Gamma Ray Spectra Analysis for Gold and Yttrium Samples

Gamma Ray Spectra Analysis for Gold and Yttrium Samples 

David Hervas 

July 2, 2013 

This analysis pretends to calculate the weighted average for the yield of 88 Y , 87 Y , and 87m Y isotopes in two 

irradiated yttrium samples with the final purpose of calculating their cross-sections. This is done by carefully 

analizing the spectras of each sample using DEIMOS software, resulting in a series of peak areas which then 

are corrected uppon to calculate the yield for each gamma line in a measurement. 

1

1 Brief theoretical background 

Gamma ray spectroscopy consists on the detection of gamma rays being emitted by decaying atomic nuclei. 

Different detectors are used for this purpose, but this analysis focuses on the use of a solid-state detector. The 

principal mechanisms in which gamma rays interact with a detector are the photoelectric effect, the compton 

effect and pair production. As an atomic nucleus decays gamma ray’s of specific energies are emmited and 

proceed to interact with the detector. This interaction is then registered and analysed to determine the energy 

of the incoming gamma rays. The collection of this data (which forms peaks at certain energies) is called 

a gamma spectrum, with the individual peaks being called gamma lines. In this analysis the gamma ray 

spectrum is analyzed by means of DEIMOS sofware to provide the energies of the registered gamma lines and 

their respective peak areas. With this data the following equation is used to find the yield for the different 

isotopes in the sample. 

S p · C abs (E) · B a 

N Y ield = 

· treal 1 e λ·t0 λ · t irr 

· · 

I γ · ε(E) · C g · C oi · C area t live m foil 1 − e −λ·t · 

(1) 

real 1 − e −λ·tirr 

Where S p is the peak area, C abs (E) the energy dependant self absoption correction, B a the beam correction, 

I γ the gamma line intensity per decay, ε(E) the energy dependant detector efficiency, C g the correction for 

efficiency change, C oi the correction for coincidences, C area the square-emitter correction, t real the measurement 

time on the detector, t live the live time of the detector, m foil the mass of the sample, λ the decay constant, t 0 

the time elapsed between end of irradiation and beginning of measurement and t irr the irradiation time. There 

are 5 main blocks to this formula, the first, 

S p · C abs (E) · B a 

I γ · ε(E) · C g · C oi · C area 

Consists of the measured peak area corrected by all the theoretical corrections listed above, the most important 

being the detector efficiency and the intensity per decay. The peak detector efficiency describes what ratio 

of counts are counted by the detector of all the counts that are irradiated in 4π steradians while the gamma line 

intensity per decay describes the probability of a given decay to ocurr. Given the type of detector being used 

the efficiency depends on the energy of the desired gamma line, the following figure models this relationship. 

Figure 1: Efficiency of detector with respect to energy (keV) at 7 cm from detector (geom7) 

Furtheremore the efficiency of the detector depends on the distance of the sample from the detector itself. 

Given that the sample irradiates in 4π steradians the closer the sample is to the detector, the detector covers a 

1 

greater solid angle. The relationship is shown bellow, where the efficiency is of the order of 

d 

, where d is the 

2 

distance to the detector. 

2

Figure 2: Efficiency of detector with respect to geometry (distance from detector in cm) at 484 keV 

The second block, 

t real 

t live 

Is the dead time correction. After each count detected by the detector there is a small time span where 

the detector recuperates and cannot register any counts. This ratio corrects for the missed counts due to this 

1 

phenomenon. The third 

m foil 

is simply a mass normalization. While the forth and fifth 

e λ·t0 

1 − e −λ·t real 

, 

λ · t irr 

1 − e −λ·tirr 

account for the decay of the analyzed isotopes due to time elapsed during cooling and measurement, and 

time elapsed durring irradiation respectively. When the yields for each measurement are calculated all the 

yields corresponding to one isotope must be the same regardless of the sample or measured gamma line. After 

grouping these yields the weighted average is calculated using the following formula. 

¯X = 

n∑ 

x i 

(∆x i) 2 

i=1 

(2) 

n∑ 

1 

(∆x i) 2 

i=1 

Where ¯X is the weited average, n is the number of measurements for gamma lines pertaining only to one 

isotope, x i the calculated yields, and ∆x i the uncentainties of these yields expressed as area error in the results. 

Once this has been calculated one can procede to calculate the uncertainty of this weighted average by means 

of formula 3. 

1 

∆X i = 

(3) 

n∑ 

√ 1 

(∆x i) 2 

Finally 

χ2 

n−1 

is calculated using equation 4. Evedently the closer the result is to 1, the more coherent the 

results. Therefore if this value deviates signicantly from 1, further procesing is required. This may include 

excluding outliers and applying other corrections. 

i=1 

χ 2 

n − 1 = 

n 

∑ 

i=1 

(x i− ¯X) 2 

(∆x i) 2 

n − 1 

(4) 

3

In this experiment two samples of Yttrium are irradiated along with two samples of Gold, the principal 

purpose of which is to analyze the spectra of Yttrium. However, the gold samples are imcluded as a reference 

to check for consistency with know values of the Gold cross-section. The following information concerns the 

irradiation period. 

Table 1: Irradiation data 

Start of Irradiation 3/22/13 22:12 

End of Irradiation 3/23/13 6:30 

Start Energy (MeV) 27.483 

End Energy (MeV) 27.158 

The masses of the Yttrium samples are as follows. 

m NY N1 = 1.8707g 

m NY O1 = 0.7580g 

Aditionally, the relevant gamma line information for the three Yttrium isotopes is presented bellow. 

Table 2: Gamma lines for 88 Y : 106.65 day half life 

Energy (keV) Intensity per decay (%) 

1836.063 12 99.2 3 

898.042 3 93.7 3 

2734.086 13 0.71 7 

850.647 24 0.065 13 

1382.406 26 0.021 6 

3218.48 4 0.007 2 

Table 3: Gamma lines for 87 Y : 79.8 hour half life 


388.531 3 82 

484.805 5 89.7 3 

Table 4: Gamma lines for 87m Y : 13.37 hour half life 


380.79 7 78 

Finally the relevant gamma line information for the four Gold isotopes is presented bellow. 

Table 5: Gamma lines for 196 Au: 6.183 day half life 


355.684 2 87 

332.983 24 22.9 5 

426.0 1 7 



411.80205 17 96 

675.8836 7 0.804 3 

4



98.85 5 10.9 5 

Table 8: Gamma lines for 194 Au: 38.02 hour half life 


328.455 11 61 3 

293.545 13 10.4 6 

2 Results 

Results are attached at the end. 

3 Analysis 

3.1 88 Y Isotope 

Table 9: Weighted average of yield of 88 Y in NYN1 and NYO1 samples 

χ 

Sample Yield Weighted Average Uncertainty 

n−1 

NYN1 1137.8 · 10 7 1.4 · 10 7 16.5 

NYO1 1442.8 · 10 7 2.1 · 10 7 15.2 

Figure 3: Yield of 88 Y with respect to sample number (ordered by geometry) in NYN1 (blue) and NYO1 (red) 

samples. Weighted average for each sample is provided with the respective color at the value especified on Table 

9. 

It is evident from figure 3 that there are corresponding clusters in both samples that separate from the rest of 

the data. To analyze these clusters, the different gamma lines must be distinguishable while still maintaining 

the same order as in figure 3. Additionaly the weighted average for each gamma line within each sample has 

been calculated bellow. 

5

Table 10: Weighted average of yield of 88 Y in NYN1 and NYO1 samples for diferent gamma lines 


χ 2 

n−1 

1836.036 keV NYN1 1092.1 · 10 7 2.8 · 10 7 15.2 

898.042 keV NYN1 1154.2 · 10 7 1.6 · 10 7 4.19 

1836.036 keV NYO1 1398.6 · 10 7 4 · 10 7 20.8 

898.042 keV NYO1 1465.0 · 10 7 2.5 · 10 7 1.80 

Evidently the weighted average is significantly lower for the 1836.036 keV gamma line than for the 898.042 

keV gamma line. This is exemplified in the following figure. 

Figure 4: Yield of 88 Y with respect to sample number (ordered by geometry) in NYN1 (bottom left cluster) 

and NYO1 (upper right cluster) samples. The yields of the 1836.036 keV (red) and 898.042 keV (blue) gamma 

lines are represented along with their corresponding whighted average for each sample which value is specified 

in Table 10. 

This is due to the separated clusters discussed earlier. Therefore, this is further analyzed by plotting the 

same data with enphasis on the 1836.036 keV gamma line, and its different measurent geometries (distances 

from the detector). 

6


and NYO1 (upper right cluster) samples. The yields of the 1836.036 keV gamma line are specified by geometry 

(in different colors) and all the yields for all geometries in 898.042 keV (light grey) gamma line are presented 

as reference. 

It is clear that the clusters consist of measurements pertaining from the same geometry only in the 1836.036 

keV gamma line. The most evident of these are geom17 and geom7 which significantly break off from the main 

set of data. This explains why 

χ2 

n−1 

is much smaller for the 898.042 keV gamma line than the 1836.036 keV 

gamma line. To resume, all this points to a miscallibration in the 1836.036 keV region. 

3.2 87 Y Isotope 


and NYO1 (upper right cluster) samples. 

7

Table 11: Weighted average of yield of 87 Y in NYN1 and NYO1 samples 

χ 


n−1 

NYN1 2122.3 · 10 6 1.4 · 10 6 69.2 

NYO1 2704.2 · 10 6 2.2 · 10 6 74.0 

Table 11 contains significantly high 

χ2 

n−1 

values which points to errors in the data, note that outliers have been 

removed. However, there is a tendancy in the yield data that cannot be appreciated in figure 6. By reorganizing 

the samples with respect to time elapsed from the end of irradiation to begining of measurement, that is from 

earliest measurement to latest, a clear trend can be observed in figure 7. 

Figure 7: Yield of 87 Y with respect to sample number (ordered by time elapsed from the end of irradiation 

to begining of measurement) in NYN1 (blue) and NYO1 (red) samples. Weighted average for each sample is 

provided with the respective color at the value especified on Table 11. 

The yield seems to increase and then stabalize. Figure 8 also depicts this, but yield is now ploted with 

respect to time, giving an acurate scale. 

8

Figure 8: Yield of 87 Y with respect to time elapsed from the end of irradiation to begining of measurement in 

NYN1 (blue) and NYO1 (red) samples. 

The conclusion is that a correction is clearly missing; just as if the correction for decay durring cooling and 

measurement was eliminated one can observe the yield decaying with respect to time. This is explained by the 

presence of the isotope 87m Y , analyzed in the following section. This isotope decays quickly in comparison to 

the 87 Y isotope. When it decays, however, it decays into the 87 Y isotope itself, originaly increasing the yield for 

said isotope. These values close to the end of irradiation must be eliminated (or corrected uppon), as in table 

13, to only analyze the yield when it stabalizes. Nevertheless, the weighted average of the yield was calculated 

separately for the different gamma lines to rule out any energy dependance as follows. 

Table 12: Weighted average of yield of 87 Y in NYN1 and NYO1 samples for diferent gamma lines 


χ 2 

n−1 

484.805 keV NYN1 2139.5 · 10 6 2.1 · 10 6 26.4 

388.531keV NYN1 2108.7 · 10 6 1.9 · 10 6 108 

484.805 keV NYO1 2734.1 · 10 6 3 · 10 6 48.0 

388.531keV NYO1 2680.5 · 10 6 3 · 10 6 97.5 

9

Figure 9: Yield of 87 Y with respect to sample number (ordered by time elapsed from the end of irradiation to 

begining of measurement) in NYN1 (bottom) and NYO1 (top) samples. The yields of the 1836.036 keV (red) 

and 898.042 keV (blue) gamma lines are represented along with their corresponding wheighted average for each 

sample which value is specified in Table 7. 

Since there is no significant deviation due to energy, the first 15 measurements are eliminated. 

Table 13: Weighted average of yield of 87 Y in NYN1 and NYO1 samples eliminating 15 first measurements 

(lowest t 0 ) for each sample 

χ 


n−1 

NYN1 2159.8 · 10 6 1.7 · 10 6 6.74 

NYO1 2806.5 · 10 6 3 · 10 6 4.99 

Concluding, the 

χ2 

n−1 

value is significantly lower when eliminating the uncorrected values, pointing towards 

a more coherent and consistent result. 

10

3.3 87m Y Isotope 

Figure 10: Yield of 87m Y with respect to sample number (ordered by geometry) in NYN1 (bottom left cluster) 

and NYO1 (upper right cluster) samples. 

Eliminating the two clear outliers in figure 10, the results are as follows. 

Table 14: Weighted average of yield of 87m Y in NYN1 and NYO1 samples 

χ 


n−1 

NYN1 1356.7 · 10 6 2.7 · 10 6 1.59 

NYO1 1761.8 · 10 6 4 · 10 6 0.870 

Figure 11: Yield of 87m Y with respect to sample number (ordered by geometry) in NYN1 (blue) and NYO1 

(red) samples. Weighted average for each sample is provided with the respective color at the value especified 

on Table 14. 

Again, the low 

χ2 

n−1 

value points towards a consistent result. 

11

3.4 Au Isotopes 

Table 15: Weighted average of yield of 196 Au in NAU1 and NAU2 samples 

χ 


n−1 

NAU1 818 · 10 7 1.1 · 10 7 19.2 

NAU2 191 · 10 7 4 · 10 7 32.8 

Figure 12: Yield of 196 Au with respect to sample number (ordered by geometry) in NAU1 (top left cluster) and 

NAU2 (lower right cluster) samples. 


χ 


n−1 

NAU1 2950 · 10 6 9 · 10 6 1.46 

NAU2 835 · 10 6 5 · 10 6 1.12 

12




χ 


n−1 

NAU1 608 · 10 7 5 · 10 7 1.32 

NAU2 221 · 10 7 3 · 10 7 0.602 




χ 


n−1 

NAU1 33.1 · 10 6 1.2 · 10 6 135 

NAU2 22.5 · 10 6 1.2 · 10 6 0.0111 

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4 Conclusions 

Besides a miscalibration in the detector in the 1836 keV region and a yet uncorrected increase in 87 Y yield 

due to 87m Y decay, the results are consistent both theoreticaly and experimentaly. This is shown by low 

uncertainties and low 

χ2 

n−1 

values. The yields for all the different yttrium and gold isotopes were calculated 

succesfuly. Nevertheless, the yield for both samples should be the same for the same Isotope; evidently this is 

not so. This difference is partly due to the placement of the samples themselves due to an intrinsic difference 

in their geometries. Their thickness is diffent, thus the approximation of taking the sample as a point source 

fails to some extent. Therefore further work must be done on this aspect to obtain one final coherent result for 

each Isotope, additionaly the correction must be introduced for the 87 Y isotope. 

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References 

[1] J. Frana, Deimos, NPI Rez, Czech Republic. 

[2] O. Svoboda, Experimental Study of Neutron Production and Transport for ADTT. (Czech Technical University 

in Prague, Prague, 2011). 

[3] P.Chudoba, Use of Activation Detectors for Neutron Field Measurement in Models of ADTS, (MFF UK 

Praha, 2013) 

[4] S.Y.F. Chu, L.P. Ekström, R.B. Firestone, Nuclear Data Search. 

(http://nucleardata.nuclear.lu.se/toi/index.asp, 1999). 

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Gamma Ray Spectra Analysis for Gold and Yttrium Samples

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