The compound nucleus

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... 

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. 

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 ... 

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... 

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... 

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... 

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... 

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... 

Fig. 3. Two decay chains measured in experiments at SHIP in the cold fusion reaction 70Zn + 208Pb —> 278112. The chains were assigned to the isotope 277112 produced by evaporation of one neutron from the compound nucleus. The lifetimes given in brackets were calculated using the measured a energies. In the case of escaped a particles the alpha energies were determined using the measured lifetimes.

The cross sections for elements lighter than 113 decrease by factors of 4 and 10 per element in the case of cold and hot fusion, respectively. The decrease is explained as a combined effect of increasing probability for reseparation of projectile and target nucleus and fission of the compound nucleus. Theoretical consideration and empirical descriptions, see e.g. [61,62], suggest that the steep fall of cross sections for cold fusion reactions... 

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