1 Chapter NP-5 Nuclear Physics Nuclear Reactions TABLE OF CONTENTS INTRODUCTION OBJECTIVES NEUTRON INTERACTIONS 2.1 ELASTIC SCATTERING 2.2 INELASTIC SCATTERING 2.3 RADIATIVE CAPTURE 2.4 PARTICLE EJECTION 2.5 FISSION ENERGY RELEASED FROM FISSION FISSION PRODUCTS FISSION: THE LIQUID DROP MODEL 3.0 NUCLEAR REACTION CROSS SECTIONS 4.0 SUMMARY NP-5 Page 1 of 16
2 INTRODUCTION A nuclear reaction is a process whereby a nucleus is transformed from one species to another. Radioactive decay is one example of a nuclear reaction. A broader definition would include those processes which are initiated by the absorption of a particle by a nucleus, the result being a transformation of the original nucleus to a different species accompanied by the appearance of one or more elementary particles or rays. There are any number of particles which can initiate a nuclear reaction, although the most common in nuclear power generation are those initiated by neutrons. The absorption of a particle by a nucleus results in the formation of an excited or "compound" nucleus. One possible result is the ejection of another particle and the formation of a different nucleus. Another result may be simply the release of gamma ray energy, with the compound nucleus returning to its ground state. Finally, the nucleus may split into two or more new nuclei (fission reaction). In this lesson, each of these reactions will be discussed in detail. NP-5 Page 2 of 16
3 OBJECTIVES TERMINAL OBJECTIVE The Contractor Health Physics Technician will describe the characteristics, sources, and interactions of neutrons. ENABLING OBJECTIVES Upon completion of this lesson, the Contractor Health Physics Technician will be able to: 1. Define the characteristics of neutrons including charge, relative mass, and stability. 2. Describe the difference between fast and slow neutrons. 3. List the sources of fast neutrons. 4. Describe the scattering and absorption neutron interactions. 5. Describe the relationship between linear attenuation coefficient and mean free path. NP-5 Page 3 of 16
4 1.0 Many types of particles can be used to bombard a nucleus, these include: neutrons (η), protons (ρ), alphas (α), and even photons. When a target nucleus is bombarded with a particle, the two combine to form a compound nucleus. This is writ ten in equation form as: a + X C* where: a = nuclear particle X = target nucleus C* = compound nucleus The asterisk indicates that the compound nucleus contains excess energy, called excitation energy. The compound nucleus will rid itself of this excess energy by the release of a particle and/or photon. The complete reaction is then: a + X C* Y + b where: Y = resultant nucleus b = resultant particle and/or photon The following are examples of nuclear reactions which are results of bombarding target nuclei with various particles. Example: proton. Nitrogen-14 bombarded with alpha particles yields Oxygen-17 and a 7N α 4 9F 18 * 8O H 1 Comment: α NP-5 Page 4 of 16
5 Example: Example: neutron. Boron 10 bombarded with neutrons results in Lithium-7 and an alpha. 5B η 1 5B 11 * 3Li 7 + 2α 4 Beryllium-9 bombarded with alpha particles yields carbon-12 and a 4Be α 4 6C 13 * 6C η 1 General rules to follow when writing nuclear equations: Conservation of nucleons - the sum of the A values on both sides of the equation must be equal. Conservation of charge - the sum of the Z values on both sides of the equation must be equal. 2.0 NEUTRON INTERACTIONS Reactions, which are initiated by neutrons, are of primary concern in the study of nuclear reactors. When charged particles approach the nucleus, they must overcome the repulsive electrostatic force before getting close enough for the strong nuclear force to act. This requires that the incident particle possess a significant amount of energy in order for the reaction to occur. Neutrons have no charge and therefore are not subject to overcoming electrostatic repulsion in order to penetrate the nucleus. This means that neutrons need not possess large amounts of kinetic energy to initiate nuclear reactions. In fact, low energy neutrons initiate the reactions, which are of prime importance to power production (fission reactions). In nuclear work, there are several terms, which are commonly used to classify neutron energies. Neutrons with energies below approximately 1 ev are referred to as "slow" neutrons. Neutrons with energies in the range of approximately 1 ev to 10,000 ev are called "intermediate" neutrons. Finally, neutrons with energies above approximately 10,000 ev or 0.01 Mev are called "fast" neutrons. There is no upper limit on the fast region, but from a practicality point of view, neutrons in the reactor rarely exceed 10 Mev. A low energy neutron (Kinetic energy less than about.65 ev) which is in temperature equilibrium with its surroundings is called a thermal neutron. NP-5 Page 5 of 16
6 2.1 ELASTIC SCATTERING The elastic scatter (or elastic collision) is one of the simplest interactions a neutron can undergo. This type of reaction can be compared to two billiard balls colliding. There is no energy transferred into excitation of the target or neutron. The only energy transfer involves changes in the kinetic energy of the neutron and target. Physically, the neutron may touch the target and bounce off; it may only come close to the target and be deflected; or it may directly collide with the target and bounce off. The criterion is that no energy be transferred into nuclear excitation; as long as this holds, the collision may be considered elastic. Figure NP-5-1 illustrates an elastic scattering reaction NP-5-1 Elastic Scatter The equation for elastic scattering is: o η 1 + Z X A Z X A + o η 1 Remember, in elastic scattering reactions the only energy transfer is a change in the kinetic energy of the neutron and target nucleus. The target nucleus is normally considered to be at rest (no kinetic energy) prior to the reaction 2.2 INELASTIC SCATTERING Inelastic scattering differs from elastic scattering in that the target nucleus is raised to an excited state as a result of the collision. Physically, the neutron may only touch the nucleus, or it may enter the nucleus and exit at a reduced energy. The energy transformations are then a change in the kinetic energy of the neutron, a change in the nuclear energy level of the target nucleus, and possible a change in the kinetic energy of the target. When the excited target nucleus returns to the ground state, excess energy is released by the emission of a gamma ray. Figure NP-5-2 illustrates an inelastic scattering reaction. NP-5-2 Inelastic Scatter NP-5 Page 6 of 16
7 The equation for inelastic scattering is: o η 1 + Z X A Z Y A+1 * Z X A + o η 1 + γ Remember, inelastic scattering results in nuclear excitation of the target nucleus, followed by gamma emission when the excited nucleus returns to the ground state. The neutron leaves the collision site at reduced kinetic energy. 2.3 RADIATIVE CAPTURE In a radiative capture reaction, the incident neutron enters the target nucleus and remains. This results in a "new" nucleus with a mass number increased by one. The new nucleus contains excess energy in the form of nuclear excitation. This excess energy is released by the emission of a gamma ray and the nucleus returns to the ground state. The equation for a radiative capture reaction is: η 1 + Z X A Z Y A+1 * Z Y A+1 + γ Figure NP-5-3 illustrates a radiative capture reaction. Remember, in radiative capture reactions, the neutron is absorbed by the target nucleus resulting in an excited nucleus resulting in an excited nucleus with a mass number increased by one. The excited nucleus returns to the ground state by emitting a gamma ray. NP-5-3 Radiative Capture NP-5 Page 7 of 16
8 2.4 PARTICLE EJECTION In some cases, the incident neutron is absorbed by the target nucleus and the newly formed nucleus is raised to a sufficient energy level to immediately eject another particle. This is a particle ejection reaction. The ejected particle can be a proton, neutron, or in some cases an alpha. Even after the particle is ejected, the nucleus normally is still in the excited state and releases a gamma ray to return to the ground state. Figure NP-5-4 illustrates particle ejection upon bombardment with a neutron. The equation for particle ejection is: NP-5-4 Particle Ejection o η 1 + Z X A Z Y A+1 * Y + b + γ where: Y = resultant nucleus b = ejected particle The atomic mass number of the resultant nucleus is dependent upon the particle ejected. 2.5 FISSION The fission process is defined as the splitting of a heavy nucleus (A ~240) into two approximately equal parts, accompanied by the release of a large amount of energy and one or more neutrons. When uranium-235 absorbs a low energy neutron (~0.025 ev), 85% of 236 the time the compound nucleus ( U*) 92 will fission. NEUTRONS FISSION REACTION FISSION PRODUCTS O NP-5-5 Fission NP-5 Page 8 of 16
9 The other 15% of the absorption s result in radiative capture as discussed in Section 2.3. Figure NP-5-5 illustrates the fission process. In order for a nucleus to undergo fission, it must be excited to an energy level called "critical energy". The absorption of a neutron raises the energy level of the nucleus to an amount equal to the binding energy of the neutron. Any kinetic energy that the neutron may possess at the time of absorption also contributes to the nuclear excitation. If the total energy supplied to the nucleus by the incident neutron (neutron binding energy + neutron kinetic energy) exceeds the critical energy (Ec), the nucleus may fission. Table 1 lists the critical energy and the excitation energy due to absorption of a thermal neutron for important fissionable isotopes. TABLE 1 - EXCITATION ENERGY REQUIRED FOR FISSION Target Nucleus Compound Nucleus Excitation Energy Critical Energy from Thermal Neutron U-233 (U-234) 6.6 Mev 4.6 Mev U-235 (U-236) 6.5 Mev 5.3 Mev U-238 (U-239) 4.9 Mev 5. 5 Mev Th-232 (Th-233) 5.1 Mev 6.5 Mev Pu-239 (Pu-240) 6.4 Mev 4.0 Mev NP-5 Page 9 of 16
10 Sample: Using U-235 as an example, show the net excitation energy upon absorption of a neutron, assuming kinetic energy is insignificant. oη U 235 (92U 236 )* Energy (mass o η 1 + Mass U Mass U-236) 931 MEV = AMU Excitation AMU AMU AMU = AMU MEV AMU x 931 AMU = 6.5 Mev This calculation indicates that U will fission by absorption of a neutron with no kinetic energy. Referring to Table 1, the same holds true for Pu and U When an isotope is capable of fissioning by absorption of a thermal neutron, it is called "fissile". U is the only natural fissile isotope. U and Pu are man - made. The other isotopes listed in Table 1 require that the incident neutron possess kinetic energy for a fission to occur. For instance, in order for U to reach critical energy, the incident neutron must possess 1.6 Mev of kinetic energy. Fission results in the emission of major pieces of the original nucleus, called fission fragments or fission products, plus the release of gamma rays, beta particles, neutrinos, and neutrons. The emis sion of neutrons from fission makes it possible to achieve a self sustaining fission chain reaction. o η 1 + Z X A Z Y A+1 * 2FF + o η 1 s + γ + E ENERGY RELEASED FROM FISSION It is important to see why there are large amounts of energy released in the fission process and where the energy manifests itself. NP-5 Page 10 of 16
11 In the Nuclear Stability Concepts (Chapter NP-5-2) binding energy of nuclei was presented. It is more useful to speak in terms of binding energy per nucleon (BE/A), which is merely the binding energy of a nucleus divided by the number of nucleons in the nucleus. When BE/A is plotted as a function of A number a curve such as that shown in Figure NP- 5-6 results. The binding energy per nucleon increases up to about 8.6 Mev at a mass number of 60 and slowly decreases thereafter. NP-5-6 Binding Energy per Nucleon Figure NP-5-6 can be used to calculate the energy released by fission. The binding energy per nucleon of U is 7.58 Mev, assuming the U nucleus split exactly in half, the fission fragments would have mass numbers of about 117. The binding energy per nucleon of nuclei with mass number 117 is about 8.5 Mev. The difference in binding energy per nucleon between the original nucleus and the resultant products multiplied by the total number of nucleons yields the energy released: (8.5 Mev/nucleon Mev/nucleon) x 235 nucleons = 211 Mev per fission (approximately) Energy released in the fission of a U nucleus appears in the form given in Table 2. TABLE 2 ENERGY RELEASED FROM FISSION Kinetic Energy of Fission Fragments 168 Mev Kinetic Energy of Fission Neutrons 5 Mev Prompt Gamma Ray Energy 7.5 Mev Decay of Fission Fragments 14.5 Mev Neutrinos Energy 12 Mev TOTAL ~207 Mev NP-5 Page 11 of 16
12 It is apparent that the majority of the energy appears as kinetic energy of the fission fragments. Immediately after the split, the two positively charged fission fragments are in close proximity and repel each other with great force. Neutrons are released by the fission fragments immediately after their formation; on the average 2.5 neutrons are released for each fission of a U nucleus. These neutrons have very high velocities, but because of their lesser mass have kinetic energy only on the order of 2 Mev. These are called "prompt" neutrons, because they are promptly emitted by the fission fragments after their formation (within seconds). These prompt neutrons are slowed by collisions and eventually one neutron from a previous fission causes another fission and the chain reaction is sustained. Even after releasing neutrons upon their formation, fission fragments have a η / ρ ratio, which is too high for stability. The fission fragments decay by beta-minus decay and in some cases neutron emission. The neutrons emitted by fission fragments in this manner are termed "delayed neutrons". Delayed neutrons are generally born at lower energy levels than prompt neutrons. Delayed neutrons play an important role in making a fission chain reaction controllable in a nuclear reactor, by effectively slowing down the fission chain reaction. If the chain reaction were dependent upon prompt neutrons alone, changes in the fission rate would occur too quickly for safe reactor operation FISSION PRODUCTS NP-5-7 Fission Product Yields When a fissionable nucleus splits, one would expect that the two fission fragments would be equal in size. That is, each fission fragment would be approximately 117 AMU. This is called symmetrical fission and the probability of its occurrence is very low. For reasons not fully understood, the most likely mass of the fission fragments of U-235 are 95 and 139. These are the most probable fission product masses; many other combinations are possible. Figure NP-5-7 plots the distribution of fission products for U and Pu NP-5 Page 12 of 16
13 2.5.3 FISSION: THE LIQUID DROP MODEL The mechanism by which nuclei fission is best represented is the liquid drop model. Considering the nucleus to be a special drop of liquid can approximate the collective behavior of all the nucleons. The liquid drop is held together by surface tension (nuclear forces). When the drop is deformed, the surface tension forces may be insufficient to restore the drop to its original shape. Splitting may occur. Figure NP-5-8 illustrates this model in the case of a nucleus. Normally, the nucleus is at its minimum energy level (ground state), i.e., spherical form (I). If the nucleus receives excitation energy (incident neutron binding energy + kinetic energy), it will start to oscillate, first going into an ellipsoidal shape (II), and then a "dumbbell" form (III). If the excitation energy is not sufficient, it will oscillate between these two shapes until the excess energy is given off, probably in the form of a gamma ray. Then it will return to special form (ground state). However, if the excitation energy is in excess of the critical energy, the dumbbell will neck down until the width is zero (IV). At that point, two positively charged nuclei are formed and they repel each other with great force (V). NP-5-8 The Liquid Drop Model of Fission NP-5 Page 13 of 16
14 3.0 NUCLEAR REACTION CROSS-SECTIONS In order to better understand the physics of neutron reactions, the probability of a certain reaction occurring must be ascertained. The method used to determine the probability of a reaction occurring between a neutron and target nucleus is to represent the target as an "effective" cross-sectional area to the neutron. This effective cross-sectional area is termed the "microscopic cross section", F is pronounced sigma. Different nuclei have different probabilities of a certain reaction occurring. Thus, each nucleus presents a different effective target area. Remember, this is not a measure of the actual cross-sectional area of the nucleus, but an effective target area for a certain reaction. The units for microscopic cross sections are "barns". where: 1 barn = cm 2 We can divide the probability of interaction of any kind (σt) into the probability of an absorption reaction (σa) and the probability of a scattering reaction (σs). σt = σa + σs The absorption cross-section can be further subdivided into a cross-section for capture (σc) and a cross-section for fission (σf). σa = σc + σf The scattering cross-section can also be subdivided into elastic and inelastic scattering cross-section. It is important to note that these cross-sections are dependent upon neutron energy. Generally, as neutron kinetic energy increases, probability of a reaction decreases. Table -3 lists absorption cross-sections of some common nuclides for thermal neutrons. NP-5 Page 14 of 16
15 TABLE 3 - Cross Sections for Absorption of Thermal Neutrons Nuclide symbol 115 \f "Symbol" \s 12σ (barns) He 4 ~0 O C U U Pu 239 1,011 B 10 3,840 Sm ,800 Xe 135 2,650,000 As Table 3 indicates, cross-sectional area varies a great deal for different nuclides and it is not significantly affected by the actual physical size of the nucleus. When describing interaction of radiation with matter, we tend to describe these interactions in terms of scattering and absorption for neutron interaction and photoelectric effect, Compton Scattering, and pair production for photons or gammas. The average distance that the radiation travels before undergoing a given reaction is called the mean free path. This means that there will be separate distances that a neutron will have to travel before undergoing a scattering or absorption reaction. The same hold true for gamma interactions. Now, when we take a substance and direct the radiation through the substance, there will be a constant fractional decrease in the radiation intensity per unit thickness of the substance. The value of that decrease in the radiation intensity is called the linear attenuation coefficient. Therefore, if the substance has a high ability to attenuate neutrons, the substance will have a high linear attenuation coefficient and the neutrons will have a low mean free path within the substance. NP-5 Page 15 of 16
16 4.0 SUMMARY There are five basic types of nuclear reactions: elastic scattering, inelastic scattering, radiative capture, particle ejection and fission. Elastic scattering reactions involve kinetic energy transfer through collision; no energy is transferred into nuclear excitation. Inelastic scattering, on the other hand, results in the nucleus being raised to an excited state. In the case of radiative capture, the incident particle is absorbed into the nucleus, thus raising the energy level of the nucleus. The compound nucleus then emits a photon to rid itself of the excess energy. In a particle ejection reaction, the compound nucleus releases excess energy by emitting a particle. The fission reaction results in the nucleus breaking apart into 2 fission fragments and releases a large amount of energy. Fission reactions produce additional neutrons which may be available to initiate further fission reactions. NP-5 Page 16 of 16
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