# Estimation of relative cross-sections from activation analysis

Department of Physics, Banaras Hindu University, Varanasi 221005

Prof. Maitreyee Saha Sarkar

Nuclear physics Divsion, Saha Institute of Nuclear Physics, Kolkata 700064

## Abstract

Activation Analysis is a method of identification and quantification of radionuclides formed by irradiating a sample by different charged and uncharged particles such as neutrons, protons, alpha particles etc. The charged particle's energy should be more than Coulomb barrier; however, reaction proceeds even if energy of the bombarding particle is less because of the quantum tunnelling. Charged particles like proton, deuteron, and tritium alpha are most favourable to be used in activation. In the present work, activities in a natural tin foil of thickness 20.385 mg/cm2 irradiated with alpha of beam energy 37 MeV have been analysed. At first I have calculated the energy loss of alpha particle passing through the foil using standard computer code SRIM. Cross-sections of different isotopes produced due to irradiation with alpha were calculated using standard statistical model code, PACE4. The product isotopes thus formed have half-lives of the order ranging from few seconds to several years. As the irradiation was done about 1.5 years ago, only those isotopes whose half-lives are around a year are considered for the study of remaining activity. Decay gamma spectroscopy with high resolution HPGe detector is done. For the energy calibration I have used the spectra of the radio isotopes like Cs-137, Co-60, and Am-241. Using Ba-133, Eu-152, I have determined the efficiency of the detector over a wide range of energy (from ~50-1450 keV). Presently I am analysing the gamma spectra obtained from irradiated foil to estimate the activities of the radioactive species. Later after correcting for the efficiency of the detector and considering the decay half-lives - the experimental yields of products will be determined and compared with theory.

Keywords: energy loss, statistical model, efficiency, detector, radioactive decay, gamma spectroscopy

## Abbreviations

Abbreviations
 CE conversion electron HPGe High Purity germanium Detector CPAA Charged Particle Activation Analysis

## INTRODUCTION

When an ion beam interacts with matter different types of reactions occur. The penetration of charged particles through matter is accompanied by various processes of interaction with atoms, electrons, nuclei. The nature and type of interaction depends upon the nature, energy and intensity of incident beam and the shape, size, state, nature and the composition of target material. On the basis of this principle different ion beam techniques are used for material characterization. Several such ion beam techniques are PIXE (Particle Induced X-ray Emission), RBS (Rutherford Back scattering spectroscopy) and nuclear reaction based Activation Analysis. Here using the technique of activation analysis the relative cross-sections for product isotopes of the alpha irradiated tin foil is estimated and is compared with the reported value.

## Activation Analysis

Activation analysis is a process of elementary analysis in which a stable nuclear isotope is made radioactive by irradiating it with a suitable beam of particles. In other words we can say that the qualitative and quantitative analysis of a material is done by using the method of induced radioactivity. Both charged and uncharged particles can be used in the process of activation analysis for irradiating a sample. Charged particles like Proton (1H+), Deuteron (2H+), Tritons(3H+), Helium-3 ions (2He3), Alpha particles(2He4) are used in this process. Uncharged particles like neutrons and photons are used.

NUCLEAR REACTION

Generally thermal neutrons are mostly used in the activation analysis because of several reasons like as neutrons are uncharged particles so they can penetrate deeply into a matter with least possibility of interaction and with negligible amount of energy loss. Another reason is that the higher cross section of n-gamma reaction in the target materials. The method is quite non-destructive because the materials are moderately radioactive. Small samples can also be analysed easily using this method. Along with many advantages there are also certain limitation such as for lower atomic number element it is not suitable because the cross section for the reaction is too low.

Net production rate of the radio active isotope is given by

$\phantom{\rule{0ex}{0ex}}\frac{d{N}_{{2}_{}}}{dt}=R-{N}_{{}^{2}}$λ

R= rate of production of that isotope

N2 λ =decay rate of the radio isotope

R=N1στ where σ=Reaction cross section τ=particle flux

## Charged Particle Activation

Charged particles like Proton (1H+), Deuteron (2H+), Tritons (3H+), Helium-3 ions (2He3), Alpha particles (24He) are used in this process. The charged particles unlike uncharged particles can not penetrate deeply into the matter. Because they carry charge they are stopped in certain thickness of the material. The range of the bombarding particle varies depending upon their charge. The range decreases with increasing the charge of the bombarding particle and increasing the atomic number of the target material. For heavy ions, the range varies as m/z2 , where m and z denotes the mass and charge of the bombarding ion beam respectively.

Due to the interaction of the ion beam with target material and the high kinetic energy of bombarding particles heat is produced in the target material. So in case of CPAA the target material used should be non volatile and should not be decomposed by heat. Preferably they should be good conductors of heat or metals. In the case of CPAA the energy of the bombarding ion beam should be more than that of coulomb barrier; however reactions also occur because of the quantum tunnelling effect.

## Target

Target selection is one of the most important factor in activation analysis. On the basis of thickness there are targets like thin target and thick target. Thick targets are those in which thee energy loss will be more as the charged particle enters into the target. In case of thin target the amount of energy loss of the ion beam through the target is negligible. So usually thin targets are mostly preferable. In order to avoid damage of the target material due to heat production targets should not be decomposed by the heat or in other words we can say the target should be a good conductors of heat or any cooling arrangement should be done in the case of CPAA.

## Statement of the Problems

• The method of Activation analysis is applied with remarkable success in finding the impurity amount in a material by forming radio isotope of that sample.
• This method is also used in the study of cross- sections of various product isotopes formed due to the nuclear reaction.
• In this context we are studying the relative cross sections of the products of alpha- induced activation process.
• The activation cross section data is to be estimated and to be compared with that of statistically obtained cross-section value.

## Objectives of the Research

• To learn about how energy loss of the charged particle occurs by passing through any thickness of the matter and to calculate the stopping power and energy loss.
• To learn about the use of statistical model of calculation for finding the cross-sections of various products obtained from a nuclear reaction.
• To analyse the experimentally obtained spectra through energy calibration, and to use in the detector efficiency determination.
• To learn about the calculation of internal conversion coefficients for different transitions.
• To study decay schemes of different product isotopes and different branching.
• To make corrections for intensity, half lives, branching ratio and finally to reach at our aim for finding the relative cross sections for different products.

## LITERATURE REVIEW

The application of charged particle activation analysis is found extensively in the field of nuclear research for studying the trace impurity amount in the sample material. This technique has also been extensively used in the nuclear astrophysics for study of stars.

For the systematic study of light ion induced nuclear reaction, platinum activation cross-sections for deuteron induced reaction were studied by F.Tarkanyi, S.Takacs. [1]

G.G Kiss, T.szucs, p.Mohr studied the α induced reaction on In-115 to test the applicability of α+nucleus optical model potential measurement of α radiative capture and α-induced reaction cross sections on the nucleus 115-In at low energy was studied. They measured the activation cross-section and measured the produced activities from the offline detection of gamma rays and x-rays the produced activities were also measured. The theoretical analysis was performed with the statistical model. [2]

A.Hermanne, F.Trakanyi made a comprehensive study on ion (p,d,alpha particles) induced reaction cross-section on natural Pd. The purpose for studying activation cross-section of ion induced reaction on natural Pd was to determine the behaviour of cross section in a systematic way and compare with that of model calculations.

## Concepts

The prime intention is to obtain the cross sections of various product resulting from the irradiation of the natural tin foil with the alpha particles. As the foil was irradiated about 1.5 years ago, we can understand about the remaining activity of various product of different isotopes of tin and the understanding about various low energy and high spin states in such nuclei will be achieved that will help us to develop a better idea about the decay scheme of such heavy nuclei.

## Experimental Setup

There is a natural tin foil of thickness 20.385 mg/cm2. The foil is irradiated with Alpha particles of beam energy 37 MeV. As the irradiation was done about 1.5 years ago, only those isotopes whose half-lives are around a year are considered for the study of remaining activity. Decay gamma spectroscopy with high resolution HPGe detector is done.

## Methods

• As natural tin foil was used, it contains various isotopes of tin in different abundancies. Using the data sheets of National Nuclear Data Centre, all possible isotopes of tin are listed out. Among them 116-120 isotopes are more abundant.
ISOTOPES OF TIN AND ABUNDANCIES
 ISOTOPES ABUNDANCY 112 0.97 114 0.66 115 0.34 116 14.54 117 7.68 118 24.22 119 8.59 120 32.58 122 4.63 124 5.79
• As the alpha particle passes through target material it loses some amount of its energy. Using the code SRIM the stopping power is determined. Then the energy loss of the alpha particle passing through that thickness of the Sn foil is determined.
• Energy loss of alpha = 2MeV
• As the nuclear reaction occurs, different product nuclei are formed in different cross-sections. Using the code PACE-4 (based on the statistical mode of calculation), different product nuclei and their cross-sections are determined for bombarding alpha particle energy 37 Mev and 35 MeV (after energy loss).
• FOR BEAM ENERGY=37 MeV BEAM ENERGY= 35MeV

•114-126 Te=88.179% 114-125 Te=89.6754 %

•114-122 Sb=5.839% 114-122 Sb= 4.387%

•111-123 Sn=4.776% 111-124 Sn=4.546%

• Out of these products some are stable and some are unstable having half life ranging from few minutes to several days. Isotopes like 114-Te, 117-Te, 114-Sb, 116-Sb have half life of few minutes only. Isotopes such as 116-Te, 119-Te, 117-Sb, 119-Sb have half life of 2-20 hours. Isotopes 118-Te, 120-Sb, 122-Sb have half life from 2-6 days. 121-Te and 111-Sn have half lives 19.17/164.2 days, 119 days respectively. 123-Te is a stable isotope but it has a meta-stable state at 247 KeV having half life of 119.2 days.
• The net abundancies for different product isotopes of Te of irradiated tin foil with alpha of beam energy 35Mev are found to be-
ABUNDANCY OF ISOTOPES OF Te CALCULATED FROM PACE4
 ISOTOPES NET ABUNDANCY HALF LIFE 114-Te 0.231 15.22 m 116-Te 0.367 2.49 h 117-Te 2.671 62m 118-Te 12.74 6d 119-Te 14.77 16 h 120-Te 15.35 stable 121-Te 26.089 19.17d(g.s)/164.2d(m.s) 122-Te 5.79 stable 123-Te,123m-Te 4.27 stable,119.2 days(m.s) 124-Te 0.31 stable 125-Te 5.44 stable 126-Te 0.151 Te=88.179%

• As in the experiment the irradiation was done about 1.5 years, so here the remaining activity of the isotopes like 121-Te, 123-Te should be found.
• Characterization of the detector used in the experiment is done using the spectrum of some standard radioactive sources. Using the spectra of 137-Cs, 60-Co, 241-Am the energy calibration is done because these sources emit one or two prominent gamma lines.
• For a precise cross-section measurement, the determination of the detector efficiency is very important. Using the spectra of 133-Ba and 152-Eu the efficiency of the detector is determined. Then the energy versus efficiency curve for 133-Ba is obtained and polynomial fitting is done. Normalising with it, the efficiency for Eu-152 is obtained. The normalised efficiency corresponding to a wide range of energy up to 1408 KeV is determined.
efficiency using 133-Ba
efficiency using152-Eu
Determination of efficiency of detector
fitting of energy vs efficiency curve for 133-Ba

NORMALISED EFFICIENCY CORRESPONDING TO DIFFERENT ENERGY
 ENERGY NORM.EFF 53.16 152440.92 80.8 161612.74 121.7 150418.929 160.6 118211.81 223.23 85906.07 244 63297.2438 276.3 63751.98 302.8 56895.08 344 50344.0377 356.01 47446.31 383.85 40746.03 411 38147.2695 443.9 37832.329 778.9 19806.1051 867.3 15395.5241 964 14885.1763 1112.07 13388.156 1212.9 11718.0028 1299.1 11910.6593 1408 10462.8713
• The decay channels of corresponding gamma transitions are as following.
ENERGY VS EFFICIENCY FITTED CURVE
• The experimentally obtained spectrum of irradiated tin foil is analyzed. The gamma lines obtained from the spectrum are- 159 KeV, 212 KeV, 507 KeV, 573 KeV, 1102 KeV lines.
• The decay channels and their half lives of corresponding gamma transitions are as following.
Experimentally obtained gamma transitions
 DECAY GAMMA ENERGY(KeV) HALF LIFE 123Te-123Te (IT DECAY=100%) 159 119.2 days 121Te-121Te (ITDECAY=88.6%) 212 164.2 days 121Te-121Sb (%∈+%β+=100%) 507, 573 19.7 days 121Te-121Sb (%∈+%β+=11.4%) 1102 164.2 days
DECAY SCHEME OF 121 Te

• The isotope 121-Te has an isomeric state of life time 164.2 days and the life time of it ground state is 19.7 days. There are three parallel ways of decay of 121-Te. About 11.4% of population of the isomeric state makes transition directly to some of the energy level of 121-Sb. Then it goes to ground state of 121-Sb by the 1102 Kev gamma line. The rest 88.6% makes transition to its ground state by subsequent 81 Kev and 212 KeV transition.
• Then from the ground state of 121-Te, it feeds the 507Kev and 573Kev level of 121-Sb. Then it comes to ground state through the transitions 507 KeV and 573 KeV.
• In case of 123-Te, there is an isomeric state of life time 119 days. From the isomeric state it comes to the ground state by IT decay =100%, through two subsequent transitions 88 keV and 159 KeV.
DECAY SCHEME OF 123-Te WITH 159 KeV GAMMA LINE
• In the spectra of irradiated tin foil we are able to observe all these transitions except the 81KeV of 121-Te and 88 KeV line of 123-Te. This is because the higher spin states are involved in these two transitions so, these transitions are M4 transitions and are highly converted transitions. The conversion co-efficients for these two transitions are calculated using BRICC code.
• The conversion coefficient for 81 KeV transition = 1735.
• The conversion coefficient for 88 KeV transition =1122.
• The conversion coefficient and energy for conversion electron is found out for electrons in different shells for the two transitions 81 KeV and 88 KeV in 121-Te and 123-Te.
FOR 81 KeV
 SHELL E(ce) (KeV) M4 K 49.97 677 L 77.23 820 M 80.91 197
FOR 88 KeV
 SHELL E(ce)(KeV) M4 K 56.65 481 L 83.89 498 M 87.58 118.4
• The correction for efficiency corresponding to these energy values are done then correction for intensity is done.
Corrected efficiency and area correpoing to the transitions
 Decay Energy (kev) Efficiency Area Area corrected with efficiency 123Te-123Te 159 115891.4117 60947 0.52589747 121Te-121Te 212 84861.5125 444394 5.23669667 121 te-121sb 507 30614.53975 32181 1.0511672 121 te-121sb 573 26511.01062 132260 4.98887055 121Te-121sb 1102 13133.4565 1810 0.13781597
• We need to know how much isomeric state is populated as compared to the ground state therefore we studied the in beam decay scheme of 121-Te using heavy ions. Because in case of using heavy ions, the higher spin states are populated. The in beam level scheme ​F. Stary, 1979​ of 121-Te [5] from the reaction 119-Sn(α,2nγ)121-Te is shown below-
LEVEL SCHEME OF 121-Te FROM IN-BEAM EXPERIMENT

From the level scheme it can be seen that there are several transitions going to ground state directly(indicated by yellow arrow). There are also some transitions going to the isomeric state(293KeV) (indicated by blue arrow) and from the isomeric state it goes to ground state by two successive transitions 81 KeV and 212 KeV respectively. The correction for branching ratio and intensity is done. The net intensity of all the transitions feeding the ground state is 157.2 and the net intensity of all the transitions feeding the isomeric state is 289.3.

As the level scheme is obtained from the in beam experiment, considering the duration of experiment to be 5 days and correcting it with the half life, the decayed amount is estimated. It was nearly 6. As from the isomeric state there are two parallel branches of decay i.e 88.6% goes to ground state through the IT decay and rest 11.4% goes to different states of 121-Sb by EC and β+ decay. Then correcting for branching ratio it is found that out of 6, 5 decays through the IT decay to the ground state and rest one decays through EC and β+ decay. Including that 5 within the intensity 157.2 the correction for intensity is being made.

Ground state population=157 Isomeric state population=289 Isomer decaying=6 (5 decays by IT decay and 1 by EC and β+ decay) Isomer remaining=283 So, this ground state population contains that 5. The estimation in our data for the population for 121-Te represents that 284 (283+1) but that is not the total population for 121-Te. Hence population of 121-Te = $\frac{corrected\;intensity}{284}\times\left(284+157\right)$

For the transitions 212 KeV and 1102 KeV and 159 KeV the net intensity (Iγ+ce) is given in the decay scheme shown in figure-6 . Correcting for their conversion coefficient the intensity for the gamma transition is determined.

For 212KeV transition 82.03%=5.23 so, 100%=6.3 For 1102 KeV transition 2.5%=0.13

so, 100%=5.2

These two numbers should be equal. But as there are some errors in the area for the gamma lines and the error in the efficiency due to the standard error associated with the coefficients in the 4th order polynomial fit for the energy versus efficiency curve so these numbers are not exactly equal. On average it is taken as 6. Then the initial population is calculated as

N=$\frac{{N}_{0}}{{2}^{n}}$,where n= no. of half lives= $\frac{t}{{t}_{1/2}}$ , t= 1.5 years or 550 days N0=N.${2}^{n}$and n= 550/164= 3.35

N0=6×23.5=67.8

correcting for intensity, N0 = $\frac{67.8}{284}\times\left(284+157\right)=105.2$

Total population for 121-Te produced initially=105.2

Similarly in the case of 123-Te the initial population is found out as here t1/2= 119.2 days and N=24.42 so, N0=14.8

Here no correction for intensity is needed because no such branching occurs in the 123-Te (%IT decay=100). Hence total population for 123-Te produced initially=14.8

The ratio of initial population of 121-Te to that of 123-Te = $\frac{105.2}{14.8}=7.1$

## RESULTS AND DISCUSSION

• The relative cross-section for the product 121-Te and 123-Te found from the analysis of the experimental data =7.1
• The relative cross-section for the product 121-Te and 123-Te found from the statistical model calculation using the code PACE4 =$\frac{26.089}{4.27}=6.1$
• The relative cross section values obtained from statistical code and from experimental data are in agreement with each other.
• The PACE4 value can be improved by considering all the 121-Te and 123-Te product isotopes. In my calculation I have considered only the more abundant product values.
• From the analysis of experimental data the value obtained is not so accurate because there are different types of errors involved in various steps of measurement. There is error in the determination of area and also in the fitting of energy versus efficiency curve there are errors in the coefficients of the 4th order polynomial fitted.
• The intensity values obtained from the data sheets and the decay scheme also have some uncertainty, which have not been taken into account.
• The corrections for the 507 Kev and 573KeV transitions are not considered here. It needs to be corrected firstly for the half life of the ground state of 121-Te (19.7 days) then to be corrected for branching ratio.

## CONCLUSION AND RECOMMENDATIONS

• The estimation of relative cross-section of products are performed using activation analysis.
• The result is found to be in agreement with the result of statistical model calculation to a good extent. But the results are not exactly equal due to different experimental and calculation error.
• The correction for the gamma lines 507 KeV and 573 KeV has not been done yet. This will require further modification because of the long lived ground state(19.7days) of 121-Te.

## REFERENCES

• Tárkányi, F., Takács, S., Ditrói, F., Hermanne, A., Shubin, Y.N. and Dityuk, A.I., 2004. Activation cross-sections of deuteron induced reactions on platinum.Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms,226(4), pp.490-498.
• Kiss, G.G., Szücs, T., Mohr, P., Török, Z., Huszánk, R., Gyürky, G. and Fülöp, Z., 2018. α-induced reactions on In 115: Cross section measurements and statistical model analysis.Physical Review C,97(5), p.055803.
• National Nuclear Data Centre, ENSDF data sheets. https://www.nndc.bnl.gov/​
• SRIM http://www.srim.org/SRIM/SRIMLEGL.htm​
• PACE 4 http://lise.nscl.msu.edu/pace4.html​
• Hagemann, U., Keller, H.J., Protochristow, C. and Stary, F., 1979. Collective excitations in the117, 119, 121Te nuclei.Nuclear Physics A,329(1-2), pp.157-191.
• Koch, R.C., 1958.Activation Analysis Handbook(No. AFCRC-TR-59-139; AD-214941). Nuclear Science and Engineering Corp., Pittsburgh.
• Tilbury, R.S., 1966.Activation analysis with charged particles(No. NAS-NS-3110). Union Carbide Corp., Tuxedo, NY Mining and Metals Div..T
• Meyer, R.A., Lanier, R.G. and Larsen, J.T., 1975. Two-particle, one-hole states in antimony nuclei and the decay of Te m, g 121.Physical Review C,12(6), p.2010.
• E.A.Schweikert, Analytical chemistry, Vol. 52, No. 7, June 1980, Center for Trace Characterization, Dept. Of Chemistry, Texas A & M university.

## ACKNOWLEDGEMENTS

• I would like to thank prof. Maitreyee Saha Sarkar for her continuous guidance. Being my 1st summer project I had a lot of things to learn. The knowledge and experience I learned here is matchless. I owe my heartfelt gratitude to her.
• I am thankful to Dr. Indrani Ray for her guidance and help during my project work.
• I also convey my sincere thanks to Dr.Dipayan chattopadhyaya and Sangeeta Das for their help.
• I am thankful to IAS-INSA-NASI for giving me such an opportunity for doing the summer project and their support throughout the programme.
• I thank to SAHA INSTITUTE OF NUCLEAR PHYSICS, KOLKATA for making it whole a great learning experience.

#### References

• U. Hagemann, H.-J. Keller, Ch. Protochristow, F. Stary, 1979, Collective excitations in the117, 119, 121Te nuclei, Nuclear Physics A, vol. 329, no. 1-2, pp. 157-191

More
Written, reviewed, revised, proofed and published with