Compound Nucleus Reactions

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  

The probability of decay of the compound nucleus (CN) into a given set of products (3 can be written as  

Let us first consider the case of Y/D 1. This means that at certain values of the compound nucleus excitation energy, individual levels of the compound nucleus can be excited (i.e., when the excitation energy exactly equals the energy of a given CN level). When this happens, there will be a sharp rise, or resonance, in the reaction cross section akin to the absorption of infrared radiation by sodium chloride when the radiation frequency equals the natural crystal oscillation frequency. In this case, the formula for the cross section (the Breit-Wigner single-lev el formula) for the reaction a + A — C b + B is 

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 

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Reactions may be either direct , where an energetic particle has such a small wavelength that it only sees one nucleon of the target, or compound nucleus reactions, where the projectile s energy is shared among many nucleons in successive collisions within a compound nucleus which can then decay into one of a number of exit channels (Fig. 2.6). The first case is the more common one in reactions between light nuclei, whereas the second dominates for heavier ones. 

Direct interactions proceed faster than compound nucleus reactions. The time of direct interactions is given by the time needed by the projectile to enter the nucleus and the time needed to leave the nucleus after collision. Reactions at the surface of the nucleus proceed within 10 s and reactions within the nucleus in about 10 - s. 

The average energy of the disintegration products of compound nucleus reactions is usually small compared with the excitation energy of the compound nucleus. If therefore we suppose that Eq—Qqi, is large compared with s, and if we suppose that at a given excitation energy the level densities in the compound nucleus and the residual nucleus are the same, so that Sb(E) = Sq E),... 

To date, the highest production rates of isotopes of transactinide elements have been achieved in compound nucleus reactions between light and heavy ion beams (ISq, I9p 26j g actinide targets ( U, Pu, Cm, Bk,... 

Mercuration and chloromethylation reactions as well as halogena-tion seem to proceed with preliminary coordination followed by substitution in the coordination compound. Such reactions as nitration and sulfonation in concentrated acids appear to proceed differently as evidenced by the substitution of the phenyl nucleus on nitration and by the sulfonation of phenylisoxazolcs. 

The immediate product of a reaction between two nuciei is a compound nucleus. It has a charge equai to the sum of the charges of the reactants and a mass number equai to the sum of the mass numbers of the reactants. Every compound nucieus has excess energy that must be reieased after the two reactants bind together. Compound nuciei... 

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. 

In a transmutation reaction, the incident neutron is absorbed, forming a compound nucleus that decays so that the residual nucleus is different from the target nucleus and the outgoing channel typically includes two particles. A transmutation reaction can be written as... 

Elements are fundamental substances that cannot be broken down into smaller chemical components. The smallest unit of an element is an atom, a term based on the Greek word atomos, meaning indivisible. But atoms are divisible—they consist of a nucleus containing positively charged particles called protons and electrically neutral particles called neutrons, surrounded by a swarm of electrically negative particles called electrons. In chemical reactions, atoms interact and combine to form a molecule of a compound. (Chemical reactions also occur when the atoms in molecules interact and combine to form even bigger com-... 

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. 

What will be the distribution in space of the reaction products Let us assume that because the compound nucleus has forgotten its mode of formation, there should be no preferential direction for the emission of the decay products. Thus, we might... 

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