Ghumman, B S

Sood, B S

IACS Institutional Repository

INELASTIC INTERACTIONS OF GAM M A RAYS W ITH  K-SHELL ELECTRONSB. S. GHUMMAK and  B. S. SOODPhysios Department, Punjabi UNrvERsiTy, PATTAt.A-4, India (Received June 14. 1967; Re-$iibmitted August 3. 1967)ABSTRACT. The technique of the absolilto intensity measurement of if-shell fluorescent rafliRtion by a NaT(Tl) crystal has boon omployij^d to measure the cross-soctions of the inelastic interactions of 280, 662 and 1260 kcV gamma* rays with /C-sholl electrons in lead and gold. The X-rays efficiency of the detector has boon njeaaured experimentally by comparing the ratio of gamma rays and X-rays following internal conversion from Aid®® and sources. For 280 keV gamma rays the measured cross-sections agree with tho known photo-electric cross- soctions showing tha t tho X-rays arc produced ©saontially through tho photo-electric interac­tion. For 662 and 1250 koV tho measured cross-seotions are somewhat higher than those of photo-elootric interaction indicating tho contribution of the Compton scattering from X-shell electrons, the integrated crosa-gection of which is ogtiraated to be equal to that from fro© and stationary electrons.I N T R O D U C T I O NTho inelastic interactions of gamma rays with X-sholl electrons of the target atoms result in J?'-vacancics which emit fluorescent X-rays or eject Auger elec­trons. The processes of interactions arc, (i) Photoelectric effect and (ii) Compton Hcattering from bound electrons. The number of X-vacanciea created( which is equal to the /f-shell X-rays emitted divided by the X-shell fluorescence yield, is a measure of the cross-sections of tiiesc interactions. The measurement of the number of X-rays emitted when a target is irradiated with a knowm flux of gamma rays thus provides a method to obtain information about the cross-sections of these processes.The experiments performed to determine the cross-soctions of inelastic interactions of 280, 662 and 1250 keV gamma rays with X-shell electrons in Pb and All by measuring tho absolute yield of the X-sholI fluorescent X-rays are described and an effort has been made to interpret the results in terms of the cross- sections of the above mentioned processes.e x p e r i m e n t a l  a r r a n g e m e n t  a n d  p r o c e d u r eThe experimental sot-up used is vshown in fig. 1- Gamma rays of energies 280, 662 and 1250 keV were obtained from radioactive sources of Cs«’ and Co*® respectively. The targets of the gold and lead in the form of circular foils (2.5 cm dia) were used . The thickness of the target could be varied by changing887377S8 B. 8. Ohumman and S. B. Soodthe number of foils. With one element measuremonts were made by using targets of thicknesses t, 2t  ^ etc. The fluorescent X-rays emitted from the target were counted with a single channel spectrometer with a 2.6 cm diax2.6cm height Nal(Tl) crystal. Direct radiation from the source was prevented fromFigure 1. Expenmental arrangement.reaching the counter by graded shielding consisting of lead, tin, copper and ahi- minium. Source and detector were also shielded by graded absorbers to prevent scattering from walls and surroundings[^to the detector. The graded shielding had to be used for preferential absorption of fluorescent X-rays produced in tho lead shielding. The energy spectrum of radiation emitted from the lead target in the fluorescent X-rays region is shown in fig. 2. I t  contains a prominent K-Figura 2. Spectrum of K-radiation when lead is irradiated with 280 keV gamma rays. Dotted curve is the spectrum taken with an equivalent ahuniniom.shell X-rays peak. The spectrum taken with an equivalent aluminium target is also shown. The spectrum without any target in position showed a general background lower than that with A1 target indicating that only those fluorescent X-rays which are emitted from the target and are of interest in the present investi­gations are recorded in the counter.The measurement of the cross-section for the creation of X-vacancies consisted of determining the number of X-shell fluorescent X-rays emitted from theInter<Kti(m8 of y-Raya mth K-klhctrona 739target, th e  Bouroe s tren g th , th e  nu m ber of atom s per cc. of the ta rge t, the  B catterer-detector a n d  sou rce-^catterer solid angles. Tlie num ber of X -rays em itted  from  th e  ta rg e t w as calcu la ted  by  m easuring th e  area under th e  photo­peak o f  th e  X -ra y s  sp ec tru m  and  tak in g  in to  account (i) th e  effective detection efficiency o f  th e  X -ra y s  u n d e r  th e  photo-peak  in th e  experim ental set-up used and (ii) th e  ab so rp tio n  o f  th e  in c id en t gam m a rays and  th e  em itted X -rays in th e  target. Both th ese  fac to rs  w ere de te rm in ed  experim entally  as discussed later. The effective efficiency acco u n ts  fo r (i) th e  abso rp tion  of X -rays in the air between th e  target and th e  d e tec to r  (ii) th e  ab so rp tio n  o f X-Wtys in  th e  crystal package, (iii) th e  iodine escape peak  in  c ry s ta l (C routham el, 196(^ and  (iv) photo-peak efficiency, corres­ponding to  th e  frac tio n  o f  X -ra y s  w hich lase the ir full energy in th e  crystal. The source s tre n g th  w as d e te rm in ed  in term s faf th e  area under the photo-peak of the  gam m a ra y s  u n d e r  in vestiga tion , th e  abi|olute strength  being no t needed. The source-target solid  ang le  w as calcu lated  from  the known geom etry, while the  sca tte rer-d e tec to r solid angle was determ ined experim entally by replacing the  scatterer w ith  a  w eak  source o f th e  energy under investigation and comparing this w eak source  w ith  th e  ac tu a l source used in th e  m ain experim ent. Assuming isotropic d is tr ib u tio n  o f  X -rays, th e  cross-section for th e  creation of X-vacancies is given b y®rr“ jr4jt .. (1 )where N J N 2 is th e  ra tio  o f  th e  counting  ra tes  due to  th e  -K-shell X -rays and the small source p laced  a t  th e  position  o f th e  ta rge t, th e  ratio  of th e  strengthsof the  w eak an d  a c tu a l source, €y is th e  photo-peak eflBciency of th e  detector for gamma ray s , e* is th e  effective de tec tion  efficiency of X -rays as defined above, is th e  source-B catterer solid angle, p  is th e  num ber of atom s per cc. of the target, t  is th e  th ick ness o f  th e  ta rg e t, is th e  correction th a t accounts for the absorption o f  th e  in c id en t gam m a ray s  an d  em itted  X -rays and is th e  X-shell fluorescence 3neld. Sg/iSi w as m easured  w ith  an  accuracy of 2 per cent by com­paring th e  co u n ts  in  th e  gam m a ra y  photo-peaks of th e  tw o sources. Two sources of in te rm ed ia te  s tre n g th  w ere used to  avoid corrections due to  source-detector geometry. T he  v a lu e  o f  th e  gam m a ra y  photo-peak efficiency, was tak en  from the tab les o f  C ro u th am el (1960) an d  graphs of Lcutz et a l (1965). The sequence of tak ing o b se rv a tio n s  w as a rran g ed  so as to  minimize the effects of drifts in electronics a n d  source  decays.d e t e r m i n a t i o n  o f  e f f e c t i v e  e f f i c i e n c y  o fT H E  D E T E C T O RAu»M deoays b y  f i  em ission to  *412 keV level in  Hg»“  w hich de-excltes by  gamma ra y  em ission o r  e lec tro n  conversion. T he X-shell conversion resu lts in740 B. 8. Ohumman and 8. B. SoodiC-vacancies in  H g an d  em it X -rays or Auger electrons. T he X -conversion coeffi. cien t is defined asNy€Kwhere N y  an d  N jc  a re  th e  counting ra te s  due to  gam m a rays an d  X -shell X-rays respectively  and  th e  o th e r te rm s have been defined earlier. K now ing th e  value o f oiK =  0 .030 2± 0 .0 00 4  (Suba R ao , 1966), - -  0.231 (C routham el, 1960; Leutzet al, 1966) an d  m easuring N k an d  Ny from  th e  spectrum  ob ta ined  by  ifiacing an Au^ ®® source a t  th e  position o f th e  ta rg e t, th e  value o f €k  was calcu lated  to  be0 .8 5 ± 0 .0 4  for th e  70.8 keV  H g X -rays in th e  p resen t experim ental arrangem ent. T he analysis o f  th e  Au^ ®® spectrum  to  determ ine Ny an d  Njc is show n in fig. 3.Figure 3. Pulse height distribution of Au^ ®® spectrum. Curve 1 direct spectrum and curve 2 with graded absorber to absorb X-rays.Sim ilar m easurem ents were also m ade for T1 X -rays using a  Hg®®® source which decays to  280 keV  level in  T1 an d  a  value o f 0.82 ± 0 .0 4  w as found  for Thevalue o f ejKCOK w as also de term ined  by m easuring th e  coincidence ra te  between f i  rays feeding 412 keV  level and  X -rays following in te rn a l conversion in  *nie ra tio  o f  th e  coincidence ra te  and  /? cou n t ra te  is given byNpxjNfi — ex cjg (2)The ta rg e t w as rep laced  b y  th e  sm all Au^ ®® source in  th e  m ain  experimental arran gem en t an d  a  p lastic  sc in tilla to r was used fo r coun ting  rays. T he ^-ray cou n ter was biased a t  600 keV  so th a t  th e  in te rn a l conversion e lectrons are notIn te ra c tio n a  o f  y -R a y a  w ith  K -E lecircm a 741counted. Coincidence co u n t ra te  was again measured by placing a graded X -rays abso rber before th e  N al(T l) crystal. This counting ra te  corresponds to  412 keV gam m a ra y s  w hich are  counted  in X -rays channel. Subtraction of th is normalized counting  r a te  from  th e  first gave th e  true  (counting rate. Solid angle <o, was m easured from  th e  geom etry  o f experim ental set-up. The value of as deter- m ined above cam e o u t to  be 82J-.06 .T he value  of c k  fo r gold and  lead Z -rays is expected to  be the same as th a t for H g  an d  T1 an d  <0^  also docs no t vary more th an  0.05 per cent in the Z  range for 79 to  82. T herefore a m ean value of 0 .83± 0.04  is iisecl in eq, (1) for €k <^ k .A B S O R P T I O N  O F  I N C I D E N T  G A M M A  R A Y S  A N D  E M I T T E D  X - R A Y S  I N  T H E  T A R G E TI t  can  be show n (Shute  et a l , I960) th a t  th e  effective thickness of a ta rge t of real th ick ness t  w hen th e  absorpticai of th e  incident gamma rays and em itted X -rays is tak en  in to  acco un t is given byUff (3)where 6  is th e  angle th a t  th e  incident gam m a rays and em itted X -rays m ake with the  ta rg e t a n d  [ ly  an d  [ in  a re  th e  linear absorption coefficients for gam m a rays and X -rays. T he va lue  o f was determ ined experim entally by measuring thera tio  o f th e  cou n ting  ra te s  under th e  photo-peak with ta rge t of thickness i and 2t respectively . T he ra tio  is given byU — 1 4  exp f— (4)The value o f R  was de term ined  w ith an  accuracy of 0.5 per cent and wasdeterm ined  to  be 2.85, 2.46 an d  2.41 for 280, 602 and 1250 keV gam m a rays res­pectively for lead an d  2.88, 2.63 and  2.59 for gold,R E S U L T  A N D  D I S C U S S I O N SA b o u t te n  in d ep en d en t runs wore m ade with each ta rge t a t  one gam m a ray  energy a n d  th e  resu lts  a re  shown in colum n 3 of table 1. The errors given are due to  th e  s ta tis tic s  o f th e  counting ra te  and the uncertainties involved in the com parison of source s treng ths, th e  determ ination  of cxcok and estim ation of o ther corrections. T he calcu lated  (Grodstein, 1957) X-shell photo-electric cross- sections a re  given in colum n 4. Column 5 gives the  difference between the  m easured ine lastic  cross-sections and th e  calculated X-shell photo-electric cross- sections a n d  should  give th e  con tribu tions of X-shell electron Compton scattering an d  th e  secondary  processes, e.g. X-shell excitation or ionization o f th e  ta rg e t a tom s b y  p h o to - an d  C om pton electrons. Column 6 gives th e  calculated Comp­to n  so a tte rin g  oross-section for tw o electrons if assum ed free and  a t  rest a fte r th e742 B. S. Ohumman and B. S, 8oodform ula given by K lein  an d  N ishina. I t  is seen from  th e  tab le  th a t  a t  280 keV th e  m easured cross-section agrees fairly  well w ith  th e  calcu lated  K -shell ph o to ­electric cross-section show ing th a t  for low energy gam m a ray s  an d  high-Z  elem ents th e  iT-shell fluorescent JC-rays are produced essentially  th ro ug h  pho to ­electric in terac tio n  an d  th is  m ethod  can be used to  m easure th e  iT-shell photo- electric cross-sections o f low energy rad ia tion  in h igh-Z  elem ents.T A B L E  1/T-shell int/eraction cross-sections o f 280, 662 and 1250 keV gam m a rays w ith gold and  lead.Gammaray energy Element a(exp.) (t(NBS) a(exp)—<t(NBS) aein MeV in barns in barns in bams in bams0.2800.662AnPbAuPbS2 .e± 5 ,596 .1r t0 .083.495.611.4^:0.9 1 3 . 4 i l . O10.612.40 . 8 ± 0 . 91.0±1.00.730.730.510.611.25 AuPb3 . 7 ± 0 . 64 . 2 ± 0 . 52.93.70.8±0.60 . 6 ± 0 . 50.380.38T he con tribu tion  o f K -shell C om pton sca tte ring  cross-section as given in colum n 6 increases w ith  gam m a ra y  energy  an d  a t  1.25 MeV i t  is a b o u t 20 per cent if  th e  con tribu tions o f  secondary  processes being second o rder effects are  neglected. T he d a ta  availab le on C om pton sca tte rin g  o f gam m a rays from  bound  electrons (Mote e t a l, 1961; V erm a et a l , 1962) are  qu ite  scan ty . O ur earlier experi-. m ents (A nand et a l , 1964) on sm all angle sca tte ring  o f low energy gam m a ray s have  shown th a t  for sm all values of m om entum  tran sfe r  involved in sca tte ring , th e  C om pton sca tte rin g  cross-section from  bound an d  m oving elec­tro n s  is less th a n  th a t  from  free an d  s ta tio n a ry  electrons. T he experim ents on large angle sca tte rin g  (Mote et a L  1961; V erm a e t a h  1962) o f  high energy  gam m a rays, however, show th a t  th e  s itu a tio n  is reversed a t  large values o f  m om entum  tran sfe r an d  th e  C om pton sca tte rin g  from  bound e lectrons becom es m ore intense th a n  th a t  from  free electrons. N o in fo rm ation  is y e t  availab le  a b o u t th e  in te­g ra ted  C om pton cross-section from  bound e lectrons w here th e  m om entum  tran s­fer m ay  v a ry  from  zero to  som e m axim um  value depend ing  u p on  th e  energy  o f the gam m a rays. F ro m  th e  d a ta  so fa r  availab le  i t  m ay  be  guessed t h a t  th e  in te­g ra ted  C om pton sca tte ring  cross-section from  th e  bound  electrons m ay  be either less th a n , o r  equal to , o r g rea te r  th a n  th a t  from  free electrons depend ing  upon the  m axim um  value o f th e  m om entum  tran sfe r  w hich in  tu rn  depends upon the energy o f gam m a rays. A t 662 an d  1250 keV  th e  in teg ra ted  C om pton scatteringliOeractW M  of y^Raye with K-Blectrona 743orosS'Seotion from ^-shell electrons as shown in column 5 of table 1 , may be taken to be equal to that from free and stationary electrons. Large uncertain­ties present in these values do not allow us tt> draw any precise conclusion. However, at still higher energies where the photo-electric cross-sections become comparable with the Compton scattering cross-section from -shell electrons it may be of .interest to perform rfmilar experiments to see if for still larger values of momentum transfer the overall Compton scattering cross-sections for bound electrons is more than that from free electrons,KBFEKKNCESAnand, S., 6ingh» M. and Sood, £. S., 1964, Curr. S et., 88, 139.Crouthamel, C. E., 1960, A p p lie d  Gamfna R a y  S pectroscopy, Pergamon Press, 108. Grodetein, G. W.. 1957, X -r a y  A t te m ^ io n  Coefficients from  lOKeFto 100 MeP, NB8 Ciroular, 583.Leutz, H., Schulz, G. and Van QeMeroii, L., 1966, N u c. In str , M ethod, 40, 257.Mot*, J. W. and Missoni, G., 1961, R ev ,, 124, 1458.Shut-e, G. G. and Sood, B. S., 1060, P ro c, R o y , Soc,, A257. 52.Suba Rao, B. N., 1966, N u c , I n s tr , M ethod, 45, 22.Varma, J. and Eswaran, A., 1962, P k ya . R ev ., 127, 1197.

Inelastic Interactions of Gamma Rays with K-Shell Electrons

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Inelastic Interactions of Gamma Rays with K-Shell Electrons

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