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The gamma-rays of radium Ozeroff, Michael John 1948

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THE GAMMA-RATS OF RADIUM by Michael John Ozeroff  A thesis submitted i n p a r t i a l f u l f i l m e n t of the requirements f o r the degree o f ' MASTER OF ARTS i n the Department of PHYSIOS  The University of B r i t i s h Columbia A p r i l , 1948  ACKNOWLEDGEMENT  The present study has been made possible by a Grant-in-Aid of Research to Professor K. C. Mann from the National Research Council of Canada.  The author wishes to  acknowledge a g i f t of 4060 pounds of lead from the Consolidated Mining and Smelting Company of T r a i l , B. C. f o r the construction of spectrometer b a f f l e s and protective screens. He i s indebted to the Cancer Research Group of Vancouver,  B.C.  f o r providing a Radium source, and to Mrs. E. Speers of the Chemistry Department f o r preparing a Thorium B source.  The  award to the author of a Studentship from the National Research Council has greatly f a c i l i t a t e d t h i s work.  Finally,  the author wishes to express his deep indebtedness to Professor K. C. Mann, whose u n f a i l i n g interest and helpfulness assisted greatly i n the successful completion of the study.  V  TABLE OP CONTENTS Page I.  INTRODUCTION  II.  EXPERIMENTAL METHOD 1. Spectrometer Types 2. The Thin-Lens Spectrometer 3. Source Arrangement 4. The Geiger Counter 5. Counter Power Supply -6. Magnet Current Supply 1. Earth's F i e l d Compensator 8. Alignment 9. Resolution 10. Calibration 11. Calculation of Gamma-Ray Energies  1  3 6 8 10 11 12 14 14 17 17 lo  I I I . EXPERIMENTAL RESULTS 1 . Reduction of Primary Beta-Ray Radiation . . 19 2. The Radium Gamma-Ray Spectrum . 21 3. S t a t i s t i c a l Accuracy 21 4. Error i n Energy Determination 23 5. Comparative Results 24 IV.  CONCLUSION .  26  V.  BIBLIOGRAPHY  29  ILLUSTRATIONS  Figure  Page  1. -fT-Type Spectrometer  4  2.  E l e c t r o s t a t i c Spectrometer  5  J>,  Electron Lens Spectrometer . .  4.  Thin-Lens Spectrometer . . .  7  5.  Source Arrangement  8  6.  Geiger Counter  7.  Current Regulator  12  8.  Compensator C o i l E f f i c i e n c y  15  9.  E f f e c t of Compensator Current on Peak,Shape  J>  . . . . .  10.  Thorium B Source, and E-line  11.  Reduction of Primary Beta-Radiation  12.  Radium Gamma-Ray Spectrum  . 10  , . 16 . . . 18 20 .22  Table 1.  Comparative Results  Plate I.  24 Facing Page  Thin-Lens Spectrometer  7  ABSTRACT  Th© thin-lens beta-ray spectrometer i s described, together with i t s associated equipment.  The. energies of  gamma-rays, emitted by Radium i n equilibrium with i t s d i s i n tegration products have been determined  by measuring, i n such  a spectrometer, the energies of photoelectrons ejected from lead.  These energies agree reasonably w e l l with those re-  ported by E l l i s and Skinner, although several values reported by Alichanov and Latyshev have not been found.  The  energy  calculations were based on a c a l i b r a t i o n using the E l i n e of Thorium B; (H o = 1385.6 gauss-cm.).  An i n d i c a t i o n was  of a gamma energy not previously reported.  found  1  THE GAMMA-RAYS OF RADIUM  I.  INTRODUCTION  Previous measurements of Radium gamma-ray energies nave been made by several investigators.  E l l i s and-  Skinner^ ), measuring i n t e r n a l conversion and photoelectric 1  l i n e energies i n a "IT-type spectrometer reported twenty-one gamma-rays of Radium B, C and D.  Alichanov and Latyshev^)  measured the energies of positrons formed by pair-production i n lead with a f t - t y p e spectrometer, and from these measurements reported eleven gamma-rays of Radium C, of energies greater than 2 moc  2  ( i . e . 1.02 Mev).  T s i e n ^ ) , using  selective absorption and c r y s t a l d i f f r a c t i o n i n the range  25-50  Kev, and the cloud chamber i n the range  ported s i x gamma-rays of Radium D. (Dc.D. E l l i s and H.W.B. Skinner,  7-25 Kev  re-  While i n the high energy Proc.Roy.Soc, 105A, 165  (1924). (2) A. Alichanov and G. Latyshev, (3) s.T. Tsien,  C.R.Acad.Sci. (U.R.S.S.), 20, 429 (1938). Phys.Rev., 69, 38 (1946).  region at l e a s t , a comparison of results shows f a i r agreement, there are some discrepancies and i t seemed advisable to r e peat t h i s work with the thin-lens spectrometer at our d i s posal.  2.  II.  1.  EXPERIMENTAL METHOD  SPECTROMETER TYPES The negative beta-rays from radioactive n u c l e i con-  s i s t of electrons whose energy varies continuously from a c e r t a i n maximum value down to zero*  Gamma-rays may also be  emitted from such n u c l e i , and since they represent t r a n s i tions between excited nuclear energy states, they possess discrete energies.  To observe beta-ray d i s t r i b u t i o n s , beta  spectrometers of various designs have been developed.  Under  the proper conditions the beta spectrometer may be used equally well to Investigate gamma-ray energies, either by measuring the energies of photoelectrons expelled by these gamma-rays from t h i n high atomic number lamina, by measuring Compton r e c o i l electron d i s t r i b u t i o n s ejected from thick absorbers of low atomic number, or by measuring the energies of positrons or negatrons created by pair production i n high atomic number absorbers. Pour types of instruments are i n general use. (a)  The Magnetic Semicircular Focussing Spectrometer  (1^-type), shown i n Figure 1 , was devised by D a n y s z ^ i n 1912.  I t was l a t e r improved by Robinson and Rutherford^)  ( ) j . D a n y s z , L e Radium, 9 , 1 ( 1 9 1 2 ) ; 1 0 , 4 ( 1 9 1 3 ) . Robinson and E. Rutherford, Phil.Mag., 2 6 , 717 4  (1913).  4. and has since been very widely used.  A uniform magnetic  f i e l d i s applied perpendicular to the plane of the f i g u r e . Beta-rays i n a small momentum i n t e r v a l describe c i r c l e s of approximately equal r a d i i i n the f i e l d and are therefore focussed at the same point on the photographic plate.  A  Geiger tube may be used i n place of the photographic plate, i n conjunction with a magnetic f i e l d which can be varied.  -Figure 1. (b)  The E l e c t r o s t a t i c Focussing Spectrometer, shown in.  Figure 2, was suggested by Hughes and Rojanskyt6).  This  instrument uses a r a d i a l , inverse first-power, e l e c t r o s t a t i c f i e l d to focus a bundle of electrons of the same energy i n a manner similar to that of a magnetic f i e l d .  An angle of  deviation of 1 2 7 ° 1 7 ' i s found to give the correct focussing condition.  The instrument i s p a r t i c u l a r l y useful f o r low  (^A.L. Hughes and V. Rojansky,  Phys.Rev., 34, 284 (1925).  energy p a r t i c l e s , and lias been used successfully by Backus(7) to measure the low energy negatron d i s t r i b u t i o n of C u ^ .  Figure 2. (c)  The Electron Lens type of spectrometer i s shown i h  ^1  Figure 3.  Source  Figure 3. (7) J . Backus,  Phys.Rev., 68, 59  (WJ,  6..  This arrangement was f i r s t used by T r i c k e r ^ ) i n 1 9 2 4 .  The  evacuated cylinder i s surrounded f o r i t s entire length by a solenoidal wound conductor.  For a given current through the  solenoid, electrons of a certain energy w i l l be focussed on the detector. (d)  A v a r i a t i o n of t h i s type of instrument i s the t h i n -  lens spectrometer, as introduced by Deutsch, E l l i o t t and Evans ( 9 ) .  This i s the type of spectrometer used i n the pre-  sent study.  I t i s described i n d e t a i l i n the sections which  follow.  2.  THE THIN-LENS SPECTROMETER The thin-lens spectrometer i s shown i n section i n  Figure 4 and i n a photograph i n Plate I .  I t consists essen-  t i a l l y of an evacuated c y l i n d r i c a l brass tube 8 inches i n diameter and 4 0 inches long, surrounded at i t s centre by a short magnet c o i l of heavy wire.  The c o i l i s water cooled  i n order to reduce temperature f l u c t u a t i o n s .  The tube con-  tains f i v e lead baffles which perform several functions. Baffle A transmits a conical beam of electrons from the radiator into the focussing f i e l d of the magnet.  Baffle B  prevents high-energy radiation from passing d i r e c t l y from source to counter.  C i s a.masking b a f f l e and together with  D and E serves to absorb much of the scattered r a d i a t i o n which might otherwise reach the counter and thus increase the Tricker, Proc.Camb.Phil.Soc, 2 2 , 4 5 4 ( 1 9 2 4 ) . ( ? ) M . Deutsch, L. E l l i o t t and R. Evans, Rev.Sci.Instr., 1 5 ,  ( )R.A. 8  7  (1944).  8  normal background.  -  A Genco Megavac pump i s used to evacuate'  the system, with an o i l d i f f u s i o n pump included f o r lower pressures when necessary.  The vacuum indicator i s a thermo-  couple gauge. The cone of electrons passing through the defining baffle A i s focussed by the action of the magnetic f i e l d of the c o i l .  For a given c o i l current, electrons of the appro-  priate energy w i l l pass through b a f f l e C, and be focussed on the "window" of the Geiger counter.  Electrons of other  energies would, i n the absence of b a f f l e s , be focussed at other points along the axis of the spectrometer  tube.  Since  the c o i l contains no iron, the f i e l d and hence the momentum of the focussed electrons w i l l be l i n e a r with current.  3.  SPURGE ARRANGEMENT Figure 5 shows the source arrangement used i n t h i s  study.  Figure 5.  The Radium used was enclosed i n a s i l v e r capsule 1 inch long and 1/8 inch i n diameter.  This was placed i n a small hole R  d r i l l e d through a s o l i d brass cylinder as shown.  The c y l i n -  der was sealed to the end of the spectrometer tube.  On the  end of the cylinder facing into the spectrometer was cemented a c i r c u l a r lamina of lead, 3 millimetres i n diameter and 0.044 millimetres thick, of surface density 50 milligrams per square centimetre. radiator.  This w i l l be referred to as the lead  The thickness of brass, between the Radium and the  lead was made s u f f i c i e n t to absorb a l l the primary beta-rays from the source, c a l c u l a t i o n f o r t h i s minimum thickness being made on the basis of the well known Feather formula(10), R(gms/cm2) =  0.543 E (Mev) *- 0.16.  Gamma-rays emitted from the source pass through the brass and eject photoelectrons from the lead.  In addition,  Compton electrons i n a continuous d i s t r i b u t i o n are ejected from the brass absorber.  Both photoelectrons and Compton  electrons are detected and counted i n the spectrometer with the r e s u l t that a plot of electron i n t e n s i t y versus electron momentum i s a composite curve, showing a series of monoenergetic photoelectric peaks superimposed Compton d i s t r i b u t i o n . Compton background,  upon the continuous  In order to correct the curve f o r  the lead radiator i s removed and a back-  ground curve i s plotted over the same momentum range.  This  curve, sometimes normalized to f i t the composite curve, i s (•°)j".M. Cork, L  "Radioactivity and Nuclear Physics", (Van -Nostrand) P. 121.  10. subtracted from the l a t t e r , and the r e s u l t i n g plot gives the l i n e spectrum due to photoelectrons ejected by gamma-rays from the lead.  4.  THE GEIGER COUNTER  ^1  The counter, shown i n Figure 6, i s of the b e l l type,  Wind  > s~  Figure 6, having a diameter of 0.75  0.005  inch tungsten wire.  inches, and a central anode of I t i s f i l l e d with a mixture  of Argon and Ethyl Alcohol vapor, 9.3 cm. (Hg) of Argon with 0.7 cm. of Alcohol vapor having been found to give a good pulse shape and a usable.plateau.  A sample plateau  r i s e s from 750 counts per minute at 975 volts to 1000 counts per minute at 1070 v o l t s , a rate of increase of 0.3 percent i n counts per minute per v o l t .  With a lead  shield around the counter, normal background (with source i n place, no current through the magnet c o i l ) i s of the order of 60 counts per minute.  A mica window of surface  11. density 0.89 milligrams per square centimetre was used. window was found to absorb a l l energies below 50 Kev,  This  and  t h i s automatically sets a lower l i m i t to the energies which may  be measured.  Considerable care must be exercised i n  order to avoid subjecting such a t h i n window to d i f f e r e n t i a l pressures much greater than 10 centimeters of mercury, since i t s strength i s not great.  A brass mask with a central  c i r c u l a r hole i n i t i s f i t t e d over the counter window.  The  diameter of the hole i s made about 1 millimetre greater than the diameter of the source.  The mask i s intended to improve  the resolving power of the spectrometer by eliminating from the counter electrons not.properly focussed. flange on the counter permits replacement  A removable  of the window and  easy sealing of the counter to the spectrometer tube.  Pulses  are counted by a scale-of-64 s c a l i n g unit which actuates a mechanical  5.  register.  C01INTER POWER SUPPLY The counter power supply consists of a high voltage  battery pack with a switching arrangement which gives steps of 15 v o l t s over the range from 840 to 1400 v o l t s .  A stable  supply voltage i s a necessity since changes i n voltage w i l l cause changes i n counting rate and w i l l thus d i s t o r t the r e sults.  In the absence of an accurate voltmeter, reproduci-  b i l i t y of points on a curve i s the most r e l i a b l e test of the supply voltage.  12 6. MAGNET CURRENT SUPPLY A D.C. generator supplies current f o r the magnet This current i s regulated to within 1 part i n 1000 by  coil.  means of a photocell control c i r c u i t , shown i n Figure 7«  A B C D E F  D. C. Generator Generator F i e l d C i r c u i t Generator F i e l d Supply Load C i r c u i t F i l t e r Magnet C o i l Standard Resistance  G H J K L  Galvanometer Potentiometer Photocells Amplifier 8 P a r a l l e l 6L6 Tubes  Figure 7. The operation of the regulator i s as follows.  The potentio-  meter, used as a reference voltage, i s standardized by means of a Weston Standard c e l l .  The voltage across a standard  resistance i n the load c i r c u i t of the generator i s then balanced by the required potentiometer  voltage.  When the . . . .  system i s i n balance the galvanometer reads zero current, and the galvanometer l i g h t beam takes up a p o s i t i o n midway between the two photocells.  This i s the desired operating condition.  13-. In t h i s condition, the two photocell output voltages are balanced against each other and no signal voltage reaches the next stage of the amplifier.  I f now  the magnet current  begins to change, the voltage across the standard resistance also begins to change, and t h i s deflects the galvanometer light.  The r e s u l t i n g off-balance photocell s i g n a l i s ampli-  f i e d and applied to the grids of the 6L6 tubes i n such a way that the generator f i e l d current i s altered to compensate for the o r i g i n a l change i n magnet current. diagram, the generator  As shown i n the  f i e l d i s separately excited, from  batteries of large current capacity. adds to the s t a b i l i t y of the regulator.  Such an arrangement Because of the re-  l a t i v e l y slow response of the galvanometer and the long timeconstant of the generator f i e l d , t h i s system i s useful i n c o n t r o l l i n g only, slow variations of current (greater than 0.5  seconds).  Hence considerable extra f i l t e r i n g on the  generator output as well as on the magnet load was  found  necessary. The importance of a high degree of regulation f o r the magnet current cannot be too f i r m l y stre'ssed.  A varying  current has the e f f e c t of reducing peak height and increasing peak width, thereby reduc'ing both the resolving power and s e n s i t i v i t y of the spectrometer.  the  Since many of the gamma-  rays are only weakly converted, t h e i r resultant photoelectric peaks are very small, and an instrument with poor s e n s i t i v i t y w i l l not detect them. At the same time i t must be admitted that t h i s  14. control c i r c u i t which holds the current constant to 0.1 percent i s hotter than i s actually needed when we consider the r e l a t i v e l y low resolution of the spectrometer.  ?.  EARTH'S FIELD COMPENSATOR Two rectangular c o i l s connected as Helmholtz c o i l s -  were arranged i n horizontal planes, one above and one below the spectrometer tube and placed symmetrically with respect to i t s axis.  Their function i s to compensate f o r the effect  of the v e r t i c a l component of the earth's f i e l d , which could cause defocussing of beta p a r t i c l e s .over t h e i r long path. Current f o r the c o i l s i s supplied from .batteries and must be held as nearly constant as possible.  Further remarks r e -  garding the importance of the compensator w i l l be made i n the following s e c t i o n .  8.  ALIGNMENT .Four major factors must be considered i n the a l i g n -  ment of the thin-lens spectrometer. (a)  The spectrometer tube axis should l i e i n the plane  of the earth's magnetic meridian.  The earth's f i e l d strength  ( v e r t i c a l component} and d i r e c t i o n (horizontal component) are plotted over the area a v a i l a b l e . i n the laboratory.  An  optimum p o s i t i o n is, then chosen f o r the spectrometer, taking into account the rate of v a r i a t i o n of v e r t i c a l f i e l d strength with distance along the tube axis. (b)  The current through the compensator c o i l s must be  15. adjusted to counteract the e f f e c t of the v e r t i c a l component of the earth's f i e l d .  I f t h i s f i e l d strength i s not sensibly-  constant throughout the length of the spectrometer tube, then obviously some compromise must be made i n the current value chosen f o r the c o i l s .  A plot of the resultant f i e l d , with  compensating c o i l s i n operation at an optimum current i s shown i n Figure 8.  r  "1  VevV;«i\ F \ e U  ] <L«HI  art-  3*.  to  Figure 8. (c)  The spectrometer tube was placed  with respect to the f i e l d of the magnet.  symmetrically F i r s t the tube  was aligned v i s u a l l y so that i t s axis and centre point coincided as nearly as possible with those of the magnet coil.  Then as a f i n a l adjustment, sample counts were taken  with a source i n place and a constant current through the magnet, f o r d i f f e r e n t positions of the tube.  The p o s i t i o n  of each end of the tube was changed ( v e r t i c a l l y or h o r i zontally only) i n turn, and the f i n a l p o s i t i o n chosen was  16. that f o r which the counting rate was a maximum.  The tube  was then clamped i n t h i s p o s i t i o n . (d)  The chosen value of compensator c o i l current should  give good peak shape, which implies maximum peak height combined with minimum width and least d i s t o r t i o n .  As a f i n a l  c r i t e r i o n f o r t h i s current value, a strong photoelectron peak was located i n the spectrum of the Radium source, and this peak was plotted using several d i f f e r e n t values of compensator current.  A sample plot i s shown i n Figure 9, with  the jvarious compensator currents indicated thereon.  It is  seen from t h i s that l i t t l e doubt a r i s e s as to the required compensator current value.  Such a current value i s then  used i n the earth's f i e l d compensator c o i l s for a l l subsequent work.  Figure 9.  17.  9.  RESOLUTION The resolving power of the instrument, whioh i s  defined as the peak width (expressed as a percentage) at half-maximum intensity, was found to be approximately 4 percent.  10.  CALIBRATION As was mentioned previously, the f i e l d of the  magnet i s l i n e a r with current, because of the absence of iron.  Therefore only single-point c a l i b r a t i o n i s required.  The instrument was calibrated with the very strong (conversion) F l i n e of Thorium B (Hp  =  138j?.6  gauss-cm)^ K 11  Using a very t h i n source i n order to obtain as sharp a l i n e as possible, and mounted on a t h i n sheet of mica to reduce back-scattering* the Thorium F l i n e was plotted as shown i n Figure 1 0 .  The Thorium source arrangement i s also shown i n  the same figure.  The potentiometer reading which corres-  ponds to the H f> value of 1 3 8 5 . 6 gauss-cms f o r the F l i n e was found to be 0 . 2 2 8 v o l t s . Hp  From t h i s a l l the required  values are found.  C.D. E l l i s , Proc.Roy.Soc, 1 3 8 , 3 1 8 ( 1 9 3 2 ) , K.C. Wang, Zeits.f.Phys., 8 7 , 633 ( 1 9 3 4 ) .  and  18.  r W  ISO Counts | M V  "T"V>oriuwr>  Source f \ r range merit"  B  F \00  So  O.t  0.3  0.3L  Potentiometer  Setting Bw>«  mask  Figure 1 0 ,  11.  CALCULATION OF GAM.iIA.-RAY ENERGIES Using the well known equation  Hp where H^  i2l  | T(T + 1 . 0 2 )  represents the electron momentum i n gauss-cm, and  T the kinetic energy i n Mev, the l a t t e r can be determined. For a photoelectron peak, hV  (gamma-ray energy) = T + Efc  where Efc i s the electron binding energy, and hence the energy of the gamma-ray can be found. For lead, the value of E  D  f o r the K s h e l l i s  8 7 . 6 K e v ^ ) , and f o r the L s h e l l 1 5 . 8 Kev, t h e i r difference 12  being 7 1 . 8 Kev.  (  12J  J . M . Cork,  l o o . c i t . p. 3 0 1 .  19.  III.  1.  EXPERIMENTAL RESULTS  REDUCTION OP PRIMARY BETA BACKGROUND An attempt was made to improve the s e n s i t i v i t y of  the spectrometer i n the following way.  The brass absorber  over the source has one function only, and that i s to prevent the intense primary beta r a d i a t i o n from the souroe from arr i v i n g at the counter.  This i t does, but a Compton back-  ground i s introduced i n i t s place, though much less intense than the primary beta r a d i a t i o n i t replaces. this Compton background  Nevertheless  s t i l l imposes a l i m i t upon the photo-  electron l i n e intensity that can be observed because of the unavoidable s t a t i s t i c a l fluctuations of i n t e n s i t y of both background and photoelectric peaks. Therefore an attempt was made to remove the primary beta r a d i a t i o n by replacing the brass absorber with a strong magnetic f i e l d , which could not of course give r i s e to Compton secondaries.  The gamma-rays would be unaffected and  this beam would then eject photoelectrons from the lead with l i t t l e or no background. shown i n Figure 11.  The experimental arrangement i s  20*  Figure  11.  The d i f f i c u l t i e s proved to be as follows: (a) .With a primary beta energy of the order of 2.5 strength of f i e l d s available about  7000  Mev,  gauss, and the geo-  metry employed, minimum source-to-radiator distances of the order of 1.5  centimetres were required to d i v e r t the most  energetic beta-rays from the spectrometer beam. (b)  Such a source-to-radiator distance proved to be so  great that with the source a v a i l a b l e (10  m i l l i c u r i e s ) the  photoelectron peaks were too small to detect, even without any appreciable background. (c)  I t was necessary to have the d e f l e c t i n g magnetic  f i e l d cut o f f sharply short of the lead radiator i n order to avoid i n t e r f e r i n g with the focussing properties of the spectrometer magnet. Various arrangements of source, f i e l d and radiator were tested.  Because of the d i f f i c u l t i e s noted above, and  21.  the l i m i t a t i o n s imposed by'the geometry of the source, which were unavoidable as t h i s was the only source available, t h i s method was not found to be f e a s i b l e .  Indications are, how-  ever, that i t would be useful f o r a source of greater i n tensity, and perhaps even with a source of the strength used but with a more suitable shape.  As was noted before, the  source used was not a point source but a cylinder 1 inch long and 1/8  inch thick, and t h i s shape complicated the problem  considerably.  2.  THE RADIUM GAMMA-PvAY SPECTRUM A graph of the photoelectron peaks over the entire  momentum range covered i n t h i s study i s shown i n Figure  12.  The upper curve i s the composite curve referred to e a r l i e r . The dotted l i n e indicates the Compton background, and the lowest curve represents the difference between the other two. The horizontal scale i s such that the momentum i n t e r v a l at any point i s a constant percentage of the t o t a l momentum at that point.  (Electron momentum i s l i n e a r l y proportional to  the Potentiometer voltage shown.)  3.  STATISTICAL ACCURACY The average intensity per point (on peak outline)  i s approximately 640  counts per minute.  For the average  counting time of 12 minutes t h i s gives a t o t a l count per point of about 7700.  On the Compton background curve the  average intensity per point i s about 600  counts per minute,  \000|  Gramma - R o y s 8001  i  600  +c5  of  Radium.  I  4 0  O 00©  Cut-otff  o f o.osK  •I*  .n  3P  Potentiometer  .3?  Voltage Figure  .50  "~  .60  .7*.  .86  \J>  \.9L  \.S  23. which leads to a t o t a l count of of 6 minutes.  3&00,  f o r the counting time  The s t a t i s t i c a l accuracies of these two mea-  surements are 1.1 and 1.7 percent respectively.  The r e s u l -  tant s t a t i s t i c a l accuracy u of the points which give the peak outline i s given by the formula  where x and y are the errors i n each of the two independent measurements.  This leads to an average s t a t i s t i c a l accuracy  of ± 2 percent.  4.  ERROR IN ENERGY DETERMINATION The accuracy of the energy determination i s o f  course an important factor.  The error i n potentiometer  standardization i s small enough to be neglected.  The pro-  bable maximum error i n determining the " c a l i b r a t i o n point" i s estimated to be less than 1 percent.  S i m i l a r l y the maxi-  mum error i n reading the highest point of a given photoelectron l i n e i s estimated to be also less than 1 percent. These are considered to be the major sources of error.  They  lead to a probable maximum error i n calculated gamma-ray energy of ± 1.5 percent. the experiment  An i n d i c a t i o n of the accuracy o f  i s given by the binding energy difference  which was found between the K and L conversion l i n e s of the  0,598  Mev gamma-ray.  This difference was found to be  73  Kev,  a value which agrees reasonably well with the quoted value of 71.8 Kev, noted e a r l i e r .  24.  5.  COMPARATIVE RESULTS Table 1 snows a comparison between the values  found i n t h i s study and those of e a r l i e r investigators.  TABLE 1 E l l i s and Skinner Gamma-ray Energy s  Mann and Ozeroff  Alichanov and Latyshev Gamma-ray Energy  Relative Intensity  .0472 .0536 .0589  Gamma-ray Energy  .243  .237  .260 .275 .297 .332 .354  .289 .428 .448. .478  .471 .503 .612 .773  .59®  .768  .941  1.248 1*39 1.43  1.21 1.29 1.39 1.52 1.62  1.78  2.22  0.6 * s  11** 2 8  .429  1.13  Relative Intensity  1.69 1.75 1.82  2.09  2.20 2.42  2 1.2 i : i  18 49  2  1.40  3BE  6 2.2 11 53 11 78 33  22  29 22  17  100 17  15 41 21  1.7?  100  2.1?  22  (2.4)  Relative i n t e n s i t i e s not given. Not corrected f o r photoelectric cross-section.  25. Relative i n t e n s i t i e s of the gamma-rays are included a l s o . The i n t e n s i t i e s shown here have been corrected to take into account the decreasing cross-section f o r the photoelectric effect with increasing energy, using p u b l i s h e d ^ ^ cross1  section curves.  (^C.D. Coryell, M. Deutsch, R.D. Evans, W.J. Ozeroff et a l The Science and Engineering of Nuclear Power, (Addison-Wesley) p. 40.  26.  IV.  CONCLUSION  An examination of the graph i n Figure 12 shows that i n the lower energy portion of the spectrum the photoelectron peaks are very prominent, while i n the high energy section they become very weak.  This condition i s due i n part to the  fact that the photoelectric cross-section decreases very rapidly with increasing photon energy.  For gamma-rays i n  lead, the absorption c o e f f i c i e n t decreases from a value of 1.6 cm" at an energy of 0.4 Mev to 0.03 cm" at 2.5 Mev. 1  1  This means that we must expect the photoelectron peaks to become weaker.and weaker as we pass to higher gamma energies. From the Compton background end-point at the upper l i m i t we can f i n d an approximate value f o r the energy of the gamma-ray which i s responsible f o r the Compton background i n that region, but which i s apparently too weak to show as a photoelectron l i n e . Table 1.  This value i s l i s t e d i n brackets i n  I t was calculated from the equation  ',  .  -.51 T (Mev)  h V (Mev) = _ ^ 0  T  T  (  T  + 1  .o2) cos 0  which i s developed from the Compton Scattering Formula. h V  Q  represents the energy of the incident gamma-ray, 0 the  angle between the d i r e c t i o n of the incident gamma-ray and that of the r e c o i l electron and T the maximum r e c o i l electron  27. energy, i n t h i s case 2.14 Mev; In the experimental arrangement, because of the r e l a t i v e l y large size of the source as compared to that of the radiator, 0 may have values from 0° to about 60° upon which portion of the source i s considered. we get h V  0  = 2.4 Mev (approx.).  depending  For  0=0°  A d i f f e r e n t value of 0*,  say 15°, leads to a higher gamma energy which i n turn would give r i s e to a maximum r e c o i l electron energy greater than 2.14 Mev.  Since the-maximum r e c o i l electron energy detected '  was 2.14 Mev, i t was concluded that the gamma-ray responsible for i t was that at 2.4 Mev. As noted previously, cut-off at the lower end of the spectrum occurs at 50 Kev, because of window thickness. Therefore the spectrometer i s not e f f i c i e n t i n the detection of gamma-rays whose energies are below about 138 Kev (50 Kev plus the lead K-shell binding energy of 88 Kev).  L-shell  photoelectrons might s t i l l be ejected but the fact that the probability of t h e i r ejection i s f a r less than that f o r the K-shell e f f e c t i v e l y rules out the p o s s i b i l i t y of detecting them. The comparative chart i n Table 1 shows fourteen gamma-ray energies found i n t h i s study.  One of these, that  at 2.4 Mev i s quoted only approximately since i t i s calculated from the Compton end-point.  Of the fourteen, a l l but  one correspond reasonably well to values found by e a r l i e r investigators.  The remaining one, at 0.45 Mev i s a very  weak l i n e , as may be seen from Figure 12, and occurs between  28. two r e l a t i v e l y strong l i n e s .  Because of i t s low i n t e n s i t y ,  much time was spent i n making observations on i t and r a i s i n g i t s s t a t i s t i c a l accuracy to a figure comparable to that of the more intense l i n e s .  Should such a l i n e actually exist,  i t i s certain that i t s i n t e n s i t y i s near the l i m i t of detect i o n of the spectrometer  used.  Many gamma-ray energies, reported by other workers were not observed here.  This might be due to t h e i r low i n -  tensity or perhaps to the fact that they are highly converted and hence have l i t t l e intensity l e f t f o r photoelectron emission.  I t may be noted that i n the region of the spectrum  above 1.1 Mev, according to the present study the picture i s similar to that given by E l l i s and Skinner.  Of the several  other energies given by Alichanov and Latyshev i n t h i s region no trace could be found, i n spite of the f a c t that they are quoted as being of r e l a t i v e l y high i n t e n s i t i e s .  29.  V.  BIBLIOGRAPHY  A.. Alichanov and G. Latyshev  C.R.Acad.Sci. (U.R.S.S.), 20, 429  J.  Phys.Rev., 68, 5 9 (194-5).  Backus  J. M. Cork  (1938).  "Radioactivity and Nuclear Physics", (Van Nostrand).  C. D. C o r y e l l , M. Deutsch, R. D. Evans, W. J . Ozeroff et a l "The Science and Engineering of Nuclear Power", (Addison-Wesley). I. Danysz  Le Radium, 9 , 1 ( 1 9 1 2 ) ;  M. Deutsch, L. E l l i o t t and R. D. Evans  Rev.Sci.Instr., 1 5 , 7 (1944).  C. D. E l l i s  P r o c R o y . S o c , 138, 318 (1932).  C. D. E l l i s and H. W. B. Skinner  P r o c R o y . S o c , 1 0 5 A , 165 (1924).  A. L. Hughes and V. Rojansky  Phys.Rev., 3 4 , 284 ( 1 9 2 5 ) .  H. Robinson and E. Rutherford  Phil.Mag., 2 6 , 717  R. A. Tricker  Proc.Camb.Phil.Soc, 2 2 , 4 5 4 (1924).  S. T. Tsien  Phys.Rev., 6 9 , 38 ( 1 9 4 6 ) .  K. C. Wang  Z e i t s . f u r Phys., 8 7 , 633 ( 1 9 3 4 ) .  10, 4 (1913).  (1913).  


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