Nuclear reactions compound-nucleus

C22-0016. The following partial nuclear reactions show one reactant, the compound nucleus, and one product. Identify the other reactant and any additional products ... 

C22-0054. Identify the compound nucleus and final product resulting from each of the following nuclear reactions (a) carbon-12 captures a neutron and then emits a proton (b) the nuclide with eight protons and eight neutrons captures an a particle and emits a y ray and (c) curium-247 is bombarded with boron-11, and the product loses three neutrons. 

C22-0057. Draw a nuclear picture (see Figure 22-1 for pictures of nuclei) that illustrates the nuclear reaction responsible for the production of carbon-14. Include a picture of the compound nucleus. 

A substance can be classified chemically in many ways. One of the simplest ways to classify a substance is as an element or a compound. An element is a pure substance that cannot be changed into a simpler substance by chemical means. Elements are the building blocks of nature all matter is composed of elements. The periodic table is a concise map that organizes chemical elements into columns (groups) and rows (periods) based on their chemical properties. Currently, there are 118 known chemical elements, with whole numbers 1 to 118. These numbers are referred to as the element s atomic number and give the number of protons in the nucleus of an atom of the element. For example, carbon s atomic number is 6 and each carbon atom has 6 protons in its nucleus. The first 92 elements occur naturally, and those above atomic number 92 are synthesized through nuclear reactions using particle accelerators. Element 118 was just confirmed in the fall of 2006, and by now, more elements may have been produced. 

ATOMIC DISINTEGRATION. The name sometimes given to radioactive decay of an atomic nucleus and occasionally to the breakup of a compound nucleus formed during a nuclear reaction. See also Radioactivity. 

PHOTONUCLEAR REACTION. A nuclear reaction induced by a photon. In some cases the reaction probably takes place via a compound nucleus formed by absorption of the photon followed by distribution of its energy among the nuclear constituents. One or more nuclear particles then "evaporate from the nuclear surface, or occasionally the nucleus undergoes pliotofissioii. In other cases the photon apparently interacts directly with a single nucleon, which is ejected as a photoneutron or photoproton without appreciable excitation of the rest of the nucleus. 

Example Problem In a certain nuclear reaction, a beam of lsO was combined with 233U nuclei to form a compound nucleus of 256Fm. The nuclei were produced with an excitation energy of 95 MeV. Calculate the nuclear temperature assuming that y = 1, and then the relative probability of neutron to fission decay of the excited system. 

The compound nucleus is a relatively long-lived reaction intermediate that is the result of a complicated set of two-body interactions in which the energy of the projectile is distributed among all the nucleons of the composite system. How long does the compound nucleus live From our definition above, we can say the compound nucleus must live for at least several times the time it would take a nucleon to traverse the nucleus (10-22 s). Thus, the time scale of compound nuclear reactions is of the order of 10 18-10 16 s. Lifetimes as long as 10-14 s have been observed. These relatively long times should be compared to the typical time scale of a direct reaction that takes place in one transit of the nucleus of 10-22 s. 

The cross section for a compound nuclear reaction can be written as the product of two factors, the probability of forming the compound nucleus and the probability that the compound nucleus decays in a given way. As described above, the probability of forming the compound nucleus can be written as ... 

Let us now consider the case where Y/D 1, that is, many overlapping levels of the compound nucleus are populated. (We are also tacitiy assuming a large range of compound nuclear excitation energies.) The cross section for the reaction a+A- -C -b + B can be written as... 

The neutron-capture cross section of any isotope represents the probability with which it is able to capture free neutrons passing by it. This quantity is important for the s process of nucleosynthesis. This process was named s owing to the need to patiently make the s isotopes of the heavy elements by the slow capture of free neutrons, neutrons liberated by other nuclear reactions within the gas in stellar interiors. It was one of the first nucleosynthesis processes identified historically. The capture of a free neutron by a nucleus increases its mass number A by one unit. As the captures continue, each nucleus in the gas is rendered heavier, little by little, capture by capture. When an isotope of mass number A of an element with atomic number Z captures a neutron, the compound nucleus formed from their union becomes an isotope of the same element but having mass number greater by one unit (i.e. A + l). 

You have seen some chemical reactions that involve the formation and decomposition of different compounds. These reactions involve the rearrangement of atoms due to the breaking and formation of chemical bonds. Chemical bonds involve the interactions between the electrons of various atoms. There is another class of reactions, however, that are not chemical. These reactions involve changes that occur within the nucleus of atoms. These reactions are called nuclear reactions. 

Most low-energy nuclear reactions proceed via formation of a compound nucleus (eq. (8.5)). In the compound nucleus model that was proposed in 1936 by Bohr it is assumed that the energy of the incident particle and its binding energy are distributed evenly or nearly evenly to all nucleons of the target nucleus. The excitation energy of the compound nucleus is... 

If the excited states of compound nuclei overlap, statistical methods are applied which also allow prediction of the emission of particles by a compound nucleus and of the cross section of a certain nuclear reaction. 

Fig. 8.11 gives a survey of the location in the chart of the nuclides of the products obtained by various low-energy nuclear reactions. By reactions with neutrons an isotopic compound nucleus is formed which may emit particles or photons, depending on its structure and excitation. In (n, y) reactions the excitation energy of the compound nucleus is given off in the form of y-ray photons. In (n, p) reactions the compound nucleus emits a proton and the product is an isobar of the target nuclide. 

Many nuclear reactions proceed through the formation of a compound nucleus. The compound nucleus, formed after particle x, collides with X2, is highly excited and lives for a time of the order of 10 to 10 s before it decays to X3 and X4. A compound nucleus may be formed in more than one way and may decay by more than one mode that does not depend on the mode of formation. Consider the example of the compound nucleus 7N ... 

For pedagogic reasons we treat this reaction as if an intermediate compound nucleus is formed. The compound nucleus f is in square brackets to indicate its transitory nature and marked with an asterisk to indicate that it is excited. Induced nuclear reactions are often written in an abbreviated manner indicating first the target and then, in parentheses, the projectile and the smaller product, followed by the major product outside the parentheses. In Ae case of the sanqile reaction, we would write N(a,p) 0 The abbreviations used for He, H, (=D), (=T), etc., are a, p, d, t, etc. The reactions may be classified by... 

If the reaction passes through formation of a compound nucleus, having a lifetime of many nuclear vibrations, we should expect that the amounts and types of reaction products were independent of the projectile — target combination used to produce a specific compound nucleus and only depend on its excitation energy. This has indeed been found to be the case for some kinds of nuclear reactions, see Ch. 14. 

There are two ways in which the compound nucleus can release this excess energy (1) it may radiate gamma rays, or (2) it may emit one or more nuclear particles (neutrons, protons, or alpha particles). Which of these two processes predominates depends on the total excitation energy of the compound nucleus. If sufficient energy is available, more than one reaction can take place. 

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