Compound nucleus excited

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... 

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 ... 

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. 

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... 

In this equation, jjl is the reduced mass of the system, and o-inv is the cross section for the inverse process in which the particle b is captured by the nucleus B where b has an energy, Eb. The symbols p(E B) and p( c) refer to the level density in the nucleus B excited to an excitation energy E% and the level density in the compound nucleus C excited to an excitation energy, . The inverse cross section can be calculated using the same formulas used to calculate the compound nucleus formation cross section. Using the Fermi gas model, we can calculate the level densities of the excited nucleus as... 

Figure 10.23 Schematic illustration of the l dependence of the partial cross section for compound nucleus (CN), fusionlike (FL), deep inelastic (D), quasi-elastic (QE), Coulomb excitation (CE), and elastic (EL) processes. [From Schroeder and Huizenga (1984, p. 242).]...

Consider the Ca + Cm reaction where the lab energy of the Ca is 300 MeV. What is the excitation energy of the putative compound nucleus 296116 What is the expected total reaction cross section ... 

Consider the reaction 12C(a, n) where the laboratory energy of the incident projectile is 14.6 MeV. What is the excitation energy of the compound nucleus The reaction cross section is 25 millibars. Assuming a carbon target thickness of 0.10 mg/cm2 and a beam current of 25 nA, compute the lsO activity after a 4-min irradiation. 

In nuclear reactors one has neutrons with energies ranging from thermal (0.025 eV) to several MeV. There are a series of sharp peaks in the total cross section for neutrons with energies between 0.2 and 3000 eV that are called resonances. These resonances correspond to exciting a specific isolated level in the compound nucleus that can decay by fission. The situation is particularly interesting for the neutron irradiation of even-even nuclei, such as 240Pu at subthreshold energies... 

Fig. 11.8). The resonances associated with fission appear to cluster in bunches. Not all resonances in the compound nucleus lead to fission. We can understand this situation with the help of Figure 11.9. The normal resonances correspond to excitation of levels in the compound nucleus, which are levels in the first minimum in Figure 11.9. When one of these metastable levels exactly corresponds to a level in the second minimum, then there will be an enhanced tunneling through the fission barrier and an enhanced fission cross section. 

Solution The excitation energy of the compound nucleus E will be... 

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... 

The fate of a compound nucleus depends on its composition and its excitation energy, not on the way it is formed. It may be formed and decay in different ways ... 

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. 

In the first reaction the compound nucleus decays immediately into two a particles and the energy A = 17.35 MeV which is set free in the reaction is distributed equally to both a particles. In the second reaction excitation energy of the compound nucleus is given off in the form of a y-ray photon and the unstable Be decays with the very short half-life of 2 10 s into two a particles. 

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