DEPARTMENT OF PHYSICS 1 Detection of uranium fission products through neutron activation August Barot, Mikael Andersson Advisor: Torbjorn¨ Back.¨ DEPARTMENT OF PHYSICS 2 CONTENTS I Introduction 3 II Neutron activation theory 3 II-A Mathematical model of the neutron ac- tivation process . 3 III Fission yields 5 IV Detector setup 5 V Calibration 6 VI Results 8 VI-A Measured data . 8 VI-B Analyzed peaks . 9 VI-C Isotope analysis: 97Zr . 12 VI-D Isotope analysis: 92Sr . 13 VI-E Isotope analysis: 91Sr . 13 VI-F Isotope analysis: 135I . 13 VI-G Isotope analysis: 143Ce . 14 VI-H Isotope analysis: 142La . 14 VI-I Isotope analysis: 133I . 15 VII Conclusion 15 VII-A Error sources . 16 VII-B Improvements . 17 References 17 DEPARTMENT OF PHYSICS 3 Abstract—Uranium compounds are used in many nuclear results from the amount of isotopes generated during a power plants, and the neutron-induced fission reactions produce neutron activation, and thus also from the intensity of the many decay products. Some of these are of interest from an characteristic photon energy levels measured in the detector. efficiency or safety point of view. For this reason, it is important to quantitatively and qualitatively know these nuclides.The objective These are proportional to both the neutron capture cross of this study is to experimentally determine these properties section of the parent isotope as well as the amount of parent through neutron activation and gamma ray spectroscopy. Using isotopes in the sample. To increase the capture rate during the a germanium semiconductor detector, gamma rays emitted from activation through neutron moderation, the uranium sample fission daughter isotopes produced from neutron irradiation of and the neutron source are separated by 5 cm of water. a uranium sample are measured. The resulting spectra are analyzed, proving the existence of fission daughter isotopes in the specimen. The data also provides experimental estimations of initial half-life of these isotopes. A. Mathematical model of the neutron activation process I. INTRODUCTION To understand the relation between the different variables ETERMINING the content of a sample through the and to summarize the mechanics at work, a theoretical D use of neutron activation requires a source that is model is used to relate the variables of the experiment to the moderated by water to provide a flux of thermal neutrons. A quantitative results. The model used is the following: 252Cf source is used to irradiate a uranium nitride specimen, causing several fission processes which yield gamma rays. A neutron source releasing S neutrons per second is Detection is conducted through gamma ray analysis using a known. The goal is to know how many gamma rays will be germanium semiconductor detector operating at 77 K. This emitted by the specimen, as well as how many gamma rays device measures electrical impulses caused by electromagnetic will be registered by the detector. waves primarily through the photoelectric effect. The nature of the reactions makes the complete analysis elaborate, and 1. Calculation of the neutron flow per unit area a theoretical proportionality model is useful to relate the The neutron flow Φ per unit area at a given distance r from properties such as the resulting spectra and the sample content the source is given by the following equation[8]. to each other. Se−r=L In the model the source neutron flux is approximately Φ(r) = (1) known, and a model of neutron diffusion in water is used. 4πDr Since the specimen mass as well as the neutron capture Here S is the total flow per second from the source, L is cross sections of the isotopes 235U and 238U are known, the diffusion length, and D is the diffusion coefficient. the number of nuclide irradiations per unit time can be estimated. Knowing the half-lives and reaction processes of 2. Calculation of neutron absorption of the specimen the nuclides, an estimation of the number of emitted gamma This flow will hit the specimen of mass m. Note that m may rays per unit time is made possible. A spherical geometry be an effective mass if the specimen is impure (the mass of flux approximation is used in relation to the germanium the active substance in the specimen). If this is the case, a detector geometry, which together with the attenuation calculation of m = m0q is required, where m0 is the total coefficient of the detector gives an estimation of the number mass and q is the (mass) concentration of active substance. of photoelectric reactions per unit time. These properties The mass m corresponds to n number of atoms, where n is are analyzed through an efficiency calibration. This gives given by a quantitative approximation of the registered gamma ray mN n = A (2) counts. M Here N is Avogadro’s number and M is the molar mass of The method is useful for trace amounts of nuclides, po- A the substance. tentially allowing measurement of many different elements, Furthermore, the effective cross section area A of the including specimen contamination nuclides. 0 specimen is given by II. NEUTRON ACTIVATION THEORY mNAa A0 = na = (3) When exposed to a neutron flux, nuclei can capture and M interact with neutrons. The rate of capture of an isotope where a is the absorption cross section of the substance for sample is determined by the neutron capture cross section thermal neutrons. which depends on the isotope as well as on the kinetic energy To calculate the probability that a neutron which hits the of the flux. Unstable isotopes generated by this method will specimen is absorbed, the quotient decay and deexcite with photon emission of well defined A mN a energy levels (gamma radiation) as a result. Studying these s = 0 = A (4) characteristic photon energies allows identification of the A MA isotopes generated by the neutron activation and thus of is calculated, where A is the area of the specimen surface. the sample composition itself. The quantitative analysis The number of neutrons hitting the specimen per second is DEPARTMENT OF PHYSICS 4 Se−r=L given by ΦA, which is equal to 4πDr A. This means that the quotient factor qγ , corresponding to the fact that not all decays average number of absorbed neutrons per second is equal to cause emission of the specific gamma ray. Let us call the number of emitted gamma rays Z , therefore ASe−r=L mN a Se−r=LmN a 0 ΦAs = A = A (5) yielding 4πDr MA M4πDr −λt2 −λt1 −λ(t1+t2) This product will be referred to as T . Z0 = N1(1 − e )qγ = N0(e − e )qγ (8) 3. Calculating the number of emitted gamma rays Every time a neutron is absorbed a new,usually radioactive, 4. Calculation of the number of gamma rays that hit atom is formed. In this case the atom’s decay constant the detector (retrieved for specific cases from NuDat [4]) will be known With Z0 known the next objective is to determine how here as λ. Depending on the process of interest the specific many gamma rays the detector will actually register. An nuclide may not always be formed. This fact requires an assumption that the specimen can be considered a point insertion of a quotient qnuclide. In the fission case qnuclide is source is made (requiring a fair distance from the detector). the fission yield (see below). The approximation that the rays will be evenly distributed on a sphere of radius X, the distance between the detector and the specimen, is then used. Therefore the number of gamma Therefore, calling the number of generated atoms N, this rays reaching the detector will be given by yields the differential equation[5] Adetector dN Z1 = Z0 2 (9) = −λN + T q (6) 4πX dt nuclide where Adetector is the detector’s surface area (assumed to dN This equation can be simplified by assuming dt = 0 be perpendicular to the gamma rays). With the value of Z0 (stationary state), which yields T qnuclide= λN and therefore (calculated above) inserted in this formula, the full formula T qnuclide N = λ . Of course, the differential equation only works for the number of gamma rays reaching the detector reads as if the first isotope in the decay series is the one of interest[5], in follows: other cases more complicated models (e.g. equation systems) −r=L Se mNAa Adetector Z = q (1−e−λt0 )(e−λt1 −e−λ(t1+t2))q are required. 1 M4πDrλ nuclide γ 4πX2 If the equation is not simplified, its solution reads as follows: (10) −λt N(t) = T qnuclideλ(1 − e ) The number of registered gamma rays will not be equal to This number will be known as N0. This is the number of Z1, due to the properties of the detector. The corresponding atoms in the specimen when a balance between the neutron calculations can be found below, under section IV. flux creating new atoms of the isotope and the natural decay of said isotope has been achieved. The requirement for the simplification of the differential equation to be accurate is that steady-state has been reached, which requires the measurement time t0 to be significantly longer than the isotope half-life. As seen below, this is generally not the case. Therefore, the T −λt0 formula N0 = N(t0) = λ (1 − e ) will be used in the calculations.Note that as t0 tends to infinity, this formula tends towards the steady-state formula. Once the specimen is removed from the neutron flow the above described balance will be shifted. The atoms will decay according to the formula −λt N(t) = N0e (7) Let t1 be the time that it takes to remove the specimen from the neutron source and put it in front of the detector.