As discussed in Section 5.5.3, neutrons are classified according to their kinetic energy as cold, thermal, slow, epithermal, and fast neutrons. Since neutrons are neutral, there is no Coulomb repulsion between them and nuclei. As a result, even thermal neutrons can initiate nuclear reactions. When the neutron collides with the nucleus, an excited nucleus forms, which can emit a neutron whose energy is dif­ferent from the neutron that initiated the process.

The cross section of nuclear reactions with neutrons versus neutron energy is shown in Figure 6.4. The plot has two general features. First, the cross section decreases when the energy and velocity of the neutron increase. This means that at

	Table 6.1 Classification of Nuclear Reactions
	Irradiating Particle	Nuclear Reaction
Neutral particle	Neutron	n, Y; n, p; n, a; n,2n; n, f (fission)
	Gamma photon	Y, n; Y, p
Charged particle	Proton	p, Y; p, n; p, a
	Deuteron	d, p; d, n; d,2n; d, a
	Alpha	a, n; a, p
	Other nuclei	See the discussion of the production of transuranium elements in Section 6.2.6.

Figure 6.4 Cross section of nuclear reactions with neutrons versus neutron energy. The cross section is inversely proportional to the velocity (energy) of neutrons up to b1 eV.

lower velocities, the neutron spends more time near the nucleus, so the probability of the nuclear reaction increases.

Second, the cross section is enormously high at certain energy values, so-called resonances can be observed. This is explained by the discrete energy state of the compound nucleus. The resonances are observed at the energies equal to any excitation energy of the compound nucleus. The two effects are observed simultaneously.

The most frequent nuclear reactions with neutrons are the (n, Y) reactions:

An (n, y) a +An (6.12)

In this process, the emitted particle, a gamma photon, is also neutral, so there is no Coulomb barrier for either neutrons or gamma photons. Therefore, the (n, Y) reactions are simple, and they take place for each element except helium. They are exoergic, releasing about 8 MeV of energy. The disadvantage of the (n, Y) reactions is that the target and the product nuclei have the same atomic number—only the mass number increases by 1. This means that carrier-free radioactive isotopes
cannot be produced directly by this nuclear reaction; the product radioactive nuclide is diluted with the stable nuclide of the same element. Since the product number is rich in neutrons, it usually emits negative beta particles. An example of (n, Y) reactions, the production of 24Na isotope is shown:

23Na(n, Y)24Na (6.13)

The (n, Y) reactions are applied in the neutron activation analysis and prompt gamma activation analysis (PGAA discussed in Sections 10.2.2.1 and 10.2.2.2).

The competitive reaction of the (n, Y) reactions is the (n, p) reactions:

An (n, p) z _An (6.14)

Since the emitted particle (proton) is heavier than a gamma photon, the (n, p) reactions should have a greater cross section. The proton, however, is positively charged, so its emission is inhibited by the Coulomb barrier of the product nucleus (similar to the emission of the alpha particles, as discussed in Section 4.4.1). As a result, light elements react in the (n, p) reactions, while heavier nuclides prefer the (n, Y) reactions. Similar to (n, Y) reactions, the (n, p) nuclear reactions are also exoer — gic. The atomic number of the product nucleus is reduced by 1, and both the target and the product nuclei have the same mass number. The product nuclear is rich in neutrons, so it is a negative beta emitter. Since the target and the product nuclei have different atomic numbers, they are chemically different, so they can be sepa­rated by chemical procedures. In this way, carrier-free radioactive isotopes can be prepared. For example:

64Zn(n, p)64Cu (6.15)

After irradiation with neutrons, the compound nuclide can emit alpha particles too:

AN (n, a)A _ 2n (6.16)

The (n, a) nuclear reactions are endoergic. Only light elements can react in this way because of the high Coulomb barrier between the alpha particle and the prod­uct nucleus. For example:

6Li(n, a)3H (6.17)

If the reaction (6.17) takes place in heavy water (D2O), the product nucleus, tritium, can react with the nucleus of deuterium as follows:

2H(t, n)4He = a or 3H(d, n)4He = a (6.18)

As a result, the neutron is recovered. The irradiating neutrons are thermal neu­trons with different energies; the produced neutrons, however, are fast and have a well-determined energy, в 14 MeV. This reaction takes place in the hydrogen bomb too.

The (n,2n) reactions such as

A N (n, 2n)A "An (6.19)

are also endoergic, since the mass of the neutron increases when emitted from the nucleus (as discussed in Section 2.2). Since the number of the neutrons in the pro­duced nucleus decreases, the product nucleus decays with positive beta decay or electron capture. Since the atomic number remains the same, carrier-free radioac­tive isotopes cannot be obtained directly. Some examples of (n,2n) reactions are:

63Cu(n, 2n)62Cu, 115In(n, 2n)114In, and 23Na(n, 2n)22Na (6.20)

A very important type of nuclear reaction with neutrons is the fission of heavy nuclei under the effect of thermal neutrons. This is called the “(n, f) reaction.” From the natural nuclides, only the fission of 235U has a high cross section. As a result of this fission, two nuclei with intermediate mass, called “fission products,” and more than one neutron are produced:

235U 1 n! A1n 1 A2n 1(2.4 — 2.8)n (6.21)

The binding energy of the two fission products is less than the binding energy of the target nucleus, meaning that the fission reaction is exoergic, releasing 200 MeV of energy. This energy can be used for energy production in nuclear power plants and has been used in the atomic bombs (see Chapter 7). The fission is usually asymmetric; the ratio of the masses of the fission product is about 2:3. In Figure 6.5, the ratio of the fission products of 235U by thermal neutrons and the

Figure 6.5 Products of the fission of 235U by thermal neutrons.

main ranges of elements are illustrated, including the small — and high-fission yields. Strontium and cesium, the most important fission products of the low- and interme­diate-level nuclear wastes, are labeled with bold letters.

A significant number of the fission products are radioactive, and some of them have long half-lives. Therefore, the treatment of the radioactive fission products is a very important environmental and safety problem with the production of nuclear energy.

The fission products can be the parent nuclides of decay series. For example, the simplified scheme of the formation of strontium isotopes is shown in Figure 6.6.

In addition to 235U, three artificially produced isotopes, namely, 239Pu, 241Pu, and 233U, also have high fission cross sections. They can be produced from iso­topes, which are more abundant naturally than 235U: the plutonium isotopes can be produced from the 235U isotope (the ratio of 235U to 238U is 1:139, as detailed in Section 4.3.1), U can be obtained from Th. The nuclear reactions of the pro-

239 241 233

duction of Pu, Pu, and U isotopes are as follows:

238U(n, y)239U -—-! 239Np -—-! 239Pu(n, Y)240Pu(n, y)241 Pu (6.22)

232Th(n, Y)233Th ——! 233Pa ——! 233U (6.23)

The irradiating neutrons are obtained from neutron sources, neutron generators, or nuclear reactors (see Section 5.5.2).

4 3.0	4 3.5	4	Figure 6.6 A simplified
		-—-88Sr	scheme of the formation of
— 88Kr ——	4z 00 00 £	strontium isotopes by fission of
4 4.5	4 4.8	4"	235U. The numbers next to the
vertical arrows indicate the
)89Kr -,Y	— 89pb.	—- , 89Sr — , 89Y	fission yield of the given
> Kr 3min		15 min 51 days	isotope; the half-lives are
4 5.0	4 5.8	4 5.9 4 5.8	shown below the horizontal

88Br-

89Br —

>90Kr

в" ,y

>90Rb

>90Sr-

>90Y-

3min * 29 years ‘ * 64 h 4 4.9 4 5.8 4 5.9

arrows. (Thanks to Dr. Nora -90Zr Vajda, RadAnal Ltd., Budapest, Hungary, for the scheme.)

0Br-

*91Rb ——- 91Sr——- 91Y—

1s 9s 58s 10 h 59 days

41.6 4 5.2 4 5.9 4 6.0

P" ,Y no P" ,Y no P" ,Y no P" no

92Br -—— 92Kr —— 92Rb —— 92Sr —-— 92Y —— 92Zr

0.3h 2s 5s 3h 4h

4 0.6 4 4.1 4 6.3 4 6.4

93 в" ,Y 93 в, Y 93 в" ,Y 93 в 93

93Kr—— > 93Rb—— > Sr———- > 93Y—— > 93Zr

1s 6s 7min 10h

41.8 4 4.8 4 6.3

94 P" ,Y 94 P" ,Y 94 P" ,Y 94

94Rb —94Sr ———> 94Y ——-—> Zr

Some isotopes of the transuranium elements have great cross sections for neu­trons, but their produced quantity is too low to be used as fuel in nuclear reactors. Their only application is neutron bombs, which contain 252Cf (see Section 7.5).