Page 220 - Radiochemistry and nuclear chemistry
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204                 Radiochemistry  and  Nuclear  Chemistry

              pair together and the sum of their individual rates,  the resolving time is calculated using the
               equations"

                                           X  =  R a R b  -  Rab R 0

                                  y  =  R a Rb (Rab  +  R 0)  -  Rab R0 (Ra  +  R b)

                                       z  =  y (R a  +  R b - Rab  -- Ro)/X 2

                                          t r  =  x[1  -  (1  -  z) '/~ ]/y         (8.9)

               where  R a,  R b,  and Rab,  are the  measured  count  rate of samples  a and  b  separately,  a  and
               b together,  respectively.  R 0 is the background count rate for the system.  The correction for
               the  resolving  time can  then be  made according  to  (8.8a).
                A  more  accurate  technique  is based on  the use of a short-lived  radionuclide,  e.g.  99roTe
               or  116rain" The count  rate is then measured a number of times during  at least  one half-life
               with the source left untouched in position all the time. When the background count rate can
               be neglected (which is usually the case) combining  (8.8a) with the equation  for radioactive
               decay  gives  after  some  algebra

                                         Rob se kt--R 0  -R  0t rRobs              (8.10)

               where  t  is  the  time of measurement,  X the decay constant  and R 0 the  initial  count  rate.  A
               plot  of  Rob s e xt  as  function  of  Rob s  should  yield  a  straight  line  with  slope  -  R 0 t r  and
               intercept  R 0 on  the  vertical  axis.  The  dead  time  is  then  obtained  as  the  absolute  value  of
               slope  divided  by  intercept.  If  the  plotted  data  deviates  strongly  from  a  straight  line  it
               indicates  that  the  system investigated  is paralyzable.



                                            8.3.  Gas  counters

                All  gas-filled  counters  are  in  principle  ion  chambers  (with  the  exception  of  the  less
               common  gas scintillation  counters).  The ionization produced in an ion chamber by a single
               nuclear  particle  produces  too  low  a  charge  pulse  to  be  easily  detectable  except  for  c~-
               particles.  However,  an ion chamber can be designed so that the number of ion pairs formed
               in  each  event  is multiplied  greatly.
                Consider  an  ion chamber with a hollow  cylindrical cathode and a  thin  central  wire as an
               anode  (Fig.  8.8(a)  shows  an  old  type GM-tube).  The  ion  pairs  formed  in  the  gas  by  the
               passage  of  the  ionizing  radiation  are  separated  from  each  other  by  their  attraction  to  the
               electrodes.  The  small,  very  mobile electrons  are rapidly  collected  on  the anode,  which  is
               maintained at a high positive potential above ground,  >  1000 V.  Most of the voltage pulse
               which  appears  on  the  anode  arises  by  induction  by  the positive  ions  as  they  move  away
               from  the  immediate  region  of the  anode.  This  step  is  responsible  for  the  rise  time of the
               pulse,  curve  I  in Figure  8.3(b).  The potential  decrease  is only  momentary as  the anode  is
               rapidly  recharged by the power supply.  The time necessary to restore the original potential
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