Neutron Capture Cross Sections of Selenium Isotopes

Home , Isotopes of selenium, Neutron capture, Neutron cross section

Howard D. Dearmon

Department of Physics

Oregon State University

1 Oct 2018

Advised by Dr. Kenneth Krane

In partial fulfillment of the requirements of PH403

Table of contents

Abstract ...... 1

Introduction ...... 2

Theory ...... 5

Methods ...... 10

Results ...... 18

Conclusion ...... 20

References ...... 21

Acknowledgements ...... 22

Abstract

The thermal cross sections and resonance integrals for neutron capture by 74,78,80,82Se were measured using the same procedure and equipment for all of the isotopes. Uncertainty and absence of accurate previous values for several isotopes introduces a need of measuring these parameters using similar techniques. This was done using OSU’s TRIGA reactor and four of its facilities: the fast pneumatic transfer facility, cadmium-lined in-core irradiation tube, G-ring in- core irradiation tube, and thermal column. These new measurements are made using high resolution detectors, improved parameter values and more consistent methods for each isotope, yielding more precise values than were made in past experiments.

Introduction

In the neutron capture nuclear reaction, a neutron collides with an atomic nucleus, which either absorbs the neutron to form a heavier nucleus or scatters it away. The neutron capture cross section is defined as the probability that the nucleus of an atom will absorb a neutron incident upon it. This probability is expressed as an area and measured in units of barns (10-28 m2). Since neutrons carry no electric charge, they are more easily able to penetrate an atom’s nucleus than other charged particles. This absorption, being dependent on the neutron’s energy, occurs in stars and nuclear reactors. The capture cross sections are further divided into two measures, which are the effective cross-sections for the nucleus at different neutron energies; the thermal neutron capture cross section (σ) for the lower energy thermal neutrons , and the resonance integral (I) for higher energy neutrons. This resonance integral consists of summing up all the contribution of absorption peaks at specific neutron energies for a particular atom.

Accurate measurements of neutron capture cross sections for different elements are crucial for applications such as neutron activation analysis, where the elements in a material capture neutrons and change to radioactive isotopes of that element and can be used to find the composition of bulk materials. This technique is used to measure the amount of selenium in things like crops and cereals due to its importance for a healthy immune system and protection against certain diseases and cancers [1].

In this series of experiments the neutron capture cross-section (NCCS) for the selenium isotopes 74,78,80,82Se, which are irradiated to produce the

2 radioactive isotopes 75,79m,81g,81m,83gSe, are measured. A list of the different isotope reactions is found in the following theory section. The neutron capture cross section of these selenium isotopes has been measured irregularly [2]; measurements for certain isotopes vary significantly from experimenter to experimenter and in some cases there is only one measurement or none. Even the values that appear accurate due to agreement with others were in some cases taken over 35 years ago and can be improved using current technology like improved high resolution solid-state Ge detectors and more accurate values of parameters like half-lives and isotope abundances. Past measurements studied only a couple of the isotopes at a time, making comparisons of their results with others less reliable than doing all 7 of them with the same sample and methods. It is with this reasoning that determining the NCCS for most of the selenium isotopes using the same procedure and technique at the same time is necessary to ensure accurate values.

Several isotopes of selenium have metastable states; these metastable states are excited states that, due to greater spin difference between the metastable state and the ground state, are occupied for far longer than other excited states. This occupation time is on the order of minutes for 79m,81mSe, whereas regular excited states are occupied for around 1-10 ns [3]. These metastable states then decay and are fed back into the ground state, which increases the difficulty of finding the number of atoms in the ground state. The correction and its theory are explained in the following theory section. With this correction, the cross-section of isotopes like the 81gSe decay can be found instead of just the ratio of metastable state cross-section to the ground state cross- section.

To find the values of σ and I of the selenium isotopes several samples of selenium oxide containing the isotopes were irradiated by the OSU TRIGA reactor using the facilities described in the methods section. 198Au, 97,95Zr and 60Co samples were also irradiated along with the selenium. Since the cross-sections and resonance integrals of these elements are well known they can be used to determine the thermal flux and epithermal flux used to find the cross-sections and resonance integrals of the selenium isotopes; these fluxes will be explained in more detail in the following sections. Next the irradiated samples were put in front of the germanium detectors and the specific gamma-rays of each isotope are counted using a multi-channel analyzer computer program called MAESTRO. The activity is then calculated and used to find the cross-sections and resonance integrals; this is described in more detail in the theory and method sections.

Theory

To find the cross-sections and resonance integrals for each of the selenium isotopes an indirect approach is used, as they are not quantities that can be directly measured. One parameter that can be used is the activity of each selenium sample. This can be measured using a high-resolution Ge detector to measure the gamma rays emitted from the radioactive isotope. This process is shown in Figure 1.

Figure 1: Decay process for neutron capture

When an isotope is bombarded by neutrons with a high enough energy, its nucleus can sometimes capture this neutron and change into a new nucleus. This new isotope is in an unstable state and will release its extra energy to get to a more stable lower energy state. It does this by emitting high energy gamma rays while inside the reactor, bringing it down to what is known as a “metastable” state. This state, while above the ground state, is lower in energy than the initial higher energy resonance state from before and longer lasting as well. Finally the isotope transitions to the ground state by emitting more gamma rays; it is these gamma rays that are measured and used for calculating the neutron capture cross sections.

Sometimes, instead of a metastable state, the isotope transitions to a radioactive ground state that beta decays into a daughter element like bromine or krypton. After this beta decay occurs the new element is in an excited state that decays to the ground state; the gamma rays it emits in this process are also measured.

There are two parts that make up the total neutron capture cross section: the thermal neutron cross section, which is the cross section of the isotope when it absorbs a low energy neutron in the thermal temperature range, and the resonance integral, which is the sum of multiple resonance peaks due to the isotopes interaction with epithermal neutrons. Higher energy neutron interactions are neglected due to the probability of interactions being minuscule. Figure 2 illustrates the different areas of cross sections we look at.

Figure 2: Cross section of 74Se with respect to energy.

The thermal cross section (below 1 eV) depends on the inverse velocity of the neutron 1/v, making it easier to calculate without having to integrate the many resonances like in the epithermal neutron range. We call this value the thermal cross section σ. The individual resonance peaks in the epithermal range can’t be individually isolated so they are summed up into an integral we call the resonance integral Ӏ.

Since the neutron capture cross section can’t be directly measured we need to calculate it using certain equations and other parameters that can be directly

7 measured, mainly the thermal and epithermal fluxes. We begin by using the activity equation:

-λt Activity=N0(σфth + Iфepi)(1-e ) (2.1)

Here N0 is the number of atoms that is initially present in the sample material, фth is the thermal flux, фep is the epithermal flux and λ is the exponential decay constant. Neutron flux is defined as the amount of neutrons passing through a square centimeter area per second, usually measured in units of cm-2s-1. We take these measurements in three different types of locations inside the reactor: The Thermal Column where most of the neutrons captured are in the thermal energy range, the Cadmium Lined In-Core Irradiation Tube (CLICIT) where most of the neutrons captured are in the epithermal (medium) energy range and the G-Ring In-Core Irradiation Tube (GRICIT) and fast pneumatic transfer system (rabbit) with a mixture of thermal and epithermal neutrons. Each is used because neutrons in certain energy ranges are more prevalent in different facilities, making it possible to neglect other neutrons due to the small amount present. These fluxes, when each multiplied by the thermal cross-section and the resonance integral respectively, can be used with the number of gamma-ray counts to find the activity of the irradiated Se sample. We then can neglect the thermal or the epithermal flux, depending on the irradiation process and solve for either the resonance integral I or thermal cross section σ respectively.

The activity can also be calculated using the following equation:

Activity=Ncount/bεt (2.2)

Where Ncount is the number of times we count a gamma ray at a specific energy, b is the branching ratio (ratio of an atoms which decay by a single decay mode and the total atoms which decay), ε is the detector efficiency and t is the counting time.

Methods

1. Detector efficiency

Before any data is taken the efficiency of the detectors needed to be determined. This efficiency is the probability that an emitted gamma ray will interact with the detector and produce a count. The detectors are cylinder- shaped and contain a germanium diode of high purity cooled with liquid nitrogen to reduce thermal excitations and electrical noise so that only the gamma rays are being detected. Figures 3 and 4 show some pictures of the germanium detectors used in the lab.

Figure 3: High resolution single crystal Ge detector with shielding

Figure 4: Expanded view of lab

To calculate the efficiency of the radiation detectors the formula,

N=abεt (3.1)

Is used, where N is the number of counts at a particular energy, a is the activity (number of decays per second) of our test sample, b is the branching ratio of the isotope, ε is the efficiency of the detector and t is the time interval of the counting. First we purchased some pre-irradiated test samples of 133Ba and 152Eu and measured the number of counts from all the low- and high-energy gamma rays at 10, 15 and 20 cm. This was done in order to minimize the efficiency uncertainty since the isotope activity is well documented and the counts (# of γ-rays) can then be compared to the expected number of counts. The program MAESTRO was used to analyze and record the gamma rays net

11 counts and uncertainty in the counts due to the dead time (period of inactivity due to γ-ray analysis) in the detector.

Next we found the activity of the calibration sources by using the familiar exponential decay formula

− ln 2∗푡 푎 = 푎0푒 퐻 (3.2)

Where a0 is the initial activity, H is the half-life, -ln 2/H is the decay constant and t is the time elapsed since the initial calibration of the source. The initial activity was known and half-lives were found by looking in an isotope data sheet compiled at several reputable facilities [4]. The branching ratios were also found in the same compilation and used in our efficiency calculations.

After calculating the detector efficiency for each of the three detectors used for each of the test isotopes a data plot was created in Excel showing the various efficiencies for each of the energies. Next a function was fitted to our data to model the efficiency for our selenium isotopes. It was found that by using a logarithmic scale a fairly linear fit could be used for the efficiency in the high energy gamma ray range, with it being

d eff = cEn , ln 푒푓푓 = ln 푐 + 푑 ln 퐸푛 (3.3) Where c is some coefficient needed for the fit, n being the subscript for the isotope being used and d is some power needed for the fit. The low energy calculation involved using both the 152Eu and 133Ba as activity sources and used a 6th degree polynomial fit shown in figure 5a. Figure 5b shows a graph of the high energy detector efficiency for only the 152Eu for the first detector at different distances as a function of energy.

Low Energy Efficiency Calibration at 20cm -4 3 3.5 4 4.5 5 5.5 6 6.5 -4.5 -5

-5.5 y = 0.0501x6 - 1.3164x5 + 13.509x4 - 65.519x3 + 131.44x2 + 19.674x - 312.33 -6 -6.5

Efficiency -7 -7.5 -8 -8.5 -9 Energy (keV)

Figure 5a: Detector efficiency for low energy gamma rays.

High Energy Efficiency Calibration at 20 cm -6.6 6 6.2 6.4 6.6 6.8 7 7.2 7.4 -6.7 -6.8 -6.9 -7 y = -0.7368x - 2.1697 -7.1

Efficiency -7.2 -7.3 -7.4 -7.5 -7.6 Energy (keV)

Figure 5b: Detector efficiency for high energy gamma rays.

2. Sample irradiation

The Se sample, containing a mixture of Se-74, Se-76, Se-78, Se-80 and Se- 82, was irradiated in the Oregon State TRIGA reactor. The samples were irradiated in three different facilities: a fast pneumatic transfer facility (“rabbit”), a cadmium-lined in-core irradiation tube (CLICIT), and a thermal column (TC) located near the core. We also used the G-ring in-core irradiation tube (GRICIT) for isotopes with longer half-lives.

Below is a picture of the reactor core used in the experiments. The Rabbit and CLICIT tubes are in the center, with the GRICIT tube in the ring on the outside. The TC is a couple of meters away and not shown in the picture. The blue glow is due to the Cherenkov radiation, which is caused by charged particles moving through a dielectric (in this case the reactor coolant) faster than the light travelling through it [5].

Figure 6: Picture of reactor core

The irradiation process started with preparing the Se samples; this consisted of measuring out pieces of the sample to be used for each of the irradiation facilities as well as the Au and Co alloys used in the flux monitors and wrapping each in Al foil. The samples were then inserted into a plastic tube to contain them in a specific spot so as to not have the neutron flux vary on the sample. Next was having the facilities irradiate the sample and transfer it to the rabbit lab; 10 minutes for the Rabbit irradiation, an hour for the CLICIT and GRICIT and 2 hours for the TC. We use these different facilities for a couple of reasons;

15 some isotopes, like 77mSe and 79mSe, have short half-lives and needed to be irradiated closer to the reactor core using the Rabbit. The Thermal Column was used to find the thermal cross sections of the isotopes that had longer half-lives due to the epithermal neutron flux being negligible. The CLICIT uses cadmium lining to block most of the thermal neutrons, letting the sample being bombarded with just epithermal neutrons and used to find the resonance integrals. These resonance integrals are then used to correct for the epithermal neutrons in the Rabbit and GRICIT and solve for the thermal cross section.

After receiving the irradiated samples they were put under a fume hood and taken out of the plastic irradiation tube. The samples were then moved to the detector lab and put in front of each detector to have the resulting γ-rays counted. Each detector would count for a certain period of time, stop, and start counting again to give enough data to make good statistics for analysis. For redundancy three samples were irradiated in the rabbit and counted, and another three runs were done using the rabbit with a cadmium lining to isolate the epithermal neutrons.

Figures 7 and 8 below are some of the gamma ray spectra created by MAESTRO for our Se samples.

Figure 7: Gamma ray spectrum for Se sample 6, series a.

Figure 8: Gamma ray spectrum for Se sample 6, series c.

Results

Table 1 shows results for the thermal cross sections and resonance integrals for the isotopes experimented on (measured in barns):

7475 7879m 8081g 8081m 8283g GRICIT 48.2 0.045 0.0036 Rabbit1 52.3 0.188 0.575* 0.047 0.0043 Rabbit3 51.8 0.238 0.590* 0.049 0.0045 Rabbit5 54.8 0.204 0.483 0.046 0.0041 Rabbit6 54.4 0.203 0.486 0.045 0.0040 Thermal 48.0 0.047 0.0036 column Average 52.0 0.203 0.485 0.046 0.0040 Previous 52.2 0.38 0.53 0.048 0.0030 values *Not used in final average because peaks have too much 81m content

Table 1: Thermal cross sections of the Selenium isotopes from each facility used.

7475 7879m 8081g 8081m 8283g CLICIT 515 0.214 0.044 Rabbit2 500 2.15 1.07 0.207 0.038 Rabbit4 510 2.22 1.025 0.200 0.043 Rabbit7 532 2.32 0.924 0.197 0.040 Rabbit8 533 2.31 0.940 0.200 0.040 Average 518 2.25 0.932 0.201 0.041 Previous 576 3.7 0.994 0.147 0.12 values

Table 2: Resonance integrals of the Selenium isotopes from each facility used.

The tables show the thermal cross sections and resonance integrals measured in this experiment next to the previous ones that mere measured or calculated in the past. As you can see, the results of this experiment give measurements that have reduced uncertainties and even increased accuracies in some cases. This can be partially attributed to more high-tech equipment like single crystal germanium detectors, improved parameter values for half-lives and branching ratios, using separated isotopes and same methods for each isotope. Also different irradiation facilities were used to further improve measurements, as well as to check if any were considerably off from what was predicted.

The uncertainties in the measurements are not shown above, as it would be too cumbersome to put here in all its entirety. It involves combining all the uncertainties of the parameters used like branching intensities, flux measurements, detector efficiencies and others. This amounts to about a +/- 5% in the measured cross sections.

Conclusion

The thermal cross sections and resonance integrals of the radioisotopes 75,79m,81g,81m,83gSe from neutron capture of 74,78,80,82Se were measured using neutron activation at OSU’s TRIGA reactor at the four facilities mentioned before (rabbit, CLICIT, GRICIT, TC). This entailed the normally stable isotopes capturing neutrons produced inside the reactor in the different facilities. The γ-rays produced by the irradiation were measured with a high resolution germanium detector and analyzed with MAESTRO and spreadsheets.

These measurements were needed in some cases due to there being no previously recorded values for the cross section or resonance integral. Also past measurements were made before the creation of high resolution detectors to more accurately measure the γ-rays emitted. Better parameter values, multiple facility measurements and consistent methods for each isotope helped in acquiring more precise measurements of these cross sections. These new measurements are made using high resolution detectors, improved parameter values and more consistent methods for each isotope, yielding more precise values than were made in past experiments.

References

[1] Galinha, Catarina & Freitas, M & M. G. Pacheco, A & Kamenik, Jan & Kučera, J & Anawar, Hossain & Coutinho, José & Maçãs, Benvindo & Almeida, Ana. Selenium determination in cereal plants and cultivation soils by radiochemical neutron activation analysis. Journal of Radioanalytical and Nuclear Chemistry (2012)

[2] S. F. Mughabghab, Atlas of neutron resonances: Resonance parameters and thermal cross sections Z=1-100 (Elsevier, Amsterdam, 2006)

[3] “Excited-State Lifetime and Natural Linewidth” http://www.files.chem.vt.edu/chem-ed/spec/atomic/theory/lifetime.html

[4] National Nuclear Data Center: http://www.nndc.bnl.gov

[5] Hadiseh Alaeian, “An Introduction to Cherenkov Radiation”, http://large.stanford.edu/courses/2014/alaeian2/

Acknowledgements

I want to thank Dr. Krane for helping me every step in the way, from deciding how to prepare samples to polishing up my final revision. Without him I would have gave up on this long ago. I also want to thank the whole physics department for the help they have given me and pushing for me to succeed.