Nuclear Reactions– changing the hearts of atoms
Simple Theories on Nuclear Reactions
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- Bu səhifədəki naviqasiya:
- Energy Dependence of Cross Sections
- Types of Nuclear Reactions
Simple Theories on Nuclear ReactionsThere are many theories on nuclear reactions and we shall consider some simple ideas such as cross section for the probability of reaction and the types of nuclear reactions. Reaction Cross Sections
In mixtures of alpha emitters and beryllium or boron as neutron sources using (, n) reactions, only fractions of particles were effective for the production of neutrons. In the three mixtures listed earlier, the fractions range from 60 to 500 per million particles.
The alpha particles have to almost collide with the atomic nuclei to be captured. The chances of an particle hitting the nuclei is proportional to the area seeing by the as its cross section, , from a distance. When the bombarding particle strikes an area slightly larger than the disk-like area of a nucleus seen from a distance, the two particles make a contact leading to a reaction. The larger the cross section, the higher is the probability of the projectile hitting the (target) nucleus. Since the radius of a nucleus is in the order of 10 14 meters, and the area of the cross section of a nucleus will be in the order of 10 28 m2 (or 10 24 cm2). For convenience, an area of 10 28 m2 is defined a barn (b). On the other hand, many kinds of interaction take place when a particle collides with a nucleus, and there are specific areas in the nucleus for certain interactions. Thus, pure collision theory suggests the cross section for nuclear reactions to be smaller than 1 b, but measured values of cross sections suggest a much more complicated model. Cross sections for nuclear reactions are not calculated values from the radii of the nuclei, but they are experimental values representing the probability of reaction. The rate of reaction (number per unit time) in an experiment equals the product of the cross section, , the number of target atoms per unit area N, and the intensity of the flux (number of particles per unit area per unit time s–1 cm–2) I. That is, rate = N I. Thus, the cross section is really a measure of the probability of a given reaction, and the total cross section of absorption of a particular accelerated particle is the sum of all partial cross sections. A sample irradiated in the core of a nuclear reactor differs from irradiated by a unidirectional beam. Neutrons in reactor bombard the sample from all directions. For neutron irradiation in reactor core, the cross section is calculated by dividing the rate of reaction by the total number of nuclei, and the intensity of the flux, = Note that the unit of the cross section so calculated is cm–2 or m–2, depending on the unit used for I. The unit barn (=10 28 m2 or 10 24 cm2) has been used for the tabulation of cross sections of nuclides. Cross sections have a very large range, 106 to 10–6. T The values of cross section depend on the nucleus, particle, and particle energy. The cross section for boron, for example, is 120 b for neutrons travelling at 10 km/s. It is 1,200 b for neutrons travelling at 1 km/s. These large cross sections indicate that boron is an excellent absorber for slow neutrons and an effective absorber for moderate fast neutrons. The metal zirconium is rather transparent to neutrons; it has an absorption cross section of 0.18 barn for the low-energy neutrons that cause fission in nuclear reactors. Zirconium experiences little damage by neutrons and it is used to clad reactor fuel rods. Boron is used to absorb neutrons.
Energy Dependence of Cross SectionsCross sections of reactions depend on both the bombarding particle and the nuclide. They not only have a very large range, they also depend on the (kinetic) energies of the incident particles.
Energy is the driving force of all reactions, including nuclear reactions. The kinetic energy of the bombarding particles must be included and considered in nuclear reactions.
Let us focus on the neutron capture reactions. In general, the cross section decreases as the energy of the neutron increases. However, the cross section increases suddenly at some specific energies of the neutron, but the cross section rapidly decreases from the high points. A typical variation curve is depicted here. The sudden increase has been attributed to the energy states of nuclei. Neutrons moving with these particular energies can be accommodated easily by the target nuclide. The rise in their capture cross section is known as resonance absorption. The resulting nuclei correspond to some excited states of the newly formed nuclei, and the excited energy may be emitted as gamma rays. Gamma ray spectroscopy often confirms the existence of these excited energy states.
There is no reliable prediction of the reaction path for a particle of certain energy. Each case must be studied individually. For a picture of total neutron cross sections of variety of nuclides U, Th, Pb, Hg, Au, to some very light nuclides 6Li, 7Li, and B, see a recent graph in the web site: http://www-phys.llnl.gov/N_Div/APT/TotalCrossSections/stotgraph.html. Skill Building Questions
Types of Nuclear Reactions
When the target nuclei are bombarded by particles, there are some general types of nuclear reactions. Net nuclear reactions occur when collisions result in combining or rearranging nucleons in the nuclide and particle. Exchange of energy between the incident particle and the target nuclei also takes place.
A particle colliding with a nucleus may be scattered (deflected) without leading to a net nuclear reaction. In this scattering process, a particle may or may not transfer any energy to the nucleus. When a particle losses no energy, it is called elastic scattering whereas inelastic scattering refers to one that a particle losses or gains energy. A subatomic particle may be captured (absorbed) by and become part of an atomic nucleus. A capture reaction increases the mass number of the nuclide and leads to a new nuclide. One or more atomic particles may be released in a particle-nucleus encounter, and such a process is called a rearrangement reaction. A particle may induce a fission reaction, in which case the nucleus splits into fragments. When light particles combine, the capture reaction is called fusion. Elastic Scattering: This process can be represented by the equation, 208Pb (n, n) 208Pb. It does not imply that neutrons scattered off the target nuclei are the same neutrons entering the target area. Inelastic Scattering: If the particle transfers energy to a nucleus, the nucleus is left excited, 40Ca (,') 40mCa where and ' have different kinetic energies. In cases when the incident particle is a complicated nuclide, it may also be left in excited state, 208Pb (12C, 12mC) 208mPb This process is called mutual excitation. Capture Reactions take place for charged and neutral incident particles. In capture reactions, excess energy is usually spent on the emission of a photon. Some examples are, 197Au (p, ) 198Hg 238U (n, ) 239U As mentioned earlier, neutron capture reactions are responsible for the synthesis of 239Pu and 236U. These reactions are responsible for the production of many radioactive nuclides.
Various rearrangement reactions are possible, and they lead to the formation of a nuclide, changing both the numbers of neutrons and protons. The transformations of nuclides in nuclear reactions are summarized in a diagram here. For example, an capture reaction (, ) increases both numbers of neutrons and protons by two. The original nuclide is transformed to one on the top right corner marked by (, ). When more nucleons are released than captured, a nuclide is transformed to the left or lower portion of the diagram. Energetic photons ( rays) also induce nuclear reactions of various types. Fission Reactions: Spontaneous fission is considered a mode of radioactive decay, and relatively few nuclides have high fission activity. Fission can be induced by neutrons, and well known fission reactions are given below, 239Pu (n, 3 n) fission products 235U (n, 3 n) fission products These fission reactions release large quantities of energy. Atomic bombs and nuclear reactors make use of them. Fusion Reactions are of great interest, because future energy supply depends on them. Fusion reactions are treated in another chapter, but they are mentioned here in this summary of nuclear reactions. One of many well-known fusion reactions is 2 2D 3He + n However, fusion is not necessarily the combination of two light nuclides. For example, the probability for the reaction 2 2D 4He is very low.
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