As seen in Figure 2.2, the fusion of light elements also can be used for energy pro­duction. These thermonuclear processes provide the energy in stars (see Sections

6.2.4 and 6.2.5) and in the hydrogen bomb (see Section 7.5).

The potential of controlled thermonuclear reactions has been studied for several decades. These processes should provide the energy requirements of the Earth for a million years by the fusion of deuterium in the oceans. In addition, the fusion reac­tions produce no nuclear waste.

The thermonuclear reactions have two basic requirements. First, the temperature must be about 108 K because the ignition temperature of the 2H—2H reaction and the 2H—3H reaction are 3 X 108 and 3 X 107 K, respectively (Section 6.2.4). Second, the пт value, the so-called Lawson limit, must be higher than 1021 parti­cles s/m for the H— H reaction and 10 particles s/m for the H— H reaction, where п is the particle density and т is the confinement time. The Lawson limit indicates the ability of the plasma to retain heat. The two conditions depend on each other; that is, a given temperature needs a certain пт value.

There are two approaches to achieving a controlled thermonuclear reaction. A part of the reactors is based on the magnetic confinement of the hot (>108K) plasma containing the isotopes of hydrogen (deuterium and tritium). The most successful results with this method have been obtained in the Tokamak instrument, in Moscow. In this instrument, the plasma is toroid shaped. The other type of con­trolled thermonuclear reactor operates in pulsed mode (inertia confinements) when small pellets of solid deuterium and/or tritium are injected into a chamber and irra­diated by an intense beam of photons from lasers. Recently, there are experiments with the combination of the magnetic and inertia confinement.

The controlled thermonuclear reactors are in the experimental stage. Some examples of important experimental fusion reactors are JET (Joint European Torus, United Kingdom), DIII-D (USA, San Diego), EAST (Experimental Advanced Superconducting Tokamak, China), TFTR (Tokamak Fusion Test Reakctor, USA, Princeton), K-Star (Korea Superconducting Tokamak Advanced Research, South Korea), JT-60 (Japan Torus 60, Japan), TCV (Tokamak a configuration variable, Switzerland), and T-15 (Russian). The International Thermonuclear Experimental Reactor (ITER) in France is under construction. This reactor is scheduled to be operational in 2018. Its objectives are to demonstrate the feasibility of fusion power and to prove that it can work without negative impact. This includes to ignite self­sustaining plasma for at least 8 min, and to produce more than enough energy to ignite the fusion. Commercial reactors may be produced in the second part of the twenty-first century at the earliest. There are still many technical problems to be solved. For example, when heating to a suitably high temperature, the fuel sepa­rates from the walls of the vessels (no substances are able to withstand this temper­ature). In addition, the injection of fuel (deuterium and tritium) and the withdrawal of the product (helium), and the control of the fusion are problematic at this time.

The main constituents of atoms are protons, neutrons, and electrons. After the revision of Dalton’s atomic theory, these particles were considered to be elementary particles, the basic constituents of matter. Later, Yukawa recognized that the nucleons interact with each other through the meson field, and a new elementary particle, the meson, had to be postulated. Moreover, several different kinds of mesons with different rest masses and charges have been discovered. In addition, new elementary particles have been observed in different nuclear and cosmic processes. Today, more than 300 ele­mentary particles are known (this fact raises the ironic question: How can something be called elementary if there are hundreds of them?).

The elementary particles can be classified on the basis of rest mass: light and heavy elementary particles are called leptons and hadrons, respectively. Hadrons can be divided into two groups: mesons (with medium rest mass) and baryons (with large rest mass). They are characterized similarly to the nuclei; as listed at
the end of Section 2.3, they have rest mass, electric charge, spin, parity, statistics, magnetic moment, and electric quadruple moment. In addition, an important prop­erty of the elementary particle is the mean lifetime.

The heavy particles, hadrons, consist of more fundamental particles, which are called “quarks.” Particles are referred to as fundamental if they exhibit no inner structure. Quarks can be experimentally demonstrated, for example, by irradiating protons with 50 GeV electrons. The magnetic momentum of neutrons implies the presence of charged particles inside the neutron as well.

The physics of the elementary particles postulate six types and three families of quarks (up—down, charm—strange, top—bottom). Within the atomic nucleus, the up and down quarks are the most important. The rest mass of up and down quarks is about 1/3 a. m.u. and their charge is +2/3 and —1/3, respectively. The proton consists of two up quarks and 1 down quark; the neutron contains one up quark and two down quarks. The sum of the rest masses of the three quarks gives 1 a. m.u. for both proton and neutron. In addition, the net charge of the nucleons (+1 for protons and 0 for neu­trons) is the summation of the individual charges of the quarks. Table 2.3 illustrates the important properties of some elementary particles. The particles with half-integral spin (fermions) are the fundamental constituents of matter; the particles with integral spin (bosons) are the exchange particles between quarks, which are similar to the exchange of photons in the electromagnetic force between two charged particles.

Interactions in the last column of Table 2.3 can be ordered on the basis of their relative strength as follows:

Interaction Relative Strength

Strong 1

Electromagnetic 10—2 Weak 10—14

Gravitation 10—39

The range of the interactions is inversely proportional to their relative strength. In nuclear processes, strong interactions are dominant. The range of strong interac­tions is about 10—15 m.

The antiparticles of all the particles listed in Table 2.3 could and should exist. The electric charge of these antiparticles is the opposite of their corresponding par­ticles. When the particle—antiparticle pairs interact with each other, they form other particles with lower or zero rest masses. As an example, the annihilation of positron and electron could be mentioned, which have a great practical importance (as discussed in Section 5.3.3).

Beta decays take place when the ratio of protons and neutrons is not optimal. Beta decays tend to allow the nucleus to approach the optimal proton/neutron ratio. When there are too many neutrons related to the protons, negative beta decay occurs; when there are too many protons related to the neutrons, positive beta decay takes place. As a result of beta decays, the mass number of the atoms remains the same, but the atomic number changes: the atomic number increases in the negative beta decay and decreases in the positive beta decay, respectively. Besides the beta particle, another particle is also emitted: antineutrino in the nega­tive beta decay and neutrino in the positive beta decay.

Negative beta decay: | + 1M 1 в-+ V (4.99)

Positive beta decay: A-M! A — 1M 1 в+ 1 v (4.100)

In Eqs. (4.99) and (4.100), в — are в+ are the negative and positive beta particles, i. e., electrons and positrons. It is important to note that the term “beta particles” means only electrons (positive or negative) emitted from nuclei. Electrons emitted from the extranuclear shell are called “electrons” and designed by e2.

Similar to alpha decay, the emitted energy of beta decays can be calculated from the rest masses of the parent and daughter nuclide plus the emitted particles:

Negative beta decay: E = (£m — A + 1M) 931 MeV (4.101)

Positive beta decay: E = (AM — A __ 1M — 2me) 931 MeV (4.102)

The rest mass of the neutrino can be ignored because its rest mass is about 10,000 times lower (150 eV at most) than the rest mass of the electron (0.51 MeV). As seen in Eqs. (4.101) and (4.102), besides the differences between the rest masses of the parent and daughter nuclides, there are differences between the rest masses of two electrons since the increase of the atomic number in the negative beta decay requires the uptake of another electron, while the decrease of the atomic number in the positive beta decay causes the emission of another electron. This means that positive beta decay can take place only if the rest mass of the parent nuclide is at least two electron masses (1.02 MeV) heavier than the rest mass of the daughter nuclide.

Since the radioactive decay always releases energy (in the exothermic process), it takes place only if the rest mass of the parent nuclide is greater than the rest mass of the daughter nuclide + the emitted particle(s). (As mentioned previously, the rest mass of the neutrino can be ignored.) For negative beta decay, this can be

expressed as:

Am — Zme > A + jM — (Z 1 1)me 1 me (4.103)

Similarly, for positive beta decay:

AM — Zme > A — 1M — (Z — 1)me 1 me (4.104)

The solution of Eqs. (4.103) and (4.104) is:

AM > A і M (4.105)

Am > A — 1M 1 2me (4.106)

As seen in Eqs. (4.105) and (4.106), the differences in the rest masses give dis­crete values for the emitted energy. The spectrum of the beta radiation, however, is continuous (Figure 4.10), and the calculated energy is equal to the maximum energy. (The electrons with discrete energy are emitted from the electron shells.)

The continuous beta spectra can be interpreted by the two emitted particles, the beta particle and the neutrino. The energy of beta decay is divided into two parts: both beta particles and neutrinos have some energy. The emission of two particles explains the changes of the spin of the nucleus as a result of the decay: the spin of the nucleus changes by 1, the spin of both beta particle and neutrino is 1/2 (see Table 2.3).

Figure 4.10 General shape of beta spectra: the number of beta particles with a given energy (N(E)) versus beta energy (E).

The elementary process of the beta decay can be described as follows:

Negative beta decay:

n! p+ + (Г+ V (4.107)

Positive beta decay:

p1! n 1 (3+ + v (4.108)

It is important to note that the processes in Eqs. (4.107) and (4.108) do not mean the free nucleons, but bound in the nucleus. Since the rest mass of the neutron is larger than the rest mass of the proton, the difference of masses in the process of Eq. (4.107) produces energy. The negative beta decay is obviously exothermic. In positive beta decay, however, a proton is transformed to a neutron. This requires energy because of the differences between the rest masses (1.3 MeV; see Table 2.1), which is provided by the decrease of the mass of the nucleus. In addition, the emittion of the positron requires more 0.51 MeV energy, which is also to be provided by the decrease of the mass of the nucleus. The sum of the two energies is 1.8 MeV.

The neutrino emitted in the beta decays cannot be detected directly because it is neutral and its rest mass is very small. However, because of the conservation of lin­ear momentum at beta decay, the momentum vectors (i. e., the pathways of the par­ticles) of the daughter nuclide and the beta particle should be at an angle of 180°. However, as photographed in a cloud chamber in the beta decay of 6He by Csikai and Szalay in 1957 (Figure 4.11), another particle (neutrino) has to be released during the decay as well.

The antineutrino can be detected using the following reaction: p 1V! n 1 в1 (4.109)

Since the cross section of the reaction (4.109) is very low (as discussed in Chapter 6), the high flux of antineutrinos is required similar to those present in nuclear reactors. When an aqueous solution of CdCl2 is placed into a nuclear

reactor, antineutrinos react with the protons of water in the reaction (4.109). The two products, namely, the positive beta particle and the neutron, can be detected simultaneously in the following way. The positive beta particles and electrons are annihilated, and as a result, photons of 0.51 MeV are emitted (see Section 5.3.3). The neutrons are thermalized in a few microseconds and initiate the nuclear reac­tion 113Cd(n, Y)114Cd. The gamma photons emitted in this nuclear reaction of 113Cd follow the emission of the photons with 0.51 MeV after a few microseconds. The two photons can be detected by coincidence measurements.

In beta decays, the nuclei usually emit one beta particle. However, two beta par­ticles are emitted in a single process in some cases. This process is called double beta decay. Theoretically, two types of double beta decays can exist: in the first, two beta particles and two neutrinos are emitted [(3(3(vv)], in the other, only two beta particles (no neutrinos) are formed [(3(3(0v)]. In the first case, the two neutrinos annihilate each other; and in the second, the emitted neutrino is absorbed by another one.

Decay products of the double beta decay [(3(3(vv)] (by extraction of crypton and xenon from very old selenium and tellurium minerals) in geological samples were detected in 1950. Under laboratory conditions, double beta decay was observed in 1986 when the double beta decay of 82Se was measured:

82Se!82Kr 1 2e2+ 2v (4.110)

In the laboratory experiments, 1.1 X 1020 years was obtained for the half-life of the double beta decay of 82Se. This value is similar to the results obtained in geochemical measurements.

More than 60 naturally occurring isotopes are capable of undergoing double beta decay. Only 10 of them were observed to decay via the two-neutrino mode: 48Ca, 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 128Te, 130Te, 150Nd, and 238U.

The neutrinoless double beta decay [(3(3(0v)] has not been demonstrated beyond any doubt.

Some examples of the nuclear reactions with alpha particles ((a, n) and (a, p)) have been shown in previous discussions of the first nuclear reaction (see Eqs. (6.1) and (6.3)) and neutron sources (see Section 5.5.2). The (a, xn) reactions are important in the production of the transuranium elements (see Section 6.2.6).

Living organisms can react with the isotope molecules in different ways. As dis­cussed in previous chapters, the cause of the physical and chemical isotope effects can be easily understood, but the biological effects are much more complicated. The most important isotope effects occur in the case of the isotope of hydrogen since the hydrogen bond plays a very important role in the secondary and tertiary structures of the proteins and nucleic acids. When substituting deuterium for hydro­gen, the strength of the hydrogen bond increases, i. e., the cleavage of a deuterium bond requires more energy. This increase is similar to the differences in the partial pressure of water under the effect of hydrogen—deuterium substitution. Heavy water (D2O) inhibits or can stop the proliferation of cells. The experience shows that living organism may die when the deuterium—hydrogen substitution happens quickly. However, when the deuterium—hydrogen substitution is slow, the living organisms can adapt to the heavy water. During the adaptation phase, cell destruc­tion or cell proliferation may be observed. After the adaptation, the cells develop as usual.

Recently, there have been some reports claiming that drinking deuterium-free water has desirable physiological effects, such as reducing the risk of cancer. This effect may have been observed in vitro. However, because of the fast isotope exchange of deuterium and hydrogen in the environment (air, nutrients, etc.), deute­rium concentration of the human body cannot be lowered in this manner.

In a sample containing the beta emitter, the beta particles can also be absorbed by the sample itself in a process called “self-absorption.” The precise and accurate measurement of the samples containing beta emitters requires taking into consider­ation the effect of self-absorption, except when the sample is “infinitely thin.” In every other case, the radioactive intensities measured for the same radioactivity

depend on the thickness of the sample, the quantity of the carrier (an excess of inactive atoms of the same elements in the same chemical state), or an inactive matrix (every other substance). In some cases, the molecule itself containing the radioactive isotope can absorb a part of the beta radiation. In solutions, the solvent can absorb the radiation to such a high degree that it becomes impossible to mea­sure the activity. For this reason, beta emitters are usually measured in the solid phase. (It is important to note here that there is a special technique for the measure­ment of beta emitters, namely, the liquid scintillation technique, which utilizes this absorption. It will be discussed in Section 14.2.1.)

When the beta energy is low (so-called weak beta, e. g., 14C, 35S), the self­absorption is significant at thin layers. However, it cannot be ignored at high beta energies, either, especially when the sample is thick because of the presence of the inactive matrix. Depending on the quantity of inactive matrix, the measured inten­sity of the same radioactive substance can differ.

The effect of self-absorption can be corrected in two ways: the method of con­stant activities for high beta energies, and the method of constant specific activities for low beta energies. In the method of constant activities, the intensity is extrapo­lated for the infinitely thin layer, while in the method of constant specific activities, the intensity is measured at the so-called saturated thickness (>10 X d1/2). The two methods of the correction of self-absorption are discussed as follows.

In the method of constant activities, the total radioactivity of the sample is con­stant and the quantity of the matrix changes. The samples are arranged as shown in Figure 5.16.

The thickness of the sample is d (g cm-2), and the total intensity of the radiation (the intensity without matrix) is I0. From here, the intensity of the radiation in a unit thickness is I<jd. Consider a dx elementary thickness at a distance x from the upper sur­face of the sample; the intensity in this elementary thickness is I0 dx/d. Passing through the distance x, the radiation is absorbed and the intensity decreases. The intensity reach­ing the upper surface (dl) is expressed by the radiation absorption law (Eq. (5.48)):

dl = — exp(- nx)dx (5.59)

d

where д is the mass absorption coefficient.

By integrating Eq. (5.59) for the total thickness of the sample (d), we obtain the total intensity reaching the surface:

I = — [1 — exp(—pd)] (5.60)

pd

If the intensities of samples with constant radioactivity in different quantities of matrix are measured, the intensity decreases as the quantity of the matrix, i. e., the thickness of the samples increases. The I0 can be obtained by extrapolating to zero thickness. It can be done graphically or by a parameter-estimating computer pro­gram from the I versus d function. The measurements can be done up to 1 —2 half­thickness (Figure 5.17).

For thin layers (up to the 30% of the half-thickness), I0 can be determined by the series expansion of Eq. (5.60):

I = I0 1 — 2 pd (5.61)

In the method of constant specific activities, the characteristic properties of self­absorption (mass absorption coefficient and half-thickness) can be determined as follows. Samples with different thickness are produced from a substance having the same specific activity. In this case, the intensity of a unit thickness is defined as I0 (its dimension is intensity/surface density). The intensity reaching the surface decreases because of the absorption as described by the radiation absorption law (Eq. (5.48)): I0 exp(—pd). The total intensity reaching the surface is:

Since

from Eq. (5.62), we obtain the following:

I = I®[1 — exp(-pd)]

where IN is the intensity at the saturation thickness. This is the maximal intensity, which does not increase even if the thickness increases. The intensity as a function of the thickness is shown in Figure 5.18.

In the method of constant specific activities, the half-thickness can be defined (dm) as:

The half-thickness can be determined from Eq. (5.64) graphically or by a param­eter-estimating computer program.

The method of constant specific activities can be used if the thickness is at least 7—10 times greater than the half-thickness. In this case, the specific intensities of the samples can be compared since they are proportional to the radioactivity.

In nuclear reactors, shielding against neutron and gamma radiation is essential. When planning the shielding for neutron radiation, it is important to take into con­sideration that the cross section for the fast neutron is rather small (see Figure 6.4). So, for shielding material, those substances should be chosen that efficiently slow down the neutrons and then efficiently absorb the thermal neutrons. The same mod­erators discussed in Section 7.1.1.4 are suitable for this purpose; therefore, the active zone of the reactors is usually surrounded by a mantle consisting of the mod­erator (water, graphite, etc.).

In nuclear reactors, the gamma radiation is very intense. The intensity of the gamma radiation continuously increases because of the increase of the quantity of the fission products. For protection against the gamma radiation, substances with a high atomic number and density are suitable. The stainless steel reactor vessel itself provides some shielding against gamma radiation. The nuclear reactors are sur­rounded by a thick concrete wall.

There are cases when more than one radionuclide is present at the same time. The radioactivity, as well as the activity— time function, depends on all the radionu­clides that are present. The identification of each nuclide requires the mathematical decomposition of the activity—time function into components. Then, the identifica­tion of the radionuclides present can be done on the basis of the type of decay, the energy, and the half-life of the emitted particles.

When the decays of the radioactive nuclei present are independent, the radioac­tivities of the mixed nuclides are the sum of the radioactivities of all nuclides. Consequently, the activity—time function cannot be described by the kinetic of the simple radioactive decay (Eq. (4.8)). This means that the radioactivity—time curve must be decomposed. In principle, the decomposition could be done easily by using computing techniques. However, since the functions have to be fitted to the experi­mental activity—time function, it has some limitations; for example, the activity/ intensity and the half-life of the individual isotopes can be determined only by the decomposition of the activity/intensity—time function if there is at least one order of magnitude difference in the half-lives, and if the isotope mixture does contain only a limited number of different radioactive isotopes. If these conditions are not met, adding or neglecting additional nuclides does not improve the accuracy of the mathematical decomposition of the activity—time function.

Since neutrons have no charge, detecting them is difficult. For this reason, neutrons were discovered relatively late, although Rutherford had postulated their existence in 1920.

In 1930, during the study of the energy levels of nuclei, Bothe and Becker irra­diated beryllium with alpha particles and observed the emission of radiation with a very long range and high energy (5 MeV). Since the energy levels of nuclei were studied, the emitted radiation was supposed to be gamma radiation of beryllium. This experiment was repeated in 1932 by Irene Curie and Frederic Joliot-Curie; however, they detected the emitted radiation by other techniques and found that the energy of the radiation was much higher than what was given by Bothe and Becker. Similarly, Chadwick measured energy readings that were as high as 50 MeV. As a consequence, Chadwick stated that if the energy of the “gamma” radiation of the beryllium depends on the detection method, it cannot be “gamma” radiation, or at least another particle must be emitted besides gamma radiation. In addition, Chadwick postulated that the long-range radiation should consist of neu­tral particles that transfer energy only by colliding with nuclei. These particles were called “neutrons.”

Chadwick measured the rest masses of the neutrons by elastic collision with hydrogen and nitrogen nuclei and found that the ratio of the neutron to the hydro­gen nucleus (proton) is about 1.1:1.

The nuclear reactions that are used for energy production are also used for military purposes. Nuclear weapons utilize both the fusion reaction and the combination of the fusion and fission reactions.

In the fission bomb (better known as the atomic bomb), the unregulated fission of 235U (Eq. (6.21)) or another fissile, plutonium, takes place. The fissile is placed in pieces, each containing less fissile than the critical mass. The chain reaction is ignited by a chemical explosion, which causes the addition of the pieces so that the mass will become more than the critical mass. During the unregulated chain reac­tion, the very high energy of the fission reaction releases in a very short time, caus­ing another explosion. As mentioned in Chapter 1, the first two nuclear bombs were exploded at the end of World War II in Japan. On August 6, 1945, a bomb known as “Little Boy” was exploded in Hiroshima; the fission of 235U took place in the bomb. On August 9, 1945, the “Fat Man” bomb was detonated in Nagasaki; the fissile in this bomb was plutonium.

The combination of the fusion and fission reactions is the thermonuclear or hydrogen bomb. The first hydrogen bomb was developed in 1952. The high tem­perature needed for the ignition of the fusion reaction of hydrogen isotopes (deute­rium and tritium; see Eqs. (6.47) through (6.50)) is provided by a fission reaction; that is, by an atomic bomb. The fusion fuel is tritium, deuterium, or lithium deuter — ide. As mentioned in Section 6.2.4, the ignition temperature is the lowest for the 2H—3H reaction; so the most favorable fusion reaction is the 2H—3H reaction. The production of tritium, however, is expensive, and in addition, its half-life is 12.4 years. For this reason, lithium deuteride is frequently used. From lithium, tritium is produced in the reaction (6.17) under the effect of neutrons formed in the fission reaction.

Recently, fission—fusion—fission bombs have been developed. In these bombs, there is an outer mantle, and the fission reaction takes place. In the so-called salted bombs, the nuclear weapon is surrounded by a substance such as cobalt or gold, from which radioactive isotopes are formed via the nuclear reactions initiated by neutrons that are produced in the fission reactions. These bombs can be considered “dirty bombs” because of their high radioactive contamination.

A special type of thermonuclear weapon is the neutron bomb, in which the fis­sile has low critical mass (e. g., californium). The fusion fuel is the mixture of deu­terium and tritium. The bomb is surrounded by a substance that has a very low level of neutron absorption. In this way, the main destructive impact is caused by the escaping neutrons. The mass of the neutron bombs is only a few kilograms, and therefore it can be transported very easily. Because of the small quantity of fissile, the radioactive contamination is relatively low.

Further Reading

Choppin, G. R. and Rydberg, J. (1980). Nuclear Chemistry, Theory and Applications. Pergamon Press, Oxford.

Friedlander, G., Kennedy, J. W., Macias, E. S. and Miller, J. M. (1981). Nuclear and Radiochemistry. Wiley, New York, NY.

Lieser, K. H. (1997). Nuclear and Radiochemistry. Wiley-VCH, Berlin.

McKay, H. A.C. (1971). Principles of Radiochemistry. Butterworths, London.

Prawitz, J. and Rydberg, J. (1958). Composition of products formed by thermal neutron fission of 235U. Acta Chim. Scand. 12:369—377.

Vajda, N. (1994). Atomreaktorok futoelmeinek ellencSrzeise uj analitikai mcidszerek segitsegevel (Analysis of nuclear fuel elements by new methods). Candidate’s Thesis. Budapet Technical University, Budapest.

European Nuclear Society, 2003. Nuclear power plants, world-wide. < www. euronuclear. org/info/encyclopedia/n/nuclear-power-plant-world-wide. htm (IAEA, August 2011). > (accessed 25.03.12.)