NUCLIDES ACTIVITIES ESTIMATION IN SCINTILLATION GAMMA-SPECTROMETRY

V.A. Muravsky, S.A. Tolstov

International Sakharov Institute of Radioecology
23, Dolgobrodskaya Str., 220009 Minsk, Belarus

     Optimal estimation   of  nuclides  activities  for  scintillation
g-spectra is considered. A set of non-linear equations for calculation
of  the  maximum  likelihood  estimates of the nuclides activities has
been  derived  for  Poisson  distribution  in  spectrum  channels.  An
effective   iteration  algorithm  for  solving  the  obtained  set  of
non-linear equations has been developed.  The algorithm allows to  get
the  maximum  likelihood estimates of nuclides activities in two-three
iterations.  A comparison  of  the  methods  for  nuclides  activities
estimation  has  been  made.  It  has  been  shown  that  in  case  of
low-intensity nuclear radiation spectrometry  the  maximum  likelihood
estimates   of   nuclides   activities   have   substantially   better
characteristics then  estimates  obtained  by  the  other  methods.  A
problem  of  choosing  a  spectrum  model in the case of low-intensity
scintillation spectra with a mixture of 2,  3 or 4 nuclides  has  been
studied. It has been shown that usage of a superfluous initial spectra
of the nuclides in a spectrum model would lead to deterioration of the
activities estimates accuracy.  A statistically grounded criterion has
been developed for  choosing  a  spectrum  model  which  provides  the
minimum  errors  of  activities  estimates.  This  criterion allows to
exclude the superfluous initial  spectra  of  the  nuclides  from  the
spectrum   model,  thus  increasing  an  accuracy  of  the  activities
estimates.
       The research  carried  out  has  shown  a  real  possibility of
creation on the basis of the maximum likelihood method  an  algorithms
and  programs  for calculating nuclides activities from the spectra of
nuclear  radiation.  In  a  case  of  spectrometry  of   low-intensity
radiation,  the  algorithms  have significantly better characteristics
than other methods used for spectrum processing such as weighted least
squares method, etc.
       A realization  of  the  developed  algorithms  in   specialized
software  for  processing  the spectrometric information will allow to
create a qualitatively new kind of spectrometers of nuclear  radiation
where  the  high  accuracy  of  measurements  will  be  reached due to
application  of  perfect  mathematical  programs  for  processing  the
nuclides  spectra,  but  not  due  to  expensive  improvement  of  the
measuring  instruments  (application  of  unique  detectors,   massive
shielding,  complex  systems  for  stabilization  of  the spectrometer
parameters,  etc.).  In addition, the developed programs will allow to
choose an optimal (adequate) model for experimental data processing on
the basis of  definite  statistical  criteria,  without  involving  an
"intuition"  of  a  user.  On  the basis of the developed criteria the
systems for nuclides identification can be constructed.