Page 219 - Radiochemistry and nuclear chemistry
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Detection  and Measurement  Techniques             203

               time,  which  in  the  figure  is  something  like  10  #s,  any  new  events  would  not  produce  a
               pulse crossing the discriminator level.  This interval is properly called dead time, see Figure
               8.6.  Somewhat  later  the  initial  operating  conditions  are  still  not  fully  restored  but  the
               detector  is  now  able  to  produce  a  pulse  of  larger  magnitude  which  triggers  the
               discriminator.  Still  later,  after  the recovery time,  the  initial  conditions  are restored.  If the
               second event occur within  a short  time, peak pile-up will occur.  At a somewhat  later time
               the new pulse overlaps with the tail of the pulse  from the previous event causing  so called
               tail pile-up.  Pulse pile-up  may make two or more closely spaced  events  look  like a  single
               more energetic  event,  Figure  8.6.  The time needed  to separate two events  is referred to as
               resolving time (for simplicity dead time and resolving time will be used as synonyms in this
               text).  Thus  the  detector  and  measuring  circuit  needs  a  certain  time  to  register  each
               individual  event  separately with correct magnitude.  In many cases the measuring  circuitry
               is much  faster than the detector and  the dead time is a  function of the detector only.  Since
               radioactive  decay  is  a  statistical  random  process  and  not  one  evenly  spaced  in  time,  see
               w     even  for relatively low count  rates a certain percentage of events will  occur within
               the  resolving  time  of the  system.  In  order  to  obtain  the  true  count  rate  it  is  necessary  to
               know  the correction  that must be made for this random coincidence loss.  In systems using
               a  MCA  for pulse height  analysis,  the MCAs  pulse conversion  time is usually dete~ining
               the  system dead  time and  not  the detector.
                Two  different  models  exist  for  the dead  time  of counting  systems  depending  on  system
               behavior after a pulse.  In a nonparalyzable system the pulses following  the first within  the
               dead  time  are  lost,  but  the  system is  ready  to  accept  another  event  immediately  after  the
               dead time has expired.  The fraction of all real time during which the system is dead is then
               given  by  the  product  between  the  registered  count,  Rob s,  and  the  dead  time,  t r.  The  true
               number  of events,  Rcorr,  is  then  given  by


                                         Rcorr =  Robs/(1 -  Rob s tr )             (8.8a)
                In  a paralyzable  system  each  event  starts  a  new  dead  time  period  whether  or  not  it
               generates  an  output  signal.  This,  in combination  with  the  time distribution  of radioactive
               decays  (8.21),  yields  the  following  implicit  expression  for  the  true number  of counts

                                           Robs =  Reor r e-Rcorr t,                (8.8b)

                At  very low  count  rates it can be shown  the result is independent  of the  type of system,
               i.e.  Rob s  ~  Rcorr (1  -  Rcorr t r ).  However,  the behavior of these  two  system types  at high
               count  rates  are  different.  A  nonparalyzable  system  shows  an  asymptotic  approach  to  a
               maximum count rate with increasing source strength whereas the count rate on a paralyzable
               system  passes  through  a  maximum  and  then  decreases  again.  Hence  each  reading  on  a
              paralyzable  system  corresponds  to  one  of  two  values,  one  low  and  one  high.  Dangerous
               mistakes  can  occur by  misinterpreting  the  reading  from a  paralyzable dose  rate meter.
                The  simplest  technique  for measuring  the resolving  time t r of a nonparalyzable  counting
               system  uses  a  method  of  matched  samples.  Two  samples  of  similar  counting  rates  are
               counted  separately  and  then  together.  The  combined  sources  should  give  about  20%
               fractional  dead  time,  Rob s t r.  From  the difference  between  the  measured  count  rate of  the
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