gamma ray spectra analysis for gold and yttrium...

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 88Y , 87Y , and 87mY isotopes in twoirradiated yttrium samples with the final purpose of calculating their cross-sections. This is done by carefullyanalizing the spectras of each sample using DEIMOS software, resulting in a series of peak areas which thenare corrected uppon to calculate the yield for each gamma line in a measurement.

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1 Brief theoretical backgroundGamma 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. Theprincipal mechanisms in which gamma rays interact with a detector are the photoelectric effect, the comptoneffect and pair production. As an atomic nucleus decays gamma ray’s of specific energies are emmited andproceed to interact with the detector. This interaction is then registered and analysed to determine the energyof the incoming gamma rays. The collection of this data (which forms peaks at certain energies) is calleda gamma spectrum, with the individual peaks being called gamma lines. In this analysis the gamma rayspectrum is analyzed by means of DEIMOS sofware to provide the energies of the registered gamma lines andtheir respective peak areas. With this data the following equation is used to find the yield for the differentisotopes in the sample.

NY ield =Sp · Cabs(E) ·Ba

Iγ · ε(E) · Cg · Coi · Carea· trealtlive

· 1

mfoil· eλ·t0

1 − e−λ·treal· λ · tirr

1 − e−λ·tirr(1)

Where Sp is the peak area, Cabs(E) the energy dependant self absoption correction, Ba the beam correction,Iγ the gamma line intensity per decay, ε(E) the energy dependant detector efficiency, Cg the correction forefficiency change, Coi the correction for coincidences, Carea the square-emitter correction, treal the measurementtime on the detector, tlivethe live time of the detector, mfoil the mass of the sample, λ the decay constant, t0the time elapsed between end of irradiation and beginning of measurement and tirr the irradiation time. Thereare 5 main blocks to this formula, the first,

Sp · Cabs(E) ·BaIγ · ε(E) · Cg · Coi · Carea

Consists of the measured peak area corrected by all the theoretical corrections listed above, the most impor-tant being the detector efficiency and the intensity per decay. The peak detector efficiency describes what ratioof counts are counted by the detector of all the counts that are irradiated in 4π steradians while the gamma lineintensity per decay describes the probability of a given decay to ocurr. Given the type of detector being usedthe 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 agreater solid angle. The relationship is shown bellow, where the efficiency is of the order of 1

d2 , where d is thedistance to the detector.

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

The second block,

trealtlive

Is the dead time correction. After each count detected by the detector there is a small time span wherethe detector recuperates and cannot register any counts. This ratio corrects for the missed counts due to thisphenomenon. The third 1

mfoilis simply a mass normalization. While the forth and fifth

eλ·t0

1 − e−λ·treal,

λ · tirr1 − e−λ·tirr

account for the decay of the analyzed isotopes due to time elapsed during cooling and measurement, andtime elapsed durring irradiation respectively. When the yields for each measurement are calculated all theyields corresponding to one isotope must be the same regardless of the sample or measured gamma line. Aftergrouping these yields the weighted average is calculated using the following formula.

X̄ =

n∑i=1

xi

(∆xi)2

n∑i=1

1(∆xi)

2

(2)

Where X̄ is the weited average, n is the number of measurements for gamma lines pertaining only to oneisotope, xi the calculated yields, and ∆xi 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 meansof formula 3.

∆Xi =

√√√√√√1

n∑i=1

1(∆xi)

2

(3)

Finally χ2

n−1 is calculated using equation 4. Evedently the closer the result is to 1, the more coherent theresults. Therefore if this value deviates signicantly from 1, further procesing is required. This may includeexcluding outliers and applying other corrections.

χ2

n− 1=

n∑i=1

(xi−X̄)2

(∆xi)2

n− 1(4)

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In this experiment two samples of Yttrium are irradiated along with two samples of Gold, the principalpurpose of which is to analyze the spectra of Yttrium. However, the gold samples are imcluded as a referenceto check for consistency with know values of the Gold cross-section. The following information concerns theirradiation period.

Table 1: Irradiation dataStart of Irradiation 3/22/13 22:12End of Irradiation 3/23/13 6:30

Start Energy (MeV) 27.483End Energy (MeV) 27.158

The masses of the Yttrium samples are as follows.

mNYN1 = 1.8707g

mNYO1 = 0.7580g

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

Table 2: Gamma lines for 88Y : 106.65 day half lifeEnergy (keV) Intensity per decay (%)1836.063 12 99.2 3898.042 3 93.7 32734.086 13 0.71 7850.647 24 0.065 131382.406 26 0.021 63218.48 4 0.007 2

Table 3: Gamma lines for 87Y : 79.8 hour half lifeEnergy (keV) Intensity per decay (%)388.531 3 82484.805 5 89.7 3

Table 4: Gamma lines for 87mY : 13.37 hour half lifeEnergy (keV) Intensity per decay (%)

380.79 7 78

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

Table 5: Gamma lines for 196Au: 6.183 day half lifeEnergy (keV) Intensity per decay (%)355.684 2 87332.983 24 22.9 5426.0 1 7

Table 6: Gamma lines for 198Au: 2.695 day half lifeEnergy (keV) Intensity per decay (%)411.80205 17 96675.8836 7 0.804 3

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Table 7: Gamma lines for 195Au: 186.09 day half lifeEnergy (keV) Intensity per decay (%)

98.85 5 10.9 5

Table 8: Gamma lines for 194Au: 38.02 hour half lifeEnergy (keV) Intensity per decay (%)328.455 11 61 3293.545 13 10.4 6

2 ResultsResults are attached at the end.

3 Analysis

3.1 88Y Isotope

Table 9: Weighted average of yield of 88Y in NYN1 and NYO1 samplesSample Yield Weighted Average Uncertainty χ2

n−1

NYN1 1137.8 · 107 1.4 · 107 16.5NYO1 1442.8 · 107 2.1 · 107 15.2

Figure 3: Yield of 88Y 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 Table9.

It is evident from figure 3 that there are corresponding clusters in both samples that separate from the rest ofthe data. To analyze these clusters, the different gamma lines must be distinguishable while still maintainingthe same order as in figure 3. Additionaly the weighted average for each gamma line within each sample hasbeen calculated bellow.

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Table 10: Weighted average of yield of 88Y in NYN1 and NYO1 samples for diferent gamma linesSample Yield Weighted Average Uncertainty χ2

n−1

1836.036 keV NYN1 1092.1 · 107 2.8 · 107 15.2898.042 keV NYN1 1154.2 · 107 1.6 · 107 4.191836.036 keV NYO1 1398.6 · 107 4 · 107 20.8898.042 keV NYO1 1465.0 · 107 2.5 · 107 1.80

Evidently the weighted average is significantly lower for the 1836.036 keV gamma line than for the 898.042keV gamma line. This is exemplified in the following figure.

Figure 4: Yield of 88Y 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) gammalines are represented along with their corresponding whighted average for each sample which value is specifiedin Table 10.

This is due to the separated clusters discussed earlier. Therefore, this is further analyzed by plotting thesame data with enphasis on the 1836.036 keV gamma line, and its different measurent geometries (distancesfrom the detector).

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Figure 5: Yield of 88Y 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 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 presentedas reference.

It is clear that the clusters consist of measurements pertaining from the same geometry only in the 1836.036keV gamma line. The most evident of these are geom17 and geom7 which significantly break off from the mainset of data. This explains why χ2

n−1 is much smaller for the 898.042 keV gamma line than the 1836.036 keVgamma line. To resume, all this points to a miscallibration in the 1836.036 keV region.

3.2 87Y Isotope

Figure 6: Yield of 87Y with respect to sample number (ordered by geometry) in NYN1 (bottom left cluster)and NYO1 (upper right cluster) samples.

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Table 11: Weighted average of yield of 87Y in NYN1 and NYO1 samplesSample Yield Weighted Average Uncertainty χ2

n−1

NYN1 2122.3 · 106 1.4 · 106 69.2NYO1 2704.2 · 106 2.2 · 106 74.0

Table 11 contains significantly high χ2

n−1 values which points to errors in the data, note that outliers have beenremoved. However, there is a tendancy in the yield data that cannot be appreciated in figure 6. By reorganizingthe samples with respect to time elapsed from the end of irradiation to begining of measurement, that is fromearliest measurement to latest, a clear trend can be observed in figure 7.

Figure 7: Yield of 87Y with respect to sample number (ordered by time elapsed from the end of irradiationto begining of measurement) in NYN1 (blue) and NYO1 (red) samples. Weighted average for each sample isprovided 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 withrespect to time, giving an acurate scale.

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Figure 8: Yield of 87Y with respect to time elapsed from the end of irradiation to begining of measurement inNYN1 (blue) and NYO1 (red) samples.

The conclusion is that a correction is clearly missing; just as if the correction for decay durring cooling andmeasurement was eliminated one can observe the yield decaying with respect to time. This is explained by thepresence of the isotope 87mY , analyzed in the following section. This isotope decays quickly in comparison tothe 87Y isotope. When it decays, however, it decays into the 87Y isotope itself, originaly increasing the yield forsaid isotope. These values close to the end of irradiation must be eliminated (or corrected uppon), as in table13, to only analyze the yield when it stabalizes. Nevertheless, the weighted average of the yield was calculatedseparately for the different gamma lines to rule out any energy dependance as follows.

Table 12: Weighted average of yield of 87Y in NYN1 and NYO1 samples for diferent gamma linesSample Yield Weighted Average Uncertainty χ2

n−1

484.805 keV NYN1 2139.5 · 106 2.1 · 106 26.4388.531keV NYN1 2108.7 · 106 1.9 · 106 108484.805 keV NYO1 2734.1 · 106 3 · 106 48.0388.531keV NYO1 2680.5 · 106 3 · 106 97.5

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Figure 9: Yield of 87Y with respect to sample number (ordered by time elapsed from the end of irradiation tobegining 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 eachsample 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 87Y in NYN1 and NYO1 samples eliminating 15 first measurements(lowest t0) for each sample

Sample Yield Weighted Average Uncertainty χ2

n−1

NYN1 2159.8 · 106 1.7 · 106 6.74NYO1 2806.5 · 106 3 · 106 4.99

Concluding, the χ2

n−1 value is significantly lower when eliminating the uncorrected values, pointing towardsa more coherent and consistent result.

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3.3 87mY Isotope

Figure 10: Yield of 87mY 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 87mY in NYN1 and NYO1 samplesSample Yield Weighted Average Uncertainty χ2

n−1

NYN1 1356.7 · 106 2.7 · 106 1.59NYO1 1761.8 · 106 4 · 106 0.870

Figure 11: Yield of 87mY 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 especifiedon Table 14.

Again, the low χ2

n−1 value points towards a consistent result.

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3.4 Au Isotopes

Table 15: Weighted average of yield of 196Au in NAU1 and NAU2 samplesSample Yield Weighted Average Uncertainty χ2

n−1

NAU1 818 · 107 1.1 · 107 19.2NAU2 191 · 107 4 · 107 32.8

Figure 12: Yield of 196Au with respect to sample number (ordered by geometry) in NAU1 (top left cluster) andNAU2 (lower right cluster) samples.


n−1

NAU1 2950 · 106 9 · 106 1.46NAU2 835 · 106 5 · 106 1.12

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n−1

NAU1 608 · 107 5 · 107 1.32NAU2 221 · 107 3 · 107 0.602



n−1

NAU1 33.1 · 106 1.2 · 106 135NAU2 22.5 · 106 1.2 · 106 0.0111

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4 ConclusionsBesides a miscalibration in the detector in the 1836 keV region and a yet uncorrected increase in 87Y yielddue to 87mY decay, the results are consistent both theoreticaly and experimentaly. This is shown by lowuncertainties and low χ2

n−1 values. The yields for all the different yttrium and gold isotopes were calculatedsuccesfuly. Nevertheless, the yield for both samples should be the same for the same Isotope; evidently this isnot so. This difference is partly due to the placement of the samples themselves due to an intrinsic differencein their geometries. Their thickness is diffent, thus the approximation of taking the sample as a point sourcefails to some extent. Therefore further work must be done on this aspect to obtain one final coherent result foreach Isotope, additionaly the correction must be introduced for the 87Y 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 Uni-versity in Prague, Prague, 2011).

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

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