girardi et al .   introduced the single comparator method for neutron activation analysis ( naa ) in 1965 . with this method it became possible to automate the analysis to a large extent and to perform multi element analysis at the same time .
the values of the experimentally determined k - factors in this method depend on the full energy photopeak efficiency and the irradiation conditions .
as such they are specific for the detector and counting geometry , and the irradiation facility and remain valid as long as the neutron energy distribution in the irradiation facility does not change significantly .
de corte and simonits redefined the measurement equation in the single comparator method in such a way that the k - factors became independent of the neutron energy distribution and counting geometry . to this end , they introduced the neutron spectrum parameters f and  in the measurement equation of their k0-method as well as the full energy photopeak efficiency parameter . de corte et al .
[ 2 , 3 ] suggested in 1979 the bare triple comparator method as an alternative for the cd - covered method to measure the neutron spectrum parameters f and  for in k0-naa .
bode et al .   reported in 1992 about large variations in the determination of f and  between individual irradiations .
the values of some of these f and  values were difficult to explain on basis of the physics and operation of a nuclear research reactor .
as an example , two irradiations of five zr  au sets carried out within a few months interval without changing the reactor core configuration resulted in f values of 5063 and 6490 and  values of 0.070.11 and 0.020.08 , respectively .
similar inconsistent results for f and  estimation by the bare triple monitor were reported by others [ 57 ] . at the mtaa-11 conference in 2004 koster - ammerlaan et al . introduced the cr 
this monitor results also in smaller uncertainties for f and  under the same statistical conditions .
the monitor has been used in delft during the past 3 years to measure f and  after each rearrangement of the fuel elements but without changing the core configuration in number and positioning of the fuel  and reflector elements .
mo  au monitor has proven to give consistent result for practical applications in routine inaa .
it is , however , still unsatisfactory that the large variations in f and  resulting from the use of the zr  au monitor can not be explained on basis of the physics of naa .
de corte et al .   cast doubt on the validity , for every reactor ( type ) of the original assumption that the neutron energy dependency of the cross section in the epithermal region can be described by the 1/e relation .
describe the hardening of the neutron spectrum due to the li - build up in the be - reflector elements .
the hardening of the spectrum due to the li build up does not explain yet the large variations in f and  between successive irradiations reported by bode et al .
beryllium indeed has an impact to the energy distribution of the neutrons on the outside of the reactor core  the position of the irradiation facilities used for naa .
both epithermal photoneutrons ( be (  , n ) 2 he , cross section  0.8  mb ) and fast neutrons ( be ( n , 2n ) 2 he , cross section  580  mb ) are produced in the beryllium .
these neutrons will be moderated and will result in contributions to the normal epithermal spectrum of the uranium fission .
it can not be excluded that these photoneutrons and fast neutrons produced in beryllium have an impact on the shape of the neutron spectrum , with consequences for the 1/e model used in k0-naa . the extent of this has been studied using mcnp modeling of the neutron spectrum in the irradiation facilities of the delft hoger onderwijs reactor ( hor ) used for inaa .
the neutron energy distributions of the in - core irradiation facilities were calculated by modeling the reactor core ( fig .  1 ) and its facilities using mcnp .
the simulations were performed using mcnp version 1.51 and the endf7 database as supplied with in - house addition of be (  , n ) data for photon neutrons via njoy processing , running 20,000 cycles of 10 source neutrons each . the facilities , including high purity quartz vials and their location with respect to the core were precisely modeled .
the uncertainty of the modeling varies from 1% in the thermal neutron range of the spectrum , to approximately 5% in the epithermal range and 10% in the fast neutron energy range.fig . 
1schematic presentation of the reactor core and the irradiation facilities of the delft hor schematic presentation of the reactor core and the irradiation facilities of the delft hor the results of the modeling have been verified by naa of cr  mo  au monitors .
the neutron flux and the neutron spectrum parameters f and  determined by modeling and measurement were in very good agreement , as already presented in the 5th k0-users workshop   ( belo horizonte , brazil , 1317 september 2009 ) .
the energy of the neutrons is plotted as a function of lethargy . in the lethargy presentation
the 1/e - relationship changes into a horizontal line and the deviations described by  can be schematically represented as shown in fig . 
2modeled neutron spectra of the pneumatic tube , the reflector and in - core irradiation facilities .
3the lethargy presentation of the 1/e 
  model modeled neutron spectra of the pneumatic tube , the reflector and in - core irradiation facilities .
the energy of the neutrons is plotted as a function of lethargy the lethargy presentation of the 1/e 
  model the output of the modeling in the epithermal range of the spectrum is shown in more detail in fig . 
as can be seen from this figure the 1/e model is valid for epithermal neutrons up to 10  kev and both the in core as well as the reflector irradiation facility tends to have a negative -value . in the energy range of 10100  kev , however , the modeled spectrum is clearly deviating from this model . radionuclides mo and au have their resonance energies in the epithermal range up to 10  kev where the 1/e model is in good agreement with the modeled spectra , zr , however , has its resonance energies mainly the epithermal part of the spectrum above 10  kev .
small variations in the production of be - neutrons may have effects on the activation of zr and therefore the determination of f and .fig . 
4modeled epithermal neutron spectrum of the pneumatic tube , the reflector and the in - core irradiation facilities .
the energy of the neutrons is plotted as a function of lethargy modeled epithermal neutron spectrum of the pneumatic tube , the reflector and the in - core irradiation facilities .
the energy of the neutrons is plotted as a function of lethargy it may be obvious that the degree of distortion of the neutron energy distribution in the epithermal range depends on the reactor core configuration , the amount of beryllium surrounding the fuel elements and the moderators used . in the irradiation facilities of the hor in delft , used for this experiment the difference in the value of  determined by either the zr  au or the cr  mo 
the results from the calculations and experiments indicate that neutrons produced in be reflector material may perturb the neutron spectrum in the epithermal range to such an extent that the applicability of the 1/e model in k0-naa may render a significant bias in the naa results .
this phenomenon may also explain the differences of the k0 values of zr ( and the related cross sections ) determined in different reactors .
it is recommended to evaluate the perturbation of the 1/e range by the be epithermal and fast neutron production in different reactor types ( e.g. , light water  +  be reflector , triga , slowpoke / mnsr ) to fully understand the neutron energy distribution and its impact to the currently universal model used for describing this distribution .
it sets , however , high demands to the precise detailing of the input model used in these calculations .
 the assumption that the shape of the epithermal neutron spectrum can be described , in any research reactor , by the 1/e1+ function is a fundamental starting point of the k0 standardization . 
 this assumption may be questioned from a reactor physics viewpoint . the type of moderator , the existence of neutron reflectors , the additional production of (  , n ) neutrons and resonance capture by construction materials may be different for each reactor , with consequences for the shape of the neutron spectrum . 
 this dependency may explain that various practitioners reported contradicting experiences with the use of zr  au flux monitors for the determination of the -parameter . 
 an objective view on the influence of the design of the reactor and irradiation facility on the shape of the neutron spectrum can be obtained by modeling . 
 this has been applied in the reactor institute delft for reactor configurations in which the irradiation facilities face the fuel elements with the presence of beryllium reflector elements . 
 the monte carlo calculations indicate a distortion of the 1/e1+ relationship at the higher energy edge of the epithermal neutron spectrum . this distortion is attributed to the formation and thermalisation of both photoneutrons and ( n , 2n ) produced fast neutrons in the beryllium , and has a direct impact on the resonance activation of 95zr , other than represented by the 1/e1+ function . 
 the obtained relationship between neutron flux and neutron energy was also used for estimating the f - value and compared with the value obtained by the delft cr  
 mo  au flux monitor . 
Introduction
Experimental
Results and discussion
Conclusions