i o n s c a l c u l a t e d by t h e method (Chapter Hilger  in  A typical  Table  the  of  Tolansky  I I , S e c t i o n 6 ) . The measurements were made w i t h a  c o m p a r a t o r , and i n some c a s e s  trace.  readily  example  Table  from  the  photometric  o f t h e r e c t a n g u l a r a r r a y i s shown  3, t h e d a t a b e i n g  fringes  also  o b t a i n e d from  the diameters  of  of the l i n e 3:  Rectangular  a r r a y f o r A = yo 77 /J . s-  v  .Vtsr/ • 9930  .977 9  . i n 3 .  — ,  MM  ff£STL  ^  • 72/7 -  • VO* 2Z2^  3ton  /  0  V6V/  • 22 Yf _  .2.2 9/ /•tsrj?  /t?S  A/=  •  from  the data  y*3v2.//7J . if t  s-s-  o f B r i x and Kopferman;  I I I ) , and the s e p a r a t i o n s f o u n d  by S c h u l e r and K e y -  (23). Table  \ 4:  Hyperfine  S t r u c t u r e of  Hg ". 1  CCM.  V  &  scffvt, ex  -o. r8  -oVof7  3 3 (// 3 / 2S~  2s~?  -O- 2/2;  -<?.  2rf  -0-  2ST9/  -0-279  *  *•*•//3 2  y3  -<?. 2 33  3S~2.  -e>f  -  ex M/f s)/  (.CoHMCATo/t) 93  23VJ/  t h e m e a s u r e d wave number s e p a r a t i o n s  separations calculated  (Appendix  • Y(ss" /879  V/2S-2227  In T a b l e 4 a r e l i s t e d the  /•  3 2/3  220(,  /  .y(yr  o.  i-0- 36 3 3  2S-s77  o. 23 2  - o 2 y f  r  +0-  2jy  -o  76 f  to.  77y?  /- o •  22/y  •f-0-34 2-  •23y6  + 0 2  33  Except  f o r the v a l u e s  separations are each case. as  zero  of  the  relative  S c h u l e r and  i n some c a s e s isotope s h i f t  The  t o the Hg- " 1  Keyston's  (-*)  between H g  o n l y one  The  Values  f o r the  measurement and o f the  determinations the p h o t o m e t r i c Section  different  3:  The  Neutron  U g l 9 9 . H g l 9 8 were made f r o m The  mean o f t h e s e  u  '99  T h i s m e r c u r y was with  a neutron  distilled  flux  the  half-life  of A u  the  decay constant  equation  cross s e c t i o n  The  (3.17) we  i n the It  attained  f o r a l l the  is felt  lines.  result  error. seven from  accurate. Cross  S e c t i o n of  Au^  9 8  o f the  ratio  the f o u r l i n e s  on  different  g i v e s f o r the  from  six  a g o l d sample per  days e q u a t i o n  irradiated cm.  sec.  2  (3.5)  Since  gives for  _  1 • 6> 7 <(  then  get f o r the neutron  tr, =  t h a t an a c c u r a c y  i n the d e t e r m i n a t i o n  /. 7 > * x /o o f the  .  ratio:  capture  of Aul98  common u n i t s ,  ^  values  evaluations  cr, = (/. 7 9 ± a. /oJ Or  2 0  determinations  2 =  2 0 0  t h e means o f s i x o r  Capture  i s 2.69  1 9 8  Hg  give their  subject to  o f 4.6X10-*-^ n e u t r o n s  A /  Using  as  to  3341A i s t h e  plates.  t r a c e s are not  Twenty-one i n d e p e n d e n t  plates.  are  not Hg  line be  zero i n  is relative  and  so may  other l i n e s  from  data  1 9 8  the  component as  98  s i n c e t h e y do  comparator value  of  o f S c h u l e r and K e y s t o n ,  X/o V  -*>~barns.  o r d e r o f 5%  o f the mercury r a t i o .  was The  47. c h i e f reason  why  almost  case  ing  every  the  the  error  t h e Hg- 1  s h o u l d e r of the  were s h o r t e n e d on  t o the t o e  by  the  to prevent of the  98  reduced  maxima p r o d u c e d  characteristic this,  curve.  s i x s t e p s o f the  more s t e p s a  c o u l d not be  then  The  sector,  and  that  a density  curve.  t h e Hg-*-  99  curve  was  itself  in  approach*..-  I f the  exposure  maxima  receded  was  determined  i t i s possible  that  corresponding i n c r e a s e i n accuracy might  with  be  gained. , The was  second  the d r i f t  important  resulting  from  o t h e r hand t h e n o i s e f r o m particularly Variations pattern  troublesome  in clear  and  the  factor  affecting  the  the  lead  trace  determinations  thermocouple,  o r on  sulphide c e l l .  i n measuring  plate  the  the Hg- 1  between t h e  c a l i b r a t i o n marks may  also  the  These were  maxima.  99  interference have a f f e c t e d  the  result. The is  value  o f 1.78  and  o f 3.5  i s i n support  X 10  4  barns  In o r d e r t h a t standard  t h e Hg- 1  98  ensure value  the green  than  o f the n e u t r o n 2  line  prepared  the freedom from  cm.  sec.  value  cross  of 1.6  section  X 10  that  barns  4  his f i r s t  estimate  i s too h i g h ( 4 ) .  i s t o be less  f o r the  of h i s assumption  o f l e n g t h I t s h o u l d be  of g o l d , then  per  barns  i n good a g r e e m e n t w i t h H i l l ' s  (5)>  If  X 10^  free by  1% o f Hg hfs.  flux  o f Hgl98 ^ from  e  u  e  d  as  s h o u l d be  irradiation present  T h i s i n t u r n g i v e s as  t o be  used  1.7  the  a l l structure.  the n e u t r o n s  s  X 10^-  2  to  a maximum  neutrons  48  Appendix I:  Method of Focussing a Prism Spectrograph.  Assuming that a focus in the v i s i b l e region may  readily  be obtained by d i r e c t observation (although the considerations of Section 3 to follow may be applied as a f i n a l  adjustment  even in the v i s i b l e region), an approximate focus f o r the u l t r a - v i o l e t regions may  be found by simple calculations.  The f i n a l adjustments may difficulty.  then be made with a minimum of  In most spectrographs regulation of prism  rotation and translation and plate t i l t may be made, and we s h a l l consider these In turn. 1.  Prism Rotation:  By Snell's law the angles of incidence, i , and r e f r a c t i o n , r, and the refractive'index of the prism, n, are related thus:  ^,. -  .  In most spectrographs the prism i s at the position of minimum deviation so that / i = prism.  , where A i s the angle of the  Equation (7.1) becomes  <7-*J Suppose now that the instrument has been focussed i n the v i s i b l e region, and that the wave-lengths at extreme ends of the plate are respectively A/ and  X*  ( A, > A )  •  A  P°r a focus  in the near u l t r a - v i o l e t the prism must be rotated so that i s moved to the opposite end of the plate. the variation of n with A  we may  From tables of  calculate i f o r any A  equation (7.2), and In p a r t i c u l a r we may  X*  calculate i  /  from  and i g  49. Xe/  for  a  n  X2  d  •  To move  X2 to the desired position f o r  the new focus we must rotate the prism through an angle ( A.  z  - yC )  .  y  In general the amount of rotation w i l l be some-  what less than this to allow f o r overlap i n the two regions. The procedure may be repeated f o r the f a r u l t r a - v i o l e t focus. 2.  Prism Translation:  The new region i s now centred on the plate. to  In order  focus the spectrum we must consider the variation of the , r w • We have  f o c a l length, f , of the camera lens with  y-  =  ^ - / J  (7?)  C  where C i s the sum of the curvatures of the lens surfaces. Prom the v i s i b l e focus we may measure f f o r X/ ( f / y ) > sa  (7.3) since f , X/ >  hence calculate C from equation  t  known.  C i s a constant of the lens.  we f i n d  m  ^\  .  x  a n d  a n d  -  - n, are  Prom the tables again  f o r X i and using the value of C calculate  Since f o r the near u l t r a - v i o l e t focus  the position of X/  > i  n  X 2 occupies  the v i s i b l e focus, we must translate  the prism through a distance  ~ )  •  3 . - Plate T i l t : Suppose that f o r a given plate t i l t at  prism translation  ^ a n d X*  a  t  \  t  i s focussed  -prism translation  X* •  We wish to know by how much we must increase the plate t i l t to  give a focus across the whole plate.  We s h a l l consider  the general case where the axis of rotation of the plate holder i s not i n the plane of the plate. In Figure 1%, 0 i s the axis of rotation of the plate AP.  The angle of incidence i Is to be increased by ctO?  Let the difference  (x* " X/)  be denoted by <4>r.  50.  Figure  1Z:  Regulation  Note t h a t t h e angleUO .  Q i s also'  •  For AB  o( i a c o n s t a n t  tilt.  and hence t h e a n g l e a t  From t h e g i g u r e  «  =  %  ~  p + * J  d $ t h e a r c AB  small  of plate  so t h a t i n t r i a n g l e  ( .yJ 7  is essentially  Q&B  e q u a l t o the chord  by t h e la?; o f s i n e s  (J.r) By e q u a t i o n  Again  (7.4) t h i s  becomes  s i n dtP <-~ d0  f o r s m a l l dO  I  [r~(r*f*J]h aU  also  ^  , =  <sLt. Equations  (7.6) r e d u c e s t o  -  <U -  or and  equation  -  /x  Now  , and s i n c e  Ax =  (7.8) a n d  ^ * &  X  (S-<*J  (7- fj  -*-<-^  (7.9) g i v e f o r  d0  AX  To g i v e a f o c u s plate  tilt  over  t h e whole p l a t e we must  by an amount  <d&  i n c r e a s e the  g i v e n by e q u a t i o n  (7.10).  51. 4.  Example of Method:  The  procedure o u t l i n e d was used to focus the H i l g e r E - l  quartz spectrograph.  Table 5 gives the v a r i a t i o n of n w i t h  X [2?). Table  5*.  V a r i a t i o n of n w i t h X ( 2 8 ) .  1(A)  XL*J  1.5405 1.5442 1.5497 1.5540 1.5674  7065 5893 4861 4341 3404  2749 2573 2313 2195 1990  1.5875 1.5962 1.6140 1.6250 1.6509  Cauchy's d i s p e r s i o n formula may be w r i t t e n  where A, B are c o n s t a n t s . /jty  /l^  and  Xj  I f we s u b s t i t u t e i n turn and s u b t r a c t :  Table 6 g i v e s the values of  <4/>» ,  4  (^J,  .the wavelength i n t e r v a l s of Table 5. Table 6:  E v a l u a t i o n of B.  0.089 X 10 0.133 0.108 0.331 0.451 0.202 0.357 0.206 0.449  0.0037 0.0055 0.0043 0.0134 0.0201 0.0087 0.0178 0.0110 0.0259  4.17 X 10 4.13 3.98  4.05  4.46 4.31  5.00  5.36 5.79  and B f o r  52. Note t h a t B i s not decreasing  actually  .  constant  hut  increases with  wavelength.  0 For  the  L i t t r o w mount  s&C*. si = and  2  ~s  A.J  is  * /*  rf  from  = /• s-7Vf  Since  1 prism  rotate  the  60  ,*>that  by  equation  . I n the v i s i b l e r e g i o n .  b o u r h o o d o f 3125A and extrapolate  /?=  a value  , and  rotation 393  formula  5 t o f i n d sr\. f o r 3125A. hence  '* -  division  S"/ * 2 7 ' ,  equals  divisions,  ~ 7o-p^>/f  /  of B i n the  Cauchy's d i s p e r s i o n  Table  prism  Using  \  15.17  or to give  neigh-  we  The **, =  (7.2)  may result &  J  s e c o n d s we  o v e r l a p say  J  .  must 370  divisions. In (7.3)  the v i s i b l e ,  Hence we  For of  C~ 37-2  gives  inches.  - 6 f  the  inches  must  regulation  of p l a t e  For  the  G0r* 2 2*} Hence e q u a t i o n  Z) x that  order  s e t f o r an e s t i m a t e d  calculated.  a  essary  •  (7.10) r e d u c e s  to  slight  from  the f i r s t  compensation  since in increasing  ment may  be  Table  not  o n l y the  calculated 7 shows t h e  focus.  from  then  yi -  plate  plate  3  4.2  inches.  theory  plate  is  correct  tilt  2- S~6 A^c^te^,^  equation  alO  and  tilt  both  The  ~  calculated.  t r a n s l a t i o n may  o u t e r end.  agreement  the  ^ -£y?  get  that the The  equation  i n question  i n prism the  we  through  note  f o c u s , and  spectrograph -v  prism  tilt  hence  2  correction.  22'36'  Is f o u n d  p l a t e move and  actual  </-  the  and  for A  , and  translate  S e c t i o n 3 i s a second  first  inches  be  the adjust-  (7.12)  between  calculated  Note  nec-  ends o f  necessary  9  and  53. Table 7:  prism rotation  Agreement of calculated focus with actual focus.  near U.V. calculated actual  far U .V . calculated actual  1330  prism translation  30  33  15  15  plate  8.0  8.0  15.2  15.4  tilt  920  920  1330  54.  Appendix I I :  Method of Focussing a Microphotometer.  In the Moll microphotometer a l i g h t beam i s focussed in the plane of the plate holder by a small objective. An exactly similar lens collimates this l i g h t , which i s then focussed upon the thermocouple.  With the beam focussed i n  the plane of the holder we wish to calculate by how much the lenses must be moved when plates of varying thickness are inserted.  Two cases a r i s e , depending on whether the emulsion  is placed against the holder or away from the holder. (a)  Emulsion against holder:  I f the objective and collimator be respectively L , and L , then L, remains f i x e d . a  For a plate o f thickness d,  L j must be moved away from the holder a distance d. (b)  Emulsion away from holder:  The focus must always be i n the plane of the emulsion. In this case, i f the plate has r e f r a c t i v e index n, then L, must be moved a distance ^ and L a plate of thickness  x  a distance d.  I f further  replaces that of thickness  d, L , must be moved a distance ^  and L  x  a distance x. The  two lenses are always moved i n the same d i r e c t i o n . Case (a) has the advantage of a simpler adjustment since only L j need be moved.  Case (b) has the advantage that the  emulsion w i l l not be scratched by resting against the plate.  55.  Appendix  III:  The H y p e r f i n e S t r u c t u r e  The h f s . o f 30 l i n e s  In the spectrum  c a l c u l a t e d by the procedure all  cases the d a t a used  The r e l a t i v e  by means o f t h e i n t e n s i t y Ornstein. T a b l e 8. ponent Hg  1 9 8  The r e s u l t s Note t h a t  gives line.  o f Hg- 1  1 9 9  99  3.  In  o f B r i x and K o p f e r m a n ( 1 3 ) .  o f t h e components sum r u l e  have been e v a l u a t e d  o f B u r g e r , D o r g e l o , and  of the i n v e s t i g a t i o n  are l i s t e d i n  t h e wave number a s s i g n e d t o e a c h  the separation  .  has been  of Chapter I I I , Section  i s that  intensities  of H g  of that  component  com-  from the s i n g l e  Structure  Trans i t i o n Wavelength 6716.4 6234.4 6123.5 6072.6 5790.7 5789.7 5769.6 5675.9 5460.7 4916.04358.3 4347.5 4339.2 4108.1 4077.84046.6 3801.7 3663.3 3662.9 3654.83650.2 3341.5 3131.8 3131.6 3125.7 3023.5 2893.6 2752.8 2536.5 2464.1  ' P ;  6s7s 'S. 6 a' 6p 6s7s 'S„ 6 s 9p 'P," 6 s 7s *S, 6 s 6p "D; 6 s 7 s 'S, * 6 s 6 p 'P/ 6s6p ' E % •6s6d 'D. 6s6p •6s6d D, 6 s 6 p 'p;- •636d D 6s7s'S, 6s 9p ' P ; 6s6p'p,''S, 6 s 6 p ' P ; 6s7s 6s8s 'S. 6s6p J P / •6s7s 'S, 6 s 6 p 'P/6s6p 'P,°- 6s 7d 'D 6s6p 'P/- •6s7d 'D 6 s 6 p - P , 1 - 6s9s 'S, 6s6p 'P.". •6s7s 'S. 6s6p 'P/- 6s7s 'S, 6s6p*P."- 6 s l 0 s 'S. 6 s 6 p 'Pa'- 6 s 6 d 'D 6s6p *PT- .636d*D, 6 s 6 d *D •6a6d'D, 6s6p * P ; • 6 s 8 s S, 6s6p'Pa"•6s6d 'Dj 6s6p*P/•6s6d*D, 6s6p*P/6s6p*P/- •6s6d *D 6s6p *P a # - • 6 s 7 d ' % 6s 6p 'p;- •6s8s *S, 6 s 6 p * P . * ' •638s *S, 6s* 'S ••6s6p * P , ° 6s6p p; • •6s9s 'S, J  J  a  J  3  3  a  a  a  CO i n  a  J  a  #  J  (1)  (cm."' )  -38.5? 128 -124.8; 261.6 -401.3; -281.3; 676.5 -397.8; -231.3; 680.0, 846.5 -635; -459.5; 400.5 -247.5; -72;138; 313.5 -137.5; 163; 332.5 -483.6; -97.2; 594.2; 980.6 -259.1; 59.7; 818.7 -119; 56.5 -961.0; -221.6; 116.8; 856.2 -416; -240.5; 254.5 -35.5; 19; 194.5 -119; 56.5 -242.5; 496.9 -714.5; 363.3 - 1 1 9 ; 56.5 -819.6; -60.6; 40.4; 799.4 -432.1; 326.9; 712.4 -491.6; -21.6; 267.4; 737.4 -741.6; 17.4; 24.9 -234.6; 41.4; 800.4 -762.5; -23.1; 97.5 -375.0; 10.5; 364.4; 749.9 -434.5; 35.5; 774.9 -395.6; 165.6; 363.4; 593.4 -936.5; -197.1; 98.5; 837.9 -690; 345 -518.0; 221.4 -690; 345  intensity 2 ;1 2tl 1 :9:5 5:1 :1:2 5 :l:9 1:5 : 2:1 9 .5:1 5:1 :1:2 5 :9:1 1 \2 1:2 :5:1 ' 5' 1:9 9 :5:1 1- 2 2 .1 1 .2 1 :2 1:3 : 5 : l 9 :l:5 5:1 :1:3 1:14:20 5:9:1 1: 5:9 5:1:1:2 9:1:5 5:1:1:3 1:2: :5:1 1:2 1:2 1:2  57.  <*}  Bibliography.  1.  S c h l f f , D.  and M e t z g e r ,  2.  M e g g e r s , W.F.:  3.  N a t i o n a l Bureau of S t a n d a r d s :  "Nuclear  4.  Hill,  A.D.  P h y s . Rev.  5.  Hill,  R.D.:  6.  Meissner,  K.W.:  7.  Tolansky,  S.:  8.  Valasek,  and  10.  Candler,  P h y s . Rev  79,  413,  J.O.S.A. 31, 32,  7,  90,849,1953.  1949. Data." 79,  275,1950.  1950.  405, 185,  1941 1942.  "High R e s o l u t i o n Spectroscopy", Methuen and Co., 1947. " T h e o r e t i c a l and  and  and  Barrell  Experimental Optics,"  Sons,  , H:  1947.  P r o c . Roy.  Soc.  A122,122,1929.  C:  "Modern I n t e r f e r o m e t e r s " , H i l g e r and W a t t s , 1951. G.: " A t o m i c S p e c t r a and A t o m i c S t r u c t u r e , " Dover P u b l i c a t i o n s , 1944.  11. H e r z b e r g ,  12.  Tolansky,  13.  Brix,  14.  Strong, J . :  S.:  "Hyperfine Structure i n Line Spectra and N u c l e a r S p i n , " Methuen and Co., 1948.  P. and K o p f e r m a n , H.: L a n d o l t - B o r n s t e i n , 6: A u g l a g e , " Z a h l e n w e r t e und P u n c t i o n e n " , I . Band, Atom-und M o l e k u l a r - p h y s i k ; 5. T e l l , Atomkerne und E l e m e n t a r t e i l c h e n , S p r i n g e r - V e r l a g , 1952, pp.53. "Procedures i n E x p e r i m e n t a l P h y s i c s , " Prentice-Hall, 1938.  15. G e i g e r , P.S.  Jr.:  16.  Hughes, D.S.  andEckart,  17.  Breit,  18.  Brix,  19.  Breit,  G.:  J.O.S.A. 39,  P h y s . Rev.  C:  G:  Jacobsen,  Phys, Rev.:  42,  M.  and  E . and  22. Webb, J.H.:  78,  348,  1949. 36,  694,  390,  157, 316,  1942.  1950.  P h y s . Rev.85, 1047L,  H a r r i s o n , G.R.:  1930.  1932.  P h y s . Rev.85, 1050L,  Brown, S.C.:  J.O.S.A. 23, 23,  249,  P h y s . Rev.  P. a n d K o p f e r m a n , H:  20. D e u t s c h , 21.  48,  M i h e l i c h , J.W.:  Wiley R o l t , P.H.  P h y s . Rev.  S c i e n . Monthly  J.:  9.  P.R.:  J.O.S.A. 39, 1933. 1933.  1952.  1054,1949.  58. 23.  S c h u l e r , . H. a n d K e y s t o n ,  J.E.:  Z . f . Phys.  72, 423,  1931. 3, 185, 1935.  24.  H a r n w e l l , C P . : Amer. P h y s . T e a c h e r  25.  M e g g e r s , W.P.  and W e s t f a l l , P.O.: J . Res. Nat. Bur. S t a n d . Wash. 44, 447, 1950.  26.  M e g g e r s , W.P.  a n d K e s s l e r , K.G.:  27.  B u r n s , K. and Adams, K.B.:  28.  Glazebrook,  J.O.S.A. 4 0 , 737, 1950.  J.O.S.A. Ji2, 56, 1952.  S i r R.: "A D i c t i o n a r y o f A p p l i e d P h y s i c s , " V o l . I V , pp.323,. M a c M i l l a n a n d Co., 1923.  «  PLATS I :  Fabry-Perot pattern angstroms two  of the l i n e  s h o w i n g t h e h f s . due  components,  rig  1 9 8  and  5461 t o the  Hg ". 1  60.  PIATE I I : At  the r i g h t ,  the f r i n g e  due t o t h e l i n e Note t h a t at  4077 a n g s t r o m s .  the l i n e  the l e f t  also  system  4046 a n g s t r o m s  exhibits h f s .  61  PLATE I I I : Interference  pattern  of t h e  3341  angstroms  ring  s y s t e m s due t o t h e two  components.  showing  the  line two Hg  62  PLATE IV: Off-centre  Fabry-Perot  of the l i n e the  right  and 3131.6  pattern  3125 a n g s t r o m s .  i s the d o u b l e t , angstroms.  At  3131.8  

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