Noise analysis

Usually samples of interest are placed directly on top of the detector to increase the detection efficiency. Therefore, for a lot of nuclides a reasonable chance ex-ists that two γ rays emitted in the decay of the same nucleus are hitting the de-tector simultaneously and the resulting dede-tector signal corresponds to the sum of both energy depositions. Since this effect, called true coincidence summing (TCS) (see also Section 2.3.2), lowers the FEP of the single γ ray it is necessary to take this effect in the FEP efficiency determination into account. It is therefore desirable to use a MC primary particle generator that is able to reproduce the emission characteristics of a certain nuclide. This requirement is in general ful-filled by the Geant4 radioactive decay module (GRDM), which is usually used in the VENOM MC tool, although some problems of this generator like the identical simulated spectral shape of β decays independent of their transition classification are known.

As it was in part already discussed in Section 5.2, the usage of GRDM relies on the correctness of the underlying physical data. By using GRDM, actually the product of the FEP efficiency ε and the emission probability p (compare Equa-tion (4.31)) of a certain γ line is determined from the MC simulaEqua-tion. Conse-quently, any bias of the emission probability in the MC simulation inevitably leads to the same (relative) bias of the determined nuclide activity but with the opposite sign (if TCS is unlikely). To allow for the correct determination of sam-ple activities the emission probabilities used by GRDM of Geant4 9.5.p01 were checked. Since usually only some or even single γ lines are used as references for a certain nuclide (see also Section 4.4 and [Gil08, Wah07]) only these were

checked as well. For this check 10⁶ decays were generated per nuclide (for¹³³Ba,

60Co,¹³⁷Cs and¹⁵²Eu 5×¹⁰⁶each) and stored with a special option in VENOM to a ROOT output file. The simulated emission probabilities were calculated and compared to the DDEP data. For many γ lines the relative deviations between simulation and measurement were found to be compatible with 0, but some emis-sion probabilities deviate significantly from the literature data. A compilation of the calculated data comparison can be found in Table F.1.

For example the emission data for the decay of ²⁰⁸Tl, in which TCS is likely due to the complicated decay scheme, are completely compatible with the data given in [Lab13]. Other isotopes like ²¹⁰Pb and ²²⁶Ra deviate significantly. The by far worst results were found for²³⁵U, which is unfortunately the only nuclide of the²³⁵U decay chain usually analysed. As one can see in Table F.1 for the orig-inal Geant4 data set deviations of up to 365 % were calculated. A corrected so called ‘PhotonEvaporation’ data file, describing the de-excitation characteristics of a certain nuclide, in this case the daughter nuclide, was taken from the Geant4 users forum²and integrated into the used data set. Although the deviations were reduced, smaller ones still remain and originate probably from wrong data in the corresponding ‘RadioactiveDecay’ data file, describing the branching ratios and decay characteristics of the mother nuclide. Due to the complexity and correla-tion between both data sets it is nearly impossible to correct the data manually, although this was tried by the author with a certain success. Since at least in all checked cases the data set of the newer Geant4 version 9.6 did not differ from the used data set an improvement was not expected and the newer version therefore not tested. An updated physics data set is under development by the Geant4 developers at least since 2011³ but up to now (2013-06-01) unfortunately not yet released.

In case TCS is unlikely in the decay of a nuclide, which is obviously the case for nuclides emitting a single γ line or reference γ lines, since they are selected due to a low summing probability in the first place, it is possible to correct the result of the MC simulation using the factors given in Table F.1 as well. For nuclides with a decay scheme supporting TCS a correction after the MC simulation in-evitably leads to still wrong results unless one knows the summing probabilities for the different combinations of emitted γ rays, which are dependent on the used measurement geometry. The probabilities can be in principle calculated from MC simulations using single γ ray emissions of the same energies but this is due to the complexity of the subsequent calculations beyond the scope of this work. In-stead the as significant regarded correction factors given in Table F.1 are used in the calculations of Chapter 6. These are applied in cases where there is a certain chance for TCS as well unless the activity of a certain nuclide can be derived from

2http://hypernews.slac.stanford.edu/HyperNews/geant4/cindex, for the thread see http:

//hypernews.slac.stanford.edu/HyperNews/geant4/get/hadronprocess/1270/1.html

3https://indico.fnal.gov/getFile.py/access?contribId=60&sessionId=7&resId=

0&materialId=slides&confId=4535, last accessed 2013-06-01

the activities of in the decay chains pre- or succeeding nuclides. Although the cor-rection of peaks in the spectrum of a decay with TCS is not completely correct, it is likely that the results improve since the summing effect should be relatively small.

As an alternative, single γ lines emitted in decays of nuclides can be simu-lated by using the Geant4 General Particle Source (GPS) neglecting any X-ray or bremsstrahlung emission by β particles (see also discussion in Section 5.2.1). In this case, the result of the MC simulation does not contain the emission probabil-ity p of the γ line. As one major drawback for the usage of GPS one has to define a volume by its dimensions and position in the geometry in which vertices are generated. Although it is possible to confine the position generation addition-ally to a certain volume of the MC geometry there is no mechanism ensuring that the volume used as a confinement is completely included in the defined position generation volume. The definition of the volume used by GPS for vertices gener-ation is complicated, since one has to calculate the position of a certain geometry part in global coordinates, which is usually hierarchical defined and only local co-ordinates are known. The sophisticated position generator used in VENOM was implemented by T. Köttig (for details see [Köt12]) but is only available for the gen-erators in VENOM based on GRDM. With this extension it is sufficient to provide the decay generators with the name of the volume and the minimal dimensions of the bounding box including the volume are retrieved from Geant4 internal meth-ods. Because of this, the decay generators based on GRDM are usually preferred to the Geant4 provided GPS generator, although the above discussed drawbacks remain.