Nucleus compound

The effects of a rather distinct deformed shell at = 152 were clearly seen as early as 1954 in the alpha-decay energies of isotopes of californium, einsteinium, and fermium. In fact, a number of authors have suggested that the entire transuranium region is stabilized by shell effects with an influence that increases markedly with atomic number. Thus the effects of shell substmcture lead to an increase in spontaneous fission half-Hves of up to about 15 orders of magnitude for the heavy transuranium elements, the heaviest of which would otherwise have half-Hves of the order of those for a compound nucleus (lO " s or less) and not of milliseconds or longer, as found experimentally. This gives hope for the synthesis and identification of several elements beyond the present heaviest (element 109) and suggest that the peninsula of nuclei with measurable half-Hves may extend up to the island of stabiHty at Z = 114 andA = 184. 

From these various processes, one can separate at least three simple prototype pathways whereby the compound nucleus may get rid of its several million electron volts which constitute the neutron binding energy. These should encompass essentially all other possibilities, as far as chemical... 

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... 

Therefore, the compound nucleus must have >1 = 4 and Z = 2 (He). It then loses a proton,... 

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. 

C22-0055. Identify the compound nucleus and final product resulting from each of the following nuclear... 

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. 

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. 

When the compound nucleus has an excited level coinciding in energy with that of the projectile in the CM system, i.e. the projectile energy E is close to Ep where... 

When there are only two possible decay channels for the excited state of the compound nucleus, i.e. T = Va + Vh, two simple limiting cases arise ... 

When a slow neutron is captured by the nucleus of element X, another isotope of the same element is instantaneously formed, in an excited state because of the impact (labelled compound nucleus in Figure 2.13), which then de-excites by the emission of a gamma particle (and possibly other particles) from the nucleus to produce a radioactive nucleus. For example, when 23Na captures a neutron (signified by on, since neutrons have a mass of one unit, but no electrical charge), it becomes the radioactive nucleus 24Na, as follows ... 

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... 

The scattering lengths discussed so far refer to a fixed nucleus. If the nucleus is free to vibrate, it will recoil under the impact of the neutron. In that case the effective mass is that of the compound nucleus, consisting of the neutron and the scattering nucleus. This means that the neutron mass m must be replaced by the reduced mass of the compound nucleus (i = mM/(M + m), where M is the mass of the scattering atom. As a result, the scattering length of the free atom is related to that of the bound atom by... 

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. 

Figure 6.20 A representation of the branching decays from a highly excited compound nucleus. In the statistical model, the relative probability for the excited nucleus to decay into a specific channel is proportional to the number of possibilities or statistical weight of that channel divided by the sum of all of the statistical weights of all of the channels.

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 ... 

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

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