1
Neutron-Nuclear Reactions

The physics of nuclear reactors is determined by the transport of neutrons and their interaction with matter within a reactor. The basic neutron nucleus reactions of importance in nuclear reactors and the nuclear data used in reactor physics calculations are described in this chapter.

1.1 Neutron-Induced Nuclear Fission

Stable Nuclides

Short-range attractive nuclear forces acting among nucleons (neutrons and protons) are stronger than the Coulomb repulsive forces acting among protons at distances on the order of the nuclear radius (R ~ 1.25 × 10-13 A1/3 cm) in a stable nucleus. These forces are such that the ratio of the atomic mass A (the number of neutrons plus protons) to the atomic number Z (the number of protons) increases with Z; in other words, the stable nuclides become increasingly neutron-rich with increasing Z, as illustrated in Fig. 1.1. The various nuclear species are referred to as nuclides, and nuclides with the same atomic number are referred to as isotopes of the element corresponding to Z. We use the notation (e.g., ) to identify nuclides.

Fig. 1.1 Nuclear stability curve. (With permission from Ref. [1]. Copyright 1996, McGraw-Hill.)

Binding Energy

The actual mass of an atomic nucleus is not the sum of the masses (mp) of the Z protons and the masses (mn) of A - Z neutrons of which it is composed. The stable nuclides have a mass defect:

This mass defect is conceptually thought of as having been converted to energy (E = ?c2) at the time that the nucleus was formed, putting the nucleus into a negative energy state. The amount of externally supplied energy that would have to be converted to mass in disassembling a nucleus into its separate nucleons is known as the binding energy of the nucleus, BE = ?c2. The binding energy per nucleon (BE/A) is shown in Fig. 1.2.

Fig. 1.2 Binding energy per nucleon. (With permission from Ref. [1]. Copyright 1996, McGraw-Hill.)

Any process that results in nuclides being converted to other nuclides with more binding energy per nucleon will result in the conversion of mass into energy. The combination of low A nuclides to form higher A nuclides with a higher BE/A value is the basis for the fusion process for the release of nuclear energy. The splitting of very high A nuclides to form intermediate-A nuclides with a higher BE/A value is the basis of the fission process for the release of nuclear energy.

Threshold External Energy for Fission

The probability of any nuclide undergoing fission (reconfiguring its A nucleons into two nuclides of lower A) can become quite large if a sufficient amount of external energy is supplied to excite the nucleus. The minimum, or threshold, amount of such excitation energy required to cause fission with high probability depends on the nuclear structure and is quite large for nuclides with Z < 90. For nuclides with Z > 90, the threshold energy is about 4-6 MeV for even-A nuclides, and generally is much lower for odd-A nuclides. Certain of the heavier nuclides (e.g., and ) exhibit significant spontaneous fission even in the absence of any externally supplied excitation energy.

Neutron-Induced Fission

When a neutron is absorbed into a heavy nucleus (A, Z) to form a compound nucleus (A + 1, Z), the BE/A value is lower for the compound nucleus than for the original nucleus. For some nuclides (e.g., , , , ), this reduction in BE/A value is sufficient that the compound nucleus will undergo fission, with high probability, even if the neutron has very low energy. Such nuclides are referred to as fissile; that is, they can be caused to undergo fission by the absorption of a low-energy neutron. If the neutron had kinetic energy prior to being absorbed into a nucleus, this energy is transformed into additional excitation energy of the compound nucleus. All nuclides with Z > 90 will undergo fission with high probability when a neutron with kinetic energy in excess of about 1 MeV is absorbed. Nuclides such as , , and will undergo fission with neutrons with energy of about 1 MeV or higher, with high probability.

Neutron Fission Cross Sections

The probability of a nuclear reaction, in this case fission, taking place can be expressed in terms of a quantity s that expresses the probable reaction rate per unit area normal to the neutron motion for n neutrons traveling with speed v, a distance dx in a material with N nuclides per unit volume:

The units of s are area that gives rise to the concept of s as a cross-sectional area presented to the neutron by the nucleus, for a particular reaction process, and to the designation of s as a cross section. Cross sections are usually on the order of 10-24 cm2, and this unit is referred to as a barn, for historical reasons.

The fission cross section, sf, is a measure of the probability that a neutron and a nucleus interact to form a compound nucleus that then undergoes fission. The probability that a compound nucleus will be formed is greatly enhanced if the relative energy of the neutron and the original nucleus, plus the reduction in the nuclear binding energy, corresponds to the difference in energy of the ground state and an excited state of the compound nucleus, so that the energetics are just right for formation of a compound nucleus in an excited state. The first excited states of the compound nuclei resulting from neutron absorption by the odd-A fissile nuclides are generally lower lying (nearer to the ground state) than the first excited states of the compound nuclei resulting from neutron absorption by the heavy even-A nuclides, which accounts for the odd-A nuclides having much larger absorption and fission cross sections for low-energy neutrons than do the even-A nuclides.

Fission cross sections for some of the principal fissile nuclides of interest for nuclear reactors are shown in Figs. 1.3-1.5. The resonance structure corresponds to the formation of excited states of the compound nuclei, the lowest lying of which are at less than 1 eV. The nature of the resonance cross section can be shown to give rise to a 1/E1/2 or 1/? dependence of the cross section at off-resonance neutron energies below and above the resonance range, as is evident in these figures. The fission cross sections are largest in the thermal energy region E < ~1 eV. The thermal fission cross section for is larger than that of or .

Fig. 1.3 Fission cross sections for . (From www.nndc.bnl.gov/.)

Fig. 1.4 Fission cross sections for . (From www.nndc.bnl.gov/.)

Fig. 1.5 Fission cross sections for . (From www.nndc.bnl.gov/.)

Fission cross sections for and are shown in Figs. 1.6 and 1.7. Except for resonances, the fission cross section is insignificant below about 1 MeV, above which it is about 1 barn. The fission cross sections for these and other even-A heavy mass nuclides are compared in Fig. 1.8, without the resonance structure.

Fig. 1.6 Fission cross sections for . (From www.nndc.bnl.gov/.)

Fig. 1.7 Fission cross sections for . (From www.nndc.bnl.gov/.)

Fig. 1.8 Fission cross sections for principal nonfissile heavy mass nuclides. (With permission from Ref. [2]. Copyright 1963, Argonne National Laboratory.)

Products of the Fission Reaction

A wide range of nuclides are formed by the fission of heavy mass nuclides, but the distribution of these fission fragments is sharply peaked in the mass ranges 90 < A < 100 and 135 < A < 145, as shown in Fig. 1.9. With reference to the curvature of the trajectory of the stable isotopes on the n versus p plot of Fig. 1.1, most of these fission fragments are above the stable isotopes (i.e., are neutron rich) and will decay, usually by ß-decay (electron emission), which transmutes the fission fragment nuclide (A, Z) to (A, Z + 1), or sometimes by neutron emission, which transmutes the fission fragment nuclide (A, Z) to (A - 1, Z), in both instances toward the range of stable isotopes. Sometimes several decay steps are necessary to reach a stable isotope.

Fig. 1.9 Yield versus mass number for fission. (From Ref. [2].)

Usually either two or three neutrons will be emitted promptly in the fission event, and...