UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

The decay of [formula omitted] Nagpal, Tarlok Singh 1964

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1964_A1 N3.pdf [ 5.16MB ]
Metadata
JSON: 831-1.0085854.json
JSON-LD: 831-1.0085854-ld.json
RDF/XML (Pretty): 831-1.0085854-rdf.xml
RDF/JSON: 831-1.0085854-rdf.json
Turtle: 831-1.0085854-turtle.txt
N-Triples: 831-1.0085854-rdf-ntriples.txt
Original Record: 831-1.0085854-source.json
Full Text
831-1.0085854-fulltext.txt
Citation
831-1.0085854.ris

Full Text

THE DECAY OF  55  .^Cst^ (9  by TARLOK SINGH NAGPAL B.A., The Panjab University (India), 1 9 5 2 M.Sc, The Aligarh Muslim University '(India), 1 9 5 6  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  i n the Department .' of PHYSICS  We accept t h i s thesis as conforming to the required  standard  THE UNIVERSITY OF BRITISH COLUMBIA September, 196k  In presenting the  this thesis i n partial fulfilment  r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t the U n i v e r s i t y  B r i t i s h Columbia, I agree that available  f o r r e f e r e n c e and  mission for extensive p u r p o s e s may his  be  cation  study,  Library  I f u r t h e r agree that  the  Head o f my  written  Department  of  permission*  The U n i v e r s i t y of B r i t i s h C o l u m b i a , V a n c o u v e r 8, Canada  c o p y i n g or  s h a l l not  of freely per-  scholarly  Department or  I t i s understood that  of t h i s t h e s i s f o r f i n a n c i a l gain  w i t h o u t my  s h a l l make i t  c o p y i n g of t h i s t h e s i s f o r  g r a n t e d by  representatives.  the  of  be  by publi-  allowed  The U n i v e r s i t y  of B r i t i s h  Columbia  FACULTY OF GRADUATE STUDIES  PROGRAMME. OF THE FINAL, ORAL EXAMINATION FOR. THE  DEGREE OF  DOCTOR OF PHILOSOPHY  of TARLOK  SINGH NAGPAL  B.A,, •. The Panjab U n i v e r s i t y M.Sc.j  (India) , 1.952  The A l i g a r h Muslim U n i v e r s i t y  ( I n d i a ) , 19.56  MONDAY, SEPTEMBER 14, 1964, AT 1 % 30 P.M, IN ROOM 10, HEBB BUILDING (PHYSICS)  COMMITTEE IN CHARGE Chairman-  I . McT. Cowan  M.P. Beddoes J.W. B i c h a r d K.L.,Erdman External  G. Jones K.C. Mann J . F . Scott-Thomas Examiner:  University  R.D. Connor  of Manitoba  DECAY OF  5  5  Cs^  ABSTRACT The  t e s t s of performance of the m o d i f i e d  magnetic spectrometer extended  u s i n g r i n g - d e t e c t i o n have been  u s i n g improved mechanical  position.  thin-lens  c o n t r o l s of d e t e c t o r  The r e s u l t s show only a small improvement, over  the performance o b t a i n e d p r e v i o u s l y i n t h i s l a b o r a t o r y . We conclude that, the l i m i t  of performance w i t h the  l e n s magnet has been reached.  F u r t h e r improvement: may  be achieved only w i t h a precision-wound which w i l l  thin-  produce a completely  magnet  symmetric  coil  field.  The decay of 55^8^^ has been i n v e s t i g a t e d u s i n g t h e m o d i f i e d t h i n - l e n s spectrometer, spectrometer  and beta-gamma, c o n v e r s i o n - e l e c t r o n gamma  coincidence techniques.  The r e s u l t s support, t h e  simpler decay scheme proposed Connor.  a scintillation  by Van Wijngaarden and  The beta decay has t h r e e components w i t h end-  p o i n t e n e r g i e s and i n t e n s i t i e s of 659+3 kev(67 .37o), 411  kev (2.5%) and 89 kev (30.3%), estimated from t h e  energy  level  i n t e n s i t y balances  i n Ba^ ^. 3  These  i n t e n s i t y balances  show d i s c r e p a n c i e s of l e s s than 3%  of the t o t a l  intensity.  decay  The c o n v e r s i o n c o e f f i c i e n t s ,  calculated  from t h e  c o n v e r s i o n e l e c t r o n and gamma-ray i n t e n s i t i e s l e a d t o the f o l l o w i n g m u l t i p o l a r i t y i d e n t i f i c a t i o n s f o r t h e transitions i nB a  1 3 4  ; 473 kev (Ml or.E2)j 563-569 kev  (Ml or E2), 605 kev (E2), 797-803 kev (E2), 1036 kev (Ml or E2), 1168 kev (E2) and 1366 kev (E2), i n agreement w i t h other work.  The M l or E2 c h a r a c t e r of t h e  47 3 kev and 1036 kev t r a n s i t i o n s makes i t p o s s i b l e t o a s s i g n a spin, of 3+ or 4+ t o the 1641 kev l e v e l which was u n c e r t a i n b e f o r e . evidence  An u n s u c c e s s f u l search f o r  of a 960 kev gamma-ray r e p o r t e d by o t h e r s  puts an upper l i m i t of 0„27o on i t s i n t e n s i t y ,  GRADUATE STUDIES  Field  o f Study"Physics  Quantum Mechanics  F. A.Kaemp f f er J.C.  Waves  CM,  E l e c t r o m a g n e t i c Theory Nuclear  Savage Volkoff  J.B. Warren  Physics  Related Studies; Applied  M.P.  Electronics  Differential  Equations  J.F.  Beddoes  Scott-Thomas  ii. ABSTRACT  The tests of performance of the modified thin-lens magnetic  spectrometer  using ring-detection have been extended using improved mechanical controls of detector position.  The results show only a small improvement over the  performance obtained previously i n this laboratory.  We conclude that the l i m i t  of performance with the thin-lens magnet has been reached. may be achieved only with a precision-wound a completely  Further improvement  magnet c o i l which w i l l produce  symmetric f i e l d . 13^  The decay of ^ C s y ^ has been investigated using the modified thin-lens spectrometer,  a s c i n t i l l a t i o n spectrometer  gamma coincidence techniques.  and beta-gamma, conversion-electron  The results support the simpler decay scheme  proposed by Van Wijngaarden and Connor.  The beta decay has three components  •with end-point energies and i n t e n s i t i e s of 659+3 kev(67-3$)> ^'H kev ( 2 - 5 $ ) and 89 kev (30-3$)> estimated from the energy l e v e l intensity balances i n Ba^-^. These i n t e n s i t y balances show discrepancies of less then 3$ of the t o t a l decay intensity. The conversion c o e f f i c i e n t s , calculated from the conversion electron and gamma-ray i n t e n s i t i e s lead to the following multipolarity i d e n t i f i c a t i o n s f o r the transitions i n  Ba S 13  i+73 kev (Ml or E2), .563-569 kev (Ml or E2), 605 kev (E2),  797-803 kev (E2), IO36 kev (Ml or E2), -11.68 kev (E2) and 1366 kev (E2), i n agreement with other work.  The Ml or E2 character of the ^73 kev and IO36 kev  transitions makes i t possible to assign a spin of 3 l e v e l which was uncertain before.  + o  r  ^+ "to the l6kl kev  An unsuccessful search f o r evidence of a  96O kev gamma-ray reported by others puts.an upper l i m i t of 0.2$ on i t s intensity.  iii. TABLE OF CONTENTS Page INTRODUCTION CHAPTER I  1  . ..  3  THEORY OF BETA AND GAMMA DECAY  3  BETA DECAY Theory of Beta Decay (i) (ii) (iii) (iv) (v) (vi)  . . . .  ....... . . .  5  Beta Interaction Beta'Spectrum  ......................  (ii)  CHAPTER II  7 10  Selection Rules Kurie Plot  . . 11  .. . .. .  Comparative Half L i f e  13  . .  O r b i t a l Electron Capture  ......... ... . . . . ik 15  GAMMA DECAY; (i)  k  Multipole Radiation  16  .  Internal~Conversion and Conversion C o e f f i c i e n t s  METHODS OF DETECTION AND MEASUREMENT  DETECTION SYSTEMS  . ... . •  MAGNETIC SPECTROMETERS  . . . . . • 19  • • •• •  ...... • • • 2.1 21  ......... . . ..  Spectrometer C l a s s i f i c a t i o n  ......... . . .  F l a t Spectrometers. .  ... ... .  Lens Spectrometers  19  . ..  ..."  P r i n c i p l e s ,of Operation  17  2k . 2k ... . • '25  .•  Spectrometer Measurements of Beta -and Internal Conversion Spectra .. • . . . . . . . ... . . 26 Spectrometer Measurement of" Photoelectron Spectra . . . . 27 THE SCINTILLATION GAMMA-RAY SPECTROMETER .  27  COINCIDENCE SPECTROMETERY . . . . . . . . . . . . . . . . . . . . . . . . . . Gamma-GammaAngular Correlation  29 31  CHAPTER I I I  THE THIN LENS MAGNETIC SPECTROMETER  Introduction  . . . . ......... 33  . . . ... . ......... . . . . . . .  THE MODIFIED THIN LENS SPECTROMETER -. • ....... . .  . . . . . 33 -. . 3^  THE ASSOCIATED CIRCUITS 38 (a) The F i e l d Current Control C i r c u i t . . 38 (b) Beta Spectra Counting C i r c u i t . . . . . . . ... . . 38  iv. Page 38  SPECTROMETER ADJUSTMENT . . . . . . . . . . . . . . .  39  ......................  39  .  Lo  Discriminator Level Setting Spectrometer Alignment  Variation of the Parameters  CHAPTER. IV  THE DECAY OF Cs " ^ 55 EXPERIMENTAL PROCEDURES 3  3  The "Coincidence System  . ......  .  L3 . .  . . . .. . . . . . . . . . .  ... .  L5  51 .52  THE DECAY SCHEME Beta-group Intensities  L3  U7  EXPERIMENTAL RESULTS Coincidence Results  .......  .. •• .. .. . . . . . . .. ... . . . .. . . 53  Conversion Coefficients and Transition M u l t i p o l a r i t i e s .. . 53  Appendix 1  NUCLEAR MODELS  .  60  The Shell Model  60  The C o l l e c t i v e Model  6k  Appendix 2  BIBLIOGRAPHY  SOME CIRCUIT DIAGRAMS  68  69-71  V.  LIST OF ILLUSTRATIONS AND TABLES To follow page Figure 1.  2  Typical Decay Schemes  CHAPTER I Figure 2.  A t y p i c a l beta spectrum with conversion l i n e s . . . 12  CHAPTER I I Figure 3>  Main features of the spectrometer due to Rutherford and Robinson  ,  2k  Figure-J+.  Double focusing  Figure 5-  P r i n c i p l e of t h i r d order focusing  2k  Figure 6.;  "Orange" spectrometer  2k  Figure 7-  Prism and S e c t o r f i e l d spectrometers  Figure 8. Figure 9*  Electron t r a j e c t o r i e s i n t h i n lens spectrometer • • 2k Block diagram of gamma ray s c i n t i l l a t i o n spectrometer 27  Figure 10.  Pulse spectrum of homogeneous gamma radiation • • • 27  . . .  . . 2k  . . . . . . . ... 2k  Figure l l ( a ) . Block Diagram of gamma gamma coincidence system • 29 (b).  29  Rossi coincidence c i r c u i t . . .  Figure 12.  Fast-slow coincidence system  Figure 13-  Two gamma rays i n cascade  30 . . . . . . .  31  CHAPTER III Figure lk.  The bell-shaped f i e l d i n a thin lens spectrometer • 33  Figure 15-  Modified t h i n lens spectrometer  Figure l 6 .  The detector assembly  Figure 17-  Defocusing  Figure l 8 .  Control c i r c u i t  Figure 19-  Counting c i r c u i t  38  Figure 20.  Typical Discrimination plateau  39  Figure 21.  Noise l e v e l setting corresponding  • •• • • • ^ • • • 36 36  e f f e c t on photomultiplier noise  electron energies  • • • • 37  • • • • • . . . . . . . . . . . 38  to d i f f e r e n t 39  vi.  To follow page Figure 2 2 . Variation of peak shape with detector distance . . Figure 2 3 .  Variation of R, T and T/R with s  Figure 2k.  Graph showing matqh condition  kl  . . ... . . . . . . kl . . . ......... .. . kl k2  Table I.  Results of c a l i b r a t i q n measurements  . .  Table II.  Comparison of present work with that of Mann and Payne . . . ..... . ... . . . . . ... . . . . k2  •CHAPTER IV Figure 2 5 .  Decay of ^ C s  . . . . . . . . . . . . . . . . . . . .1+3  Figure 2 6 .  Photoelectron source  Figure 27-  Gamma-ray detector  Figure 2 8 .  Gamma-ray detector assembly i n the magnetic  . kk ..... . . . kk  .  spectrometer  kk  . ...  Figure 29- Block diagram of gamma-beta coincidence system  . . 4-5  Figure 30*  . . 1+5  Block diagram of beta-gamma coincidence system  Figure 31-  Beta-gamma coincidence response as a function of delay on the gamma side . . . 46 Figure 3 2 . Beta spectrum o f Cs * ' . . . . . ............. . . 1+7 13  4  Figure 33- Kurie analysis of beta spectrum of Cs"*"^ 3  • Figure 34. Figure 35Table I I I .  Internal conversion spectrum of Cs" " ^ 1  3  . . . ... 1+7 ..... . ... k'J  Part of photoelectron spectrum of C s ^ ..... ... .k'J "Conversion electron i n t e n s i t i e s (Beta scale) . . . kQ  Figure 36.  S c i n t i l l a t i o n spectrum of gamma rays of " C s ^  Figure 37-  Gamma spectrum of C © ^  Table IV..  Gamma ray i n t e n s i t i e s  . . .. 49 ... .' . 49  . . ..... . . . . . . . ... . 50  Figure 38- Kurie analysis o f beta spectrum i n coincidence with 7 9 7 \ gamma rays . . . . . . . . . . . . . . -51 803j 134 Figure 39- S c i n t i l l a t i o n spectra of gamma rays o f Cs in coincidence with different, gate points . . . . . . . 51  0  vii. To. follow page Figure. U O .  Table V.  Analysis of composite conversion peaks . . . . . . .  T r a n s i t i o n i n t e n s i t i e s and conversion coefficients"  Table VI. Comparative gamma ray i n t e n s i t i e s  . . . . ....  Level structure, of M Xe  5^ 56  l^U  T O O  Figure U X -  53  and'/Ba.  (comparison)  Appendix 1 Figure A l . Energy l e v e l s i n a p o t e n t i a l well intermediate between square well and o s c i l l a t o r p o t e n t i a l . .  6l  Figure A2. Coupling scheme f o r angular momentum of deformed n u c l e i . . ........... . . ... . . . . .  65  Figure A3- Single p a r t i c l e states i n a spheroidal p o t e n t i a l as -a function offi  66  Figure Ah. V i b r a t i o n a l l e v e l s i n even-even n c u l e i  67  . . ... .  Appendix 2 Figure A5. Magnet current c o n t r o l c i r c u i t  . ....... . . .  Figure A6. Components of the phototube bleeder  ........  Figure A7- C i r c u i t diagram of the fast coincidence d r i v e r Figure A8. S c i n t i l l a t i o n detector-electronics  .  -  68 68 68 68  59  viii.  • ACKNOWLEDGEMENTS The work reported upon i n t h i s thesis has "been made possible by the. assistance and cooperation of a number of people i n the Department of Physics, and to them I am most grateful. Dr. J.B. Warren and Dr. B.'L. White made the multichannel pulse height analyzer available to me and gave me advice on i t s use.  Dr. Garth Jones  was very h e l p f u l with some electronics'problems. "Mr. A. Fraser, Mr. J . Lees, Mr. E. Price, and members of the workshop s t a f f provided valuable technical assistance.  To a l l of these, I express my sincere thanks.  To Dr. K.C. Mann, who suggested the research problem, f o r h i s advice and guidance throughout the course of t h i s work, I express my sine ere st thanks.. The project was supported by the National Research Council of Canada, through Grants-in-Aid of Research to Dr. K.C. Mann.  1. INTRODUCTION  It was established i n 1912 by the alpha scattering experiments of S i r Ernest Rutherford that an atom has a c e n t r a l massive core c a l l e d the nucleus, where a l l the p o s i t i v e charge and a l l but a small f r a c t i o n of the t o t a l mass are  concentrated.  positively  charge.  Positive  charged p a r t i c l e s  charge on the nucleus called protons,  i s due t o t h e p r e s e n c e of  e a c h c a r r y i n g a u n i t electronic  The number of protons i n a nucleus i s generally denoted by Z and i s  known as i t s atomic number.  Surrounding the nucleus are Z electrons i n various  states of motion. Modern theories of the atomic nucleus begin with the discovery of the neutron by Chadwick i n 1932 and the suggestion of Heisenberg, shortly thereafter, that the elementary constituents of n u c l e i are protons and neutrons, often referred to indiscriminately as nucleons.  The number of nucleons i n a  nucleus i s i t s mass number and i s denoted by A.  Thus a nucleus of mass number  A and atomic number Z i s composed of Z protons and A-Z=N neutrons.  Nuclei of  equal Z and^equal N are c a l l e d isotopes, those of equal N and d i f f e r e n t Z are c a l l e d isoton&s, while n u c l e i of the same mass number A are isobars.  A  nuclear species or nuclide i s generally denoted by the symbol X ( A , Z ) , where X stands f o r the chemical symbol of the nuclide. Quantum mechanical invesigations into the behaviour of a nucleus as a proton-neutron system reveal that such a system can exist only i n certain discrete energy states which correspond to c e r t a i n allowed arrangements and motions of the nucleons.  Each state i s characterized by properties such as  energy, angular momentum (or spin), p a r i t y , * etc.  The state of the lowest energy  i s c a l l e d 'ground' state and a l l others are known as 'excited' states. * In quantum mechanics a nuclear state i s described by a wave function. On changing the sign of the coordinates .of the wave function (mirror r e f l e c t i o n ) i t s sign may or may not change. P a r i t y describes t h i s behaviour. In the former case i t i s said to be odd, in'the l a t t e r even.  2. A nucleus i n an excited state i s unstable or radioactive, and may  attain  s t a b i l i t y through a variety of processes depending, among other things, upon the e x c i t a t i o n energy available.  The process of de-excitation may  involve a  change i n the atomic number of the nucleus (beta emission and o r b i t a l electron capture) or no change i n the atomic number (gamma emission, i n t e r n a l conversion and i n t e r n a l p a i r formation). to another which may  In the former case, the nuclide i s transformed  also be l e f t i n an excited state; i n the l a t t e r the  nuclide remains unchanged.  The p r o b a b i l i t i e s of the d i f f e r e n t events.are  complicated functions of the energies and the spins and p a r i t i e s of the i n i t i a l and f i n a l energy states involved i n the process.  It i s useful'to represent  a l l such processes on energy l e v e l diagrams such as are' shown i n Figure 1 . These representations are c a l l e d decay schemes. One important function of nuclear spectroscopy i s the establishment of decay schemes f o r a l l nuclides with spin and p a r i t y assignments to each l e v e l , and a comparison of experimental measurements with t h e o r e t i c a l predictions. Decay schemes of a large number of nuclides have been investigated but •only the simplest of them are well-established.  The modes of decay of many  nuclides are very complex and the data that can be c o l l e c t e d i n such cases generally are inadequate to lead to an unambiguous determination of the decay schemes. Therefore, i t i s not surprising to f i n d that -a p a r t i c u l a r decay has been investigated by many workers using a v a r i e t y of techniques without reaching agreement on the decay process.  The decay of C s l 3 ^ "the analysis of which  forms part of the present work, i s an example.  To f o l l o w p a g e 2.  Fig.l.  T y p i c a l Decay  Schemes  3CHAPTER THEORY OF BETA AND  1 GAMMA DECAY  BETA DECAY In t h i s process an unstable nucleus (parent) emits a negatron or a positron, or captures an o r b i t a l electron.  The product nucleus (daughter) has,the same  mass number but i t s atomic number d i f f e r s from the parent by one u n i t .  Thus  beta decay takes place between isobars. Emitted negatrons and positrons have a continuous energy d i s t r i b u t i o n from zero to some maximum energy which i s related to the energy available f o r the decay.  Since the decay takes place between discrete i n i t i a l and f i n a l  states, the emitted electrons do not carry away the entire energy available. Electrons are not fundamental nuclear constituents so they must be created during the decay.  The-conservation of-energy, momentum, and  angular momentum i n the beta decay process and the d i s t r i b u t i o n i n energy of the emitted electrons .can be understood only i f i t i s assumed that i n addition to the electron, a second p a r t i c l e c a l l e d the neutrino ( )) ) i s emitted.  The  neutrino i s assumed to have no charge, p r a c t i c a l l y zero mass and an i n t r i n s i c spin angular momentum of -g-h .  These assumptions o r i g i n a l l y proposed by P a u l i ,  .1 led Ferpi  to construct h i s theory of beta decay.  It i s only recently that 2  the d i r e c t evidence f o r the existence of the neutrino has been .found . Since the number of nucleons A remains -unaffected, beta decay e s s e n t i a l l y consists of' the transformation of-a neutron (or proton) i n the parent nucleus into a proton (or neutron) i n the daughter nucleus.  Thus beta t r a n s i t i o n s  may be indicated by: (A,Z)~^> (A,Z+l)+ e + + U  (l)  (negatron or positron emission) (A,Z)+ e " — ^ (AjZ~L) + » (capture of the o r b i t a l electron)  (2)  Processes ( l ) and ( 2 ) are energetically possible only i f , M(A,Z)  y M(A,Z+l)  M(A,Z)  >  M(A,Z)  > M(A,Z-l)  negatron emission  M(A,Z-l)+2mQ  positron emission o r b i t a l electron capture  where M(.A,Z) i s the mass of an atom of mass number A and atomic number Z.., and mQ i s the rest mass of electron. In the description of processes ( l ) a n d - ( 2 ) above, we have assumed that the neutrino accompanying a negatron i s i d e n t i c a l with that accompanying a positron.  This i s the assumption made by Majorana . The alternative assumption k  i s that of Dirac  whereby the p a r t i c l e emitted with a positron i s the -'normal'  neutrino and that -emitted with a negatron i s i t s ' a n t i p a r t i c l e ' or antineutrino. In Dirac's theory of spin-^ p a r t i c l e s , the emission of an a n t i p a r t i c l e i s equivalent to the absorption of a normal p a r t i c l e and therefore a l l nuclear beta processes can be conveniently expressed by a basic r e l a t i o n , i . e . , P + e~  -<  s-  n  + y;  ^j  which i s interpreted as the annihilation of a neutron (n) and a neutrino ( V ) leading to the creation of a proton (p) and a negatron ( e~) or vice versa. Theory of Beta Decay Fermi's basic assumption i s that the .leptons (electron and neutrino) i n nuclear beta decay are created as a r e s u l t - o f the transformation of a neutron state into a proton state, .or vice versa, inside a nucleus i n much the same way that a photon i s born with the change i n state of a charged radiating system.  Beta t r a n s i t i o n p r o b a b i l i t i e s , therefore, can be calculated using,  the same 'golden rule' of time dependent perturbation theory which i s used for c a l c u l a t i n g electro-magnetic t r a n s i t i o n p r o b a b i l i t i e s i n the theory of radiation.  The golden rule gives as the t r a n s i t i o n p r o b a b i l i t y , £ per unit time;  5-  where  ^ are i n i t i a l and f i n a l wave functions of the system, ~  i s the  density of f i n a l states available to the emitted p a r t i c l e s and H i s the force or  'interaction' which brings about the transformation of the system from an  i n i t i a l to a f i n a l state.  In the theory of r a d i a t i o n the i n t e r a c t i o n i s taken  over from c l a s s i c a l theory and the -elementary electronic charge e the strength of the injt-eraction. analog exists.  measures  For beta decay, however, no such c l a s s i c a l  The beta interaction, therefore, has to be invented to f i t  the experimental r e s u l t s .  (i)  Beta Interaction Fermi proposed that the i n t e r a c t i o n i s proportional to a four vector  current associated with the beta decay process. mathematical  convenience  i t can be written as:  '•#• H  = 8  (Vp  From the viewpoint of  -3fr  K  P- %  ) - +  h  c  ( 5 )  where 'g' measures the strength of interaction. 1  Starred  V/Z's represent the  corresponding wave functions of the p a r t i c l e s created and simple of the p a r t i c l e s annihilated.  's those  0 i s an operator which brings about the  •annihilation of the two p a r t i c l e s to create two new ones.  h.c. i s the  hermitian conjugate of the -expression preceeding i t and i s included f o r the sake of completeness  and accounts f o r the creation of positrons.  P a r t i c l e s involved i n beta decay are - a l l spin-5- p a r t i c l e s , each of which i s represented by a four-component vector (spinor) i n Dirac's theory. be any operator containing spin coordinates. construct the  O's and'then combining  of interactions are possible.  Q.  c  a  Using Dirac four matrices to  the l a t t e r with ^ " s , a large number  Of these, only those are accepted that are  invariant under rotations and Lorentz transformations.  Physically this  n  defines the way the interactions depend upon the spin coordinates.  Using  t h i s c r i t e r i o n we end up with just f i v e types of interactions c a l l e d respecti v e l y scalar (s), vector (v), tensor (T), a x i a l vector (A) "and pseudoscalar (p). Fermi's o r i g i n a l hypothesis quoted the vector interaction as an example. There i s no a p r i o r i reason why each of these f i v e interactions cannot bring about beta decay and hence an a r b i t r a r y l i n e a r combination of these i s a possible choice.  The most general interaction therefore i s -x-  H =g J S c ^ where  Q  ±  =  Oiy )( %  ) .+ h.c.  n  Os,V,T,A,P >  3 1 1 ( 1 c  l •= S,V,T,A,P C  a  r  e  (6) a r b i t r a r y constants •  The interaction (6) i s invariant under space r e f l e c t i o n or i t conserves p a r i t y and i s c a l l e d 'even'.  A similar interaction biit 'odd', i n nature can  also be constructed and i s obtained by replacing  i n (6) w i t h ^ l ^ ^  has a pseudoscalar character, which imparts an ''odd' behaviour to the interaction. 5  Before Yang and Lee  advanced t h e i r hypothesis of p a r i t y non-conservation  i n weak interactions, the even and odd interactions had been used as equivalent alternate ways i n which one could-formulate a theory of beta decay. The p o s s i b i l i t y of t h e i r coexistence i n any decay was .rejected to maintain the then secure view that p a r i t y was conserved i n weak interactions.  (Beta  decay i s a weak interaction.) Immediately following Yang and Lee's hypothesis, a large number of experiments were performed,  the f i r s t being the c l a s s i c measurement of  Wu.et.al^ on the s p a t i a l d i s t r i b u t i o n of beta p a r t i c l e s emitted from nuclei.  aligned  They proved that the hypothesis was correct and hence both odd and  even interactions can coexist i n a decay.  A general form of interaction, then,  may be:  +h.c.  •H =  (7)  7 To simplify (7) use i s made of the available 'experimental evidence , which shows that the negatron and neutrino emitted i n beta decay are longi t u d i n a l l y p o l a r i z e d with spin a n t i p a r a l l e l to t h e i r momentum.  When tracked  down t h e o r e t i c a l l y , t h i s means that Ci  = Ci  and that only vector and a x i a l vector interactions should be included. The presently accepted interaction therefore i s + h . c (8)  H = gS.C V,A V,A with C •= - 1 . 2 C A  8 y  ( i i ) .Beta Spectrum ..In c a l c u l a t i n g beta decay rates using (U) Fermi made the following assumptions; (l)  the nuclear extension ,,—> r = 0;  (.2)  U i i s the wave function of the i n i t i a l nucleon, whereas U  =  ; y£  say  are respectively the  wave functions of the f i n a l nucleon, electron and'(anti) neutrino; (3)  electrons and antineutrinos are considered emerging as plane waves with momentum  and Py respectively.  Therefore  1 where  ~ ^ v ~ "*"  the nucleus;  S &  n o r m a l  i  z a t i o n  f  & c  '  t o r  using an a r b i t r a r y volume V around  8.  (U)  the transition prohahility is proportional to the expectation value for the electron and the antineutrino at the nucleus, i . e .  °c \y0)1*1 %(o)\  z  Using these assumptions with  q dn  = V ) ^ ~~ —ITS 2  d E  2  t  dp '  V (E -E g ) , U,6 2  =  0  /  2 P/9  d  P/g  (  1  0  )  where ^0,p respectively are disintegration energy and beta particle: energy, and making use of equation (4), the probability per unit time that a beta particle w i l l be emitted with momentum between p^  =  where  and p^ + dp^g  is  » - f ! _ . i M p p |  "(ID  M = In deriving ( l l ) i t was assumed that the nuclear charge of the  transforming nucleus allows the electron plane wave to emerge undistorted. Physically, negatrons will.be 'held back' and positrons 'pushed forward* as a result of the Coulomb forces between the nuclear and the-electronic charges, resulting in a characteristic distortion of the spectrum.  Correction factors  for  either case and for different values of p and Z have been calculated and  are  available.  These are known as Fermi functions, F(Z,p).  The corrected  form of (ll)., therefore, is ptyOdfc  .= 2  JL=_ ^Jn'd'J  P(Z,P)  |M|V(E -J) ^ 0  2  (13)  A more u s e f u l form of equation (13) i s obtained as follows: n(p), the number of beta p a r t i c l e s having momentum between p .and p+dp i s related to P(p) through a constant m u l t i p l i e r . Further, i t i s customary to use units i n which TOQ = "H  = c - 1, and  p a r t i c l e momentum p and energy W are expressed as :  P ,=  • and W = /3 E  m c  —  0  T  O ™cf  d  This, then, leads to the following form of the momentum d i s t r i b u t i o n of beta p a r t i c l e s n(p)dp = const. |MJ F(Z,p)p (W -W) dp 2  2  (lk)  2  0  2 In (lU)  2  p (E -E.) i s known as the- s t a t i s t i c a l - w e i g h t ' . 1  I t i s this  factor that describes the s t a t i s t i c a l d i v i s i o n of the disintegration energy between the beta p a r t i c l e -and the neutrino. In. c a l c u l a t i n g the t r a n s i t i o n p r o b a b i l i t y , plane.'wave functions were used f o r the l i g h t p a r t i c l e s .  These were evaluated at the nuclear-centre on  the assumption that the nuclear dimensions were n e g l i g i b l e compared with the wave length  /\ = -^2  of the plane wave.  The product of the wave  K  functions may be expressed as: * ur %TV  = I  V  e"  1  %  1  h  1e "  .=  1  Actually the nuclear extension for moderate energies and therefore  e  '  00  (2i+l)i^  ^  |.r| i s such that  = 1 - i ( k . r ) + ^(11.7)' =S  1  v  (kr)j£(cos 9)  |kr|  1  may be expanded as  (15)  •10.  where  i s the spherical Bessel function and P^ (cos 0) are Legeridre  Polynomials. Using ( l 5 ) > "we .can write  f * <U | H J U ^ r ^ f  lj?  ^  f  r Ot^dt- i -  [M|  Yf k  |Mi| +  r  £Yi  d t  +  '(16)  —  |MP|  where successive terms decrease by a factor of approximately 1 0 " f o r energies 1 Mev.  M  i s momentum independent, while  |M-jJ , \^\ > etc. are a l l  momentum dependent. The orthogonality properties of the wave functions may, under' c e r t a i n conditions involving spin and p a r i t y changes i n the t r a n s i t i o n , cause any of the matrix elements to vanish.  This being so, i t i s the f i r s t  element which p r i m a r i l y determines the decay p r o b a b i l i t y . leading to equation (lh)  meant that |'M| only was used.  most probable, and are c a l l e d 'allowed' t r a n s i t i o n s .  non-vanishing  The assumption  Such t r a n s i t i o n s are Where |M[ i s zero, and  JMJ non-zero, we have a ' f i r s t - f o r b i d d e n ' t r a n s i t i o n , etc. The t r a n s i t i o n rate i n the case of a forbidden t r a n s i t i o n may be expressed by an equation similar to equation ( l 3 ) > 2 PCP/a  =  —  S ( )P(Z,p)(E -E n  P  0  /3  ) p | dp^  ^  where S ( p ) i s c a l l e d the 'shape-factor'. n  The p r o b a b i l i t y of observing forbidden t r a n s i t i o n s decreases r a p i d l y with increasing order of forbiddenness.  (iii)  Selection Rules The conditions whereby a t r a n s i t i o n f a l l s within a c e r t a i n c l a s s i f i c a t i o n  (allowed, forbidden, e t c ) are c a l l e d 'selection rules. conditions whereby the element | M±\ does not vanish.  These obviously are As: might be expected  the quantum descriptions involved are angular momentum and p a r i t y .  11. The angular momentum - I"h of any nucleus i s considered to be a vector sum of a l l angular momentum components of the constituent nucleons. are of two types: o r b i t a l angular momentum :  These  /tfi f o r the i t h v nucleon, where Jj. . i .  i s an integral,and i n t r i n s i c spin angular momentum s/h , where s i = \. The p a r i t y of the wave function for the i t h nucleon i s odd or even i f (-1) i i s odd or even. It can be shown that f o r the p a r t i c l e s involved i n the t r a n s i t i o n , the f i r s t element | MI i s non-vanishing i f  =0, that i s , i f the p a r i t i e s of  the i n i t i a l and'final states are the same.  These are•the allowed transitions.  There are two p o s s i b i l i t i e s whicjh-can s a t i s f y t h i s p a r i t y condition.  Since  the decay involves two spin--|- particle's, the beta p a r t i c l e and the neutrino, the t o t a l angular momentum change i s that of t h e i r i n t r i n s i c spins.  The two  p a r t i c l e s may come out with t h e i r spins •antiparallel, i n which case AI=0. This i s the so c a l l e d singlet state and i s the basis of the Fermi hypothesis and h i s selection rules.  The other p o s s i b i l i t y i s that both p a r t i c l e s are  emitted with spins p a r a l l e l , i n which case A I = 1 . postulated by Gamow and T e l l e r .  This i s the t r i p l e t state  To summarize f o r allowed t r a n s i t i o n s  A 1=0,no .  (Fermi)  AI=+1 or 0 (except 0«-^0), no  (Gamow T e l l e r )  For the f i r s t forbidden t r a n s i t i o n  (l8)  |Ai|=l, i . e . change i n angular  momentum of one unit with change i n p a r i t y , (-l)^*= -1; therefore A l •= + 1, 0 , yes  (19)  A I = + 2,,+ 1, 0, yes (iv)  Kurie Plot The s t a t i s t i c a l shape of the continuous beta spectrum has been predicted  by the Fermi theory as n(p) vs. p.  Since the spectrometer  resolution*  i s not zero, the measured counts per unit time at any momentum setting N(p) = n(p) A p-  But ^P- = R, a constant.  * Spectrometer  P  P  Hence the d i s t r i b u t i o n function n(p)c>C N(  resolution i s defined i n d e t a i l on page 22  P  12. A p l o t of N(p)  vs.. p gives the true spectral d i s t r i b u t i o n and i s shown i n  P Figure 2. From Figure 2 i t i s obvious that the spectrum approaches i t s end point energy W  Q  t a n g e h t i a l l y making i t d i f f i c u l t to determine accurately.  d i f f i c u l t y i s removed i f ,  The  instead, a Kurie p l o t i s used. K  Counts,  Conversion  minute,  lines  AP = A B •. p Bf  p Fig. 2.  or B  A t y p i c a l beta spectrum with conversion  For allowed t r a n s i t i o n s  lines  |M| i n equation (ik) i s independent of energy and  therefore i t follows that:  H(p) P^FCZ,?)  where | M |  has been absorbed i n the constant factor.  the function F(Z,p) corresponding and hence  N(p)  (22)  const (WQ-W)  N ( p ) i s known experimentally,  to Z and p involved i s available i n tables 10  can be computed to p l o t against W.  A p l o t constructed  p F(Z,p) 3  i n t h i s fashion y i e l d s a straight l i n e f o r allowed t r a n s i t i o n s and i s known as Kurie plot..  The extrapolation of the straight l i n e i s the usual method of  determining WQ.  13A complex beta spectrum may be resolved into i t s components through Kurie analysis. ,2  For forbidden t r a n s i t i o n s , the Kurie p l o t may not be l i n e a r , since |'Mi| i s no longer energy independent. included.  In these cases, a shape factor must be  A shape factor which produces a l i n e a r Kurie p l o t can provide  information on the degree of forbiddeness.  It i s important to note that a  curved Kurie p l o t i s a strong indication that the t r a n s i t i o n i s forbidden although the reverse i s not always true. The Kurie analysis does have inherent d i f f i c u l t i e s where many beta groups are involved.  Any r e l a t i v e l y weak group may be l o s t i n the subtraction  processes the method demands. together cannot be resolved.  Groups whose end-points are too close F i n a l l y , and p a r t i c u l a r l y i n the low energy  region of the spectrum, the thickness o f the source and backing become important, leading to spectral d i s t o r t i o n s caused by absorption and hack scattering.  (v)  Comparative H a l f - L i f e The decay constant,  (13)  A  for beta t r a n s i t i o n i s obtained by integrating  which y i e l d s  Pmax  (23)  0 where  C  =  and Numerical values f o r f ( Z , p Since the half l i f e t = define the comparative  m a x  11 ) are .available i n tabular form'  (tn2)^  where the mean l i f e ,  h a l f l i f e ( f t ) as  r£  —_  we  Ik.  The product f t i s thus a measure of the t r a n s i t i o n matrix element.|.]VL[. l  The  magnitude of M i s a measure of the decay p r o b a b i l i t y and hence of the degree of forbiddenness.  Therefore allowed t r a n s i t i o n s have the smallest f t values,  the f t value increasing with increasing forbiddenness, so that they may  be  3 They range from 10  used f o r the c l a s s i f i c a t i o n of beta t r a n s i t i o n s .  sec  l8 to 10 sec. It i s , therefore, more convenient to use log^Qft values instead. Experimental evidence" .. leads to the following crude c l a s s i f i c a t i o n s . Transition  log &  10  ft  Allowed  .3 to 6  F i r s t forbidden  7 to 9  Second forbidden  13  Third forbidden  18  Log-j^ft values f o r any decay can be conveniently calculated from the  12 nomographs prepared by Moszkowski (vi)  O r b i t a l Electron Capture An unstable nucleus may  electrons.  a t t a i n s t a b i l i t y by capturing one of the atomic  While any electron may be c a p t u r e d , i t w i l l most probably be a :  K-shell electron ( i f the decay energy i s s u f f i c i e n t ) because K s h e l l wave functions overlap the nucleus the most.  This process i s known as K-capture.  No observable p a r t i c l e i s emitted but the f i n a l atom emits an 'X-ray when a bound.electron from a higher s h e l l drops into the vacancy i n the K s h e l l . X-rays emitted are soft and so the capture process i s hard to observe.  The  so c a l l e d Auger electrons also accompany the process. Theoretically, K-capture i s similar to positron emission (p+e-^—$-n+)) ) but i s energetically favoured over the l a t t e r because no positron rest mass has to be;created and the rest mass of the captured electron i s added to the •energy release.  15Where K-capfrure because l e s s e r energy a normal K-capture  I s e n e r g e t i c a l l y i m p o s s i b l e , L-capture w i l l take p l a c e i s r e q u i r e d t o .ionize an L s h e l l e l e c t r o n .  Along w i t h  p r o c e s s , c a p t u r e from t h e L and h i g h e r s h e l l s i s always  present. The c a l c u l a t i o n o f t h e decay c o n s t a n t f o r t h e o r b i t a l e l e c t r o n decay d i f f e r s from t h a t o f e l e c t r o n e m i s s i o n i n two r e s p e c t s .  capture  In the f i r s t  p l a c e I n s t e a d o f f r e e e l e c t r o n wave f u n c t i o n s , K, L, etc.. • s h e l l e i g e n f u n c t i o n s of  t h e atom a r e used;  secondly, t h e s t a t i s t i c a l  (W  Q  .+ m ^  f a c t o r has t h e form,  - W.)  where'Wj_ i s t h e i t h s h e l l b i n d i n g energy  o f the -electron.  The decay c o n s t a n t  can s t i l l : b e w r i t t e n I n a form s i m i l a r t o ( 2 3 ) , v i z ,  Z i n e q u a t i o n .(29) r e f e r s t o t h e p a r e n t and not t h e daughter  nucleus.  Log-^Qft v a l u e s f o r t h i s p r o c e s s have a l s o been t a b u l a t e d .  GAMMA DECAY In,the m a j o r i t y o f b e t a p r o c e s s e s , a daughter excited state with too l i t t l e l o s e i t s e x c i t a t i o n energy  energy  n u c l e u s -is l e f t  t o emit a n u c l e o n .  i n an  I t w i l l , therefore,  e i t h e r b y t h e e m i s s i o n o f gamma r a y s o r b y t h e  e j e c t i o n o f • a n e l e c t r o n from an o r b i t o f t h e daughter p r o c e s s i s known as •-' i n t e r n a l c o n v e r s i o n  r  atom.  The ' l a t t e r  and w i l l be d i s c u s s e d l a t e r .  D e - e x c i t a t i o n b y gamma r a d i a t i o n may take p l a c e i n a s i n g l e . s t e p o r through several steps.  16..  ( i ) ,Multipole Radiation By treating the nucleus as a system of charges and c u r r e n t s , . i t s radiation can be sorted out into d i s t i n c t types.  In. quantum .theory, t h i s  corresponds to sorting the emitted quanta into what i s known as -'multipojie orders'L', according to the angular momentum L ( i n units of "h) c a r r i e d o f f by each quantum. radiation: parity.  For each inultipole order, there are two possible classes of  e l e c t r i c 2'^pole (EL) and magnetic 2^pole (ML), which d i f f e r i n  C l a s s i c a l l y EL and ML r e f e r to the radiation emitted by a v i b r a t i n g  e l e c t r i c or magnetic 2^ pole.  Generally the electromagnetic radiation f i e l d  of a system contains a l l the multipoles expressed as a converging power series with the f a m i l i a r c l a s s i c a l r e s t r i c t i o n that R «  in R  t y p i c a l radius of the charge current system and  1, where R i s a  A i s the radiated wave-  length/2^ • This means that only the 'lowest multipole order "L allowed Iby .the symmetries of the system can make an. appreciable contribution, f o r gamma rays up ta> .quite high energy.. I t also turns out that the strength of an e l e c t r i c multipole exceeds that of a magnetic multipole of the same order by a factor.c, where V i s the v e l o c i t y of the charged p a r t i c l e s . Y e l e c t r i c and magnetic multipoles may be radiated.  Mixtures of  So f a r only (MI+E2) has  been detected. The conservation of angular momentum and p a r i t y f o r the nucleus plus gamma rays imposes selection rules on the possible m u l t i p o l a r i t i e s of a gamma t r a n s i t i o n between two states of s p e c i f i e d angular momenta (lj.>If) and p a r i t i e s ( 7^, 7tf)z i.e., and  - I -I ±  f  < 'L € "I-i+I  = —— Ai  f  = ( - l ) ^ f o r EL radiation ,  (28) •= - ( - l ) Here  L  f o r ML radiation  AT;= +1 means no change i n p a r i t y and A ' A .= -1 means change i n p a r i t y .  17It i s noted that radiative t r a n s i t i o n s cannot occur f o r L - 0.  If  1^=1^=0, ordinary radiation i s wholly: forbidden though such t r a n s i t i o n s may take place by p a i r production or by. internal-conversion. The gamma t r a n s i t i o n p r o b a b i l i t y t i s calculated using the skme we'll:  known equation from perturbation theory:  l<U |H|VI§  M  f  The operator corresponding to H depends upon the multipole order. For example i n the case of e l e c t r i c dipole radiation i t w i l l have the form 5 i i e  x  -  Estimates of the t r a n s i t i o n p r o b a b i l i t i e s f o r various multipole  orders can be made.  These estimates, of course, depend upon the choice of  13 •a nuclear model.  Moszkowski  , f o r example, has made such estimates using  an extreme single p a r t i c l e model, namely a proton i n a central v e l o c i t y independent p o t e n t i a l .  These estimates, although very crude, do i n many  cases provide a basis f o r the analysis of experimental data. (ii)  Internal Conversion and Conversion C o e f f i c i e n t s Internal conversion processes result from a direct interaction between  the multipole f i e l d of a nucleus and a bound.atomic electron.  The k i n e t i c  energy Ej_ of the emitted electron, i s given by %  =W-Bi  where W i s the e x c i t a t i o n energy -and electron.  (29) the-atomic binding energy of the  Equation ( 2 9 ) becomes I d e n t i c a l • i n form with Einstein's photo-  e l e c t r i c equation, i f W i s replaced'by.the energy hp of the unsuccessful photon.  This l e d to an erroneous picture of the process that the excited  nucleus f i r s t emits a photon which i s then absorbed by the atom to produce a photoelectron.  This hypothesis known as 'internal photoelectric effect' was  rejected because of the fact that t r a n s i t i o n s l i k e 0->0 are observed i n i n t e r n a l conversion though such t r a n s i t i o n s cannot produce any gamma rays.  18.  If gamma emission i s -allowed, i n t e r n a l conversion and photon emission are two competing de-excitation processes with t r a n s i t i o n p r o b a b i l i t i e s <CUfjH|u*i>  depending upon the matrix element  If i n a de-excitation process IT and N y are respectively e  the number of  internal conversion electrons .and photons, the conversion c o e f f i c i e n t ; i s defined as:  -(30). •Since conversion electrons can come from d i f f e r e n t atomic N  e  ='.+ K e  N L  e  + N M e  C<  where  shells  + ... . t h e r e f o r e .=  o <  K  +  e<_. .+ L  o <  M  +  ...  i s the K .shell conversion c o e f f i c i e n t N 06  =  e  Irj_  + N  e  Lp  + N  e  i s the L s h e l l conversion c o e f f i c i e n t ,  and so on. Theoretical values of the i n t e r n a l conversion c o e f f i c i e n t are •independent of 'any p a r t i c u l a r .nuclear model but depend strongly on W, the t r a n s i t i o n energy Z, the atomic number of the transifdrmihg nucleus L, the multipole order of the t r a n s i t i o n AA  , change i n p a r i t y  Extensive t h e o r e t i c a l calculations of internal conversion c o e f f i c i e n t s ••lk are available  . ,A comparison between experimental and-theoretical values  of conversion c o e f f i c i e n t s i s a useful t o o l f o r determining p a r i t y and angular momentum of nuclear states.  .19-. CHAPTER I I METHODS OF DETECTION AND  MEASUREMENT  Our knowledge -of n u c l e a r p r o p e r t i e s began when experimenters l e a r n e d how nuclei.  t o d e t e c t .and a n a l y z e o p a r t i c l e s o r r a y s e m i t t e d by  first  radioactive  Even today, the study o f n u c l e a r s t r u c t u r e i s -a m a t t e r o f c o u n t i n g  and a n a l y z i n g what comes out o f such n u c l e i e i t h e r s p o n t a n e o u s l y o r when induced by p a r t i c l e bombardment."  In what f o l l o w s we  s h a l l describe b r i e f l y  o n l y those t y p e s o f deibectors and a n a l y z e r s ( s p e c t r o m e t e r s ) t h a t are g e n e r a l l y used w i t h b e t a and gamma r a y work.  DETECTION SYSTEMS Some important c h a r a c t e r i s t i c s t h a t determine the q u a l i t y and  suitability  o f a d e t e c t i o n and measurement system f o r a p a r t i c u l a r r a d i a t i o n are l ) i t s e f f i c i e n c y of detection (i.e.  i t s a b i l i t y to detect a reasonable f r a c t i o n of  the r a d i a t i o n t h a t p a s s e s through i t ,  2)  i t s r e s o l v i n g power ( a b i l i t y t o  d i s t i n g u i s h between r a d i a t i o n s o f - almost e q u a l energy o r momentum) and 3) i t s r e s o l v i n g time ( a b i l i t y t o d i s t i n g u i s h between two almost simultaneous e v e n t s ) . I f the energy o f a p a r t i c l e  i s E and  the r e s o l u t i o n i s measured by — — E  x  AE  i s the u n c e r t a i n t y i n i t s measurement,  100.  While the l a s t few y e a r s has seen the e v o l u t i o n o f a wide v a r i e t y o f b a s i c d e t e c t o r s f o r a l l t y p e s o f p a r t i c l e s , those used i n b e t a - r a y s p e c t r o s c o p y may  be c l a s s i f i e d i n t h r e e groups, the gaseous  s c i n t i l l a t i o n phosphor, The gaseous  i o n i z a t i o n , d e t e c t o r , the  and more r e c e n t l y , the s o l i d - s t a t e  i o n i z a t i o n d e t e c t o r was  detector.  one o f the e a r l i e s t used.  c o n s i s t s o f a volume o f gas i n an e l e c t r i c  field.  which p a s s e s through the gas, produces i o n - p a i r s .  It  Any I o n i z i n g p a r t i c l e These move under the  i n f l u e n c e o f the f i e l d t o c o l l e c t i n g e l e c t r o d e s and produce -an e l e c t r i c a l p u l s e i n an e x t e r n a l c i r c u i t .  The f i e l d  s t r e n g t h may  be low enough t o produce  no secondary i o n i z a t i o n , o r i t may be h i g h enough t o produce  secondary i o n  20. m u l t i p l i c a t i o n or even an avalanche.  The Geiger counter i s an example of the  l a s t case and the output pulse size i s .independent of the number of ion-pairs o r i g i n a l l y produced by the p a r t i c l e . the a r r i v a l of the p a r t i c l e .  Such a pulse gives no information except  Where avalanches are not produced, the output  pulse height i s proportional to the o r i g i n a l number of ion-pairs, and hence to the energy l o s t i n the gas by the p a r t i c l e .  The proportional counter i s  such a detector, and p a r t i c u l a r l y i n the case of low energy.electrons, the pulse height can be correlated with the electron energy. These detectors suffer i n comparison with others i n t h e i r time resolution c and i t i s d i f f i c u l t to resolve p a r t i c l e s which arrive less than 10 apart.  seconds  Also, f o r weakly i o n i z i n g radiations, such as gamma-rays, the gas  volume must be large. The s c i n t i l l a t i o n detector makes use of the fact that i o n i z a t i o n and excitation produced i n materials such as zinc s u l f i d e , calcium tungstale, anthracene, rjapthalene or thallium-activated sodium iodide, results i n the emission of photons to which the materials are transparent.  Such materials  •are known as phosphors, and the photon bursts are c a l l e d s c i n t i l l a t i o n s . The number of photons produced i s proportional to the energy l o s t i n the phosphor by the p a r t i c l e .  The photons are converted into an e l e c t r i c a l  pulse, usually by means of a secondary electron device c a l l e d a photomultiplier, the output pulse height being proportional to the energy of the p a r t i c l e . The s c i n t i l l a t i o n detector i s usually much smaller than gaseous detectors, has a very short resolving"time, and a high detection e f f i c i e n c y .  I t has  been the most popular detector f o r gamma-rays, even though i t s energy resolution i s somewhat poor. It was discovered as early as 19^-5 that semiconducting materials such as diamond, zinc sulfide and s i l v e r c h l o r i d e , when exposed to an i o n i z i n g radiation, became e l e c t r i c a l l y conducting.  The charge thus released can be  21. c o l l e c t e d .to produce an e l e c t r i c a l pulse just as i n the case of the gaseous detector.  They suffered from c e r t a i n inherent disadvantages however.  There  are -a number of charge c a r r i e r s already present i n such c r y s t a l s caused by thermal e x c i t a t i o n and impurities, and these frequently outnumber those produced by the incident p a r t i c l e .  Also, c r y s t a l • i m p u r i t i e s provide trapping  centers f o r the charges which lead to a storage of charge and ultimate crystal polarization.  Recently, these defects have been reduced by exploiting  the junction properties of a "semiconductor. vacancies or 'holes* are the charge c a r r i e r s . c a r r i e r s are electrons.  In a p-type semiconductor, In an n-type semiconductor, the  At a junction between p- and n type materials, the  charge c a r r i e r s from each region cilose tb the junction migrate into the other and a shallow layer at the' interface i s cleared of charge.  This zone i s  c a l l e d the 'depletion layer' and i t s thickness can be increased to over 1 cm by applying an external e l e c t r i c a l f i e l d i n the d i r e c t i o n of the migration. The depletion layer behaves l i k e an i n t r i n s i c semiconductor, and i s used as the sensitive region of detection.  "Very recently "^, s o l i d state detectors 3  have shown outstanding promise i n low energy nuclear physics.  Their  i o n i z a t i o n p o t e n t i a l i s about 3 ev/electron-hole p a i r as compared with 30 ev f o r the gaseous.detector.  The l i t h i u m - d r i f t techniques applied- to s i l i c o n  and germanium c r y s t a l s can give energy resolutions^—^10ev f o r p a r t i c l e s . They have a l i n e a r energy response, a very f a s t pulse rise-time (r—<10 ^ seconds) and are the smallest i n size of a l l detectors.  MAGNETIC SPECTROMETERS P r i n c i p l e s of Operation The momentum p of a charged p a r t i c l e may be deduced from i t s trajectory i n a magnetic f i e l d . •F = e(7xE)  The force on the p a r t i c l e i s (31)  22, In t h e s p e c i a l case o f an e l e c t r o n o f charge e and mass m and moving w i t h v e l o c i t y v i n a f i e l d B a t r i g h t a n g l e s t o v, we have  E£  .=  f  where  evB  o r Bf  =  EL = P e  (32)  e  f •= r a d i u s o f c u r v a t u r e o f t h e p a t h .  The gauss-cm u n i t o f Bf  Thus'B/  1  i s p r o p o r t i o n a l t o p.  i s a c o n v e n i e n t measure o f e l e c t r o n momentum and  i s r e l a t e d t o t h e e l e c t r o n energy b y  E  =  m c  /_£. .  2  +  1  .1]  (33) 16 '  Extensive tabulations of t h i s r e l a t i o n are available The magnetic f i e l d a l s o p o s s e s s e s f o c u s i n g p r o p e r t i e s , and may f o c u s an i n i t i a l l y d i v e r g e n t beam o f monoenergetic e l e c t r o n s . i n t o a c o n v e r g e n t one, forming, an image o f t h e s o u r c e .  W i t h a s u i t a b l e b a f f l e arrangement,  electrons  i n a s m a l l chosen momentum i n t e r v a l o n l y w i l l r e a c h a d e t e c t o r p l a c e d a t t h e focal position.  I n s t r u m e n t s - w i t h t h i s p r o p e r t y a r e known as a n a l y z e r s o r  spectrometers. There i s a wide v a r i e t y o f magnetic s p e c t r o m e t e r s , whose p r i n c i p l e o f performance i s b a s e d upon e q u a t i o n (3l)-  A c o m p a r i s o n O f performance i s  b e t t e r u n d e r s t o o d b y f i r s t d e f i n i n g some o f t h e commonly-used p a r a m e t e r s . a) as  JLL ABf  The r e s o l v i n g power f o r momentum-selective .  instruments i s defined  I t i s u s u a l l y e v a l u a t e d from t h e shape o f a monoenergetic  c o n v e r s i o n l i n e o f momentum B at half-maximum  , where  as shown i n F i g u r e 2.  A ^ / ) i s t h e f u l l w i d t h o f t h e peak The i n v e r s e r e s o l u t i o n R = A(Ef  ) .  ay  more g e n e r a l l y used.  The momentum s p r e a d A ( B J ° ) a r i s e s from t h e s p e c t r o m e t e r  field characteristics. as R i s s m a l l o r l a r g e .  The' r e s o l u t i o n R i s r a t e d ' h i g h ' o r 'low' a c c o r d i n g  23. b)  The dispersion  , defined as  W 7 i s a measure of the s p a t i a l spread of momentum f o c i , x i s a suitable coordinate f i x i n g the p o s i t i o n of the image of the focused p a r t i c l e .  Obviously,  c l o s e l y spaced spectral l i n e s can be resolved only i f the distance between the images of two l i n e s i s greater than the s p a t i a l width of the l i n e s . c)  The gathering power 4)measures the geometrical e f f i c i e n c y of the  instrument.  The emission of b e t a - p a r t i c l e s from an unpolarized point source.is i s o t r o p i c . The size and p o s i t i o n of the entrance b a f f l e s define a s o l i d angle of •acceptance SL , so that the f r a c t i o n entering the spectrometer i s  Depending upon the f i e l d c h a r a c t e r i s t i c s , i t may be that only part of these reach the detector, and some of these may.in^ss detection ;if the detector e f f i c i e n c y i s not 100%.  Thus, the transmission T which measures the f r a c t i o n  of the t o t a l emitted beta-rays which i s detected i s the expressed as a f r a c t i o n of 4 A T< d)  .  e f f e c t i v e s o l i d angle'  Thus  CO  In beta-ray spectroscopy,  one i s often limited, not by.the t o t a l a c t i v i t y :  of a source, but b y , i t s 'specific a c t i v i t y ' , i . e . the a c t i v i t y per unit weight.  Sources must be..thin to minimize spectral d i s t o r t i o n s caused by  absorption and scattering within the source - i t s e l f . i s low, the source area rate..  I f the s p e c i f i c a c t i v i t y  O" must be large to produce an appreciable counting  Large sources produce poorer f o c i than small sources.  In t h i s case,  the luminosity L i s a u s e f u l parameter where L =  .... crT.  An aperture luminosity L can also be defined as  cTco , and obviously  2k,. Comparisons of spectrometer performances parameters.  should properly include a l l these  However, a crude but useful figure-of-merit i s one that compares  resolution R and transmission T.  For any given instrument, the resolution may  be improved at the expense of the transmission and vice-versa.  In what  m  follows, we have selected to compare the r a t i o _ as a rough guide of performance. R The higher t h i s r a t i o , the better the instrument. Spectrometer C l a s s i f i c a t i o n There are two main groups of magnetidjspectrometers, the f l a t and the lens (or h e l i c a l ) spectrometer.  spectrometer  In the f i r s t group, the' central  trajectory i s confined largely to a plane perpendicular to the magnetic  field.  In the lens spectrometers, the trajectory s p i r a l s along the f i e l d l i n e s .  In  both types, f i e l d s may be homogeneous or inhomogeneous and produced with or without iron.  The shape of the f i e l d determines i n each case the degree and  kind of focusing.  In the so-called double focusing, electrons are focused  in both the horizontal and the v e r t i c a l planes.  The f l a t types may be single  or double focusing; while lens types, due to t h e i r r a d i a l symmetry, are always double focusing. Flat  Spectrometers Semicircular spectrometers (and spectrographs) are the prototypes of  the f l a t instruments.  Others i n t h i s family are the t h i r d order focusing  spectrometer, the double focusing spectrometer; and various sector f i e l d spectrometers, among these the 'orange' spectrometer and the s p i r a l o r b i t spectrometer.  Each spectrometer i n t h i s group has a d i f f e r e n t shape of the  magnetic f i e l d which i s responsible f o r the unique type of focusing i n each case, the p r i n c i p l e s of which are i l l u s t r a t e d f o r each case i n Figures 3 to 8.  To follow page 2k.  Baffle  lead shielding photographic plate  source Fig. 3-  Fig.h.  S  Fig. 5.  Main features of the spectrometer due to Rutherford  and Robinson  Double focussing  F (a) spherical aberration P r i n c i p l e of t h i r d order focussing  S (b) t h i r d order  F focussing  To follow page 24  Fig. 7« Prism and sectorfied spectrometers  •25'Lens Spectrometers To t h i s group belong solenoidal spectrometers, long lens and short (thin) lens spectrometers, and the intermediate image spectrometer.  The solenoidal  spectrometer 'employs a uniform magnetic f i e l d over the entire electron path which makes the computation of electron t r a j e c t o r i e s very simple.  Lens 17  spectrometers suffer excessively from inherent focusing;-aberrations.  Siegbahn  has shown that an .'upward concave' magnetic f i e l d gives a considerably reduced aberration.  The long lens i s designed to produce such a f i e l d .  image i s a special type of long lens spectrometer.  In these, the source and  the detector l i e i n regions of a strong magnetic f i e l d . t h i s proves a serious drawback.  The intermediate  For some applications  The t h i n lens spectrometer i s described i n  d e t a i l i n the next chapter. There i s such a wide range of problems studied i n nuclear spectroscopy that i t i s impossible to single out one p a r t i c u l a r -instrument which w i l l have superior q u a l i t i e s i n a l l cases. meters.  Different problems need d i f f e r e n t spectro-  In general, f l a t spectrometers such as the semicircular and the  double focusing instruments are to be preferred f o r high resolution, low transmission experiments and precise -energy measurements. are  Lens spectrometers  most suitable f o r high transmission and moderate resolution.  preferable., f o r instance, f o r coincidence measurements.  They are  Lens spectrometers  have proven useful f o r reasonably accurate energy measurements as well.  The  orange spectrometer-, however, has the unique property of showing a moderate resolution with very high transmission. l8 • A detailed study on beta-ray spectrometers has been undertaken by Gerholm Momentum or energy measurements of beta p a r t i c l e s with any of the magnetic. spectrometers usually are not absolute. c a l i b r a t e d with a known monoenergetic are  In most cases, the spectrometer i s  conversion l i n e .  A number of such l i n e s  known, t h e i r absolute momenta having been determined by other means (see  for example, Seigbahn et a l 19).Where the spectrometer magnet i s air-cored., a single point c a l i b r a t i o n i s s u f f i c i e n t .  26. Spectrometer Measurements of Beta and Internal Conversion  Spectra  The data obtained-is always the counting rate 'N(p) as a function of the f i e l d B.  From the instrument c a l i b r a t i o n , the Bf  to B i s known and  or p value  corresponding  i s p l o t t e d against p.  Regions of such a spectrum not obscured by conversion l i n e interference, may be subjected to a Kurie analysis.  I f the beta spectrum i s complex, i t  i s often possible to use the.analysis to resolve the spectrum into i t s individual beta components, yielding.information on group end-point  energies  and r e l a t i v e i n t e n s i t i e s . The i n t e r n a l conversion l i n e s , superimposed on the primary beta spectrum provide information on t r a n s i t i o n energies, where the conversion l i n e s are reasonably intense.  Also, the r e l a t i v e i n t e n s i t i e s of the conversion l i n e s  from various -electron shells can be related to the -multipole order and e l e c t r i c or magnetic nature of the'transition.  In p a r t i c u l a r , the  ^/j^  conversion r a t i o can be compared with t h e o r e t i c a l estimates, which depend upon energy, multipole order and atomic number.  Such comparisons a s s i s t i n assigning  spin and p a r i t y changes to the t r a n s i t i o n .  The r e l a t i v e i n t e n s i t i e s of the  conversion l i n e s are j u s t the r e l a t i v e areas under the l i n e s on the  ^(P)  v s  ,  p  P spectrum p l o t . It i s more d i f f i c u l t to measure absolute i n t e n s i t i e s of i n t e r n a l conversion l i n e s , since t h i s requires a precise knowledge of the parameters T and R of the instrument, and i t i s not always easy to measure these with s u f f i c i e n t l y . h i g h accuracy.  Where i t can be done,.and the accompanying gamma-  ray absolute i n t e n s i t i e s are known, the conversion c o e f f i c i e n t s may be computed and compared with theory.  27. Spectrometer Measurements of Photoelectron Spectra The photoelectron process provides-a means whereby the spectrometer may be used to give reasonably accurate measurements on gamma-ray energies. In.this method, the source i s placed i n a container of low Z material, :  thick enough to absorb a l l primary electrons and i n t e r n a l conversion electrons. To the outside of the container i s .attached a small thin f o i l of a heavy element such as lead or uranium.  Gamma rays emitted by.the source eject  photo electrons from the f o i l which i s c a l l e d a the photo electron source.  radiator' which becomes  High Z f o i l s are used because the photoelectric  cross section r i s e s rapidly with increasing'Z of the radiator-material. The photo electrons ejected from the f o i l show up as K, L and sometimes M photopeaks beyond the <Compton continuum.  Prom the peak p o s i t i o n s and the  c a l i b r a t i o n of the instrument, one may obtain the gamma ray energy by adding the appropirate s h e l l binding energy of the radiator element. Relative i n t e n s i t i e s of gamma-rays can be derived from areas under the photopeaks, i f the source-converter geometry i s simple enough to allow c a l c u l a t i o n s of y i e l d based upon the photoelectric ciross section and angular  20 distributions.  Hultberg et a l  have discussed t h i s problem i n d e t a i l .  THE SCINTILLATION GAMMA-RAY SPECTROMETER" This system i s based upon the pulse height analysis of the s c i n t i l l a t i o n spectra produced i n phosphors by gamma-rays.  The e s s e n t i a l components of  a t y p i c a l system are shown i n block diagram form i n Figure 9The e l e c t r i c a l pulses from the output stage of the photbmultiplier which are generally too small to be analyzed d i r e c t l y , are amplified with a l i n e a r amplifier, then sorted according to t h e i r size with either a sin;gle channel pulse height analyzer (P.H.A) or an automatic multichannel pulse height analyzer (Kicksorter), and f i n a l l y recorded with a scaler.  A p l o t o f the  number of pulses per unit time versus pulse height gives the i n t e n s i t y d i s t r i b ution of the charged p a r t i c l e s or the photons absorbed by the s c i n t i l l a t i o n c r y s t a l .  Uo follow page 27.  Scintillation Detector  Linear Amplifier  P.H.A.  H.T.. Scaler  Fig. 9 -  Block diagram of gamma ray s c i n t i l l a t i o n  E,  E  spectrometer  E -2mc E-mc E^, Y o tfo y 2  +3  cS  u  Compton Distribution  w a  •H  -p A  o o  Pulse height (a) Fig. . 1 0 .  (b)  (c)  Pulse spectrum of homogeneous gamma radiation  2  28. In Figure 10 are shown t y p i c a l pulse height spectra to be expected from gamma-rays of d i f f e r e n t energies. of  the photoelectron,-Compton  phosphor.  For E  These spectra r e f l e c t the r e l a t i v e  importance  and pair-production processes within the  <£, 250 Kev (Figure 10a) the photo e l e c t r i c e f f e c t fl y  predominates, and the pulse height d i s t r i b u t i o n shows a strong f u l l  energy  peak (with a lower energy 'escape' peak corresponding to the events i n which the K X-ray of iodine emerges without loss from the c r y s t a l of Nal).. The photopeak produced has an amplitude proportional to the energy of the gamma ray  and not to that of photoelectrons because most of the X-rays emitted  a f t e r the photoeffect are.absorbed i n the c r y s t a l and contribute to the i n t e n s i t y . o f the s c i n t i l l a t i o n .  For'E  >  500 Kev but <  1.02 Mev, the  Y compton e f f e c t i s also important and the f u l l energy photopeak i s accompanied by -a c h a r a c t e r i s t i c d i s t r i b u t i o n of the r e c o i l electrons with a we'll marked Compton edge (Figure 10b).  For E^,  "1.02 Mev p a i r production i s possible  and peaks w i l l be observed fit pulse amplitudes corresponding to the energies E y — 2 m Q C , Ey. — HIQC 2  2  and E^,  respectively "(Figure 10c).  These three l i n e s  result because of the three p o s s i b i l i t i e s .  F i r s t l y both a n n i h i l a t i o n quanta 2 may escape leaving behind an energy equal to E^- — 2HIQC , secondly one quantum p  of the a n n i h i l a t i o n p a i r may be recaptured giving r i s e to a l i n e of  m  o  c  and t h i r d l y both quanta may/be absorbed r e s u l t i n g i n a f u l l energy photopeak. If a very large c r y s t a l of Nal i s used almost nothing escapes and the d i s t r i b u t i o n w i l l cori'sist of only one strong peak -at E ^ . The p o s i t i o n of these peaks permits an accurate determination of gamma ray. energies.  The width of the peak i s s t a t i s t i c a l i n o r i g i n .  The pulse  height (amplitude) i s proportional to E-and to the number o f photons N produced i n the phospher by an event.  The l a t t e r process i s a s t a t i s t i c a l  process and therefore N follow a Gaussian curve with an uncertainty r^> JN^ The width of the peak i s hence proportional to  J~E.  •29. COINCIDENCE SPECTROSCOPY The coincidence method i s designed to measure •,'simultaneous'  emission  of two types of radiation with the help of two or more counters and-a coincidence c i r c u i t which produces a count when p a r t i c l e s arrive at the counters within a resolving time,T. .  Because of i t s high detection e f f i c i e n c y , energy  p r o p o r t i o n a l i t y and f a s t rise-times, the s c i n t i l l a t i o n detector i s i d e a l f o r coincidence work. As an example we may  describe -a t y p i c a l simple gamma-gamma coincidence  system, i l l u s t r a t e d with a block diagram i n Figure 1 1 a .  The mixer element  i s the Rossi coincidence c i r c u i t and i s shown i n Figure l i b . source i s placed between two detectors.  The gamma-ray  Of the pulses produced i n detector 1,  the pulse height analyzer (P.H.A.l) can be set to select only those of a c e r t a i n amplitude circuit.  ( i . e . energy) and these are fed into one input of the mixer-  This i s c a l l e d the gate pulse.  P.H.A.2 can be used to scan the  entire spectrum from .detector 2 , which i s fed into the other input of the mixer-circuit.  The l a t t e r w i l l produce an output pulse only i f i t receives  pulses on both inputs which arrive within a time i n t e r v a l ,  The -output  pulses of the m i x e r - c i r c u i t , then respresent the gamma-ray spectrum of detector 2 i n coincidence with the gate pulse. The chance (accidental) coincidence rate i s given by N  • •'•  = 2NiN r 2  c h  where Ni and N2 are the t o t a l counting rates of counter l a n d counter 2 respectively, and  T"  i s the resolving time of the system. ' To keep N ^ c  much lower than the true coincidence rate, i t i s important that TT as small as possible.  very  should be  Whereas ther.resolving time of the Rossi c i r c u i t alone  can be made as low as 10  -9  s e c , the resolving time T " of the system of  -6 Figure 1 1 a  i s never better than 10~  sec.  This i s because the resolving time  of the system i s p r a c t i c a l l y governed by the P.H.A. only.  In the process of  To follow page 29  Scintillation Detector  Amplifier  Pulse height analyzer  Scaler  Mixer circuit  Scintillation Detector  Fig.ll(a).  Amplifier  Pulse . height analyzer  Scaler  Scaler  Block diagram'of gamma gamma coincidence system  Q 'R_  Input 1  Input 2  o-Hf  -Ir—o -\\— Rr  Fig.  11(b).  Rossi coincidence c i r c u i t  O out  30.pulse-height analysis, the P.H.A. imposes a variable delay i n the output pulses depending upon the size and the shape of the input pulses. The magnitude of the time spread-associated with the variable delay i s  10  -6  sec. 21 B e l l , Graham and Petch  solved t h i s problem by performing the coincidenc  selection and the pulse height analysis -in e n t i r e l y separate channels, and combining the r e s u l t s of these operations i n a separate, r e l a t i v e l y slow coincidence c i r c u i t .  The -system used by them i s c a l l e d a Fast-Slow  Coincidence system and i s i l l u s t r a t e d i n the block diagram of Figure 12. The unselected pulses from the detectors are fed into the .fast: coincidenc c i r c u i t whose resolving time may b e l 0 ~ 9 s e c -At the same time detector pulses are also amplified, analyzed and fed into the so-called slow coincidence.  -6 c i r c u i t with a resolving time r-~' 10~  s e c At the 'end of the chain the  t r i p l e coincidence unit selects, out of a l l the fast coincidences o r i g i n a l l y formed, only those that are i n coincidence with the outputs of the two slow channels.  In t h i s way the f u l l speed of the detectors i s preserved and at  the same time pulse height selection i s c a r r i e d out without a f f e c t i n g the fast response of the Rossi c i r c u i t .  The resolving time of the fast-slow  coincidence system i s determined by the fast coincidence c i r c u i t alone. Coincidence spectrometry; . i s a very useful and widely used technique i n nuclear  spectroscopy.  When dealing with a complex beta spectrum with several beta rays, the beta gamma coincidence technique i s far more r e l a i b l e for determining the upper energy l i m i t and the spectral shape of the beta t r a n s i t i o n s than i s the conventional Kurie analysis approach.  The reason i s that by a proper  choice of gating pulse, some of the beta groups are eliminated leaving the Kurie analysis to deal with a simpler p i c t u r e .  Similarly, the use of  gamma-gamma coincidence measurements can sometimes i s o l a t e a single component from a composite gamma ray peak i n the singles spectrum.  To follow page 30.  Scintillation Detector  Scintillation Detector  Amplifier  Fast coincidence circuit  Amplifier  Pulse height analyzer  Slow coincidence circuit  Pulse height analyzer  Scaler  Fig.  Source  12.  Scaler  Fast-slow coincidence system  Scaler  :3i-  C o i n c i d e n c e s may a l s o b e m e a s u r e d b e t w e e n c o n v e r s i o n e l e c t r o n s a n d gamma r a y s w.hich w o u l d a p p e a r t o h a v e a t t r a c t i o n s  o v e r gamma-gamma m e a s u r e m e n t s .  T h i s method e x p l o i t s  thehigh resolutions.obtainable  However, t h e r e s u l t s  areusually  i n deducing, decay sequences. •and g e n e r a l l y of  of qualitative  Directional  u n k n o w n u n l e s s -a p r i o r  w i t h magnetic  interest  correlation  spectrometers.  only and merely  effects  may b e  assist  large  determination o f t h e spins and p a r i t i e s  t h e l e v e l s h a s b e e n made.  Gamma-Gamma A n g u l a r  Correlation  I t h a s b e e n shown t h e o r e t i c a l l y t h a t t h e a n g l e b e t w e e n the  directions  o f e m i s s i o n o f two p h o t o n s e m i t t e d i n c a s c a d e  depends upon t h e s p i n s o f t h e n u c l e a r l e v e l s c o n n e c t e d b y the  two p h o t o n s .  F o r e x a m p l e , i f o n e gamma r a y ^  emitted i na particular the  direction  the  e m i s s i o n o f t h e s e c o n d gamma r a y ^ g . i n  T2 " i s a f u n c t i o n  o f ,the  i s  probability of the direction  angle between r ^ and  F i g u r e '13. in  Two / - r a y s cascade  (say, 9 ) .  A c o n v e n i e n t f o r m f o r e x p r e s s i n g t h e d i r e c t i o n a l c o r r e l a t i o n W(G) b e t w e e n  X]_  The  and  ^2 i s :  W(0)  = 1 + A P ( c o s 9 ) + A P ( c o s 9 ) + . . . • A^P 2  coefficients  2  1 +  ] +  A y d e p e n d u p o n f i v e p a r a m e t e r s ; t h e m u l t i p o l e o r d e r s L-j_  a n d ' l ^ o f t h e gamma r a y s a n d t h e s p i n s I , a  The  maximum v a l u e f o r v i s e s t a b l i s h e d  v  max  =  m  n  (  Calculations of  the spin  22 Rose  (cos «)+•  2  L  i ; V> 21  2 L  1^, a n d I  c  o f thenuclear  levels.  by the condition,  2)  o f t h e c o e f f i c i e n t s A y i n (3^) f o r v a r i o u s  (35) combinations  a n d m u l t i p o l e o r d e r p a r a m e t e r s h a v e b e e n made b y B i e d e n h a r n a n d  •32-. Gamma-gamma angular correlations  are obtained by f i x i n g the d i r e c t i o n  of one detector and moving the other through small angular steps and recording the coincidence counting rate at each step.  A least square f i t to the data  of a function of the form (3*0 then y i e l d s values f o r Ay which can be compared with those calculated t h e o r e t i c a l l y .  I f m u l t i p o l a r i t i e s of  the gamma rays concerned are known from some other source (the i n t e r n a l conversion c o e f f i c i e n t s , say) then the experimentally measured values of Ay can be extremely h e l p f u l i n establishing the spins of the l e v e l s involved.  I f they are not known, then a t r i a l - a n d - e r r o r procedure must be  used to determine which parameters best f i t the r e s u l t s .  33CHAPTER III THE THIN LENS MAGNETIC SPECTROMETER Introduction This spectrometer uses a hell-shaped f i e l d produced by a r e l a t i v e l y short (compared with the source to detector distance), a x i a l l y symmetric magnetic (Boil. (Figure lk).  The  source  and the detector are located along the B:(O,Z)  c o i l axis on opposite sides of the c o i l and outside the region of high f i e l d . In t h i s spectrometer analogies with 23  o p t i c a l lenses have been much used Busdl f i r s t pointed out that the ordinary .'lens formula  ^ = — + — f u v  i s applicable i n t h i s  case and showed that Figure lk. The bell-shaped f i e l d i n a thin, lens spectrometer. .05  1  1  f  MBJF  B  7  (36)  (0,Z)dz  —00  where B (0,Z) i s the a x i a l f i e l d component and.Bf  i s the electron momentum.  2k  Deutch, E l l i o t t and Evans . c a r r i e d out a detailed study of the t h i n lens spectrometer and showed that f = C(2.) ni-  (37)  where p i s the electron momentum, n i i s the ampere-turrite,,and :  depending upon the shape and size of the magnet c o i l .  C i s a constant  Thus, f o r a f i x e d  geometry, the momentum of the focused electron i s proportional to i . Figure 8 shows the r a d i a l displacement of t y p i c a l t r a j e c t o r i e s f o r a short lens f i e l d .  It i s obvious that even f o r a narrow range of emission  angles, the a x i a l focus i s much extended, a fact which demands detectors of  large size.  The disadvantage may 'be minimized to some extent by using low  emission angles, and a symmetrical geometry of source, and detector, but t h i s inevitably leads to low transmission and dispersion, and hence to poor resolution. Even so, the t h i n lens spectrometer possesses c e r t a i n d i s t i n c t advantages over other types.  I t i s inexpensive, and easy to construct.  The source and  detector, both l i e outside the h i g h - f i e l d region and are e a s i l y accessible, so that i t i s r e a d i l y adaptable to beta-gamma coincidence-work. An unmodified thin lens spectrometer, with symmetrical geometry and a x i a l detection has a transmission of approximately 0.3$ ,-^3$  i  n  with a resolution  momentum, c h a r a c t e r i s t i c s which suffer i n comparison with, f o r  example, the Siegbahn-Slatis intermediate image spectrometer.  However, the  p o s s i b i l i t i e s of the t h i n lens are too tempting to discard i t , and from time to time, attempts have been made by various workers i n t h i s laboratory and elsewhere, to improve i t s performance. THE MODIFIED THIN LENS SPECTROMETER In Figure 8, the electron t r a j e c t o r i e s reach a region of maximum convergence Off the axis before coming to an .'extended' focus .along the ^axis. The envelope of t h i s convergence forms a ring i n a plane perpendicular to the magnetic axis.  This i s the well-known .'ring focus', which has been  exploited by many/workers  25-28  26 '  i n the past. -Keller et a l  , f o r example,  inserted suitable baffle's at the p o s i t i o n of the ring, and-with an a x i a l detector found.that f o r the same resolution, the transmission increased by a factor of two.  29 Mann and Payne d i f f e r e n t way.  took, advantage of the -ring focus property.but i n a 1  Their attack was to"place the. detector not on the axis, but  at the p o s i t i o n of the ring.  Their detector w i l l be.described i n d e t a i l l a t e r ,  but b r i e f l y , i t consisted of a ring of anthracene c r y s t a l s coupled to a  35photomultiplier.  Detection thus "-takes ••place before the electron beam diverges  •again past the ring focus.  This arrangement made i t possible to use greater  ranges of emergence angles  .  I t i s well-known that the transmission  2  increases -as  and the resolving power as &C  vacuum chamber w i l l l i m i t  •  The p h y s i c a l size of the  od i f a symmetric geometry i s used.  With ring  detection,.the symmetric geometry may be discarded, and the source moved closer to the magnet.  Using these modifications, Mann and-Payne achieved a  resolution r-o 1.2k^> with a transmission  1.1$.  Mann and Payne began t h e i r investigations by f i r s t computing a large series of ...trajectories f o r the thin lens field., a f t e r the method of Deutch 2k  et a l  .  The c a l c u l a t i o n s were made by the computing, center of the University  of Toronto.  From the f a m i l i e s of curves of which Figure 8 i s an example, the  p o s i t i o n and nature of the ring focus was (a)  source-to-magnet distance  (b)  detector-to-magnet  (c)  mean emission angle oL , and  (d)  angular divergence  distance  The r i n g focus radius was  found to be a sensitive function of  s, d,  AoC fixed, at .5•0 cm.,  a value chosen f o r convenience  because of the vacuum chamber size, and each of the four parameters was varied independently i n a systematic way.  They.placed i n front of the ring  detector and at the p o s i t i o n of the rirgfocus, .annular exit b a f f l e s of variable s l i t width.  At each p o s i t i o n , , a l i n e p r o f i l e of the "K-conversion  l i n e of C s l 3 7 was taken.  i  In a l l cases, the object was  to determine the  values of the four parameters which would produce the best l i n e , i.e., maximum peak height consistent with minimum peak width.  They were l i m i t e d to some  extent i n t h e i r search by the "length of t h e i r vacuum chamber,.and by a lack of adequate controls f o r variations of s and  d, and as a r e s u l t , they were not  certain that the r e s u l t s they achieved were n e c e s s a r i l y the ultimate attainable •with the magnet used.  36: '30 -Chaturvedi recognized that precautions should be taken to ensure alignment of the source-detector axis with the magnetic f i e l d axis, since otherwise, the arrangement could hot be a x i a l l y symmetric.  He designed a  vacuum tube mounting which could be s e n s i t i v e l y and accurately controlled. t h i s , i t was possible to rotate the tube about any axis.  With  Mann and Payne had  provided a source centering mechanism, whereby the source p o s i t i o n could be adjusted i n a plane perpendicular to the spectrometer axis, but Chaturvedi was  s t i l l l i m i t e d i n detector p o s i t i o n control. A schematic diagram of the spectrometer used i n the present work i s shown  in Figure 15-  The vacuum chamber length has been increased by.50$ and the  detector -is mounted on a c y l i n d e r i c a l carriage inside the vacuum chamber with ball-bearing r o l l e r s and p o s i t i o n controlled by an external rod passing through a vacuum seal. 's and  This gives a smooth and easy access to the detector.  Parameters  d are continuously adjustible -with t h i s device and.with the a x i a l movement  of the vacuum chamber, which i s mounted on r o l l e r s . o n the 'Chaturvedi supports, and can move f r e e l y . i n t o and out bf the magnet.  With these modifications, the  work of Mann and Payne was repeated, but with greater ranges of the four parameters. Details of the r i n g detector are shown i n Figure 16, controls, i t i s the design of Mann and Payne..  and except f o r the  The •J" photomultiplier (Dumont  636U) .was selected from several f o r the smallest dark current, and i s coupled to the anthracene ring by a shallow lucile'-'light pipe cut to a c r i t i c a l r e f l e c t i o n shape...  The anthracene  i s f i t t e d to,a shallow (3/16" deep by l/h"  c i r c u l a r r i n g cut into the l u c i t e .  wide)  The 'lucite and anthracene are coupled by  a mixture of glycerine and"Ivory soap, a mixture with good o p t i c a l properties which flows f r e e l y when-warm, but which i s s o l i d at room temperature. l u c i t e i s coupled to the face of the photomultiplier with a mixture of s i l i c o n e gel (DC kOO)  and s i l i c o n e o i l .  The  Dolly Positioning Rod Vacuum gage  1 1 w -p o u •H 0) fl H O  u  Dumont  636k  \  Exit baffle  Gamma b a f f l e  TP Chamber Support  Water-cooled Elec tromagnet  F i g . 15-  Modified thin lens spectrometer.  Source-centering control  Aluminum F o i l  Fig. l6.  The Detector Assembly  37-  The -photomultiplier i s shielded, from the r e s i d u a l f i e l d of the magnet by placing a mu-metal s h i e l d around the photomultiplier i t s e l f , and then by surrounding the entire detector assembly with a Fernetic-Conetic* jacket. Figure 17 shows the e f f e c t of t h i s shielding arrangement as a function of magnet current.  The f i r s t e f f e c t of the f i e l d occurs when the f i e l d strength i s  adjusted to focus electrons of approximately 600 kev.  This f i e l d e f f e c t  appears to be constant with time and shows no detectable hysteresisThe entrance and exit b a f f l e s , shown i n Figure lh, are made of 1/8" aluminum.  The entrance b a f f l e system-which determines , cH. and  mounted r i g i d l y . t o the source holder on aluminum stand-offs. i n turn i s mounted on the source-centering  A c C .are .  The source holder  assembly of Mann and Payne.  a simple rack and pinion arrangement-controllable  It i s  from-outside the-spectrometer.  A lead b a f f l e shields the detector - from d i r e c t gamma r a d i a t i o n from thesource.  Other b a f f l e s are used to reduce the number of electrons -and gamma-  rays scattered from the chamber walls, an e f f e c t that becomes very important when strong . sources are used. -p as  u  £  u  Potentiometer s e t t i n g ( v o l t s ) . Figure 17-  Defocusing e f f e c t on photomultiplier noise.  F i n a l l y to compensate f o r the earth's magnetic f i e l d , the entire spectrometer assembly.is enclosed by large rectangular Helmholtz c o i l s . * Available from Perfection Mica Co., -Chicago, I l l i n o i s .  38THE ASSOCIATED CIRCUITS (a)  The F i e l d Current Control C i r c u i t The e l e c t r i c current used to produce the focusing f i e l d was taken from a  110V d.c. generator.  This current was  supplied to the magnet through a k  regulator capable of regulation to 1 part i n 10 . follows (See Figure 18).  This i s accomplished as  The current through the f i e l d c o i l s also passes  through a bank of 38 p a r a l l e l e d 6AS7-G-'s and-a 0.1.ohm standard resistance made of manganin s t r i p .  The voltage produced across the standard resistance i s  compared with that from a Rubicon potentiometer.  This comparison i s c a r r i e d out  i n the b i a s - c o n t r o l - c i r c u i t which feeds the required bias "fcp the grids of the 6AS7-G's.• The b i a s - c o n t r o l - c i r c u i t consists of a Brown converter-fed d.c. control amplifier having a frequency.response from 0 / G  to 20 / c  s  s  and a gain of 30,000  in p a r a l l e l with an a.c. amplifier of.frequency,response from and-a gain of  10,000.  1 0 / to 2000 / c  c  s  s  A complete c i r c u i t diagram of the bias control c i r c u i t i s  shown i n Appendix 2, Figure A5« (b)  Beta Spectra.. Counting C i r c u i t A block diagram of the counting c i r c u i t i s shown i n Figure 19The c o l l e c t o r output of the photomultiplier i s fed to a cathode follower  to match the impedance of the signal cable leading to l i n e a r pulse amplifier (Tracerlab amplifier, model RIA-l). standard scale of 6U-.  The.amplified pulses are counted with a  High voltage f o r the photomultiplier i s , provided by .a  John Fluke Manufacturing Co.,Inc.,-Seattle (U.S.A) Power supply, model.U02M. The voltage supply c i r c u i t f o r the photomultipler i s shown in-Appendix 2, Figure A6. SPECTROMETER ADJUSTMENT The source used f o r c a l i b r a t i o n and adjustment was Csl37-  This source  has an i s o l a t e d K-conversion l i n e of - 3381.28+0.5 gauss-cm. corresponding to ,a 66l  Kev t r a n s i t i o n .  CSN0 dissolved i n  The Csl37 was obtained from Chalk River i n the form of  HNOo.  A beta source was prepared by depositing a drop of the  To follow page 38-  +110v O  Rubicon Potentiometer  Magnet  Bias Control Circuit  •v^W* 1 ohm F i g . 18.  Beta Detector  Amplifier  Fig. 19-  Control C i r c u i t  Cathode Follower  Scalar  Counting C i r c u i t  j _L  '39solution on a 2^0 pgm/ 2 thick aluminum f o i l and allowing i t to dry. cm  It was  then covered with a t h i n f i l m of collodion to contain the active material. PJ.scriminator Level Setting In any photomultiplier there are always some.-'dark' pulses or  'noise'.  I t . i s important that the signal-to-noise r a t i o should be. as large'-'as possible. For electron energies above a few hundred kev the -signal-to-noise r a t i o f o r the photomultiplier used i s high and i n consequence the discriminator l e v e l can.be adjusted f o r low background (noise) with no loss of counts.  With low energy-  electrons, however, the signal pulses overlap the noise pulses to some extent and hence a lower discriminator setting i s necessary to :'dig' out the signal. In beta spectra, we must deal with a continuum of energies from low to high under these circumstances,  and  i t i s advantageous to use d i f f e r e n t discriminator  settings f o r d i f f e r e n t .small.ranges of.electron energies.  For any. p a r t i c u l a r  small range of electron energies the discriminator setting. I s determined by measuring the peak height of a conversion setting or noise l e v e l .  l i n e as a function of discriminator  As the discriminator l e v e l i s lowered, the number of  s i g n i f i c a n t signal pulses increases u n t i l i t reaches i t s maximum value.  Further  lowering the discriminator level.'leaves the -significant peak-height unaffected. The p l o t of peak height vs. noise i s thus a plateau-shaped curve, the knee of which determines -the discriminator setting at the energy of the -electrons to t)e focused.  One  such graph i s shown i n Figure  20.  For measuring spectra covering a large energy range, the knee-points determined f o r energy i n t e r v a l s beginning with energy' E r e s u l t i n a curve of the type shown.in Figure 2 1 and from t h i s , the -optimum discriminator setting at any energy may be found. Spectrometer Alignment The -following, procedure was adopted.as the most r e l i a b l e , (a) The  source i s positioned i n i t s mounting so that i t -lies i n the centre of  the spectrometer end-plate.  A s p e c i a l j i g was  constructed f o r t h i s purpose.  To follow page 39.  Required discriminate  setting  Noise  F i g . 20.  Typical discrimination  plateau.  Noise  Fig. 21.  Noise l e v e l setting corresponding to d i f f e r e n t electron energies.  40 . This does not ensure that i t l i e s on the magnetic-axis(b) The vacuum chamber i s then v i s u a l l y centred to make i t reasonably concentric with the c i r c u l a r opening,in the magnet. (c) The p o s i t i o n of the source i s next varied with the rack and pinion arrangement and the peak p r o f i l e of.the conversion l i n e - i s studied as a function of the source position.  The p o s i t i o n of the source corresponding to the  maximum peak-height attained i s then used i n subsequent  adjustments.  (d) Following ,an o p t i c a l analogy, i t i s apparent that the performance of the instrument w i l l be optimum when,the source-detector axis and the geometric axis of the vacuiam chamber coincide or, at l e a s t , intersect each other -at the magnet-centre (lens-centre).  Whereas the above three operations may bring the  ring focus i n t o coincidence with the s c i n t i l l a t i o n detector, they may not f u l f i l t h i s condition. For t h i s reason the vacuum chamber i s rotated around an axis through the magnet-centre and the peak-height of -a conversion l i n e studied as a function of the angular displacement of the vacuum chamber.  The p o s i t i o n of  the vacuum chamber corresponding to the maximum peak height i s then taken as the correct p o s i t i o n f o r both vacuum chamber and source.  The spectrometer  i s now ready.for tests.. Variation of the Parameters 06 and A 0 6  The parameters entrance b a f f l e s .  are determined by the size and p o s i t i o n of the  Six mean emergent angles were chosen,  such that the mean  tangent of 0 6 (and the associated gathering powers 6t>), were 0 . 2 4 9 8 ( 1 - 1 $ ) , 0 . 3 0 3 0 ( 1 . 2 $ ) , 0 - 3 3 8 4 ( 1 . 1 3 $ ) , 0 . 3 4 8 1 ( 1 . 1 7 $ ) , 0 . 3 6 8 5 ( 1 . 0 9 $ ) and 0 . 3 8 3 4 ( 1 . 1 $ ) . It had been intended to keep the gathering powers constant f o r a l l . s i x b a f f l e s , but a f t e r they.had been cut, t h e i r calculated gathering powers showed the above variations-  We found that f o r higher mean tangents and larger  gathering powers, the vacuum chamber walls interfered with the beam. In p r i n c i p l e , t h i s can be 'overcome by a smaller value of s, but with our ;  arrangement, i t was physically.impossible,because of vacuum pump connections, to reduce  s s u f f i c i e n t l y f o r higher mean tangents than O.3834.  ki. For each entrance b a f f l e , and with.a wide open e x i t b a f f l e , s was varied i n steps of 0.5 cm.  At each such position, .the l i n e p r o f i l e of  measured as a function of detector p o s i t i o n  d.  Cs'137 was  An example of the results f o r  a p a r t i c u l a r value of s i s shown i n Figure 22 and Figure 23-  A comparison of  such curves f o r a l l source positions enabled a choice of optimum s and f o r that p a r t i c u l a r entrance b a f f l e , and the spectrometer was set on these. Then the exit slot width was reduced i n steps to obtain a 'match' between the focused beam and the e x i t b a f f l e s .  Where the exit s l o t i s too wide, the  transmission i s determined by the beam width, and the l i n e width by the -exit baffles.  Reducing the slot width has no e f f e c t upon the transmission u n t i l  the match point i s reached, although the line-width steadily decreases.  When,  the exit slot becomes narrower than the beam width at the focus, the l i n e height drops and the l i n e width stays constant,.since the l a t t e r i s now determined by the width of the focused beam. set of l i n e p r o f i l e s . Table I  Figure 2k represents a t y p i c a l  This procedure was followed with a l l entrance b a f f l e s .  i s a summary.of the results.  In Table  II,  we compare the results  with those of Mann and Payne, in^-the only two cases where the same mean tangents and gathering powers were used. It i s obvious that i n spite of the greater f l e x i b i l i t y of control available i n t h i s survey, the performance of the spectrometer has not been s i g n i f i c a n t l y improved, and we.are forced to conclude that we have reached the optimum settings f o r the thin lens magnet used.  I t i s most probable that  the l i m i t reached.is imposed by,the f a c t "that the f i e l d i t s e l f i s not r a d i a l l y symmetric.  Wo special precautions were taken with the windings of the c o i l .  If t h i s symmetry, i s not present., then the r i n g focus -will not be a true -circle and no c i r c u l a r exit b a f f l e s can properly match i t .  The only p o s s i b i l i t y f o r  further improvement would be to use p r e c i s i o n techniques i n winding the c o i l , e.g., square cross-section wire with accurate controls of turn radius.  d =  63cm  Fig.22.  64cm  65cm  66cm  67cm  68cm  69cm  Variation of- peak shape with detector distance (M.T.-QV3481, 6>=1.17#, slot=3mm, -s=20.5cm)  E x i t slot  Fig.. 24.  3^  2.5mm  Graph showing 'match' condition (M. tf 0*348l ,60-1.17$) 1  2mm  TABLE I Results of C a l i b r a t i o n Measurements T  T(arbitrary units)  Mean t a n  ft>R  CO  0.2498  1,1  1-39  29  26  19  O.3O3O  1.2  1.20  • 42  " 35  29  0-3384  1.13  1.09  38  ' 34  31  •O.3U81  1-17  1.07  40  34-  32  O.3685  1.09  1.02  •31  28  27  O.383U  l.l  1.03  . 3k  •31  30  Table I I Comparison of present work with that of Mann' and Payne  (^x R  Mean tan  Present work  100) Mann and Payne  0.3834  106  83.  0-3481  109  89.  ^3CHAPTER IV THE DECAY OF.' C s ^ 55 . 1 3  The 2.3 year negatron decay of Cs 55  13k  13k to Ba 56  has been investigated  ^1-52 during the past few:years by a great many workers^ ^ and while agreement has been reached on c e r t a i n aspects of the decay, there are s t i l l many differences in the proposed schemes that require c l a r i f i c a t i o n .  The published decay  schemes are becoming increasingly complex as authors present evidence f o r new beta and gamma ray t r a n s i t i o n s which have not been noted before. Fig.25(a) shows those l e v e l s and t r a n s i t i o n s i n the decay that are generally accepted.  Fig.25(b) indicates other l e v e l s and t r a n s i t i o n s that have  been reported from time to time by some laboratories. progress, the two most recent papers appeared. analyzed the decay of C s - ^ 1  the beta source.  While t h i s work was i n  Van Wijngaarden Snd Connor^ have 2  paying p a r t i c u l a r attention to the preparation of  They report -that i f the source and backing are too thick,  back scattering gives evidence of beta-groups  at klO and 280 kev which almost  e n t i r e l y disappear when thinner sources are used.  With the thinnest sources,  they could not detect any of the t r a n s i t i o n s of Fig.25(b) and have been able to place very small upper l i m i t s on t h e i r i n t e n s i t i e s .  They conclude that the  decay scheme of Fig.25(a) i s correct.  Part of t h e i r conclusions has received 51 support from the work of Schriber and Hogg who examined the  independent  decay using a sum coincidence spectrometer.  Their results indicate only the  presence of the l e v e l s i n Fig.25(a), and that therefore the only beta-groups with end-point energies less than 662 kev are those of energies UlO and 89 kev.  EXPERIMENTAI, PROCEDURES  Ilk . The Cs  used i n our measurements was obtained from Oak Ridge National 133 \ 134  laboratory where i t had been prepared by the Cs was received i n the form of CsCt  i n ECt  solution.  (n,Y ) Cs  method.  It  A small quantity of t h i s  To follow page kj.  *\  J  „ -aoo H CO o o CD  CD  o  Q  Ln o  OJ  2  co  •H  CO to oocO H E— PQ LT\  LO O io  tg  CD  c-  4  +  +  co  OO O N  H C— CO O  + o  kk. solution was evaporated to dryness and then dissolved i n d i s t i l l e d water. resultant solution was. p r a c t i c a l l y acid-free.  The  A drop of t h i s solution was  deposited on a t h i n aluminum f o i l (150 pS /cm ) and evaporated to dryness. m  2  It was then covered with a thin f i l m of collodion to keep the active material in place.  This source was used f o r the measurement of beta, gamma, internal  conversion and coincidence spectra.  This i s the type of beta source that  52 Van Wijngaarden and Connor For  predict w i l l show spurious beta groups.  the preparation of photoelectron source, a s p e c i a l l y designed brass  capsule, as shown i n F i g . 2 6 , was used.  The active material, i n f u l l concentration,  was deposited into the capsule, evaporated  ..'Brass,  to dryness and covered with a thick layer of collodion. The thickness of the brass between the source material and the radiator was 0.75 to  which i s adequate  absorb a l l expected primary betas and  conversion electrons.  The radiator was  a c i r c u l a r disc of lead, k mm. i n diameter  Fig.26  Photoelectron source.  and 15 mg/ 2 thick, fixed to the brass cm  capsule as shown i n Fig.26. For  beta and conversion electron measurements, the modified t h i n lens  spectrometer was set f o r a line-width of 1-5$ power of 1 . 6 l $ .  i n momentum and a gathering  The large photoelectron radiator gave wider l i n e s , and i n these  measurements, the photoelectron l i n e widths were approximately 3$Gamma-ray singles spectra were taken with the source i n p o s i t i o n i n the spectrometer as shown i n Fig.28.  The gamma-detector was a l^r" x 1" JNal(TJt)  c r y s t a l assembly, o p t i c a l l y coupled to an RCA 63^2 photomulitplier by a 55" long l u c i t e r o d (Fig.27)-  This arrangement moved the photomultiplier back from  the strong f i e l d of the spectrometer magnet and at the same time kept the  To f o l l o w p a g e  H a r s h a w 1" x C r y s t a l Assembly  . RCA 6342 Photomultiplier  Nal(Tl)  1^" d i a m e t e r  x 5^'" l o n g  Lucite Light  Pipe  Fig.  27-  Gamma R a y D e t e c t o r U s e d i n t h e Beta-Gamma C o i n c i d e n c e Measurements  Fig.  28. Gamma R a y D e t e c t o r A s s e m b l y i n t h e Spectrometer. •  Magnetic  kk.  45. Nal(T-t) c r y s t a l near the source.  The residual magnetic f i e l d e f f e c t on the  photomultiplier was further reduced by surrounding i t with a Fernetic-Conetic magnetic f i e l d jacket.  Even with t h i s protection, the gamma-ray pulse  heights were affected by the f i e l d , but to a small extent only, and the e f f e c t was not troublesome. A lead s h i e l d was placed around the c r y s t a l to reduce the scattered gamma-radiation reaching the c r y s t a l from the surrounding brass.  This shield  was only p a r t l y successful as evidenced by a concentration of low energy pulses in the singles spectra.  The Coincidence Systems Two separate coincidence arrangements were used i n t h i s experiment.  They  w i l l be c a l l e d the gamma-beta and the beta-gamma systems and are shown i n block diagram form i n Fig.29 and F i g . 3 0 respectively. Both are fast-slow systems and have: some elements i n common. The fast-slow mixer 'is a commercially 1  available Borg-Warner unit, model DZ4 with a resolving .time^-(10  sec.  The gamma-beta system of F i g . 2 9 was designed to measure spectrometer pulses i n coincidence with selected gamma-ray pulses. m i l l i v o l t s amplitude of the mixer.  beta  Pulses of a few  from both beta and gamma detectors feed the f a s t inputs s  Since the l a t t e r require input amplitudes  of 2 0 ma. into 1 0 0 0  ohms, the d i r e c t pulses are f i r s t amplified and converted into standard pulses of the required amplitude  and p o l a r i t y by s p e c i a l l y designed c i r c u i t s c a l l e d  'fast drivers', a schematic At the same time,  diagram o f which i s shown i n Appendix 2 , F i g . A 7 - . .  'slow' gamma pulses from the seventh dynode (see Appendix  2, Fig.A8 ) are amplified and fed to a single-channel pulse-height analyzer, whose output goes to one of the slow channels.  A p a r t i c u l a r base l i n e  setting  of the single channel analyzer selects from the slow gamma output, pulses corresponding to a selected gamma-ray.  With t h i s arrangement alone, the f a s t -  slow c i r c u i t gives an output pulse whenever a spectrometer pulse i s i n coincidence  To follow page 45r  1 '^'-detecto] —> !  .Cathode follower  Amplifier x 2  Fast Coincidence  Fast Driver  .16  Fast Driver Phase Inverter  i  Ampt and Disc.  Ampli f i e r 1  Pulse Shaper  0-7 u s  Slow Coincidence  P.H.A.  \  Scaler  Fig.29  Scaler  Block diagram of gamma-beta coincidence system  Scaler  To f o l l o w p a g e 4 5.  (3  2f- d e t e c t o r  Cathode Follower  Amplifier x 2  Fast Coincidence  Fast Driver  ,16  Fast Driver •Phas e Inver t e r  Amp, and D i s c .  CO  +  1  Amplif i e r  i Pulse  Shsper  0.7  J1S  Slow Coincidence  ^i Scaler  Attenuator and phase inverter  P h a t se Invei'ter >  Amplifier  Amplifier  Kicksorter  Fig.30  Gate  B l o c k d i a g r a m o f beta-gamma c o i n c i d e n c e  3  ps  system.  with the selected gamma-ray.  However, the f a s t beta pulses include photo-  m u l t i p l i e r noise as w e l l , which contributes heavily to the chance coincidence rate.  To reduce t h i s , the beta-detector output i s fed to an amplifier discrimin-  ator whose output feeds the other slow input, and the fast-slow output  then  represents t r i p l e coincidences between the f a s t sum pulses and the two slow channels.  Because of amplifier, discriminator, and pulse height analyzer delays,  i t i s necessary to incorporate into the system the proper external delays to ensure that a l l pulses arrive at the mixer at the same time. The beta-gamma system of F i g - 3 0 i s designed to measure gamma-ray spectra i n coincidence with selected beta-pulses. of the gamma-beta system.  The f a s t inputs are the same as those  Only the beta-slow input i s used, so that the mixer  output pulses represent a l l gamma-ray pulses i n coincidence with selected by the spectrometer  current setting.  beta pulses  This output provides a time gate  to the multi-channel pulse height analyzer and only during t h i s time i s the analyzer receptive to the gamma-ray slow input.. that i n coincidence with a preselected beta gate.  The spectrum thus analyzed i s As before, external delays  are incorporated to ensure the proper a r r i v a l times of a l l pulses. It w i l l be noted that a variable delay has been incorporated on the gammaside i n both arrangements.  This compensates f o r the difference i n t r a n s i t time  of the electrons i n the 5" photomultiplier used on the beta side and the 2" photom u l t i p l i e r on the gamma side.  The magnitude of t h i s t r a n s i t time difference was  determined by measuring the coincidence counting rate between the 605 kev K-conversion  line  and the 797 kev gamma-ray (which are known to be i n coincidence), as a function of the delay.  A t y p i c a l result i s shown  in Fig.31.  o-<=t Fig.31  Beta Gamma Coincidence response as a function of delay on the gamma side.  V7.  EXPERIMEKTAL RESULTS The primary beta and conversion electron spectrum i s shown i n Fig.32, and Fig.33 shows the Kurie analysis of the spectrum with the conversion l i n e s removed.  The highest energy beta-group that i s detectable, gives a l e a s t -  squares end point of 6^9 + 3  kev i n agreement with the more precise 52  measurement of 661.9  +_ 0 . 5 kev of Van Wijngaarden and Connor  .  The spectrum  also shows two other" groups with end points of 411 and 272 kev.  Strong  source absorption begins a t r ^ l 3 0 kev and i n consequence,the low-energy 89 kev group could not be observed.  When the data of Fig.32 i s replotted as  N vs p, the areas under each group are proportional to the group i n t e n s i t i e s .  P The actual counts under the- 662 kev group are 2730^ while the r e l a t i v e i n t e n s i t i e s of the 662, 411 and-272 kev groups are 100,  14,  and 7.6 respectively.  Fig.34 shows the i n t e r n a l conversion l i n e s taken from Fig.32 with the primary beta background subtracted. ponding to t r a n s i t i o n s  The very weak K-conversion  of energies I O 3 6 , 1168  and 1366  l i n e s corres-  kev,were d i f f i c u l t  to measure and each experimental point i n t h i s region has a minumum counting time of 60. minutes. 15$-  In t h i s region the s t a t i s t i c a l uncertainty i s approximately  Also shown i s a weak conversion l i n e corresponding to a 473  transition.  kev  'The i n t e n s i t i e s of a l l - l i n e s were compared by measuring the areas  under each peak and dividing by the peak momentum. summarized i n Table IV.  The results are  It i s to be noted that the 605 K-conversion  includes within i t a small (L+M) s h e l l contribution from the 563^  line  569  kev  transitions. Fig.35 shows the photoelectron spectrum taken with the 15 mg/cm lead 2  radiator.  The Compton d i s t r i b u t i o n , measured with the radiator removed, has  been subtracted. the 473,  The spectrum was used only to relate the i n t e n s i t i e s of  563-569, and 605 gamma-rays.  The i n t e n s i t i e s were compared i n the  same manner as f o r the conversion electrons except that corrections f o r  (1) ( li WG)2 w  = 41.2355 « 18..-005UW  2  (2) (N ^2 ) i 2/  W G  =  27.O5U8 - 14.9956W  605K  Potentiometer setting(volts).  Fig.34  Internal conversion spectrum of Cs (Not a l l experimental points are plotted).  To follow page  Table I I I  Conversion Electron  Intensities  (Beta scale) E(kev)  K-conv.  473  0.8l  + 0.30  563  2.48  + 0.60  569  4.24 + 0.60  605 797V 803/  19.2  + 1.0  8.14 + 0.4  1036  0.08  + 0.02  1168  0.086 + 0.02  1366  0.016  +0.03  ( L + M ) conv.  3.5 + 0.5 1-3  + 0-3  49v a r i a t i o n of photoelectron cross-section with energy, using the data of  53 Davisson and Evans  , were also applied.  The energy spread i s small enough  that such factors as the dependence of angle of emission of the photoelectrons on energy may be ignored.  The data from t h i s spectrum i s included i n Table TV".  Fig.36 shows the gamma-rays singles spectrum.  I t was analyzed by  successive stripping of the upper energy p r o f i l e s .  For the three high  energy gamma-rays, we used as shape standards the l i n e p r o f i l e s of the  60 gamma-rays of Co  , a source that was r e a d i l y available.  that i t s two gamma-rays of energy 1173 the gamma-rays of C s  1  a  It has the advantage  *id 1333 kev are very close to two of  ^ but i s suffers from the disadvantage that the l i n e  shapes are not resolved.  To obtain these, the C o ^ singles spectrum was 134  taken with the same geometry as with Cs  ..- This i s shown i n Fig. 37-The  kev photopeak i s s u f f i c i e n t l y resolved to measure i t s width. p r o f i l e i s constructed as shown i n the figure.  1333  The peak  When t h i s peak i s subtracted,  the residue shows the clear, leading edge of the 1173  kev photopeak.  The  correct half-width i s selected (consistent with y^E dependence) and t h i s establishes the Gompton continuum of the 1333 kev gamma-ray under:.the kev photopeak.  This i s then scaled down to provide the 1173  11.73  Compton continuum.  In t h i s region of the spectrum, the sum of the two p r o f i l e s i s i d e n t i c a l with the measured C o ^ .spectrum. The photopeak area r a t i o s , when corrected f o r correct r e l a t i v e i n t e n s i t i e s of these two gamma-rays £ ! Z 3 J = 0.96 to [1333J 54 the known v a r i a t i o n of peak/total r a t i o and c r y s t a l ..efficiency , gives the within 4$. They were then considered to be acceptable shape standards and were used to unfold the three upper energy p r o f i l e s i n Fig.36-  The  i n t e n s i t i e s of the expected Compton d i s t r i b u t i o n s of the combined IO36,  1168  and 1366 kev gamma-rays of Cs"'"^ are not l i k e l y to exceed 1$ of the 605 or 797 kev photo peaks so that even though t h e i r exact shapes are not known, t h e i r e f f e c t upon these intense photopeaks i s minimal.  Rather than ignore  Table IV Gamma-Ray Intensities Relative E (kev) Photoelec tron Intensities k  73  563 569 605  1.0  From singles  + 0.5  26.5 + 6 . 5 "\  Relative GammaRay Intensities 1.0  + 0.5  26.5  +6.5  126.5 100  100  797 803  9  1036  1-5  1168  2.U + 0 . 3  2.k + 0 . 3  1366  3.6 + 0 . 3  3.6 + 0 . 3  k  + 5 + 0,3  9 1.5  k  + 5 + 0.3  51i t completely, however, the 605 and 797 kev residues were reduced by a constant 1$ of the 605 kev photopeak. 1  The 6 6 l kev l i n e p r o f i l e of Cs"^^ was used as a shape standard f o r the  remainder of the spectrum, each p r o f i l e being adjusted f o r photopeak width and peak/total r a t i o .  We could not resolve accurately the weaker 563,569 kev  composite peak from the stronger 605 kev peak and preferred to use the i n t e n s i t y r a t i o from the photoelectron data.  A summary of a l l i n t e n s i t i e s i s given i n  Table IV r e l a t i v e to the 605 kev gamma-ray. Coincidence Results We f i r s t used the gamma-beta system with the gamma-gate set on the 797*803 134 photopeak of the Cs  singles spectrum.  The spectrometer then scanned the  beta-ray spectrum i n coincidence with these gamma-rays. the r e s u l t s i s shown i n Fig.38.  The Kurie analysis of  The 662 kev group i s present but there also  seems to be contributions from lower energy groups, i n complete  disagreement  with the decay scheme shown i n Fig.25(a). Fig.39 summarizes the r e s u l t s of measurements, with the beta-gamma system. Fig-39(a) shows the gamma-rays i n coincidence with the K-conversion electrons of the 797*803 t r a n s i t i o n .  As expected, only the 605 kev photopeak appears,  which probably includes the 563*569 gamma-rays as well.  Fig.39(h) i s the  coincident gamma-ray; spectrum when the spectrometer i s set at the gate point A of Fig. 33-  I f "the decay scheme i s correct, these should be i n coincidence  only with the 662 kev beta-group. point i s moved to'B.  Fig.39(c) shows the r e s u l t s when the gate-  This should include the kll  and 270 groups as well,  both of which should be i n coincidence with the 605 kev gamma-ray, but not with the 797* 803 kev radiation, and from the Kurie analysis, t h i s difference should not be n e g l i g i b l e .  In fact, however, the d i s t r i b u t i o n s i n Fig.39(h)  and (c) have the same shape.  ^  e v  Fig-39  S c i n t i l l a t i o n spectra of gamma rays of Cs' •with d i f f e r e n t gate points.  J  i n coincidence  •52. If we assume that our kll and 270 kev beta-groups are actually back• scattered electrons of the 662 kev group, then the spectra i at' gate points A and B should be i d e n t i c a l when corrected f o r time and the difference i n In Fig.-39(d), the s o l i d curve i s that of Fig.39( c )-  counting rate at the two gates-. The:-superimposed;crosses  are. the:'.corrected': experimental points of Fig.39(^0•  Within the experimental uncertainties, they are i d e n t i c a l . that the Ull'and 270 kev groups  We conclude then,  from our beta spectrum must be  largely  back-scattered electrons; of the 662 kev group as predicted by Van Wigngaarden  52 and Connor  .  t  THE DECAY SCHEME The transitions that we have been able to detect, f i t the decay scheme of Fig.25(a) and i n Tables III: andIVwe have the conversion and gamma i n t e n s i t i e s , each to a d i f f e r e n t scale.  From previous work, i t appears that a l l conversion  -2 c o e f f i c i e n t s are less than 10  so that f o r the purpose of estimating  t r a n s i t i o n rates,'..the' conversion i n t e n s i t i e s may be ignored.  The r e l a t i o n  between the two intensity scales may be deduced by r e f e r r i n g to Fig.25(a) and Ilk examining the intensity balances of each l e v e l of Ba |j  i n t e n s i t i e s w i l l be denoted by  .  J  A l l gamma-ray  ~j , and beta i n t e n s i t i e s by (  ).  We  w i l l reduce a l l i n t e n s i t i e s to the gamma-scale, i . e . , r e l a t i v e to the value of 100  f o r the 605 kev gamma-ray, and use mean values throughout.  The 605 kev l e v e l  9k  [563]  f?9l] +  [803]  -  so that  + 26.5j :  (569]  +  +  [1O36J  -  [569]  [803]  =  + + 'l.5|  [1366]  =  [6o|  + '3.6' = 100; :  25.6  (a)  and s i m i l a r l y from the 1168  kev l e v e l  [569]  +  [803]  •=  27.9  In what follows, we w i l l use the average value  (b) R69]  •+  §03]  =  26-7-  53(659) +  - The 1402 l e v e l  [569]  (659) = 94  or The l 6 4 l l e v e l  (4ll) =  The 1971 l e v e l  (89) =  -  =  (79^  |803] -  [473] •+  |l036J  [569]  §03]  +  [569]  = 67.3  = 2-5 +  [1366] ' = '3.0.3  Beta-group Intensities The percentage i n t e n s i t i e s of the beta groups from t h i s analysis thus are 8 9 ( 3 1 $ ) , 411(2$) and 6 5 9 ( 6 7 $ ) , i n excellent agreement with those reported by 52 Van Wijngaarden and Connor  of 28$, 1$ and 71$., who determined them by direct  Kurie analysis of the beta-spectrum from a very thin source. Conversion C o e f f i c i e n t s and T r a n s i t i o n M u l t i p o l a r i t i e s We can now reduce the conversion i n t e n s i t i e s to the gamma-scale.  The 662  kev beta group has an i n t e n s i t y of 273° counts on the beta scale and 6 7 . 3 on the gamma scale.  The conversion m u l t i p l i e r i s then 0.0247-  Table V". l i s t s the revised conversion i n t e n s i t i e s , the associated gammaray i n t e n s i t i e s and the calculated conversion c o e f f i c i e n t s .  Also included are  the t h e o r e t i c a l values f o r some m u l t i p o l a r i t i e s computed from the tables of 55 S l i v and Band . rv.;.:.  :  With the error l i m i t s , a l l m u l t i p o l a r i t i e s are.  consistent with the spin-parity assignments of F i g . 2 5 ( a ) . It was not possible to resolve either the 563, 569 or the 797., 803 kev gamma-rays from the photoelectron spectrum. data to make some estimates.  However, we can use the conversion  If. we compare the 797* 803 kev composite peaks  and the 605 kev peak i n both conversion and photoelectron spectra, we f i n d that they have the same percentage width.  I t i s p a r t i c u l a r l y evident i n the  conversion spectrum, where both peaks are "'clean', and t h i s i s shown i n F i g . 4 0 ( a ) where the 605 kev peak has been scaled up to the 7 9 7 , 803 peak. In addition, the maximum of the l a t t e r corresponds energy 797 kev.  exactly to a t r a n s i t i o n of  Therefore the. 803 kev component must be weak.  From test  To f o l l o w page 5 3 .  1 0.330  .  <  —f  0;340  Potentiometer v o l t s tt>) Fig.kO  A n a l y s i s o f composite c o n v e r s i o n peaks  0.350  Table V., Transition Intensities and Conversion Coefficients Energy  k  73  5631 569/ 605 797) 803J  Gamma-Ray Intensity  K-conversion  l.O + 0.5  0.020 +0.006,  26.5 +6.5 100  & o.kik  K-conversion coeff.  Dre±ical  IK  0 02 + °-° • ° - ± 0.011  °^2K  Identification  O.OO325 0.0130 O.OO97  Ml or E2  °<«*  O.OO63 + ° - ° 0.00215 0.008k 0.0060 - 0.0015  Ml or E2  + 0.03  0.00V7 + 0.0003 O.OOI85 0.0071 0.0051  E2 E2  32  0 2  023  9k + 5  0.20 +0.01  0.00213 + 0.003 0.0010U  1036  1-5 ± 0-3  0.0020 + 0.000U  0.00133+0.00067 O.OOO63 0.0020  1168  2.k +0.3  0.0021 + 0.000U  0.00088+0.00031 0.00051 0.0015k 0.00115  E2  " 1366  3.6 + 0-3  0.0026 + 0.0005 0.00072+0.00022 O.OOO38 0.00108 O.OOO89  E2  O.OO36 0.0026 0.00147  Ml or E2  .55p r o f i l e s of composite peaks constructed from components of varying intensity r a t i o s , we conclude that the 803 kev component cannot be much greater than about 10$ of the 797 kev conversion l i n e .  From the established decay scheme,  both should have the same multipolarity, so that t h i s should be  approximately  the r a t i o of the gamma-ray i n t e n s i t i e s . The 563,  569 composite peak i n the conversion spectrum has a much 1  greater percentage width than the 605 kev standard, and was easy to resolve into components of i n t e n s i t y r a t i o 0 . 5 8 : 1 as shown i n Fig.UO(b). Again, the decay scheme predicts the same multipolarity f o r these t r a n s i t i o n s (Ml predominantly).and  t h i s should be a measure of the gamma-ray r a t i o .  The only way we can check these conclusions i s to check t h e i r consistency I f the [563])./ C ^ 9 j  from the decay scheme i n t e n s i t y balances. then [569J = 1 6 . 8 .  Therefore, from the 1971  kev l e v e l i n Ba ^, 1  ratio i s  O.58,  [8O3J = 9 . 9  which i s roughly the i n t e n s i t y predicted from the conversion l i n e p r o f i l e s . Alternatively, from the 605 kev l e v e l , we get [797J = 8 5 . 2 . 95-1  Thus [_797] + [803] =  compared with the measured value of 94These conclusions are i n reasonably good agreement with the i n t e n s i t y  estimates of other workers who were able to make them. comparisonsof  Table VI shows the  our estimates of these four gamma-rays with some published  results. In summary; our-results support the s i m p l i f i c a t i o n of the decay scheme 52  as proposed by Van Wijngaarden and Connor^ Hogg''"'".  and supported by Schriber and  Other l e v e l s as shown i n Fig. 25(b) have been postulated f o r a variety  of reasons not the least of which are observations of beta groups other than the three i n Fig.25(a).  The i n t e n s i t y measurements of Van Wijngaarden and  52 Connor  have placed upper l i m i t s on the i n t e n s i t i e s of beta-groups  of  energies greater than 662 kev as <C-.0>05$ which to a l l intents and purposes rules out the 683,  892 and 1453 kev groups.  The only group they detect with  Table Vfr  Comparative Gamma-Ray Intensities (Percentage of decay) Author  1563]  B69J  CT97J  L803]  10  18  103  8  14  12  72  11  9-4  12.8  91  18  9  11  SchnHber & Hogg^  9-5  12.6  83  12  Present work  9-5  16.4  83  9-7  36 Bashiloy et at  41  Forster & Wiggins 42 Kiester et al..  49 Trehan et a l 0  51  93  57-  an energy between 662 and 89 kev i s t h e 1+11 kev group,: arid i t has an i n t e n s i t y o f a p p r o x i m a t e l y 1$.  The 1770  k e v l e v e l , supposedly f e d b y a I+9I+  kev b e t a group d e - e x c i t e s b y 960 and 156I+ k e v t r a n s i t i o n s .  Van W i j n g a a r d e n  52 and Connor  p l a c e an upper l i m i t on the 156k k e v gamma-ray o f <  0.02$.  We  made a s e r i o u s attempt t o d e t e c t a 960 k e v gamma-ray i n t h e p h o t o e l e c t r o n  50 spectrum b u t w i t h o u t s u c c e s s . quote i n t e n s i t i e s o f 1-5$  I t was r e p o r t e d b y S e g a e r t  and 0.6$ r e s p e c t i v e l y .  1+7 and b y G i r g i s  who  Counting times of  a p p r o x i m a t e l y one hour on each p o i n t i n t h i s r e g i o n o f t h e spectrum produced We were a b l e t o d e t e c t the 473 k e v photopeak w i t h r e l a t i v e  no d e t e c t a b l e peak.  ease and i t s i n t e n s i t y i s 1$ o f the 605 k e v gamma-ray.  I t i s true that at  96O kev, the p h o t o e l e c t r i c c r o s s - s e c t i o n f a l l s t o about o n e - q u a r t e r o f i t s v a l u e a t 1+73 k e v b u t t h i s s h o u l d be more t h a n compensated  b y t h e almost  comp'lete absence o f Compton background, and b y the much l o w e r p h o t o m u l t i p l i e r background we were a b l e t o use.  The IO36, 1168  c l e a r l y d i s c e r n a b l e as measureable peaks.  and 1366 k e v photopeaks a r e  A uranium r a d i a t o r (50 mg/cm )  i n c r e a s e d t h e l a t t e r b u t s t i l l showed n o t h i n g a t 96O kev.  We c o n c l u d e t h a t  i f t h i s t r a n s i t i o n e x i s t s , i t s i n t e n s i t y i s l e s s t h a n 0.2$. The l o g . ( f t ) v a l u e s o f t h e t h r e e b e t a - g r o u p s c l o s e l y p a r a l l e l t h e r e s u l t s of other workers.  They a r e  8.9 + 0-5, 9.6  +  and 6.2  + 0.-05.  f o r the  662, 4 l l and 89 kev components r e s p e c t i v e l y . The s p i n - p a r i t y assignment t o t h e l6kl  k e v l e v e l i s somewhat u n c e r t a i n .  The l o g ( f t ) v a l u e f o r t h e 1+11 k e v group from the k+  Cs^^  ground s t a t e t o  t h i s l e v e l i s 9-6 w h i c h l o o k s l i k e a f i r s t - f o r b i d d e n t r a n s i t i o n a l t h o u g h i t i s j u s t p o s s i b l e t h a t i t i s a h e a v i l y - r e t a r d e d a l l o w e d decay. c o e f f i c i e n t s o f b o t h t h e "1036 or a mixture o f both.  The c o n v e r s i o n  and t h e 1+73 k e v gamma-ray can be e i t h e r M l , E2  The e r r o r l i m i t s on b o t h t r a n s i t i o n s do n o t i n c l u d e o t h e r  m u l t i p o l a r i t i e s such as E l , M2'or E3-  I f these i d e n t i f i c a t i o n s a r e c o r r e c t ,  t h e n t h e s t a t e i s p r o b a b l y 3+ o r 1++ .  T h i s -agrees w i t h t h e two p o s s i b i l i t i e s  r e s u l t i n g from t h e a n g u l a r c o r r e l a t i o n s t u d i e s o f the IO36-6O5 gamma-ray  It i s not easy to f i t the decay scheme of F i g . 2 5 ( a ) i n a l l i t s d e t a i l s ^Ba^g^ has 6 protons outside a closed s h e l l  to a p a r t i c u l a r nuclear model.  and k neutron 'holes' so that the energy l e v e l s can hardly retain any s i n g l e particle characteristics.  On the other hand, the nucleus does not f a l l into  the strongly deformed group (A y 150 i n t h i s region of the periodic table) that have been treated with some success by the various c o l l e c t i v e model approaches (see Appendix i ) .  In t h e i r paper, Segaert et a l ^ have calculated  the l e v e l structure to be expected on the basis of seven d i f f e r e n t models developed f o r the medium weight n u c l e i , and the asymmetric rotor model of 62 _•' Mallmann appears to give'the closest f i t .  A l l of the l e v e l s of Fig.25(a)  appear with the correct spins and p a r i t i e s including the l 6 U l kev l e v e l which i s degenerate with spins 3  +  and k+.  In 'addition however, i t predicts l e v e l s  at about 1570 and 1770 kev which do not appear to be excited i n t h i s decay. A l l seven, models predict the f i r s t 2+ state (605: kev) and most of them the second 2+ state ( l l 6 8 kev). and 1971  It i s interesting to note that the ..ground, 605  kev states f i t almost exactly the predicted sequence of r o t a t i o n a l  band components f o r K=0. It i s also of interest to compare Fig.25(a) with the level, structure of 132 cj^Xeyg Fig.kl.  , . [2 paired protons l e s s ; .  These are shown f o r the f i r s t few l e v e l s i n  ' 132 The s i m i l a r i t i e s are quite marked, although for Xe there are J  two less protons which can interact with the core.  I t i s tempting to conclude  from t h i s that the'-many-particle shell'model, with conf igurational mixing i s a better approximation i n t h i s case tlhan one which emphasizes core excitations.  Kurath  points out that the region of the l g .  s h e l l i s one  •9k  i n which the many-particle model should work reasonably well.  The s i x  134 extra-core protons of Ba  have l g 72 7 /  states.immediately available which  59-  4f.  mo  3+4-f 14-50  \Z2.o  2.A-  14<>Z  4+-  1168  2,+ .  Zr-.  G1S  13^ 56 78  132 54 78  BA  XE  Fig.4:1  l i e above the IgcV  Go5  ZA-  • 132 13U Level structure of Xe and Ba (comparison).  configurations-.  I t i s f r u i t l e s s however, to speculate on  one model to the ^exclusion of others since i t i s probable that both types of e x c i t a t i o n contribute.  6o.. Appendix 1 NUCLEAR MODELS Attempts have been made from time to time to arrive at a model of the nucleus consistent with the available experimental evidence.  Several models  have been proposed each of which explains some aspects of the experimental data i n a more or less l i m i t e d way.  Among the models which have been proposed are  the FerWi gas model, the l i q u i d drop model, the alpha p a r t i c l e model, the s h e l l (independent p a r t i c l e ) model and the c o l l e c t i v e model.  For beta and gamma  ray spectroscopy the l a s t two have proved r e a l l y useful and hence w i l l be described b r i e f l y .  The S h e l l Model .It i s now well established that electronic energy l e v e l s i n an atom show a d i s t i n c t s h e l l structure which accounts f o r i t s c h a r a c t e r i s t i c behaviour.  For  instance, atoms such as helium, neon, krypton etc. are exceptionally stable because they have a l l t h e i r electronic s h e l l s completely f i l l e d . those containing 2, 8, 20,  Among n u c l e i ,  $0, 82 and 126 protons or neutrons are observed to  56'  be more s t a b l e ^ than others.  These numbers are known as 'magic numbers'' .  nuclear s h e l l model originated as an attempt to explain the magic numbers on l i n e s similar, to those of atomic s h e l l structure. The basic assumptions  of the s h e l l model a f t e r Mayer, Haxel, Jensen and  Suess are l)  a nucleon moves independently i n a nuclear p o t e n t i a l f i e l d created  "by a l l the others.  This p o t e n t i a l consists of two parts and i s a n a l y t i c a l l y  expressed as  , V(r') + f ( r )  1.7  '  1  The  61.  where V(r) i s the average central p o t e n t i a l due to (A-l) nucleons and f ( r ) J£.s i s that r e s u l t i n g from a strong i n t e r a c t i o n between the o r b i t a l and spin angular momentum of a nucleon. 2)  The e f f e c t of the l a t t e r i s "to s p l i t each / l e v e l into two l e v e l s with  j = L->c\ and j =t-\, the j = L->r\ l e v e l l y i n g below j.= L-\ . For V(r) the most commonly used form i s one intermediate between the square well p o t e n t i a l and the o s c i l l a t o r p o t e n t i a l and i s shown i n F i g . ( A l ) . form of f\r)  The exact  i s not yet known.  When these assumptions are incorporated into the wave mechanical treatment, the result i s that protons and neutrons form independent  s h e l l s , or subshells, • which  close at the magic numbers as shown i n Fig.(Al). In addition to explaining the magic  'If  numbers, the s h e l l model gives a' complete description of ground state spins-and p a r i t i e s , nuclear isomerism and some information about magnetic dipole  Fig.Al  and e l e c t r i c quadripole moments. To deduce angular momenta, we start  Energy l e v e l s i n a p o t e n t i a l well intermediate between; square well and an o s c i l l a t o r p o t e n t i a l .  with nuclides consisting e n t i r e l y of closed shells (N andJZ, both magic) and those-consisting o f closed shells plus or minus one p a r t i c l e .  According to the exclusion p r i n c i p l e the former must  have zero angular momentum and the t o t a l angular momentum of the l a t t e r i s just the angular momentum of the 'extra' or the 'missing' (hole) p a r t i c l e . 8 16  angular momenta of g0 2 0 _ 3 9 125' 82 19 > KR  P B 2 D 7  8 2 1  ( 1  f  20  20^  kO 126 208 > 82^  a  126^.209 1 5 3 - Tti are i - — - — and £ 83 2' 2 ' 2 ' 2" B i  8„15  are zero and those of yN  Thus the 9 17 8°'  respectively i n accordance  62.  with experimental evidence. For odd-A nuclides, the assumption made i s that l i k e nucleons i n a nucleus p a i r off" i n such a way that t h e i r angular momenta cancel.  Then the angular  momentum of an odd-A nuclide i s due e n t i r e l y to the angular momentum of the l a s t unpaired nucleon.  Actually t h i s assumption  i s i n s u f f i c i e n t unless due  account i s taken of the fact that nucleons outside the closed shells with each other.  interact  As a result of t h i s so-called p a i r i n g energy e f f e c t , a l e v e l  w i l l be depressed when i t contains an even number of nucleons compared with i t s value when i t contains an odd number of nucleons. with increasing o r b i t a l angular momentum.  Moreover, the e f f e c t increases  Thus odd A nuclides with N above  58 w i l l be expected to have angular momenta of 7/2 or l l / 2 . have angular momentum of'-g-, showing that 1  ••&jj'2  1 h]j/2  Instead they levels.are  depressed below the 3 s i l e v e l when they are f i l l e d by even number of nucleons. The assumption  that l i k e nucleons outside closed shells p a i r o f f to  produce zero angular momentum i s not r e a l l y s e l f evident. f a i l e d only i n three cases. of 5/2, 3 ° M n  55  However, i t has  12 23 They are -Q-^a with angular momentum 3/2 instead  with 5/2 instead of 7/2 and gj^Se  79  with 7/2 instead of 9/2. In  these three nuclidesthe t o t a l angular momentum i s then due to the three nucleons outside the closed s h e l l . For odd-odd nuclides, the t o t a l angular momentum must be due to at least two unpaired p a r t i c l e s , the l a s t proton and the .last neutron.  In t h i s case there  i s no simple rule tp deduce the angular momentum of the nuclide because the angular momenta of the two unpaired p a r t i c l e s can combine i n many ways. By convention, nucleons have an even i n t r i n s i c p a r i t y .  I nucleon state i s given by (-l)  The p a r i t y of a  ~~~~ . The s h e l l model predicts the o r b i t a l  angular momentum f o r each nucleon and hence the p a r i t y of each nucleon i n different nucleon states i s known.  The, p a r i t y of the nucleus, then, i s the  product of the p a r i t i e s of the individual nucleons .  63The single p a r t i c l e s h e l l model i s very successful i n predicting spins and p a r i t i e s of the ground states of odd-A nuclei, and even some of the lowl y i n g states of excitation.  Higher excited states lose t h e i r single p a r t i c l e  character, probably because some nucleons are excited out of the core to j o i n the odd p a r t i c l e . 58 Goldhaber, H i l l , Sunyar s h e l l model.  have studfced nuclear isomerism:  i n terms of the  Isomerism.- ( i . e . the phenomenon of long-lived excited states)  occurs when t r a n s i t i o n s to neighbouring nuclear stStes become forbidden because of large changes i n angular momentum involved.  The s h e l l model predicts  that the conditions f o r isomerism should exist below magic numbers 50, 82 and 126,  but not immediately above them.  This i s what i s observed when the known  long l i v e d isomers ( T A . ^ 1 sec) with odd A are p l o t t e d against t h e i r odd Z or odd N number.  Such a p l o t reveals the presence of groupings or' islands  of isomers' just below the magic numbers ^0, 82 and 126. Magnetic moments (j^) are obtained using ground state angular momenta. For even even nuclides, J=o and hence  u=o . For odd A nuclides, J=j and  magnetic moments are calculated using the following r e l a t i o n s :  H = (j-i)g/, + %  f o r 1= j - i  , .  where g^ = 1 f o r a proton and zero for a neutron; g£ = 2-79 f °  ra  proton and  -1.19 f o r a neutron. u-values calculated using the above r e l a t i o n s are known as Schmidt values and are compared with the observed magnetic moments.  Q u a l i t a t i v e l y they agree  very well but quantitatively they show deviations, and usually l i e somewhere between the two l i m i t s .  These deviations disappear (partly) i f mixing i n of  states other than the single p a r t i c l e states i s also taken into account.  There  59' i s some evidence  that the magnetic moment u of a free nucleon i s not the same  as when the nucleon i s i n a bound state.  64, Shell model predictions regarding e l e c t r i c quadrupole moments (Q) a r e : Q = o  f o r magic number n u c l e i  Q i s -ve f o r nuclei with a proton or a neutron outside a closed s h e l l and  Q i s +ve f o r nuclei with a 'hole-' .  No exceptions have been found to these predictions. Regarding the magnitudes of Q's the situation i s very discouraging. Theoretically Q, should be of the order of the nuclear radius squared i . e . 10" 5cm 2  2  . This i s found to be so f o r small A, but f o r A. ^ 100, values as  large as 10 x 10~ 5 occur. 2  Another puzzling feature i s that Q's f o r odd A-odd  N nuclides are of the same order as those ofi.oddcA^oddZ nuclides whereas jthe s h e l l model predicts the former to be much smaller. The magnitude of Q i s a measure of the deviation of a nucleus from spherical shape, and the s h e l l model seems to underestimate t h i s deviation. The large values of Q mean that the nucleus i s f a r from spherical in: shape. When, instead, a sphenoidal nucleus i s treated mathematically, theQ's turn out to" be closer to the observed values.  This modification of the s h e l l  60 model leads to- the c o l l e c t i v e model The C o l l e c t i v e Model .In the s h e l l model, i t i s assumed that nuclear properties such as angular momenta, magnetic moments and e l e c t r i c quadrupole moments are determined by the l a s t nucleon moving outside the nuclear core. core does not play any active role.  The nuclear  The c o l l e c t i v e model, however, assumes  that nucleons outside the core exert a c e n t r i f u g a l pressure on the surface of the core.  As a r e s u l t the core may undergo surface o s c i l l a t i o n s and  become deformed into a non-spherical shape. spherical p o t e n t i a l .  The nucleons thus move i n a non-  The nuclear deformation reacts on the nucleons and  modifies somewhat the independent p a r t i c l e aspect.  65The t o t a l angular momentum remains the same but now i t i s shared between the core and the l a s t nucleon outside i t . Z ~— L A  c o r e  towards the magnetic moment.  The core makes a contribution  This brings magnetic moments i n better  agreement with the observed values. The e f f e c t on the quadrupole moment i s much larger. df the core can lead to large quadrupole moments.  A small deformation  Since the quadrupole  moments are due to core deformations, odd A-oddN nuclides may show the same order of quadrupole moments as those of odd A-oddZ nuclides. The deformation of the core i s specified by parameter ^  Q=  1  where R  Q  A  R  R  °  o  "  such that  OO  5.  A  i s the average nuclear radius and A R  i s the difference between the  0  ma^jor and minor semi-axis of the e l l i p s e , n i s the number of nucleons outside the core. Variations of the p o t e n t i a l energy of the nucleus with respect to /3 reveals that 1) f o r small n, -the equilibrium shape of the nucleus i s spherical and c o l l e c t i v e motion i s a v i b r a t i o n about t h i s shape. 2)  f o r large n, the nucleus i s permanently  deformed and the c o l l e c t i v e  motion i s a rotation- of the nuclear orientation. Under these circumstances the c o l l e c t i v e angular momentum R i s given by Z  (fixed i n space)  'deformed n u c l e i .  66. where I i s the resultant angular momentum of the nucleus and K i s the sum of the i n t r i n s i c angular momenta due to a l l nucleons outside the core  (Fig.A2).  For the sake of s i m p l i c i t y i t may he assumed now that l e v e l spectrum arises from; a)  i n t r i n s i c nucleonic motion i n a spheroidal p o t e n t i a l of which s h e l l  model predictions are a s p e c i a l case  a)  b)  c o l l e c t i v e rotation  c)  collective vibration  I n t r i n s i c spectrum f o r a spheroidal f i e l d as a function of jb has been  calculated by K i l l s o n 61  A specimen of his r e s u l t s are shown i n F i g . A3.  It i s seen that each s h e l l model state s p l i t s up into -g-(2j+l) states-For ^ =0, the normal s h e l l ordering appears. For large  however, there i s a  drastic change. 13)  For r o t a t i o n a l state  J  rot "  2  (6)  2  where co i s the angular v e l o c i t y of the core and I i s the < e f f e c t i v e moment of i n e r t i a of the core. I = £  5  I i s given by MA(AR„)  2  -org  -o-a -<f\ Deformation ^3  Combining (5) and (6)  E Equation  2 h •t _ 21  Fig.A3 JCJ+I)-!? ^ 2  (7)  Single p a r t i c l e states i n a spheroidal p o t e n t i a l as a function of/3 .  (7) determines the  r o t a t i o n a l band superimposed on the i n t r i n s i c l e v e l s .  67For even even nuclei "K = o'and as i n the case o f a homonuclear diatomic moelcule,the l e v e l s are given by J=o, 2 , k, 6 , .... (parity even) For odd A nuclei K i s equal to the angular momentum of the l a s t odd p a r t i c l e as determined from Nilsson o r b i t s and the allowed values of J are J = K, K+l, K+2,  (half  integral)  P a r i t y i s determined by K and hence i s the same f o r a l l states of the r o t a t i o n a l band. c)  In t h i s case the nucleus possesses a c e r t a i n number of v i b r a t i o n a l  quanta "(phonons) each of energy httg, and angular momentum Jb\' , In the simple case of even even nuclei, the v i b r a t i o n a l spectrum i s due to quadrupole phonons and i s shown i n Fig.AU. C o l l e c t i v e model thus predicts fine structure of nuclear l e v e l s .  3nu>-  0,2,3,4,6  2IVW-  0,2 k  It retains a l l the c h a r a c t e r i s t i c s  2  +  of the s h e l l model and at the same C o l l e c t i v e Vibration  time gives better r e s u l t s f o r magnetic moments, e l e c t r i c quadrupole moments, excited states of nuclei and other phenomenon.  Fig.AU  Vibrational'levels i n even-even n u c l e i .  Appendix 2  SOME C I R C U I T DIAGRAMS  fD  CD  Fig.;"A5 Magnet current control c i r c u i t  To follow page68.  V + 1U2QV  Fig.A6  Components of the phototube bleeder.  To follow page 68.  To follow page 68.;  RCA 63^2  7A8  Scintillation Detector Electronics  69BIBLIOGRAPHY  ' 1.  E. Fermi. •.  Z e i t s . f. Physik 8 8 , l 6 l ( 1 9 3 4 ) .  2.  C L . Cowan et a l .  Science 1 2 4 , 103 (1956).  3.  E. Majoi*ana. Nuovo. Cimento 14, 171 (1937).  4.  P.A.M. Dirac. P r o c Roy. S o c (London) A 117, 6 l 0 ( 1 9 2 8 ) ; A I l 8 , 351 (1928).  5.  C N . Yang, and T.D. Lee.  6.  C S . Wu et a l .  7.  Frauenfeldes et a l .  8.  Hermannsfeld Burn et al." Phys.. Rev. Le'tters 1, 6 l ( 1 9 5 8 ) .  9-  Fermir Lecture Notes.. "University of Chicago Press 7 6 , ( l 9 5 0 ) .  Phys. Rev. 104, 254 ( 1 9 5 6 ) . . t  Phys.Rev. 105, , . l 4 l 3  (1957).  Phys. Rev. 106, .386 ( l 9 5 j ) .  10.  Appendix II '"Beta and Gamma Ray Spectroscopy" edited by K. Siegbahn.  11.  E. Feenberg and G. Trigg.  12.  S.A. Moszkowski.  13-  S.A. Moszkowski. Chapter VIII, "Beta and Gamma Ray Spectroscopy" edited by K.'Siegbahn.  lh.  M.E. Rose-. "Internal Conversion Coefficients'" Publishing Company.  Rev. Mod. Phys. ' 2 2 , -399 (.I95O).  Phys. Rev. 8 2 , 35 ( 1 9 5 1 ) .  15.  E.L. Stolyarova.  16.  A.H. Wapstra et a l .  North Holland 0  Uspenski. . v o l . 6 , no.6, 872 (196U). "Nuclear Spectroscopy Tables", North Holland  P u b l i s h i n g Co., Amsterdam, 31 (1959). 17-  K . Siegbahn.  P h i l . Mag. ( 7 ) , 3J_, 162 ( 1 9 4 6 ) .  18.  T.R. Gerholm.  Handbuch der Physik, 3 3 , 6 l 0 .  19.  "Beta and Gamma Ray Spectroscopy". 2 2 7 . ( 1 9 5 5 ) .  20.  Solve, Hultberg.  21.  R.E. B e l l , R.L. Graham.and H.E. Petch.  22.  L.E. Biedenhjarn and M.E. Rose.  23*  H. Busch. Ann. Physik 8 l , 974 ( 1 9 2 6 ) .  24.  M. Deutsch, L.G. E l l i o t and R.D. Evans.  25-  Hornyak, Lauritsen and Rasmussen.  Arkiv f o r Fysik Band 15nr 2 7 , 307 ( 1 9 6 3 ) . Can. J . Phys.. 3 0 , 35 (1952).  Rev. Mod. Phys. 2 5 , 746 ( 1 9 5 3 ) . Arch. Elektrot. 18, • 583 (1927). Rev. S c i . Inst.. 1 5 , 178 ( 1 9 4 4 ) .  Phys.. Rev. 7 6 , 731 (1949)-  70. 26.  J.M. K e l l e r , E. Koenigsberg and A. Paskin.  Rev. S c i . -Inst. 21, 713  27.  W.W.  28.  Jensen, Laslett and Pratt.  29-.  K.C. Mann and F.A. Payne.  30.  R.P. chaturvedi.  31.  L.G. E l l i o t and R.E. B e l l .  32.  J.L., Meem and F. Maienshein. Phys. Rev. 7_6_, - 328 (1949 ) .  33-  'MyA: Waggoner et a l .  3l+.  K. Gromov and B. Dzhelepov.  35-.  J.M. Cork et a l .  36.  A.A. Bashilov et a l .  37-  D-C  Lu and M. Wiedenbeck,  38..  M.C  Joshi and B..V. Thosar.  39.  T. Azuma.  40.  G. B e r t o l i n i et a l .  4.1.  H.H. Forster and J.S. Wiggins.  42.  G.L. Keister et a l .  43.  E. Klema.  44.  G. Chandra. Proc. Indian Acad. Science. A vol. 4 4 , no.4-, pp. 194-200, (Oct., 1956).  45..  C L . Peacock.  46.  T.D. French and M. Goodrich.  47.  R.K. Girgis and R. Van Lieshout.  48.  Y. Yamamoto.  49.  P.N. Trehan et a l .  50.  O.J. Segaert et a l .  51.  S.O. Schritfeer and B.G. Hogg.  52.  W. Van Wijngaarden and R.D. Connor.  53.  G.M.  Rev. See. Inst. 2 2 , .92 ( l 9 5 l ) .  Pratt, E.I. Boley and R.T. Nicholas.  Phys. Rev. 75, U58 (1949). Rev. S c i . Inst.. 30, 4.08 (1959).  Ph.D. Thesis, U.B.C. Van. -8 (1962) unpublished. ?  Phys. Rev. 7 2 , 979 (19U7). '  Phys. Rev. 8 0 , 1+20 (1950). Dokl. Akad. Nauk. SSSR 8 5 , 299 (1952).  Phys. Rev. 9 0 , .444 ( 1 9 5 3 ) . Izv. Akad. Nauk. SSSR Ser. F i z l 8 , . 4 3  (1954).  Phys. Rev. 9_4, ,501 (195U). Phys. Rev. 9 6 , 1022  B u l l Maniwa University 3 A , 237  (1954).  (1955)-  Nuovo Cimento 2, 273 .(1955)Nuovo Cimento 2_, ,854 (1955).  Phys. Rev. 97, .451  (1955).  Phys. Rev. 100, 66 ( 1 9 5 0 ) .  NP-6325 Microcard  (1957).  B u l l . Am. Phys-. Soc. 4 , - 3 9 1  (1959).  Nuclear Physics 12, 672  (1959).  Thesis, Osaka University, Japan ( i 9 6 0 ) . , Phys. Rev. 1 3 1 , . 2 6 2 5  (1963).  Nuclear Physics 4_3, 76  Davisson and R.D. Evans.  (1950).  (.1963).  Nuclear Physics 48, 647  (1963).  Can. J . Phys-. 42, 504 ( 1 9 6 4 ) .  Rev. Mod. Phys. 24, 79  (1952).  71. 54.  W.E.  55-  L-'A. S l i v and I.'M. Band. • " C o e f f i c i e n t s of Internal Conversion of Gamma Radiation". Unpublished.  56.  (a) .M.G.  Mayer.  (b)  Flowers. Prog, i n Nuc. Phy. 2, 235 ( l 9 ' 5 2 ) , O.R. Frisch, Academic Press.  •(c) 57.  Mott and R.B.  B.H.  M.'H.L. Pryce. Mayer.  Sutton.  Encyclopedia of Physics 45_, 111  Phys. Rev. 74, -253  :  (l958).  (1948). edited by  Rep. Prog. Phy./London Physical Society 17,  l'(l954)•  Phys. Rev. 78, -l6 ( 1 9 5 0 ) .  (a)  M.G.  (b)  0. Haxel et a l . Phys-. Rev. 75,  1766  '(l9'49).  58.  (a) .M. Goldhaber. 906 (1951)-  59-  De S h a l i t . Proc. of Int.. Conf. of Nuc. Structure, Univ. of Toronto Press ( i 9 6 0 ) .  60.  A. Bohr.  61.  S.G.  Nillson.  62.  CA.  Mallmann.  63-  Rev. Mod.  Phys-. 24, -179  ( 1 9 5 2 ) ; Phys-. Rev.  83,  Kgl. Danske Videnskab Selskab Mat. fys. Medd 26, No-l4 ( 1 9 5 2 ) . Dan. Mat. Medd. 2 9 , -No..l6 ( 1 9 5 5 ) . Nuc. Phys. 24,  535(1961).  D. Kurath. 'Nuclear Spectroscopy' edited by Fay Ajzenberg-Selove. Academic Press, page 983 ( i 9 6 0 ) .  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0085854/manifest

Comment

Related Items