Similar to alpha decay, spontaneous fission takes place with heavy nuclides. The nucleus is split into two smaller nuclei, assuming that the sum of the mass of the daughter nuclides and the emitted neutrons, if any, is less than the mass of the par­ent nuclide. The energy of spontaneous fission can be calculated from the decrease of the mass:

E = 931 MeV(|M — A1M — A2M — xmn) (4.117)

E has to be greater than zero, which is principally valid at about A > 80, as shown by the positive slope of Figure 2.2. However, spontaneous fission requires activation energy; therefore, it is characteristic of thorium and the heavier nuclides. Spontaneous fission was discovered by Petrzsak and Flerov in 1940, shortly after the discovery of neutron-induced fission by Otto Hahn (1939).

A M — A1M + A2 M 1 xn (4.118)

For spontaneous fission, the log A versus Z2/A function for the isotopes of a given element shows a maximum curve (Figure 4.13). The ratio Z2/A is called the “fissionability parameter” because the liquid drop model (discussed in Section 2.5.1) predicts that the probability of fission should increase with this ratio. The composition of the fission products is similar for both spontaneous and neutron-induced fission (see Figure 6.4).

The elements in the universe are formed through nuclear reactions. The history of the universe, in some way, could be considered to be a process consisting of nuclear reactions.

The scientific interpretation of the universe is based on observations and experi­ences of theoretical and experimental physics, astronomy, and the spectral analysis of the universe. The first observation to be considered is the relative abundance of the elements in the universe, as illustrated in Figure 6.8. As seen in Figure 6.8, about 90% of the atoms in the universe are hydrogen and about 9% are helium. The amount of all the other elements combined is <1%. The relative abundance of helium in the stars (e. g., the Sun) is about twice that in the universe. An important fact is that the amount of the elements usually decreases as the atomic number or mass number increases. The amount of the elements in the iron group, however, is higher than expected on the basis of the atomic number. Some light elements (lithium, beryllium, and boron) are very rare. The amount of the elements with even atomic numbers is higher than the amount of the adjacent elements with odd atomic numbers. As a result, a theory explaining the amount of the elements in the universe should start from hydrogen and explain how the heavier elements can be produced from hydrogen and the mentioned anomalies in the general tendency of the abundances.

As another starting point, astrophysical observations can be mentioned. The age of the Milky Way is about 15 billion years, or 15 eons. The age of the oldest

meteorites and rocks on the Moon is about 4.65 eons. The age of the oldest rocks in the Earth’s crust is about 2.6 eons. Some stars of the Milky Way are only about 1 million years old. The different ages of the stars and planets show that they were formed over a long period and they are still in the process of formation/transforma — tion. If the elements are produced in the stars, their formation is continuous.

Information on the universe originates from spectral measurements. These spec­tral data provide information on the elementary composition, surface temperature, age, density, and movement of the stars. Because of the Doppler effect, the spectra of the stars moving away shift toward higher wavelengths. This is called the “red — shift phenomenon,” and it shows the expansion of the universe, i. e., it is thought to have been much smaller during its early stages.

The first theory of the formation of the elements and the stellar revolution has been constructed by G. Gamov and R. A. Alpher, including assumptions by H. Bethe. They proposed that at the moment of the formation of the universe, all matters existed as neutrons in a gigantic nucleus, which exploded. This event is popularly known as “the Big Bang.” During this explosion, the neutrons trans­formed into protons by negative beta decay with (t1/2 = 11 min). The formation of the elements began with the combination of protons and neutrons. This theory was modified later, postulating that the gigantic nucleus may have contained some other particles heavier than neutrons, and the radiation density (i. e., the number of photons) was much higher than the density of the particles. In the Big Bang, only hydrogen and helium formed; there were no heavier elements. Approximately 25% of the expanding cloud converted to helium; the rest remained as hydrogen. This would explain the relative abundance of hydrogen and helium in the universe.

Assuming that the rate of the expansion of the universe is constant, the Big Bang occurred about 13 billion years ago. Gravity, however, decreases during the expansion, so the age of the universe may be 15—20 billion years.

Later, I. E. Segal found that the red-shift is not linearly proportional, but rather the square of the distance. If so, the most important argument of the Big Bang the­ory is put into question and that would imply that the universe is eternal.

The temperature of the neutron state has been hypothesized to be about 2—20 X 109 K. When such a hot gas cloud is adiabatically expanded, its tempera­ture decreases. From the size of the universe, Alpher, Herman, and Gamov calcu­lated that black body radiation with about 5 K has to be present. Really, black body radiation with 2.7 K can be detected in the whole universe, which proves the Big Bang theory.

The Big Bang theory, however, can only provide an interpretation for the forma­tion of hydrogen and helium. The formation of the other elements can be explained by the processes that occur in stars, assuming that the stars are formed by the con­densation of the matter of the interstellar space consisting of hydrogen and helium. In this condensation process, the density of the interstellar matter (atoms/cm3) sig­nificantly increases (by about 1000 times). At critical density, hydrogen gas trans­forms to protons and electrons, plasma is formed, and the pressure significantly decreases. The gravitation accelerates the condensation of the interstellar gas, and the release of the gravitation energy increases the temperature. When the temperature of the core reaches 5 X 106 K, a thermonuclear reaction, in which hydrogen is converted to helium, can begin. Since the thermonuclear reactions are exoergic, the temperature continues to increase. As a result, a very hot core and a much colder mantle form, as observed in the Sun.

The transformation of hydrogen to helium is not a one-step process because the probability of the collision of four atoms is negligible. Instead, the elementary steps shown in Table 6.2 are assumed to happen. Since the formation of positron occurs through weak interaction, the first elementary step is very slow. One from ~ 1022 1H + 1H collisions results in a successful reaction in the Sun. If this reaction has been going on in the Sun for 4.6 eons, about 6% of the hydrogen has to be already converted to helium.

Beside the main reaction in Table 6.2, other reactions may take place as well, such as:

2H 13H! 4He 1 n, AE = -17.59 MeV (6.52)

3He + n AE = -3.27 MeV (6.53)

2H + 2H

3H + p AE = -4.03 MeV (6.54)

2H 13H ! 4He 1 p, AE = -18.38 MeV (6.55)

3H 14He! 6Li 1 n, AE = 2.73 MeV (6.56)

!H 1 6Li! 3He 1 4He, AE = -4.02 MeV (6.57)

3He 14He! 7Be 1 y, AE = -1.59 (6.58)

7Be 1 e — ! 7Li 1 v, AE = -1.37 MeV (6.59)

In the processes (6.52)—(6.55) and (6.57), helium is formed too.

Since helium is heavier than hydrogen, gravitation acts stronger on helium. Therefore, helium tends to move toward the core of the star, and hydrogen is in the outer mantle. As the quantity of hydrogen in the core decreases, the temperature decreases as well. Gravitation in the core, however, increases, contracting and warming the core. The warming core increases the temperature of hydrogen in the outer mantle, expanding the mantle of the star. In this period, the star emits red light and becomes a red giant.

As discussed previously, the density and gravitation of helium in the core increases, the temperature rises until the thermonuclear reactions (fusions) can start. These fusion processes cause an abrupt increase in temperature, producing the nuclei with the atomic number in the range of 5—8. Two helium nuclei combine to form a nucleus, whose half-life is only 2 X 10_16 s. However, the quantity of 8Be is enough to react with a third helium nucleus, producing 12C isotope, which is stable:

3 4He! 8Be 14He! 12C 1 y (6.60)

If 12C is already present, the additional reactions with helium can produce heavier nuclei up to silicon:

12C(4He, Y)16O(4He, Y)20Ne(4He, Y)24Mg(4He, Y)28Si (6.61)

As seen in Figure 6.9, the amount of the even nuclides of the light elements is higher than the amount of adjacent odd nuclides. This is in agreement with the reactions in Eq. (6.61).

238U(n, y)239U 239Np

Iе-

239Pu(n, Y)240Pu(n, Y)241Pu(n, Y)242Pu(n, Y)243Pu

Iе-

241Am(n, Y) 242Am(n, Y) 243Am(n, Y) 244 Am

Iе — Iе-

242Cm(n, Y)243Cm(n, Y)244Cm(n, Y)245Cm(n, Y)246Cm(n, Y)247Cm(n, Y) 248Cm(n, Y) 249Cm(n, Y)250Cm

Iе — Iе-

249Bk(n, Y) 250Bk

Iе — Iе-

249Cf(n, Y)250Cf(n, Y)251Cf(n, Y)52Cf(n, Y) 253Cf

Iе-

253Es(n, Y) 254Es

Iе-

Fm

Figure 6.9 Production of transuranium elements by (n, Y) nuclear reactions.

The opportunity of helium burning that leads to the formation of the heavier elements depends on the size of the star. When the mass of the star is less than the half the mass of the Sun, the temperature cannot rise high enough for the helium burning to be initiated. When the mass of the star is <3.5 times the mass of the Sun, the burning of carbon does not take place. These stars become white dwarfs; the gravitation crack, however, can initiate the transformation of the outer hydrogen mantle into helium. This process, called a “nova explosion,” can drive out part of the core matter in the outer mantle.

In the great stars (the masses of which are more than 3.5 times the mass of the Sun), helium burning is an important source of energy. As the temperature rises above 109 K, the reactions, some examples of which are listed below, can take

place:

12C 112C! 20Ne 1 4He (6.62)

12C 112C! 23Na 1 p (6.63)

12C 112C ! 23Mg 1 n (6.64)

12C 112C! 24Mg 1 y (6.65)

16O 116O! 28Si 14He (6.66)

16O 116O! 31P 1 p (6.67)

16O 116O! 31S 1 n (6.68)

16O 116O! 32S 1 y (6.69)

The conditions such that these reactions (Eqs. (6.62)—(6.69)) occur are appropri­ate in stars with a mass of at least 7.5 times that of the Sun. The emission of the gamma photons (see Eqs. (6.65) and (6.69)) assists the emission of nucleons from the nuclides with mass numbers from 12 to 32. As a result, a so-called soup of nuclides, nucleons, alpha particles, and photons forms, in which lighter and heavier nuclides can react further as the temperature rises. These reactions are feasible until the formation of the most stable elements (namely, the elements of the iron group), where the absolute value of the binding energy per nucleon is maximal. The amount of even nuclides and nuclides with closed proton and neutron shells is higher.

The transformation of hydrogen and helium produces neutrons as well. In the formation of heavier elements, the concentration of neutrons significantly increases, so the main procedure of the formation of the elements changes: namely, neutron captures become dominant. The elements from iron and bismuth are formed in so-called slow (s) (n, y) reactions accompanied by beta decays.

The formation of elements heavier than bismuth cannot be explained by the s-process since these elements have many short-lived isotopes that prohibit additional neutron captures. Their formation is explained as follows: In stars (red giants), where the heavier elements have been accumulated in the core, energy production continues in the outer mantle. The energy release of these stars is very high because of the emission of photons and neutrinos. As a result, the core of the star becomes cooler and contracts, and the gravitation energy decreases, initiating the increase of the pressure and temperature. Under these conditions, the strong photon field causes the photodisintegration of the elements of the iron group, producing helium nuclei and neutrons. Helium burning immediately starts, increasing the temperature of both the core and the mantle. Therefore, fusion reactions start in the mantle too. This process is known as a “supernova explosion.” Because of the high pressure, we can postulate the reaction as follows:

p1 + e2 ! n + v (6.70)

The supernova explosion is a very fast process, but the emission of the neutrons is very intense, producing elements heavier than bismuth in the so-called rapid (r) process.

After the supernova explosion, a very dense (1018 kg/m3) neutron star is formed, starting a new cycle!?

As a result of the isotope effects, isotopes are fractionated in nature. The amount of natural isotope fractionation, however, is usually smaller than would be expected from the isotope effects because the cyclic processes characteristic in nature tend to compensate for the fractionation caused by isotope effects. Only the isotope

fractionation of the light elements can be easily observed. Thus, the heaviest element showing isotope separation in nature is germanium. Besides the isotope effects, the fractionation of the radioactive isotopes is also influenced by the radioactive decay.

The stable isotope concentrations of the substances are presented as the molar ratio of the heavy-to-light isotopes. Since this ratio is small, stable isotope abun­dances are usually presented relative to an international standard:

S = Rsample — 1 X 1000 (3.43)

^standard

where S is expressed in %o. In Eq. (3.43), Rsampie and Rstandard are the ratio of heavy-to-light isotopes in the sample and the standard, respectively. For example, the value of S for the stable isotopes of hydrogen is:

Traditionally, the isotope ratios of five elements (namely, hydrogen, carbon, nitrogen, oxygen, and sulfur) are used for practical, especially geochemical, pur­poses. The standard of the isotope ratios of these elements is summarized in Table 3.6. Standard materials are available from the International Atomic Energy Agency (IAEA) and the National Institute of Standards and Technology (NIST) to ensure accurate measurement and reporting of isotope ratios for unknown samples and to facilitate cross-lab comparability.

The gamma radiation (gamma photon) is very different from alpha and beta radia­tion. The most important difference is that it has no charge or mass. It forms during the transition of nucleons between the shells in the nuclei, and their energy is in a very broad range. As discussed previously, the gamma photons are always emitted from the nuclei, whereas the photons emitted by the inner electron orbitals are called “X-ray photons.” However, both gamma and X-ray radiations are electro­magnetic radiation, so their interactions with matter can be treated together.

The gamma and X-ray photons usually have intermediate interactions with mat­ter. The interactions are summarized in Table 5.6 and Figure 5.22. The dominant type of the interaction is strongly affected by the energy of gamma photons. Depending on the energy, the gamma photos can interact with the orbital electrons, the nuclear field, and the nucleus. The cross section of the interactions (the absorp­tion coefficient, in other words) also depends on the atomic number of the substance.

It is important to emphasize that one of the most important interactions is the scattering of the gamma photons. Depending on the energy, different scattering phenomena can be observed, namely, Rayleigh, Thompson, and Compton

Interaction with nuclear field

Positron

Electron

Figure 5.22 Interactions of gamma photons with the different constituents of matter. Source: Reprinted from Choppin and Rydberg (1980), with permission from Elsevier.

scattering in the interaction with the orbital electrons, and the (y, y) and (y, y ) nuclear reactions in the nuclei. In addition, gamma photons do not cause direct ion­ization; only the secondary electrons forming in the interactions of gamma radia­tion with matter can produce ions.

The first artificial reactor was built in Chicago in the early 1940s as part of the Manhattan Project. The project supervisor was Enrico Fermi, in collaboration with Leo Szilard, the discoverer of the chain reaction. The first self-sustaining chain reaction was started on December 2, 1942. The fuel was enriched uranium, and the moderator was graphite. The controls consisted of cadmium-coated rods that absorbed neutrons. The withdrawal of the rods increased neutron activity, leading to a self-sustaining chain reaction (keff = 1). The reactor had no radiation shielding and no cooling system. Fermi himself described the apparatus as “a crude pile of black bricks and wooden timbers.”

The construction of nuclear reactors for energy production started in the 1950s. As mentioned previously in this chapter, the first nuclear reactor built specifically for energy production opened in Obninsk in 1954.

When the daughter element of a parent element is also radioactive and decays fur­ther, we describe this as a successive decay series. It means that there are genetic relations between the radionuclides. There are some similar decay series in the products of uranium fission initiated by neutrons. For example, 90Sr isotope decom­poses by negative beta decay to 90Y, which also decomposes by negative beta decay to stable 90Zr. In this series, there are two successive decays; however, there are series with more than two successive decays. Three natural radioactive decay series where alpha and beta decays form long decay series are known. Their start­ing parent nuclides are 235U, 238U, and 232Th isotopes, and the last, stable nuclides are different lead isotopes, namely, Pb, Pb, and Pb. These natural radioac­tive decay series are shown in Figures 4.4—4.6.

For simplicity, the kinetics of the radioactive decay series are demonstrated for the two-member decay series (a parent nuclide and one radioactive daughter nuclide). The total radioactivity (A) is the sum of the radioactivities of the parent (Aj) and daughter (A2) nuclides:

A = Ai 1A2 (4.27)

The kinetics of the radioactive decay of the parent nuclide can be described using the kinetics of the simple decay, as discussed previously:

Aj = AiNi = A1N0 e-A1t (4.28)

The radioactivity of the daughter nuclides depends on two factors: it continu­ously forms from the parent nuclide and decays. Therefore, the quantity of the daughter nuclide is determined both by the rate of its formation and by its decay:

dN2

= A1N1 — A2N2 (4.29)

In Eqs. (4.28) and (4.29), N1 and N2 are the number of the parent and daughter nuclides, respectively; A1 and A2 are their decay constants.

For the solution of Eq. (4.29), the next substitutions are applied:

N2 = u X v

and

v = e——2 г

The total derivative with respect to t of the function in Eq. (4.30) is: dN2 d(uv)

dt

From Eqs. (4.29) and (4.32):

— u2 e—A2t 1 du e—A2t = A1N1 — A2N2

By substituting Eqs. (4.28) and (4.30) into Eq. (4.33), we obtain:

— uA2 e—A2t 1 du eA2t 1 uA2 e—A2t — A1N10 e—A1t = 0 After mathematical simplification:

du e~—2t — A1N10 e~—1t = 0 The solution of Eq. (4.35) is:

A1N10 e(A2 A)t

u = — N10 e(A2 A1)t 1 C

A2 2 A1

where C is a constant. By substituting Eq. (4.37) into Eq. (4.30):

N2 = — N10 e—A1t 1 C e—A2t

A2 2 A1

When at t = 0, N2 = N20, then from Eq. (4.38):

A1

N20 = N10 1 C

A2 2 A1

By expressing C and substituting into Eq. (4.38), we obtain:

N2 = a — a N10 e A1t 1 ^n20 — a — a N1^e —2t

After equivalent mathematical transformation:

N2 = — Nw e——1t [1 — e(Al ——2)г] 1 N20 e——2t (4.41)

—2 — —1

or

N2 = — N10 [e —1t — e —2t] 1 N20 e —2t (4.42)

Л2 — A1

Instead of the number of the radioactive nuclides, radioactivities can be written using A2 = N2A2 and A1 = N1A1:

A = — A10 e-—1t [1 — e(A1——2)t] 1A20 e-—2t (4.43)

A2 2 A1

This equation of the activity can be transformed directly to intensities only if the measuring efficiency for both the parent and daughter nuclides is the same. If not, intensity can be measured only after reaching radioactive equilibrium (see Section 4.1.6).

The first and second members in Eq. (4.41) express, respectively, the increase and decay of the quantity of the daughter nuclide compared to its quantity at t = 0. The maximum quantity of the daughter nuclide can be determined by the differenti­ation of Eq. (4.41): the quantity of the daughter nuclide is maximized when Eq. (4.41) has an extremum. For the sake of simplicity, suppose that, at t = 0, N2 = 0:

From here:

t = 1 1 —1

^^max ln

A1 2 A2 A2

At t = 0, N2 Ф 0, the equation has an additional member (which is not discussed here).

For radioactive decay series having more than two members, the formation and decay rates can be defined for the third to nth members, similar to Eq. (4.29):

= A2N2 — A3N3

dt

The solution of the rate equations can be given as follows:

n

Nn =53 C e~X“ (4-47)

where

n—1

ПA

cn = N10-^ (4.48)

П (At — A)

k=1

кфі

For three members:

‘ A1A2e—A1t, A1A2e—A2t, A1A2 e—A3t ‘

(A2 — A1)(A3 — A1) (A1 — A2 )(A3 — A2) (A1 — A3 )(A2 — A3)

(4.49)

The inelastic collision of radiation and the nuclei of a substance may result in the formation of new nuclei. Rutherford observed in 1919 that a proton and a new nucleus, 17O, form in the reaction of alpha particles with nitrogen (Figure 6.1). This nuclear reaction can be described by any chemical reaction:

^N 1 a = 17O 1 p (6.1)

The nuclear reactions have the following nomenclature:

!74N(a, p)17O (6.2)

The substance (14N) irradiated in this case with alpha particles is called the “target,” the emitted particle is the proton, and the product nucleus is 17O. A cloud chamber photograph shows the tracks of the alpha particle, the proton, and the recoiled 17O hot nucleus (described in Section 6.4) can be observed (Figure 6.1). The product (17O) is a stable isotope; thus, the first artificial nucleus produced by humans was stable.

The first artificial radioactive nucleus was produced by Joliot and Irene Curie in 1932 by the irradiation of aluminum with alpha particles. The irradiated aluminum was dissolved in sodium hydroxide solution; the product was distilled and collected on the cold wall of a glass tube. (This procedure, which is the separation by ther­modiffusion, is similar to the Marsch test for detecting arsenic.) The product emitted (3+-particles with a half-life of 2.5 min:

27Al(a, n)3°P (6.3)

The partners of the nuclear reactions are the target nucleus and the irradiating particles. The important properties, the selection of a target nucleus, and charged particles will be discussed in Section 8.5.2, and the production of the irra­diating particles was shown in Section 5.5.2 (neutrons). The opportunities for the production of a nuclide with a Z atomic number and an A mass number will be summarized in Section 6.3. Moreover, the production of the important radioactive isotopes will be discussed in detail in Sections 8.5—8.7.

Nuclear and Radiochemistry. DOI: http://dx. doi. org/10.1016/B978-0-12-391430-9.00006-8

© 2012 Elsevier Inc. All rights reserved.

As seen from nuclear reactions (6.2) and (6.3), the following rules of conserva­tion apply:

1. The number of nucleons

2. The charges In addition,

3. spin,

4. parity,

5. momentum,

6. energy, including both the kinetic energy and the energy originating from the change of the masses of the reactants and products, are conversed.

Similar to chemical reactions, the nuclear reaction can be exoergic (exothermic) or endoergic (endothermic). The energy of the nuclear reaction (AE) can be calcu­lated from the difference between the mass of the products (product nucleus + emitted particle) and the reactants (target nucleus + irradiating particle) multiplied with the energy equivalent to the atomic mass unit (931 MeV):

^E 931 MeV[(mproduct_nucleus 1 memitted particle)

(6.4)

(mtarget nucleus 1 mirradiating particle)]

When the mass of the reactants is greater than that of the products, the nuclear reaction is exoergic; when the mass of the reactants is less than that of the pro­ducts, the nuclear reaction is endoergic. The activation energy needed for nuclear reactions is provided by the irradiating particles. In case of exoergic nuclear reac­tions, the released energy will compensate for the activation energy invested. In nuclear reactions with neutrons, the activation energy can be close to zero. In the case of endoergic nuclear reactions, the energy of the irradiating particle must
provide both the activation energy and the energy of the reaction. The energy of the reaction (plus the recoiling energy of the product nucleus) gives the threshold energy, the minimal energy needed for a successful nuclear reaction. In the nuclear reactions where charged particles react (which always means positively charged particles), the Coulomb barrier of the target nucleus has to be overcome:

2Ze2

Г1 1 Г2

where Z is the atomic number of the target, e is the elementary charge, and r1 and r2 are the radii of the target nucleus and the irradiating particle.

As seen in Section 2.5.1, the binding energy of nuclei can generally be expressed well by the liquid-drop model. However, this model cannot explain certain phe­nomena. For example, some nuclei with given mass numbers (2, 8, 20, 50, 82, 126, 184) are extremely stable. These numbers are called “magic numbers.” Also, a very small difference in the nuclei results in a very great difference in stability. For example, 210Po and 212Po isotopes differ in only two neutrons, but their half-lives are 138.37 days and 10_7 s, respectively, a fact that indicates very different stabilities.

These phenomena can be explained by the shell model of nuclei. This model postulates that, similar to electrons, nucleons are arranged in shells in the nucleus. The closed shells result in the most stability, and the magic numbers indicate filled shells. The stability is indicated by the mass of the nuclei: within the isobar nuclei, the nucleus with the lower mass is stable. The radioactive nuclei have unfilled shells.

According to the shell model, there should be some transuranium elements with relatively great stability and “long” half-lives.

As a result of radioactive decay, the nuclei of the daughter nuclides can be in an excited state. The excited nucleus may return to a lower excited state or ground state emitting photons with a characteristic energy. These photons are called

“gamma photons” or “gamma radiation.” Thus, gamma radiation is not indepen­dent; it always follows another radioactive decay process. The time between the original radioactive decay and the gamma photons can range from minutes to years. This process is called “isomeric transition”; the excited state of the nucleus is known as a “metastable state.” About 150 isomer pairs are known. An empirical relation between the mean lifetime (t) and the radiation energy (E) has been found on the basis of the change in the spin (ДJ):

In Eqs. (4.119)—(4.121), energy and mean lifetime are expressed in keV and seconds, respectively.

As an example of the isomer transition, let us discuss the 137Cs isotope. 137Cs itself is a beta emitter, while its daughter nuclide is 137mBa (m means the metastable, excited

state). The daughter nuclide, 137mBa, transforms into 137Ba by emitting a gamma pho­ton. The energy of the gamma photon is 662 keV. 137Cs is frequently used to calibrate spectrometers; however, gamma photons are emitted by 137mBa, not directly by 137Cs.

4.2.5 Exotic Decay

During exotic decay, the spontaneous emission of nuclei takes place. For example,

Exotic decays are very rare, so they are difficult to observe. In the case of the 223Ra isotope, for example, the probability of the decay (4.123) is about 1011 times lower than the probability of the alpha decay. The emitted nuclei are very stable, having closed nucleon shells.

Further Reading

Burshop, E. H.S. (1952). The Auger Effect and Other Radiationless Transitions. Cambridge University Press, Cambridge.

Csikai, J. (1957). Photographic evidence for the existence of the neutrino. Il nuove cimento 5:1011-1012.

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.

Haissinsky, M. (1964). Nuclear Chemistry and its Applications. Addison-Wesley, Reading, MA.

Kullerud, K. 2003. The Rb-Sr method of dating. <http://ansatte. uit. no/kku000/webgeology/ webgeology_files/english/rbsr. html.> (accessed 24.03.12.)

National Nuclear Data Center, 2010. List of Adopted Double Beta ((3(3) Decay Values. <http://www. nndc. bnl. gov/bbdecay/list. html.> (accessed 24.03.12.)

Lagoutine, F., Ciursol, N. and Legrand, J. (1983). Table de Radionucle’ides. Comissirait a l’Energie Atomique, France.

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

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

Perkins, D. H. (2000). Introduction to High Energy Physics. 4th edition. Cambridge University Press, Cambridge.

Spalding, K. L., Buchholz, B. A., Bergman, L.-E., Druid, H. and Frisen, J. (2005). Age written in teeth by nuclear tests. A legacy from above-ground testing provides a precise indica­tor of the year in which a person was born. Nature 437:15.

The heaviest natural element is uranium. The next elements, so-called transuranium elements, have been produced artificially by nuclear reactions with neutrons, charged particles, and other nuclei. The production and names of the transuranium elements are summarized in Table 6.3.

As seen in Table 6.3, the production of the transuranium elements started in the United States in 1940, in the period of the development of the atomic bomb. The first transuranium elements (neptunium, plutonium, americium, and curium) were produced by (n, Y) nuclear reactions and the following beta decays, and the new elements (plutonium and americium) were irradiated again with neutrons, which results in additional (n, Y) reactions and beta decay. These transuranium elements are produced in nuclear power plants; some of them (239Pu, 241Pu) are fissile nuclides (as discussed in Section 6.2.1), and so play a role in the neutron balance of the nuclear reactors. In addition, plutonium isotopes are separated from the burned-out fuels and applied for production of mixed oxide fuels (see Section 7.1.1.1) or nuclear weapons (see Section 7.5).

Transuranium elements heavier than curium cannot be produced with (n, Y) reac­tions because the negative beta decay of curium isotopes is not known. These elements have been produced by nuclear reactions with positively charged particles. The charged particle is an alpha particle to californium. Then, as the atomic number of the transuranium element increases, heavier and heavier charged particles must be used for the irradiation.

Atomic Number 93 94 95 96 97 98 99 100 101 102 103 104	Name of Element Year and Place of Production	Nuclear Reaction
Neptunium	1940, United States	238U(n, y)239U-—! 239Np

From the 1960s, transuranium elements have been produced in the Soviet Union (now Russia) too. At that time, the scientific research became political competition. This is reflected in the names of the transuranium elements: every discoverer gives a name to the new element even if that element already had a name. There have been heated arguments about this issue, for example, the American scientists did not accept the production of kurtschatovium (presently known as rutherfordium) by the Russian scientists since they were said to give an incorrect half-life for the element. For this reason, there are elements in Table 6.3 that have several names. Finally, in 1997, IUPAC accepted the names, and they are official now (shown in bold in the table).

The American and the Soviet scientists had different strategies for the produc­tion of the transuranium elements. The American scientists tended to irradiate heavier targets with smaller particles; in these cases, the targets had to be produced in higher quantities. The scheme of this method is shown in Figure 6.9. The Soviet scientists, however, irradiated lighter targets with heavier particles. This procedure required greater and greater cyclotrons.

An important decay mechanism of the transuranium elements is spontaneous fis­sion. The half-life of a transuranium nuclide decreases as the atomic number increases. For example, the half-life of 241Am is 432 years and that of 252Cf isotope is 2 years, but lawrencium isotopes have half-lives measured in seconds. At Z > 108, the half-lives are milliseconds or even shorter. For this reason, the produc­tion of the element with Z = 118 is questionable because only three atoms have been produced, and this result has not been repeated by other institutes.