# Help:Gamma Spectrum Generator

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## INTRODUCTION

Nowadays the γ-spectrometry is used on a daily basis in different basic and applied fields of nuclear science and technology. A variety of instruments and measurement techniques, involving γ-spectrometry measurements, are employed routinely by nuclear and radio-chemists, health physicists, nuclear facility operators, radiation protection staff, safeguards inspectors, border police, customs and low-enforcement officers. Needs for education and training in these areas are high and, obviously, they will be increasing in the future as new challenges, such as strengthening nuclear safeguards and security, nuclear terrorism prevention and implementation of new standards in radiation safety and protection, arise.

To address these growing demands in education & training, an interactive web-assessible simulation tool, Gamma Spectrum Generator, has been developed and integrated into the NUCLEONICA nuclear science and data portal. The simulator presents an efficient visual teaching aid that is especially useful in training facilities, which have restrictions on the use of radioactive substances, or when sources of special interest (e.g. spent fuel, enriched U, weapon grade Pu or other highly radiotoxic materials) are not readily available.

This document describes the underlying mathematical approach and user interface of the Gamma Spectrum Generator. It also contains the results of the experimental validation of the simulator and some examples of its application.

## BASICS OF THE GAMMA-SPECTROSCOPY

Gamma-spectroscopy is an extremely important nuclear and radioanalytical method. Most radioactive sources produce γ-rays of various energies and intensities. When these emissions are collected and analyzed with a γ-spectroscopy system, a gamma energy spectrum can be produced. A detailed analysis of this spectrum is typically used to determine the identity and quantity of γ-emitters present in the source. The γ-spectrum is characteristic of the γ-emitting nuclides contained in the source. The equipment used in γ-spectroscopy includes an energy sensitive radiation detector, a pulse sorter (multichannel analyzer), and associated amplifiers and data readout devices. The most common detectors include sodium iodide (NaI) scintillation counter and High Purity Germanium detectors (HPGe).

For more details on the γ-spectroscopy method and system components see the following references in Wikipedia

## GAMMA-SPECTRUM SIMULATION APPROACH

### Basic assumptions

The γ-ray spectrum is modeled assuming that:

• a point-like γ-source is measured, i.e. γ-ray self-attenuation is negligibly small,
• the detector pulse pile-up effect due to both true and random coincidence summing is negligible,
• the losses of counts due to the spectrometer dead time are negligible, and
• a multi-channel analyzer with absolute linearity is used.

Based on these assumptions, the number of counts F(N) in the N-th channel of a simulated spectrum is calculated as

$F(N)=\sum_{i=1}^{N_\gamma} N_i\,\int_{\Delta N}^{\Delta(N+1)}R(E,E_i)\,dE$,

where Nγ - the number of γ-rays with different energies emitted by a source, Ei - the energy of the i-th γ-ray, keV, Ni - the total number of i-th γ-rays emitted during the spectrum measurement, Δ - the spectrum channel width in energy units, keV/channel, R(E,Ei) - the detector response for a γ-ray with energy Ei.

The number of γ-rays emitted during the spectrum measurement is calculated from the number of disintegrations of particular nuclide, which is evaluated using the Nucleonica Decay Engine. The γ-ray energies and emission probabilities are taken from the Nucleonica Database, which is currently based on the evaluated nuclear data library JEFF3.1-RDD.

### Detector response model

Figure 3.1. Illustration to the origin of the detector response components: solid and dotted photon trajectories give rise to the P(E,Ei) and S(E,Ei) components of the detector response, respectively.

The detector response is presented in the form

$R(E,E_i)=\epsilon_{p,tot} (E_i) \left \{ \, P(E,E_i) \, + \, k_s \, S(E,E_i) \, \right \}.$

Here εp,tot(Ei) is the total detection efficiency for γ-rays with energy Ei.

The function P(E,Ei) represents the main part of the detector response resulting from the detection of primary γ-rays, which are transported directly from a source to the detector sensitive volume (see solid lines in Fig.3.1). It is important to note that only those primary γ-rays, which upon arrival to the detector sensitive volume immediately undergo interaction and leave there at least part of their energy, are considered to contribute to this component of the detector response and to the total detection efficiency εp,tot.

The function S(E,Ei) presents additional contribution to the detector response and to the total detection efficiency, which is resulted from the detection of secondary γ-rays (shown by the dotted lines in Fig.3.1). These secondary γ-rays are produced in the interactions of the primary photons with materials surrounding the detector sensitive volume, such as the materials of the detector construction elements, measurement setup components, experimental room objects etc. The dimensionless factor ks determines the magnitude of this additional contribution.

#### Total detection efficiency (primary gammas)

Figure 3.2. Illustration to the total efficiency εp,tot calculation.

The detection of a primary γ-ray can be considered in terms of the following three probabilities:

• the probability εd for a γ-ray to be emitted in the direction of the detector sensitive volume,
• the probability εa for a γ-ray to escape absorption in all absorbing layers on its pathway from the source to the detector sensitive volume, and
• the probability εi for a γ-ray to interact with the detector sensitive volume, so that a signal at the detector output is produced (this porbability is ofter refered as the intrinsic efficiency of a detector).

For a collimated or pencil photon beam the total detection efficiency can be represented simply as a product of these three probabilities, i.e. εp,tot = εd × εa × εi, whereas for uncollimated sources and broad photon beams an integartion over the detector solid angle is required.

In the currently implemented approach the total detection efficiency εp,tot is calculated assuming that a point-like isotropic source located on the axis of a cylindrically symmetric sensitive volume (detector crystal) and separated from it by a number of absorbing layers, as shown in Fig.3.2. An opening at the rear side of the crystal represents a rear contact feature of the conventional coaxial HPGe detectors. The total detection efficiency calcualtion procedure implements the following formula

$\epsilon_{p,tot}(E_i)=\frac{1}{2}\,\sum_{n=0}^{3} \, \int_{t_{n}}^{t_{n+1}}\exp \left ( -\textstyle \sum_m \mu_{a,m}(E_i)\,d_{a,m}/t \right ) \, \left \{ 1- \exp (-\mu_{s}(E_i)\,x_n(t)) \right \} \,dt\,,$

where μa,m - the total photon attenuation coefficient for the material of the m-th absorbing layer, da,m - the thickness of the m-th absorbing layer, μs - the total photon attenuation coefficient for the material of the detector sensitive volume, xn(t) - the length of the photon pathway in the detector sensitive volume for a given value of the polar angle cosine t = cosθ. The formulas for the limits of the polar angle cosine intervals tn and the respective lengths of the photon pathways xn(t) are presented in Table 3.1. In the Table, z is the source-to-detector sensitive volume distance and z0 = R l / (R-r) - L, where R, L, l and r are the dimensions of the sensitive volume defined in Fig.3.2.

Table 3.1. The polar angle cosine intervals and lengths of the photon pathways used in the total detection efficiency calculation.
$n$ $t_n$ $x_n(t)$
$0$ $\frac{z}{\sqrt{z^2+R^2}}$ $\frac{R}{\sqrt{1-t^2}}-\frac{z}{t}$
$1,\, z \geqslant z_0$ $\frac{z+L}{\sqrt{(z+L)^2+R^2}}$ $\frac{L}{t}$
$1,\, z < z_0$ $\frac{z+L-l}{\sqrt{(z+L-l)^2+r^2}}$ $\frac{L-l}{t}+\frac{R-r}{\sqrt{1-t^2}}$
$2,\, z \geqslant z_0$ $\frac{z+L-l}{\sqrt{(z+L-l)^2+r^2}}$ $\frac{z+2L-l}{t}-\frac{r}{\sqrt{1-t^2}}$
$2,\, z < z_0$ $\frac{z+L}{\sqrt{(z+L)^2+R^2}}$ $\frac{z+2L-l}{t}-\frac{r}{\sqrt{1-t^2}}$
$3$ $\frac{z+L}{\sqrt{(z+L)^2+r^2}}$ $\frac{L-l}{t}$
$4$ $1$ $-$

The integrals in the above formula are computed numerically with relative precision 10-9 using optimized recursive adaptive quadratures [1]. The total photon attenuation coefficients μa,m and μs for a given photon energy are computed by the interpolation of tabulated reference photon attenuation data, taken from the Evaluated Photon Data Library EPDL-97 [2]. It must be noted that, because of its highly peaked forward angular distribution and absence of any energy deposition, the coherent scattering is not included into the total photon attenuation coefficients μa,m and μs.

#### Primary photon contribution

The function P(E,Ei) consists of several components representing the main features of a typical detector response shown in Fig.3.3. These features are the Full Energy Peak (FEP), X-ray Escape Peaks (XEP), Single Escape Peak (SEP), Double Escape Peak (DEP), and Compton continuum.

Figure 3.3. Components of the detector response R(E,Ei) for the energy of incident photons Ei = Eγ.

Mathematically the primary photon contribution is presented by the formula

$P(E,E_i)=\omega_{fep,i} \, F_{fep}(E,E_{fep,i}) \, + \, \omega_{sep,i} \, F_{sep}(E,E_{sep,i}) \, + \, \omega_{dep,i} \, F_{dep}(E,E_{dep,i}) \, +$
$+ \, \textstyle \sum_j \omega_{xep,ij} \, F_{xep}(E,E_{xep,ij}) \, + \, \left \{ \, 1 - \omega_{fep,i} - \omega_{sep,i} - \omega_{dep,i} - \textstyle \sum_j \omega_{xep,ij} \, \right \} \, F_{cp}(E,E_i).$

Here, ωfep,i = εfep,i / εtot,i, ωsep,i = εsep,i / εtot,i, ωdep,i = εdep,i / εtot,i, ωxep,ij = εxep,ij / εtot,i – ratios of the FEP, SEP, DEP and XEP efficiencies to the total detection efficiency, respectively. The index i indicates that the ratios must be evaluated for the incident photon energy Ei. The index j denotes that the corresponding value is related to the escape of the j-th characteristic X-ray from the detector sensitive volume.

The probability density distribution functions Ffep, Fsep, Fdep and Fxep describe profiles of the FEP, SEP, DEP and XEP, respectively. The peak centroids are calculated as: Efep,i = Ei, Esep,i = Ei - m0c2, Edep,i = Ei - 2m0c2 and Exep,ij = Ei - Ex,j, where m0c2 = 511 keV is the electron rest mass and Ex,j is the energy of the j-th characteristic X-ray of the constituent chemical elements of the detector sensitive volume. The probability density distribution function Fcp describes the profile of the continuum created in the primary photon interactions, which result in the partial transfer of the photon energy to the detector sensitive volume. Since all profiles are normalized to unity, so as the primary photon contribution

$\int_0^{\infty} P(E,E_i) \, dE = 1.$

#### Secondary photon contribution

The function S(E,Ei) includes contributions from two sources

$S(E,E_i)=\omega_{ann,i}\,F_{ann}(E,m_0c^2)\,+\,\omega_{cs,i}\,F_{cs}(E,E_i).$

The first term describes a γ-ray peak at 511 keV (see Fig.3.3), which is due to the full absorption of 511 keV photons from the annihilation of positrons. These positrons are created in the interactions of high-energy photons (Eγ > 2 m0c2) and supposed to annihilate outside the detector sensitive volume. The ωann is the annihilation peak efficiency εann to total detection efficiency εp,tot ratio. The probability density distribution function Fann describes the profile of the 511 keV peak.

The second term in the formula represents a part of the continuum associated with the detection of the secondary photons (see Fig.3.3). The ωcs gives the magnitude of this contribution relative to the total detection efficiency εp,tot. The probability density distribution function Fcs describes the profile of this continuum.

Since both annihilation and continuum profiles are normalized to unity, the normalization of the secondary photon distribution function S(E,Ei) is

$\int_0^{\infty} S(E,E_i) \, dE = \omega_{ann,i} \, + \, \omega_{cs,i}.$

#### Total detection efficiency (all gammas)

Taking into account the above normalizations of the primary and secondary photon distribution functions, one can easily obtain the following formula for the total detection efficiency

$\epsilon_{tot}(E_i)=\int_{0}^{\infty}R(E,E_i)\,dE\,=\,\epsilon_{p,tot}(E_i)\, \left \{ 1 \,+\, k_s\, (\omega_{ann,i} \,+\, \omega_{cs,i}) \right \}.$

Here both the primary and secondary photon contributions are included. Using the factor ks, one can scale the secondary photon contribution, thus, adapting the detector response model to different measurement conditions, i.e. different detector environment.

#### Peak profiles

The shapes of the full energy γ-peaks are simulated using the Gaussian distribution function

$F_{fep}(E,E_{fep})=G(E;E_{fep},\sigma)=\frac{1}{\sqrt{2\pi\sigma^2}}\,\exp{\left ( - \frac{(E-E_{fep})^2}{2 \,\sigma^2} \right )}.$

The energy dependent standard deviation σ is calculated from the energy resolution properties of a detector, described by the function Δ1/2(E) - the Full Width at Half Maximum (FWHM) of a peak, using the relation

$\sigma(E_{fep})=\frac{\Delta_{1/2}(E_{fep})}{2\sqrt{2\ln{2}}}\approx 0.4246609\,\Delta_{1/2}(E_{fep}).$

The energy dependence of the FWHM is treated differently for NaI and HPGe detectors. Particularly, for NaI detectors it is taken as a linear function of the photon energy

$\Delta_{1/2}(E})=a\,+\,b\,E,$

whereas for HPGe detectors it is considered to be propotional to the square root of the photon energy

$\Delta_{1/2}(E})=a\,+\,b\,\sqrt{E}.$

The coefficients a and b in these formulas are calculated based on the user-specified FWHM values for the 122 keV ( 57Co ) and 1332.5 keV ( 60Co ) full energy γ-peaks.

The SEP, DEP and 511 keV annihilation peak profiles are also modeled using the above Gaussian distribution. The only modification concerns the single escape and 511 keV peaks, whose widths include additional contribution from the Doppler broadening, i.e.

$\sigma(E_{sep,511})=\sqrt{\frac{\Delta_{1/2}^2(E_{sep,511})}{8\ln{2}} \,+\, \sigma_{Doppler}^2}.$

The conventional estimate for the Doppler shift of the annihilation photon energies σDoppler ≈ 1 keV [3] is used.

The shapes of the full energy X-ray peaks and X-ray escape peaks are modeled using the Voigt profile, defined as a convolution of the Gaussian and Cauchy-Lorentz distributions

$F_{fep,xep}(E,E_{fep,xep})=\int_{-\infty}^{+\infty}G(E';E_{fep,xep},\sigma) \, L(E-E';\Gamma) \, dE'.$

Here L(E-E';Γ) is the Lorentzian profile

$L(E-E',\Gamma)=\frac{\Gamma}{2\pi}\,\frac{1}{(E-E')^2+\Gamma^2/4}$

with Γ being the full natural width at the half maximum of an X-ray line. The standard deviation σ of the Gaussian distribution represents the detector energy resolution properties and is calculated like in the case of the full energy γ-peaks (see above). A rapid algorithm [4] is employed to calculate the Voigt profile function. The natural widths of the X-ray lines are calculated based on the widths of the atomic levels involved in the respective intra-atomic transitions, taken from the Evaluated Atomic Data Library [5].

#### Continuum profiles

The primary and secondary photon continuum profiles Fcp and Fcs are obtained by convoluting the respective physical continuum profiles Hcp and Hcs with the Gaussian distribution function

$F_{cp,cs}(E,E_i)=\int_{0}^{+\infty} H_{cp,cs}(E';E_i) \, G(E';E,\sigma) \, dE'.$

Here σ represents the energy resolution properties of a detector and is calculated based on the FWHM function Δ1/2, like in the case of the Gaussian full energy γ-peak profile (see above).

The models of the physical profiles are shown in Fig.3.4 and 3.5. They are represented as piecewise continuous functions with the continuity intervals defined based on the physical considerations, briefly explained in the Figures.

Figure 3.4. Physical continuum profile Hcp associated with the detection of primary gammas. The vertical dotted lines shows physically grounded devision of the full energy range into the intervals of the function continuity.

The continuum described by the profile Hcp is mostly formed by the Compton scattering of the primary gammas. For the primary gamma-rays with energies > 2 m0c2, an additional contribution from the Compton scattering events of annihilation gammas created within the detector sensitive volume is present.

Figure 3.5. Physical continuum profile Hcs associated with the detection of secondary gammas. The vertical dotted lines shows physically grounded devision of the full energy range into the intervals of the function continuity.

The continuum Hcs represents the contribution from the secondary photons, which, after being scattered in the detector environment, strike the detector sensitive volume, thus, forming a so-called backscatter peak. Additional contribution to this continuum component appears for photon energies > 2 m0c2. It represents the Compton continuum associated with the detection of the 511 keV annihilation photons created in the materials surrounding the detector sensitive volume.

On each of the continuity intervals the physical profiles are represented by the 8-th order polynomial function.

### Detector response database

In the course of modeling, an extensive detector response database is used for evaluating contributions of the spectrum components. The database has been created using a specially developed and validated Monte Carlo program. It contains a large set of the peak-to-total and continuum-to-total efficiency ratios as well as the parameterized continuum profiles, calculated on grids of the detector crystal dimensions, γ-ray energies and source-to-detector distances. To calculate the efficiency ratios and continuum profiles for arbitrary measurement setup and photon energy, a set of interpolation techniques described in [6] is applied. More details on the detector response database are given in the sub-sections which follow.

#### Scope of the database

The database contains tabulated response data arrays, which were pre-calculated for the generalized models of NaI and HPGe detectors shown in Fig.3.6.

Figure 3.6. Models of NaI and HPGe detectors used in the detector response database calculations (dimensions in mm).

The both models imply a point-like γ-source located on the axis of a cylindrically symmetric crystal (the detector sensitive volume), which is encompassed by a number of fixed standard construction elements (absorbing layers). For the NaI crystal (ρ = 3.667 g/cm3) these fixed elements include:

• the 0.5 mm Al detector end cap (ρ = 2.7 g/cm3),
• the 5 mm crystal packaging made of foam plastic (ρ = 0.2 g/cm3),
• the 0.5 mm Al crystal casing, and
• the 0.5 mm MgO reflector (ρ = 2.0 g/cm3).

The fixed construction elements encompassing the HPGe crystal (ρ = 5.323 g/cm3) include:

• the 1.5 mm Al detector end cap (ρ = 2.7 g/cm3),
• the 0.7 mm inactive Ge at the front and sides of the crystal (ρ = 5.323 g/cm3), and
• the 1.0 mm Al crystal holder (ρ = 2.7 g/cm3).

In both models there is the 30 mm thick Al disk, which simulates the presence of all other detector construction elements (e.g. the photomultiplier tube, cooling system, electronics etc.) behind the detector sensitive volume.

The response data have been tabulated on the grids of the detector sensitive volume dimensions (L and D in Fig.3.6), source-to-detector distance (X in Fig.3.6) and photon energy. The sensitive volume dimension grid has 10 mm step and spans 20 mm to 120 mm ranges for both length and diameter (in total 121 grid points). For HPGe detectors it corresponds to the relative efficiency range from 1.5% to more than 300%, thus, encompassing the practical range of existing high-energy photon detectors. The γ-ray energy grid consists of 61 points, which are equally spaced in logarithmic scale from 10 keV to 10 MeV, covering the useful energy ranges of radionuclide decay and prompt activation gammas. There are only 4 points in the source-to-detector distance grid, specifically 0 cm, 1 cm, 5 cm and 25 cm, which is due to a weak dependence of the response profile properties on this parameter.

Thus, in total, there are: 2 (detector types) × 121 (sensitive volume dimensions) × 61 (photon energies) × 4 (source-to-detector distances) = 59048 records in the database. Each record contains information about:

• the peak-to-total efficiency ratios for FEP, SEP, DEP, XEP and 511 keV peaks,
• the total number and energies of the XEP peaks (8 peaks per each constituting chemical element in the detector sensitive volume, assosiated with the emission of Kα1,2,3 and Kβ1,2,3,4,5 X-rays),
• the cumulative peak-to-total efficiency ratio for XEP peaks,
• the standard uncertainties for all peak-to-total and continuum-to-total ratios,
• the coefficients of the 8-th order polynomial parameterization for each continuity interval of the primary and secondary photon continuum profiles.

#### Detector response generator

The database has been filled up with the data using a specially developed Monte Carlo based Detector Response Generator program DRGen (Version 1.3). Its main features are: (a) the full control over the statistical uncertainties of the target values, i.e. uncertainties of the efficiency ratios and continuum components, (b) the separation of the primary and secondary continuum components in accordance to the definition shown in Fig.3.1, and (c) the automatic processing of the simulated data and storage of the target values in the database. Screen captures of the program main form are shown in Fig.3.7 and Fig.3.8.

Figure 3.7. Screen capture of the DRGen program main form: response calculation running for the 1 MeV incident photons.
Figure 3.8. Screen capture of the DRGen program main form: response calculation running for the 9 MeV incident photons.

For each datapoint in the detector response grid, the DRGen starts with Nmin trials and then proceeds by steps of 100 thousand trials. After the first set of trials and each subsequent step, the simulated data are processed and the statistical uncertainties of the target values are checked against the predefined uncertainty thresholds

• 1% for the peak-to-total and continuum-to-total efficiency ratios,
• 5% for the average uncertainties in each continuity interval of the primary and secondary components of the continuum.

The calculation continues until the uncertainties of all target values are below the respective thresholds or the maximum number of trials Nmax is reached. The minimum and maximum numbers of trials are chosen different in different energy intervals of the incident photons, particularly

• Nmin = 106 and Nmax = 107 for 10 keV ≤ Eγ < 40 keV,
• Nmin = 5 · 106 and Nmax = 1.5 · 107 for 40 keV ≤ Eγ < 1 MeV, and
• Nmin = 107 and Nmax = 2 · 107 for 1 MeV ≤ Eγ < 10 MeV.

The transport of photons through the detector geometry is performed by modeling the main types of interaction - coherent (Rayleigh) scattering, photoelectric effect, pair production effect and incoherent (Compton) scattering. Photon interaction cross-sections are calculated based on the EPDL-97 library [2]. The Compton and Rayleigh scatterings are simulated using GEANT Low-Energy Compton Scattering package GLECS 3.36 [7], which includes atomic electron binding effects (Doppler broadening). In photoelectric interactions the emission of characteristic X-rays of K- and L-series is modeled.

Because of the large number of the detector response grid datapoints and huge computational overhead associated with the electron transport, DRGen uses a simplified approach for tracking electrons, which is beleived, however, to be sufficient for typical dimensions of the γ-detector sensitive volumes and γ-ray energy range of interest. The energy deposited by an electron is assumed to be proportional to a part of its projected range, which entirely lies in the detector sensitive volume. This part of the range is evaluated along the straight line projected in the direction of the electron emission. The bremsstrahlung photons are sampled uniformly along the electron pathway. The photon numbers and energies are sampled using the Thick Target Bremsstrahlung (TTB) approximation. The transport of positrons is modeled using similar approach. The point of the positron annihilation is sampled from the uniform distribution along its pathway. The positron annihilation at rest is assumed by modeling the emission of two 511 keV photons in opposite directions.

To futher enhance the performance of the calculations, the directional cosines of the source photons are sampled only within the solid angle subtended by the detector. For the low-energy photons (Eγ < 40 keV), which suffer severely from the absorption, an additional variance reduction technique is applied. These photons are transported directely to the detector sensitive volume with appropriate reduction of their weight: w = exp(-Σμx), where μ = μtot - μcoh is the total photon attenuation coefficient with the coherent scattering excluded, x is the absorbing layer thickness, and the sum is over all absorbing layers separating source and detector sensitive volume along the photon pathway.

The calculation performance is also optimized through a set of the energy cut-offs / thresholds, which are

• 1 keV and 10 keV - the cut-off energies for photons and electrons respectively, below which the local deposition of their energy is assumed,
• 40 keV - the lower incident photon energy, for which the continuum is calculated,
• 1200 keV - the maximum energy of the incident photons, for which the XEP peak-to-total efficiency ratio is calculated, and
• 1200 keV - the lower threshold for the SEP, DEP and 511 keV peak-to-total efficiency ratio calculation.

#### Uncertainty of the data

The minimum, maximum and average statistical uncertainties of the data in the detector response database are summarized in Table 3.2 and Table 3.3 for NaI and HPGe detectors respectively. The uncertainties are presented for different energy regions of incident photons.

The mean uncertainties of the FEP-to-total efficiency ratio ωfep do not exceed 0.3% in the whole energy range. The individual values of the ratio are well below 0.6% for photon energies up to 3 MeV and for all crystal dimensions and detector types. For higher energies and small detector sensitive volumes (where the contribution of the FEP becomes not so important) the uncertainty of the ratio can reach about 4%.

The individual uncertainties of the cumulative XEP-to-total efficiency ratio ωxep in the low-energy interval are below 0.32% and 1.1% for the NaI and HPGe detectors respectively. The individual uncertainties of the SEP and DEP peak-to-total ratios for energies greater than 3 MeV are below 1.3% and 0.7% respectively. The mean uncertainties of the ratios do not exceed 1% in the full energy range.

The 511 keV peak-to-total ratios have greater uncertainties with the mean values in the higher energy region within 1.0-1.5% and extreme values up to 3.4%. This still can be considered as appropriate since this peak is not usually used in the quantitative γ-spectrometry.

The uncertainties of the continuum-to-total ratios are well below 0.5% in the energy intervals, where the continuum contribution is expected to be significant.

Table 3.2. The relative statistical uncertainties of the NaI detector response data. The values shown are 1σ uncertainties in percent. Cases where the contribution of a particular detector response component can be significant are marked with the grey background.
Energy range Value $\omega_{fep,i}$ $\textstyle\sum_j\omega_{xep,ij}$ $\omega_{sep,i}$ $\omega_{dep,i}$ $\omega_{ann,i}$ $\omega_{cp,i}$ $\omega_{cs,i}$
10 keV - 100 keV min
max
mean
0.017
0.22
0.081
0.10
0.32
0.16

0.29
0.39
0.33
0.12
0.17
0.14
100 keV - 1 MeV min
max
mean
0.028
0.24
0.056
0.24
2.33
0.80

0.049
0.50
0.17
0.097
0.32
0.17
1 MeV - 3 MeV min
max
mean
0.034
0.54
0.11
0.99
2.19
1.27
0.14
3.84
0.56
0.24
2.00
0.63
0.97
17.1
2.82
0.041
0.11
0.055
0.087
0.21
0.13
3 MeV - 10 MeV min
max
mean
0.063
4.18
0.29

0.11
1.25
0.23
0.20
0.69
0.27
0.65
3.36
1.35
0.042
0.110
0.061
0.12
0.26
0.17

Table 3.3. The relative statistical uncertainties of the HPGe detector response data. The values shown are 1σ uncertainties in percent. Cases where the contribution of a particular detector response component can be significant are marked with the grey background.
Energy range Value $\omega_{fep,i}$ $\textstyle\sum_j\omega_{xep,ij}$ $\omega_{sep,i}$ $\omega_{dep,i}$ $\omega_{ann,i}$ $\omega_{cp,i}$ $\omega_{cs,i}$
10 keV - 100 keV min
max
mean
0.027
0.40
0.16
0.61
1.05
0.79

0.18
1.50
0.55
0.10
0.49
0.20
100 keV - 1 MeV min
max
mean
0.022
0.31
0.054
0.89
14.4
3.30

0.043
0.19
0.077
0.078
0.21
0.11
1 MeV - 3 MeV min
max
mean
0.034
0.58
0.12
4.33
12.8
6.20
0.23
6.27
0.81
0.30
3.36
0.92
0.81
13.0
2.05
0.037
0.094
0.051
0.081
0.19
0.12
3 MeV - 10 MeV min
max
mean
0.070
3.25
0.30

0.14
1.20
0.29
0.24
0.63
0.36
0.66
2.60
1.04
0.050
0.100
0.061
0.11
0.20
0.15

#### Accuracy of the data

The accuracy of the data has been studied by comparing the DRGen results with the reference data obtained with help of the MCNP-4C [8] general purpose Monte Carlo N-Particle transport code. The MCNP calculations were performed with the detailed electron transport (mode p e) and realistic bremsstahlung creation (phys:e bnum=1) models. The reference geometries included a point-like γ-source at 25 cm distance from the bare cylindrical Ge crystals with dimensions 2 × 2 cm, 6 × 6 cm, and 12 × 12 cm. The incident photon energies considered were 1 MeV, 3 MeV, and 10 MeV. The results of the calculations are presented in Table 3.4.

Table 3.4. The reference efficiency data obtained with the use of the MCNP code. The numbers in paranthesis indicate the statistical uncertainties at 1σ level. For absolute values, multiply the respective figures by 10-6.
Crystal dimensions, cm E, MeV εtot εfep εsep εdep
2 × 2 1
3
10
168.11 (0.77)
115.69 (0.16)
105.61 (0.18)
13.91 (0.23)
3.066 (0.032)
0.131 (0.007)

1.018 (0.019)
0.823 (0.018)

5.944 (0.055)
4.428 (0.068)
6 × 6 1
3
10
2555.7 (2.0)
2018.7 (1.6)
1889.8 (2.6)
763.0 (2.0)
303.6 (0.9)
60.4 (0.7)

65.0 (0.4)
102.4 (0.9)

37.4 (0.3)
53.2 (0.6)
12 × 12 1
3
10
11101 (7)
9657 (6)
9261 (13)
5725 (9)
3308 (6)
1327 (8)

381.5 (2.1)
817.2 (6.4)

56.8 (0.8)
112.9 (2.4)

For the sake of comparison, the MCNP calculations were also performed using two simplified approaches

• MCNP-1: without electron transport and without bremsstrahlung photon creation (mode p, phys:p ides=1),
• MCNP-2: without electron transport but with bremsstrahlung photon creation modeling using TTB approximation (mode p, phys:p ides=0).

The relative deviations of the DRGen, MCNP-1 and MCNP-2 results from the reference values are summarized in Table 3.5. The data show that all approaches give perfectly accurate estimations for the total detection efficiency. However, the accuracy of the peak efficiencies is strognly influenced by the underlying physical approximations. Particularly, disregarding the electron transport and utilization of an inadequate bremsstrahlung creation model result in the overestimation of the peak efficiencies, which are about a few percent for 1 MeV photons, a few tens percent for 3 MeV photons, and several hundereds percent for 10 MeV photons.

As for the DRGen accuracies, they are perfectly below 1% for the FEP efficiencies at 1 MeV, and FEP and SEP efficiencies of the medium and large sensitive volume detectors at 3 MeV. For the smallest crystal and 3 MeV photons the accuracy of the FEP efficiency is about 4.5%, which is also quite good if one takes into account that 3 MeV is far beyond the typical practical energy range of the detectors with such small crystals. For 10 MeV photons the peak efficiencies are biased to higer values not more than by 25%, which is still very good if compared to the respective deviations of the MCNP-1 and MCNP-2 values.

Table 3.5. The relative deviations (%) of the MCNP-1, MCNP-2 and DRGen results from the reference efficiency data. Cases when the deviations are significant with the confidence probability p > 0.99 are marked with red.
E, MeV Crystal dimensions, cm Value εtot εfep εsep εdep
1 2 × 2 MCNP-1
MCNP-2
DRGen
0.19
0.23
0.00
9.15
6.06
0.25

1 6 × 6 MCNP-1
MCNP-2
DRGen
0.00
0.00
-0.18
1.79
0.74
-0.60

1 12 × 12 MCNP-1
MCNP-2
DRGen
-0.04
-0.03
-0.28
0.86
0.43
-0.57

3 2 × 2 MCNP-1
MCNP-2
DRGen
0.06
0.22
0.18
50.09
17.68
-4.46
9.65
9.31
-0.47
29.64
15.83
3.81
3 6 × 6 MCNP-1
MCNP-2
DRGen
0.02
0.01
-0.08
17.64
4.74
0.00
8.76
2.95
0.07
16.79
10.11
2.93
3 12 × 12 MCNP-1
MCNP-2
DRGen
-0.02
0.00
-0.29
8.30
2.16
-0.12
7.19
3.68
0.85
17.90
11.77
4.36
10 2 × 2 MCNP-1
MCNP-2
DRGen
0.16
0.20
0.18
1026.15
176.81
2.70
507.09
101.68
19.31
603.66
129.55
24.52
10 6 × 6 MCNP-1
MCNP-2
DRGen
0.25
0.26
0.17
182.49
29.20
17.21
183.90
39.06
22.54
237.70
55.16
22.32
10 12 × 12 MCNP-1
MCNP-2
DRGen
0.03
0.01
-0.25
76.17
14.42
13.29
107.44
27.62
15.86
144.18
29.76
-0.51

The computed continuum distributions are compared in Fig.3.9-3.11. One can see that, in contrast to the simplified MCNP-1 and MCNP-2 approaches, the DRGen distributions quite accurately reproduce the reference continuum spectra for all crystal dimensions and photon energies tested.

Figure 3.9. Comparison of the continuum distributions simulated for 2 × 2 cm bare Ge crystal.

Figure 3.10. Comparison of the continuum distributions simulated for 6 × 6 cm bare Ge crystal.

Figure 3.11. Comparison of the continuum distributions simulated for 12 × 12 cm bare Ge crystal.

## EXPERIMENTAL VALIDATION

### Coaxial 60% High Purity Germanium Detector

#### Experimental

The experimental setup consisted of the GC6020 coaxial HPGe detector with 61.8% relative efficiency and 2110 TRP preamplifier. Detector signal processing and spectrum aquisition were carried out by high-throughput electronics consisting of a DSP9660 digital signal processor and an AIM556 interface module. The energy resolution of the system was FWHM = 1.75 keV at 1.33 MeV and FWHM = 0.95 keV at 122 keV.

The measurements were performed with 137Cs, 60Co and 152Eu thin standard spectrometry γ-ray sources. The activities of the sources, as provided in the manufacturer's certificates, were known with 3% relative cumulative uncertainty at 3σ-level. The sources were located on the detector axis and measured twice, at 5 cm and 17 cm from the detector end cap. The background spectrum was measured in a separate run and appropriately subtracted from the source spectra.

The spectrum processing was performed by Genie-2000 spectroscopic software, inhanced by the interactive peak fiiting option. The experimental efficiencies at 5 cm distance were corrected for the cascade summing effect using the Monte Carlo approach described in [9].

#### Detector model parameters

The detector crystal dimensions as well as the thickness of inactive layers were taken from the detector certificate provided and used without any modifications: crystal diameter – 74 mm, crystal height – 53 mm, inactive germanium at the front and sides of the crystal – 0.7 mm, Al end cap – 1.5 mm, end cap to crystal distance – 5 mm. The rear contact dimensions of the crystal (diameter - 10 mm, length - 36 mm) were obtained from the detector manufacturer.

#### Results

Fig.4.1 shows calculated and measured FEP efficiencies for 5 cm and 17 cm distances between source and detector end cap. Open circles represent data points not corrected for cascade summing. One may see that the generator provides an excellent description of the experimental data. Small discrepancies between modelled and measured efficiencies can be caused by the uncertainties of the Ge inactive layer thickness and detector sensitive volume dimensions, which not always correspond to the certified values.

Fig.4.2-4.4 compare the simulated and experimental detector responses. All responses were generated with the value kS = 2.0 for the secondary photon contribution scaling coefficient. One can see that the model spectra reproduce the experimental data quite well in both shape and absolute values. The observed differences are due to the contribution of the secondary radiation (backscatter peak), the shape of which is highly sensitive to the peculiarities of the actual measurement geometry.

Figure 4.1. Comparison of calculated (curves) and experimental (circles) FEP efficiencies for a point source at 5 cm (upper curve) and 17 cm (lower curve) distance from the detector end cap.
Figure 4.2. Comparison of the calculated (curve) and experimental (circles) detector responses for a 60% HPGe detector and point 137Cs source located at 17 cm distance from the detector end cap.

Figure 4.3. Comparison of the calculated (curve) and experimental (circles) detector responses for a 60% HPGe detector and point 152Eu source located at 17 cm distance from the detector end cap.
Figure 4.4. Comparison of the calculated (curve) and experimental (circles) detector responses for a 60% HPGe detector and point 60Co source located at 17 cm distance from the detector end cap.

## PROGRAM INTERFACE DESCRIPTION

### Getting started

The Gamma Spectrum Generator is an interactive web-accessible application which can be used to simulate the gamma spectrum of radioactive substances. The simulator presents an efficient visual teaching aid that is especially useful in training facilities which have restrictions on the use of radioactive substances, or when sources of special interest (e.g. spent fuel, enriched U, weapon grade Pu or other highly radiotoxic materials) are not readily available.

The Gamma Spectrum Generator module interface is shown in Fig.5.1. The basic geometric arrangement of the source, filters and detector is shown schematically.The lines shown indicate some of the paths of photons which lead to a contribution in the detector. Associated with source, filters and detector are a number of input boxes in which one can specify the source and its strength, the filter materials, the source detector distance, type of detector etc.

The module is setup such that the user can run the program immediately through a simple “one-click” calculation with default parameters. To do this, press the “Start” button shown in Fig.5.1. Thereafter, the lower half of the page will immediately show the “Calculation results” tab, which displays the resulting simulated spectrum with default view settings as shown in Fig.5.2.

Figure 5.1. Gamma Spectrum Generator starting page

Figure 5.2. Calculation results of the “one-click” calculation with defaults setting

This “one-click” calculation simulates the spectrum for the 10 MBq 60Co γ-source, as specified by the default settings of the “Element”, “Mass” and “Quantity” controls below the nuclide’s image (see Fig.5.1).

The activity of the source is related exactly to the measurement starting point in time as indicated by the default setting of the “Reference point” dropdown box to the right of the “Quantity” controls.

The “Measurement time” controls at the top of the “Measurement setup” tab is defaulted to 1000 seconds. This is normally a sufficient time interval for detecting nuclide’s signatures in the real conditions.

The detector setup in the “Current configuration” dropdown box in Fig.5.1 is defaulted to an unshielded NaI detector with crystal dimensions 3" x 3" (76.2 x 76.2 mm) positioned at 25 cm distance from the source.

The graphical presentation of the results is defaulted to the spectral distribution of intensity of counts (count rate in counts per second) at the start of the measurement (see “Data displayed” dropdown box in Fig.5.2).

See the quick visual guide in Section 5.2 below for a brief overview of additional calculation settings and results presentation options available. Section 5.3 provides a detailed description of the user interface.

### Quick visual guide

Figure 5.3. Start view of the Gamma Spectrum Generator page. Controls for selecting nuclide / mixture and setting up the measurement geometry.

Figure 5.4. Measurement geometry setup controls.

Figure 5.5. Calculation options available.

Figure 5.6. Controls available on the "Calculation results" tab.

Figure 5.7. Customizing appearance of the detection efficiency graph.

### Detailed description

#### Choosing nuclide or mixture

By default the page is opened in the Nuclide Selection Mode. To select a nuclide, use "Element" and "Mass" dropdown lists (shown in Fig.5.8) for specifiying the chemical element and mass number of the isotope of interest. In the "Mass" list the stable isotopes are marked with symbol "s" (e.g. "27 s" indicates stable isotope of Al) and the isomers are marked with symbols "m", "n", and "p", indicating the first, second and third isomeric states of the nuclide respectively (e.g., "26 m" corresponds to the first isomeric state of Al-26).

Figure 5.8. Nuclide selection controls.
Figure 5.9. Nuclide selected.

A nuclide of interest can be chosen also from Nucleonica’s Help:Nuclide Explorer page, which can be reached by clicking on the corresponding link provided - the Nuclide Explorer logo box to the right of the "Mass" dropdown list (see Fig.5.8).

Once a source nuclide is selected, the box at the top left of the page (see Fig.5.9) shows an image with its basic properties (decay modes, half-live, existing isomers) indicated. The nuclide’s name to the right of the image provides a link to a part of the Nucleonica Wiki, which describes in detail properties of the chemical element.

To switch to the Mixture Selection Mode, click on the "Nuclide Mixtures Selector" link to the right of the Explorer logo box (see Fig.5.8). This will enable the "Nuclide Mixtures" dropdown list shown in Fig.5.10, which contains a set of the user-specified and pre-defined Nuclide mixtures. When the required mixture is selected, its name appears below the page title (see Fig.5.11) providing a link to the Nucleonica's Nuclide mixtures editor. Clicking on this link redirects to the Nuclide mixtures editor page, which is opened with the current mixture selected.

Figure 5.10. Mixture selection controls.
Figure 5.11. Nuclide mixture selected.

Alternatively, one can start from the selection/creation/editing of a required mixture on the Nucleonica's Nuclide mixtures page. When the mixture is prepared, one can switch to the Gamma Spectrum Generator using the corresponding link provided on the Nuclide mixtures page.

To return to the Nuclide Selection Mode, click on the "Nuclide Selector" link to the right of the "Nuclide Mixtures" dropdown list (see Fig.5.10).

#### Specifying nuclide/mixture quantity

The quantity of a nuclide or a mixture in the source can be specified using the controls shown in Fig.5.12. First, specify the quantity type using the "Quantity" dropdown list and then enter the corresponding numeric value in the edit box to the right of it. The possible quantity types are

• the activity either in Bequerrels or Curries,
• the mass in grams (only for a single nuclide), and
• the number of atoms (only for a single nuclide).

It is important to note, that switching between different types of the nuclide/mixture quantity does not convert the numeric value into the corresponding measurement unit automatically.

Figure 5.12. Nuclide quantity selection controls.
Figure 5.13. Specifying "cooling" time interval.

The nuclide/mixture quantity can be specified either at the moment of its production/certification or at the spectrum measurement starting point of time. This is defined by the selection of an appropriate item in the "Reference point" dropdown list (see Fig.5.13). Note, that the list becomes enabled only if the corresponding option in the "Options" tab, which enables the decay calculations, is selected (see section 5.3.7).

By default, the reference point of time is the "Measurement start". If the "Nuclide creation" is chosen instead, then the "Cooling time" controls for specifying the duration of the source "cooling" time interval become available (see Fig.5.13). Use the respective dropdown list to select a measurement unit for the source "cooling" time interval. The options available are "sec", "min", "hour", "day" and "year". The length of the interval must be entered in the corresponding edit box to the right. Note, that the length value is not converted automatically when a new measurement unit for the "cooling" interval is selected.

#### Specifying the measurement time interval

Figure 5.14. Measurement time controls.

The respective controls (the dropdown list and edit box shown in Fig.5.14) are provided at the top of the "Measurement setup" tab. Use the dropdown list to select an appropriate measurement unit for the time interval. The available options are shown in the figure. Specify the value of the interval in the edit box to the right.

#### Selecting and managing detector configurations

The detector configuration controls shown in Fig.5.15 are available at the top of the "Measurement setup" tab.

Figure 5.15. Detector configuration controls.

The "Current configuration" dropdown list shows available measurement setups, which include 6 default configurations with NaI and HPGe detectors. The default configurations are marked with "(default)" at the end and they appear always on the top of the list. Parameters of these pre-defined configurations are shown in Table 5.1.

Table 5.1. Parameters of the pre-defined (default) measurement setups available in Nucleonica's Gamma Spectrum Generator.
Configuration identification Crystal
L × D, mm
Rear contact
L × D, mm
Source-to-detector, mm Input window, mm Crystal packaging, mm
NaI, L × D = 3 in × 3 in 76.2 × 76.2 None 250.0 Al, 0.5 None
NaI, L × D = 1 in × 2 in 25.4 × 50.8 None 250.0 Al, 0.5 Plastic, 5.0
LEGe, 20 mm × 28 cm2, 0.5 Be 20 × 59.7 None 25.0 Be, 0.5 Vacuum, 2.5
HPGe, coaxial, p-type, rel. eff. 150% 95.0 × 82.0 60.0 × 10.0 250.0 Al, 0.5 Vacuum, 3.0
HPGe, coaxial, p-type, rel. eff. 50% 70.0 × 59.0 45.0 × 10.0 250.0 Al, 0.5 Vacuum, 3.0
BEGe, 30 mm × 50 cm2, rel. eff. 30% 30.0 × 79.8 None 50.0 Be, 0.5 Vacuum, 3.0
Table 5.1. continued
Configuration identification Inactive layer, mm Number of channels Conversion, keV/channel FWHM at 122 keV, keV FWHM at 1332 keV, keV
NaI, L × D = 3 in × 3 in MgO, 0.5 2048 1.0 18 90
NaI, L × D = 1 in × 2 in MgO, 0.5 512 3.0 20 140
LEGe, 20 mm × 28 cm2, 0.5 Be Ge, 0.0003 4096 0.07 0.75 1.64
HPGe, coaxial, p-type, rel. eff. 150% Ge, 0.8 8128 0.30 1.3 2.3
HPGe, coaxial, p-type, rel. eff. 50% Ge, 0.5 8128 0.30 0.8 1.8
BEGe, 30 mm × 50 cm2, rel. eff. 30% Ge, 0.0003 8128 0.30 0.75 2.2

The last entry "<...Edit...>" in the configurations list enables all measurement setup controls on the "Measurement setup" tab, so that new user-specific configurations can be created.

Hint: To start editing a new measurement setup based on an existing configuration, first, choose the configuration, which you would like to have as the basis, and then switch to the edit mode by selecting "<...Edit...>".

Using the "Save as" button, the new configuration can be saved in one's Nucleonica user account. Fig.5.16 shows the "Configuration save" dialog, which appears after the "Save as" button is pressed. Here the user is prompted to enter a unique (!) identification (decription) string for his new measurement setup.

Figure 5.16. Detector configuration save dialog.

After the new configuration is saved, it appears in the list of the available measurement setups after the default configurations.

An outdated user-specific configuration can be deleted using the "Delete" button (see Fig.5.15). After pressing the button the user will be prompted to confirm the deletion. Note, that both "Save as" and "Delete" buttons are disabled when one of the default configurations is selected.

#### Editing the measurement setup

The edit mode is turned on when the last entry ("<...Edit...>") in the "Current configuration" dropdown list on the "Measurement setup" tab is selected (see previous section). This enables the controls on the underlying measurement setup drawing, whereby one can configure his own γ-spectrometer.

By default the drawing displays the basic configurable parameters of the measurement setup shown in Fig.5.17 and 5.18 for NaI and HPGe detectors respectively. These basic parameters include the length and diameter of the detector crystal, the length and diameter of the rear contact of the crystal (available only for HPGe crystals), and source-to-detector distance. One can switch between models in Fig.5.17 and 5.18 by selecting the "NaI" or "HPGe" item in the "Crystal" dropdown list.

Use the "Dimensions in" dropdown list at the left top of the drawing to select an appropriate measurement unit ("mm", "cm" or "inch") for the dimensions entered in the respective text edit controls. Note that all dimensions are recalculated automatically when a new unit is chosen.

Figure 5.17. Basic configurable parameters of the measurement setup with a NaI detector.

Figure 5.18. Basic configurable parameters of the measurement setup with a HPGe detector.

More measurement setup controls appear (see Fig.5.19) when "Show more settings" checkbox at the bottom right of the measurement setup drawing is selected. These additional controls include dropdown lists with associated text edit boxes for specifying the material and thickness of

• the detector input window made of Al, Be or Mylar,
• the detector crystal packaging made of foam plastic or polyethylene in the case of NaI crystals and should be taken as void (vacuum) in the case of HPGe crystals,
• the inactive Ge layer in the front of the HPGe crystal or MgO reflector in the case of NaI detector, and
• additional absorbing filters between source and detector made of Al, Cu, Fe, Pb, Sn, or polyethylene.
Figure 5.19. Advanced parameters of the measurement setup.

The filters can be used to reduce unwanted contribution to the simulated spectrum from the intense low-energy γ-radiation. One can also use them to simulate γ-spectra from containerized or/and self-attenuating sources.

To add a filter to the measurement setup, first, choose appropriate filter material in the "Filter" dropdown box, then specify the filter thickness in the related edit text box and, finally, click the button "Add filter layer". The filter will appear in the table. Up to 6 non-redundant filter layers can be specified this way.

To remove a filter layer from the configuration, select the layer in the table by clicking somewhere within the respective row. The selection will be marked with the grey background and the button "Remove filter layer" will be enabled (see Fig.5.19). Pressing the button will remove the selected filter from the measurement setup.

• the dropdown list "Number of channels in the spectrum accumulated" for selecting the number of channels in the spectrum,
• the text edit box "Channel-to-energy conversion factor, keV/channel" for specifying the channel-to-energy conversion coefficient, i.e. Analog-to-Digital Converter (ADC) conversion gain, and
• two text edit boxes "Energy resolution (FWHM) at 122 keV, keV" and "Energy resolution (FWHM) at 1332 keV, keV" for specifying the energy resolution properties of the spectrometer, i.e. FWHMs at 122 keV and 1332.5 keV.

The available options and valid ranges of the measurement configuration parameters are summarized in Table 5.2. The properties of the materials used in the measurement setup definition are given in Table 5.3.

Table 5.2. Available options and valid ranges of the measurement configuration parameters.
Parameter Control name Control type Options / Range
Detector crystal type "Crystal" dropdown list "NaI", "HPGe"
Dimension measurement units "Dimensions in" dropdown list "mm", "cm", "inch"
Crystal length "Crystal length" text edit box 20 ÷ 120 mm
Crystal diameter "Crystal diameter" text edit box 20 ÷ 120 mm
Crystal rear contact length "Contact length" text edit box 0 ÷ "Crystal length"
Crystal rear contact diameter "Contact diameter" text edit box 0 ÷ 20 mm
Source-to-detector distance "Source to Detector distance" text edit box 0 ÷ 10300 mm
Input window material "Input window" dropdown list Al, Be, Mylar
Input window thickness "Input window" text edit box 0 ÷ 10 mm
Filter layer material "Filter" dropdown list Al, Cu, Pb, Fe, Sn, Polyethylene
Filter layer thickness "Filter" text edit box 0 ÷ 1000 mm
Crystal packaging material "Crystal packaging" dropdown list Vacuum, Foam plastic, Polyethylene
Crystal packaging thickness "Crystal packaging" text edit box 0 ÷ 20 mm
Inactive layer / Reflector material "Inactive layer / Reflector" dropdown list Ge, MgO
Inactive layer / Reflector thickness "Inactive layer / Reflector" text edit box 0 ÷ 5 mm
Number of channels "Number of channels in the spectrum accumulated" dropdown list 28, 29, 210, 211, 212 and 213
ADC's conversion gain "Channel-to-energy conversion factor, keV/channel" text edit box 0.1 ÷ 10 keV/channel
Energy resolution at 122 keV "Energy resolution (FWHM) in keV at 122 keV" text edit box 0.01 keV ÷ "FWHM at 1332 keV"
Energy resolution at 1332.5 keV "Energy resolution (FWHM) in keV at 1332 keV" text edit box "FWHM at 122 keV" ÷ 200 keV

Table 5.3. Properties of the materials used in the γ-spectrometer setup.
Material Chemical formula Density, g/cm3
Aluminium Al 2.70
Beryllium Be 1.85
Maylar C5H4O2 1.39
Foam plastic C2H4 0.20
Polyethylene C2H4 0.935
Germanium Ge 5.323
Magnesium Oxide MgO 2.00
Copper Cu 8.96
Iron Fe 7.87
Tin Sn 7.31

#### Starting calculations

The calculations can be started either in an on-line or background mode by pressing the respective button, i.e. "Start" or "Start in background", to the right of the "Measurement time" setup controls on the "Measurement setup" tab (see Fig.5.20).

Figure 5.20. Press "Start" or "Start in background" button to launch calculations.

If background mode is chosen, a notification will be sent via email and a respective alert will be raised in user’s Nucleonica account, once the task has been completed.

#### Selecting calculation options

Settings on the “Options” tab (see Fig.5.21) provide additional control over the calculation result output and spectrum simulation. These options include

• the "Display detector efficiency curves" checkbox that enables/disables the efficiency graph on the "Calculation results" tab,
• the "Consider decay transformations..." checkbox that enables/disables decay calculations, which will/will not allow a parent nuclide to decay and daugther nuclides to accumulate during the source "cooling" and spectrum measurement time intervals. When the box is checked the additional checkbox "Include gamma-rays of daugther nuclides" and text edit box "Decay Engine's accuracy factor" appear, as shown in Fig.5.21
• if the "Include gamma-rays of daugther nuclides" checkbox is disabled then the contribution to the simulated γ-spectrum from daugther nuclides accumulated during the source "cooling" and measurement time intervals is suppressed
• use the "Decay Engine's accuracy factor" text edit box to enter the value of the accuracy factor used by Nucleonica's Decay Engine in decay calculations
• the "Consider effects of backscatter radiation" checkbox enables/disables the contribution of the secondary photons to the full spectrum. If the box is checked, an additional text box "Backscatter peak normalization factor" appears, which allows specifying the value of the secondary photon contribution scaling coefficient ks (see section 3.2 for more details).
Figure 5.21. Additional settings for the simulation and output control.

Note: All settings on the "Options" tab are disabled by default !

#### Viewing simulated spectrum

The standard output, which appears in the "Calculation results" tab after the calculations have finished, is shown in Fig.5.22. It consists of a spectrum graph with a variaty of associated controls, which allow to switch between different types of the spectral information plotted and adapt appearance of the graph according to one’s needs and requirements.

Important: All new control settings come into force only after the button "Update spectrum graph" is pressed.

Different types of the spectral data can be displayed by selecting respective items in the "Data displayed" dropdown list, in particular

• "Count rate at start" and "Count rate at end" show spectral distributions of the detector count rate (i.e. spectral intensities) at the measurement starting and ending points of time respectively. The datapoints plotted present the intensity of counts in counts per second (cps) in respective spectrum channels,
• "Theoretical number of counts" shows the true mean numbers of counts in the respective channels, which one would obtain if performed averaging on the infinitely large number of spectra measured in absolutely the same conditions (general totality of spectra), and
• "Statistical number of counts" shows one of the possible realizations from the general totality of spectral distributions, i.e. the spectrum which is usually obtained in γ-spectroscopic measurements. The random number of counts in the spectrum channels are obtained from the Poisson distribution, whose mean values are taken from the respective datapoints in the "Theoretical number of counts" spectrum.

Note: If calculation is repeated with exactly the same settings, the only piece of information, which may differ, is the "Statistical number of counts" spectrum and values, which have been derived from it (e.g. count rates, total number of counts etc.).

Hint: It may happen that the statistical spectrum will not contain any significant number of counts when a source with low activity or at large distance from the detector is considered. In this case switching to the "Theoretical number of counts" spectrum is recommended.

Figure 5.22. The γ-spectrum graph with related controls on the "Calculation results" tab.

By default, the full spectrum (i.e. spectrum that is cumulative on the contributing nuclides and different spectrum components) is plotted on the graph as a function of the channel number. The checkboxes "Energy scale", "Spectrum continuum" and "Contribution of scattered photons" beneath the graph allow to convert the channel numbers on the X-axis to the energy units as well as to separate the peaks from the primary and secondary photon continuum contributions. This is demonstrated in Fig.5.23.

Figure 5.23. Use "Energy scale", "Spectrum continuum" and "Contribution of scattered photons" checkboxes to enable energy scale on the X-axis and to visualize different parts of the spectrum continuum.

The contributions of selected nuclides to the full spectrum can be visualized by checking boxes in the last column of the respective rows in the Table below the graph (see Fig.5.24). The other columns in the Table present the count rates at start and end of the measurement and the number of spectrum counts associated with individual nuclides. The last row in the Table shows cumulative count rates and number of counts in the full spectrum.

Note: All decay daugthers appear in separate rows in the Table below the graph, when a single nuclide source is considered. In the case of nuclide mixtures, only starting nuclides appear in the Table. The quotation marks around the starting nuclide name indicate that the figures shown include also contributions from all decay products of this nuclide.

Figure 5.24. Use checkboxes in the table below the graph to visualize contributions of individual nuclides to the full spectrum.

A panel of additional graph controls (see Fig.5.25) becomes available if the "More graph options" checkbox is selected. For each axis on the graph the panel provides similar blocks of controls, which include

• the "Scale" block for selecting appropriate data ranges to be displayed,
• the "Ticks" block for enabling/disabling axis ticks and tick lables,
• the "Tick steps" block for specifying appropriate values for the major and minor tick intervals, and
• the "Grid lines" block for enabling/disabling the major and minor grid lines, which are superimposed on the spectrum image.

The Y-axis can be turned to the logarithmic scale using the "Log" checkbox provided on the respective "Scale" block.

Note: The automatic mode is enabled by default for the "Scale" and "Tick steps" settings.

Figure 5.25. Use additional spectrum graph options to select a spectrum region of interest and to format the graph axises according to your preferences.

#### Viewing efficiency graph

The detection efficiency graph appears below the spectrum graph in the "Calculation results" tab, if the corresponding option in the "Options" tab is activated (see Section 5.3.7). The graph displays the total detection efficiency for the current spectrometer setup, as well as FEP, SEP, DEP and XEP efficiencies as functions of the incident photon energy (see Fig.5.26).

Figure 5.26. The efficiency graph with related controls.

Use "Efficiency displayed" checkbox controls below the graph to enable/disable plotting particular efficiency curves in the graph. A panel with additional graph options appears when the "More graph options" checkbox is selected. The panel appearance, content and function of controls are the same as shown in Fig.5.25. The only difference is the additional "Log" checkbox in the X-axis "Scale" block, which allows to enable/disable the logarithmic scale on the photon energy.

Both spectrum and efficiency graphs can be downloaded to user's computer in PNG or BMP formats. To do this, click the right mouse button when cursor is somewhere within the graph region and select "Save as" option from the context menue, which appears (see Fig.5.27). Then you will be prompted to specify the type of the graphical file and the destination folder and after that downloading begins.

Figure 5.27. Saving spectrum graph using the respective option in the context menue.

Use other options available in the context menue to print the image, or send it via e-mail, or see its properties etc.

A detailed report, containing the complete collection of spectral and efficiency numerical data, can be generated and downloaded as a text or Excel spreadsheet file. The corresponding links are provided in the "View/Save results in Text or Excel format" string located just above the right corner of the spectrum graph (see Fig.5.22-24).

The information in the files is structured as follows

• the "Parameters" block/sheet (see Fig.5.28) contains the full set of the settings, including the spectrometer parameters, source specification and calculation options, which have been used in the calculation,
Figure 5.28. An example of the "Parameters" sheet in the Excel file.

• the "Nuclides" block/sheet (see Fig.5.29) contains the cumulative and nuclide-specific information on the calculated activities, number of decays, count rates and number spectrum counts (theoretical and statistical) at the measurement starting and ending points of time,
Figure 5.29. An example of the "Nuclides" sheet in the Excel file.

• the "X- and Gamma-rays" block/sheet (see Fig.5.30) contains the properties of the γ- and X-rays emitted by the source with associated . For each γ- and X-ray the table indicates the ancestor and emitter nuclides, the photon energy and emission rates at the measurement start and end, the total number of photons emitted during the spectrum measurement, the total and FEP efficiencies, the peak and background number of counts, and the Minimal Detectable Activity (MDA(0)) of the ancestor nuclide at the measurement starting point of time. The MDA(0) values are calculated according to the approach described in [10],
Figure 5.30. An example of the "X- and Gamma-rays" sheet in the Excel file.

• the "Efficiency" block/sheet (see Fig.5.31) contains the efficiency data for the current measurement setup. The total and peak efficiencies are tabulated on the energy grid, which consists of 61 points spaced uniformely on the logarithmic scale in the energy range from 10 keV to 10 MeV. Additional pairs of energy points (one pair per each absorbing layer between source and detector crystal) are added to the energy grid to reproduce accurately the step-shaped behaviour of the efficiency curves near the K-edges,
Figure 5.31. An example of the "Efficiency" sheet in the Excel file.

• the "Nuclide's name" blocks/sheets (one per each nuclide in the source) contain the complete set of the spectral information related to induvidual nuclides (see Fig.5.32). This information includes the count rate spectral distributions at the start and at the end of the measurement time interval, as well as the theoretical and statistical distributions of the numbers of counts in the spectrum. For each type of the distributions the primary and secondary continuum contributions as well as the total spectrum are shown,
Figure 5.32. An example of the Excel sheet with the nuclide specific spectral information.

• the "Full spectrum" block/sheet presents the full spectrum information, i.e. the sum of the respective spectral distributions over all nuclides in the source. The data are structured in the same way as it is done in the nuclide's specific datasheets, shown in Fig.5.32.

## APPLICATION EXAMPLES

This section contains results of different case studies performed with the application of the Gamma Spectrum Generator. All graphs were created using the generator’s tools and downloaded directly from its web-page.

### Unshielded Co-60 and Eu-152 and 3" × 3" NaI

Fig.6.1 and 6.2 show γ-spectra simulated for the 100 kBq 60Co and 100 kBq 152Eu sources and NaI (3" × 3") detector. The detector setup includes 0.5 mm MgO reflector and 0.5 mm Al casing. The energy resolution of the detector is assumed to be FWHM = 18 keV at 122 keV and FWHM = 90 keV at 1332 keV. The sources are positioned at 25 cm distance from the detector and measured for 1000 s. The graphs demonstrate a powerful feature of the generator, which allows to visualize peak and continuum components of the spectrum. In addition, a backscatter peak contribution is shown as a separate continuum component in the graphs. The calculated total and peak efficiencies of the detector setup are shown in Fig.6.3.

Figure 6.1. γ-spectrum simulated for 60Co 100 kBq source and NaI (3" × 3") detector.

Figure 6.2. γ-spectrum simulated for 152Eu 100 kBq source and NaI (3" × 3") detector.

Figure 6.3. Total and peak detection efficiencies calculated for NaI (3" × 3") detector and point-like source at 25 cm distance.

### Spectra from thin NatU sample

The spectra were simulated for a 1 g U sample and three different measurement setups

• NaI detector (crystal dimensions - 76.2 mm × 76.2 mm (3" × 3"), crystal casing - 0.5 mm Al, MgO reflector - 0.5 mm), energy resolution - FWHM = 18 keV at 122 keV and FWHM = 90 keV at 1332.5 keV, number of channels - 2048, shielding - 1 mm Sn, channel-to-energy conversion - 1.0 keV/channel, source-to-detector distance - 250 mm,
• 30% BEGe detector (crystal length and diameter - 30 mm × 79.8 mm, crystal to end cap - 3 mm, inactive germanium - 0.3 um, input window - 0.5 mm Be), energy resolution - FWHM = 750 eV at 122 keV and FWHM = 2.2 keV at 1332.5 keV, shielding - 1 mm Sn, number of channels - 8192, channel-to-energy conversion - 0.3 keV/channel, source-to-detector distance - 50 mm, and
• LEGe detector (crystal length - 20 mm, active area - 2800 mm2, crystal to end cap - 2.5 mm, inactive germanium - 0.3 um, input window - 0.5 mm Be), energy resolution - FWHM = 750 eV at 122 keV and FWHM = 1.64 keV at 1332.5 keV, shielding - 0.5 mm Sn, number of channels - 4096, channel-to-energy conversion - 0.07 keV/channel, source-to-detector distance - 25 mm.

It was assumed that U had been separated from the ore 2 years before the measurement and had natural abundances of 234U, 235U and 238U at the date of the separation. The spectra include contributions from all decay products, which have been accumulated since this date. To obtain better statistics of counts, the spectrum measurement time was 105 s in all cases. The spectra are shown in Fig.6.4-6.9. Figures 6.4, 6.6 and 6.8 present spectrum peak and continuum components. Figures 6.5, 6.7 and 6.9 demostrate contrinbutions of different uranium isotopes to the full spectrum.

Figure 6.4. γ-spectrum simulated for 1 g natual uranium sample and NaI (3" × 3") detector. Spectrum peak and continuum components are shown.

Figure 6.5. γ-spectrum simulated for 1 g natual uranium sample and NaI (3" × 3") detector. Nuclide contrtibutions to the full spectrum are shown.

Figure 6.6. γ-spectrum simulated for 1 g natual uranium sample and BEGe detector. Spectrum peak and continuum components are shown.

Figure 6.7. γ-spectrum simulated for 1 g natual uranium sample and BEGe detector. Nuclide contrtibutions to the full spectrum are shown.

Figure 6.8. γ-spectrum simulated for 1 g natual uranium sample and LEGe detector. Spectrum peak and continuum components are shown.

Figure 6.9. γ-spectrum simulated for 1 g natual uranium sample and LEGe detector. Nuclide contrtibutions to the full spectrum are shown.

### Spectra from shielded TRU waste

Fig.6.10 and Fig.6.11 show low- and high-resolution γ-spectra for a 5.25 TBq source, which represents actinides extracted from a 1 kg sample of 6-year-aged PWR spent fuel. The isotopic composition of the fuel was calculated using NUCLEONICA’s webKORIGEN, assuming 4.2% for the original enrichment and 50 GWd/t for the final burnup of the fuel.

The low-resolution spectrum corresponds to a NaI detector with crystal dimensions - 76.2 mm × 76.2 mm (3" × 3"), crystal casing - 0.5 mm Al, MgO reflector - 0.5 mm, energy resolution - FWHM = 18 keV at 122 keV and FWHM = 90 keV at 1332.5 keV, number of channels - 2048, and channel-to-energy conversion coefficient - 1.0 keV/channel.

The high-resolution spectrum was simulated assuming 30% BEGe detector with the following parameters: crystal length and diameter - 30 mm × 79.8 mm, crystal to end cap - 3 mm, inactive germanium - 0.3 um, input window - 0.5 mm Be, energy resolution - FWHM = 750 eV at 122 keV and FWHM = 2.2 keV at 1332.5 keV, number of channels - 8192, channel-to-energy conversion coefficient - 0.3 keV/channel.

In both cases the source was assumed to be shielded with a 5 mm Pb filter and located at 25 cm distance from the detectors. The measurement time is 1000 s. From the spectra shown one can see easily the advantages of the high-resolution γ-spectrometry when accurate characterization of the sample is required.

Figure 6.10. γ-spectrum simulated for actinides in 1 kg PWR spent fuel shielded with 5 mm Pb and NaI (3" × 3") detector. Nuclide contrtibutions to the full spectrum are shown.

Figure 6.11. γ-spectrum simulated for actinides in 1 kg PWR spent fuel shielded with 5 mm Pb and BEGe (30% rel. eff.) detector. Nuclide contrtibutions to the full spectrum are shown.

### Simulation of a HPGe Detector with the GSG Pro

In this section we show how a HPGe detector can be simulated using the GSG Pro. To enter the detector edit mode select "Edit" from the "Current configuration" drop-down list. The main detector settings can then be changed directly in the schematic detector setup. Additional parameters can be set by activating the "Show more settings" check box. Once the settings have been set, the detector configuration should be given a name and save for future use.

Figure 6.12. Simulation of a HPGe detector using the GSG Pro: Detector Settings

Detector settings:

-Source to detector distance --> 111 mm

-Crystal --> HpGe

-Crystal length --> 80.4 mm

-Contact length --> 50 mm

-Contact diameter --> 10.0 mm

-Crystal diameter --> 59.1 mm

-Absorbing filter layers --> Aluminium 1 mm

-Input window --> Aluminum 0 mm

-Crystal packaging --> Vacuum 3.0 mm

-Inactive layer/reflector --> Germanium 0.0003 mm

-Number of spectrum channels --> 4096

-Channel to energy conversion factor --> 0.3

-Energy resolution at 122 keV--> 0.8

-Energy resolution at 1332 keV --> 1.95

Once the new detector parameters have been specified, the user is ready to make a simulation. As a first step the newly defined detector is selected from the "Current configuration" drop-down list. Thereafter the nuclide Ba137m (1 MBq) is selected. The final results of the simulation are shown in fig. 6.13

Figure 6.13. Simulation results for Ba137m with the new detector settings

## INFORMATION BROCHURE

Gamma Spectrum Generator

## PUBLICATIONS

N. Stefanakis, A Comparison of a Measurement using the Canberra BEGe Detector and a Simulation using Nucleonica, presented at the Nucleonica training course in April 2013. Link to pdf

A. Berlizov et al.,Fast and Accurate Approach to -Spectrum Modelling: A Validation Study with a Shielded / Unshielded Voluminous Uranium Sample, Applied Radiation and Isotopes 68 (2010) 1822–1831. http://dx.doi.org/10.1016/j.apradiso.2010.03.019

V. Kleinrath, a Study of Gamma Interference Scenarios for Nuclear Security Purposes, Measurements and Modelling using the Nucleonica Tools, JRC-ITU-TN-2010/21.

A. Berlizov, et al., A Collection of Reference HPGe Gamma-Spectra for Shielded / Unshielded Radionuclide Sources and Special Nuclear Materials, Technical Note JRC-ITU-TN-2009/25, 2009.

A.N. Berlizov and R. Dreher, Web-accessible γ-spectrum simulator with on-line Monte Carlo for voluminous and shielded γ-sources: First results of experimental validation. http://dx.doi.org/10.1016/j.nima.2009.07.010

A. Berlizov, Introduction to the Gamma Spectrum Generator, 2011

J. Magill, A. Berlizov, R. Dreher, Web-based Education & Training for Illicit Trafficking and Consequence Management Associated with Nuclear and Radiological Terrorism, NATO Advanced Research Workshop: Threat Detection, Response and Consequence Management Associated with Nuclear and Madiological Terrorism, November 17 - 21, 2008, Brussels, Belgium.

Full paper

## Experimental Gamma-Ray Spectrum Catalogues

Online experimental gamma spectrum catalogue

Heath Catalogue (NaI)

Heath Catalogue (HPGe)

## REFERENCES

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