The half-lives of known α-radioactive nuclei vary widely. Thus, the tungsten isotope 182 W has a half-life T 1/2 > 8.3·10 18 years, and the protactinium isotope 219 Pa has T 1/2 = 5.3·10 -8 s.

Rice. 2.1. Dependence of the half-life of a radioactive element on the kinetic energy of an α-particle of a naturally radioactive element. The dashed line is the Geiger-Nattall law.

For even-even isotopes, the dependence of the half-life on the α-decay energy Q α described empirically Geiger-Nettall law

where Z is the charge of the final nucleus, the half-life T 1/2 is expressed in seconds, and the energy of the α-particle E α is in MeV. In Fig. Figure 2.1 shows the experimental values ​​of half-lives for α-radioactive even-even isotopes (Z varies from 74 to 106) and their description using relation (2.3).
For odd-even, even-odd and odd-odd nuclei the general tendency of the dependence
log T 1/2 of Q α is preserved, but the half-lives are 2–100 times longer than for even-even nuclei with the same Z and Q α .
In order for α decay to occur, it is necessary that the mass of the initial nucleus M(A,Z) be greater than the sum of the masses of the final nucleus M(A-4, Z-2) and the α particle M α:

where Q α = c 2 is the α-decay energy.
Since M α<< M(A-4, Z-2), the main part of the α-decay energy is carried away by α ‑ particle and only ≈ 2% - the final nucleus (A-4, Z-2).
The energy spectra of α-particles of many radioactive elements consist of several lines (fine structure of α-spectra). The reason for the appearance of the fine structure of the α spectrum is the decay of the initial nucleus (A,Z) into the excited state of the nucleus (A-4, Z-2). By measuring the spectra of alpha particles one can obtain information about the nature of excited states
cores (A-4, Z-2).
To determine the range of values ​​of A and Z nuclei for which α-decay is energetically possible, experimental data on the binding energies of nuclei are used. The dependence of the α-decay energy Q α on the mass number A is shown in Fig. 2.2.
From Fig. 2.2 it is clear that α decay becomes energetically possible starting from A ≈ 140. In the regions A = 140–150 and A ≈ 210, the value of Q α has distinct maxima, which are due to the shell structure of the nucleus. The maximum at A = 140–150 is associated with the filling of the neutron shell with the magic number N = A – Z = 82, and the maximum at A ≈ 210 is associated with the filling of the proton shell at Z = 82. It is due to the shell structure of the atomic nucleus that the first (rare earth) region of α-active nuclei begins with N = 82, and heavy α-radioactive nuclei become especially numerous starting from Z = 82.

Rice. 2.2. Dependence of α-decay energy on mass number A.

The wide range of half-lives, as well as the large values ​​of these periods for many α-radioactive nuclei, are explained by the fact that an α particle cannot “instantaneously” leave the nucleus, despite the fact that this is energetically favorable. In order to leave the nucleus, the α-particle must overcome the potential barrier - a region at the boundary of the nucleus formed due to the potential energy of the electrostatic repulsion of the α-particle and the final nucleus and the attractive forces between nucleons. From the point of view of classical physics, an alpha particle cannot overcome a potential barrier, since it does not have the kinetic energy necessary for this. However, quantum mechanics allows for such a possibility − α ‑ the particle has a certain probability of passing through the potential barrier and leaving the nucleus. This quantum mechanical phenomenon is called the “tunnel effect” or “tunneling.” The greater the height and width of the barrier, the lower the probability of tunneling, and the half-life is correspondingly longer. Wide range of half-lives
α-emitters are explained by different combinations of kinetic energies of α-particles and heights of potential barriers. If the barrier did not exist, then the alpha particle would leave the nucleus behind the characteristic nuclear
time ≈ 10 -21 – 10 -23 s.
The simplest model of α-decay was proposed in 1928 by G. Gamow and, independently, by G. Gurney and E. Condon. In this model, it was assumed that the α particle constantly exists in the nucleus. While the alpha particle is in the nucleus, nuclear forces of attraction act on it. The radius of their action is comparable to the radius of the nucleus R. The depth of the nuclear potential is V 0 . Outside the nuclear surface at r > R the potential is the Coulomb repulsive potential

V(r) = 2Ze 2 /r.

Rice. 2.3. Energies of α-particles E α depending on the number of neutrons N
in the original kernel. Lines connect isotopes of the same chemical element.

A simplified diagram of the combined action of the nuclear attractive potential and the Coulomb repulsive potential is shown in Figure 2.4. In order to leave the nucleus, an α particle with energy E α must pass through a potential barrier contained in the region from R to R c . The probability of α decay is mainly determined by the probability D of an α particle passing through a potential barrier

Within the framework of this model, it was possible to explain the strong dependence of the probability α ‑ decay from the energy of the α-particle.

Rice. 2.4. Potential energy of an α particle. Potential barrier.

In order to calculate the decay constant λ, it is necessary to multiply the coefficient of passage of an α-particle through a potential barrier, firstly, by the probability w α that the α-particle was formed in the nucleus, and, secondly, by the probability that it will be at the core boundary. If an alpha particle in a nucleus of radius R has a speed v, then it will approach the boundary on average ≈ v/2R times per second. As a result, for the decay constant λ we obtain the relation

(2.6)

The speed of an α particle in the nucleus can be estimated based on its kinetic energy E α + V 0 inside the nuclear potential well, which gives v ≈ (0.1-0.2) s. It already follows from this that if there is an alpha particle in the nucleus, its probability of passing through the barrier D<10 -14 (для самых короткоживущих относительно α‑распада тяжелых ядер).
The rough estimate of the pre-exponential factor is not very significant, because the decay constant depends on it much less strongly than on the exponent.
From formula (2.6) it follows that the half-life strongly depends on the radius of the nucleus R, since the radius R is included not only in the pre-exponential factor, but also in the exponent, as a limit of integration. Therefore, from α-decay data it is possible to determine the radii of atomic nuclei. The radii obtained in this way turn out to be 20–30% larger than those found in electron scattering experiments. This difference is due to the fact that in experiments with fast electrons the radius of the electric charge distribution in the nucleus is measured, and in α-decay the distance between the nucleus and the α-particle is measured, at which nuclear forces cease to act.
The presence of Planck's constant in the exponent (2.6) explains the strong dependence of the half-life on energy. Even a small change in energy leads to a significant change in the exponent and thus to a very sharp change in the half-life. Therefore, the energies of the emitted α particles are highly limited. For heavy nuclei, α-particles with energies above 9 MeV fly out almost instantly, and with energies below 4 MeV they live in the nucleus for so long that α-decay cannot even be detected. For rare earth α-radioactive nuclei, both energies are reduced by reducing the radius of the nucleus and the height of the potential barrier.
In Fig. Figure 2.5 shows the dependence of the α-decay energy of Hf isotopes (Z = 72) on the mass number A in the range of mass numbers A = 156–185. Table 2.1 shows the α-decay energies, half-lives and main decay channels of the 156–185 Hf isotopes. It can be seen how, as the mass number A increases, the α-decay energy decreases, which leads to a decrease in the probability of α-decay and an increase in the probability of β-decay (Table 2.1). The 174 Hf isotope, being a stable isotope (in the natural mixture of isotopes it is 0.16%), nevertheless decays with a half-life T 1/2 = 2·10 15 years with the emission of an α-particle.

Rice. 2.5. Dependence of the α-decay energy Q α of Hf isotopes (Z = 72)
from mass number A.

Table 2.1

Dependence of α-decay energy Q α, half-life T 1/2,
different decay modes of H f isotopes (Z = 72) depending on the mass number A

Hf isotopes with A = 176–180 are stable isotopes. These isotopes also have positive α decay energy. However, the α-decay energy ~1.3–2.2 MeV is too low and the α-decay of these isotopes was not detected, despite the nonzero probability of α-decay. With a further increase in the mass number A > 180, β - decay becomes the dominant decay channel.
During radioactive decays, the final nucleus may end up not only in the ground state, but also in one of the excited states. However, the strong dependence of the probability of α-decay on the energy of the α-particle leads to the fact that decays into excited levels of the final nucleus usually occur with a very low intensity, because when the final nucleus is excited, the energy of the α-particle decreases. Therefore, only decays into rotational levels with relatively low excitation energies can be observed experimentally. Decays into excited levels of the final nucleus lead to the appearance of a fine structure in the energy spectrum of the emitted α particles.
The main factor determining the properties of α decay is the passage of α particles through a potential barrier. Other factors manifest themselves relatively weakly, but in some cases they make it possible to obtain additional information about the structure of the nucleus and the mechanism of α-decay of the nucleus. One of these factors is the emergence of a quantum mechanical centrifugal barrier. If an α particle is emitted from a nucleus (A,Z) having spin J i , and a finite nucleus is formed
(A-4, Z-2) in a state with spin J f, then the α-particle must carry away the total momentum J, determined by the relation

Since the α-particle has zero spin, its total angular momentum J coincides with the orbital angular momentum l carried away by the α-particle

As a result, a quantum mechanical centrifugal barrier appears.

The change in the shape of the potential barrier due to centrifugal energy is insignificant, mainly due to the fact that centrifugal energy decreases with distance much faster than Coulomb energy (as 1/r 2, and not as 1/r). However, since this change is divided by Planck's constant and falls into the exponent, then at large l, it leads to a change in the lifetime of the nucleus.
Table 2.2 shows the calculated permeability of the centrifugal barrier B l for α-particles emitted with orbital momentum l relative to the permeability of the centrifugal barrier B 0 for α-particles emitted with orbital momentum l = 0 for a nucleus with Z = 90, α-particle energy E α = 4.5 MeV. It can be seen that with an increase in the orbital momentum l carried away by the α particle, the permeability of the quantum mechanical centrifugal barrier drops sharply.

Table 2.2

Relative permeability of the centrifugal barrier forα -particles,
departing with orbital momentum l
(Z = 90, E α = 4.5 MeV)

A more significant factor that can dramatically redistribute the probabilities of various branches of α-decay may be the need for a significant restructuring of the internal structure of the nucleus during the emission of an α-particle. If the initial nucleus is spherical, and the ground state of the final nucleus is strongly deformed, then in order to evolve into the ground state of the final nucleus, the initial nucleus must rearrange itself in the process of emitting an alpha particle, greatly changing its shape. Such a change in the shape of the nucleus usually involves a large number of nucleons and a system with few nucleons such as α ‑ a particle leaving the nucleus may not be able to provide it. This means that the probability of the formation of the final nucleus in the ground state will be negligible. If among the excited states of the final nucleus there is a state close to spherical, then the initial nucleus can, without significant rearrangement, go into it as a result of α ‑ decay The probability of population of such a level may turn out to be large, significantly exceeding the probability of population of lower-lying states, including the ground state.
From the α-decay diagrams of the isotopes 253 Es, 225 Ac, 225 Th, 226 Ra, strong dependences of the probability of α-decay into excited states on the energy of the α-particle and on the orbital momentum l carried away by the α-particle are visible.
α decay can also occur from excited states of atomic nuclei. As an example, Tables 2.3 and 2.4 show the decay modes of the ground and isomeric states of the isotopes 151 Ho and 149 Tb.

Table 2.3

α-decays of the ground and isomeric states of 151 Ho

Table 2.4

α-decays of the ground and isomeric states of 149 Tb

In Fig. Figure 2.6 shows the energy diagrams of the decay of the ground and isomeric states of the isotopes 149 Tb and 151 Ho.

Rice. 2.6 Energy diagrams of the decay of the ground and isomeric states of the isotopes 149 Tb and 151 Ho.

α-decay from the isomeric state of the 151 Ho isotope (J P = (1/2) + , E isomer = 40 keV) is more probable (80%) than e-capture to this isomeric state. At the same time, the ground state of 151 Ho decays mainly as a result of e-capture (78%).
In the 149 Tb isotope, the decay of the isomeric state (J P = (11/2) - , E isomer = 35.8 keV) occurs in the overwhelming case as a result of e-capture. The observed features of the decay of the ground and isomeric states are explained by the magnitude of the energy of α-decay and e-capture and the orbital angular momentum carried away by the α-particle or neutrino.

The nuclei of most atoms are fairly stable formations. However, the nuclei of atoms of radioactive substances during the process of radioactive decay spontaneously transform into the nuclei of atoms of other substances. So in 1903, Rutherford discovered that radium placed in a vessel after some time turned into radon. And additional helium appeared in the vessel: (88^226)Ra→(86^222)Rn+(2^4)He. To understand the meaning of the written expression, study the topic of mass and charge number of the nucleus of an atom.

It was possible to establish that the main types of radioactive decay: alpha and beta decay occur according to the following displacement rule:

Alpha decay

During alpha decay an alpha particle (the nucleus of a helium atom) is emitted. From a substance with the number of protons Z and neutrons N in the atomic nucleus, it turns into a substance with the number of protons Z-2 and the number of neutrons N-2 and, accordingly, atomic mass A-4: (Z^A)X→(Z-2^ (A-4))Y +(2^4)He. That is, the resulting element is shifted two cells back in the periodic table.

Example of α decay:(92^238)U→(90^234)Th+(2^4)He.

Alpha decay is intranuclear process. As part of a heavy nucleus, due to a complex combination of nuclear and electrostatic forces, an independent α-particle is formed, which is pushed out by Coulomb forces much more actively than other nucleons. Under certain conditions, it can overcome the forces of nuclear interaction and fly out of the nucleus.

Beta decay

During beta decay an electron (β particle) is emitted. As a result of the decay of one neutron into a proton, electron and antineutrino, the composition of the nucleus increases by one proton, and the electron and antineutrino are emitted outward: (Z^A)X→(Z+1^A)Y+(-1^0)e+(0 ^0)v. Accordingly, the resulting element is shifted one cell forward in the periodic table.

Example of β decay:(19^40)K→(20^40)Ca+(-1^0)e+(0^0)v.

Beta decay is intranucleon process. The neutron undergoes the transformation. There is also beta plus decay or positron beta decay. In positron decay, the nucleus emits a positron and a neutrino, and the element moves back one cell on the periodic table. Positron beta decay is usually accompanied by electron capture.

Gamma decay

In addition to alpha and beta decay, there is also gamma decay. Gamma decay is the emission of gamma quanta by nuclei in an excited state, in which they have high energy compared to the unexcited state. Nuclei can come to an excited state during nuclear reactions or during radioactive decays of other nuclei. Most excited states of nuclei have a very short lifetime - less than a nanosecond.

There are also decays with the emission of a neutron, proton, cluster radioactivity and some other, very rare types of decays. But prevailing

Slide11

Alpha decay is the emission of alpha particles (helium nuclei) by an atomic nucleus in the ground (unexcited) state.

Main characteristics of half-life T 1/2, kinetic energy T α and mileage in matter Rαα-particles in matter.

Basic properties of alpha decay

1. Alpha decay is observed only in heavy nuclei. About 300 α-radioactive nuclei are known

2. The half-life of α-active nuclei lies in a huge range from

10 17 years old ()

and is determined Geiger-Nettall law

. (1.32)

for example, for Z=84 constants A= 128.8 and B = - 50,15, T α– kinetic energy of α-particle in Mav

3. The energies of α-particles of radioactive nuclei are contained within

(Mav)

T α min = 1.83 Mav (), Tαmax = 11.65 Mav(isomer

4. The fine structure of the α-spectra of radioactive nuclei is observed. These spectra discrete. In Fig. 1.5. A diagram of the decay of a plutonium nucleus is shown. The spectrum of α particles consists of a number of monoenergetic lines corresponding to transitions to various levels of the daughter nucleus.

6.Mileage of α-particles in air under normal conditions

R α (cm) = 0.31 T α 3/2 Mav at (4< T α <7 Mav) (1.33)

7. General scheme of the α-decay reaction

where is the mother nucleus, is the daughter nucleus

The binding energy of an α particle in the nucleus must be less than zero for α decay to occur.

E St α =<0 (1.34)

Energy released during α-decay Eα consists of the kinetic energy of the α particle Tα and kinetic energy of the daughter nucleus T i

E α =| E St α | = T α +T i (1.35)

The kinetic energy of an α particle is more than 98% of the total energy of α decay

Types and properties of beta decay

Beta decay slide 12

Beta decay of a nucleus is the process of spontaneous transformation of an unstable nucleus into an isobar nucleus as a result of the emission of an electron (positron) or the capture of an electron. About 900 beta radioactive nuclei are known.

In electronic β - decay, one of the neutrons of the nucleus turns into a proton with the emission of an electron and an electron antineutrino.

free neutron decay , T 1/2 =10.7 min;

tritium decay , T 1/2 = 12 years .

At positron β+ decay one of the protons of the nucleus turns into a neutron with the emission of a positively charged electron (positron) and an electron neutrino

When electronic e-capture the nucleus captures an electron from the electron shell (usually the K-shell) of its own atom.

The β - -decay energy lies in the range

()0,02 Mav < Е β < 13,4 Mav ().

Spectrum of emitted β-particles continuous from zero to maximum value. Calculation formulas maximum energy of beta decays:

, (1.42)

, (1.43)

. (1.44)

where is the mass of the mother nucleus, is the mass of the daughter nucleus. m e–electron mass.

Half life T 1/2 associated with probability beta decay relation

The probability of beta decay strongly depends on the beta decay energy ( ~ Eβ 5 at Eβ >> m e c 2) therefore the half-life T 1/2 varies widely

10 -2 sec< T 1/2< 2 10 15 лет

Beta decay occurs as a result of the weak interaction, one of the fundamental interactions.

Radioactive families (series) Slide 13

Laws of nuclear displacement during α-decay ( A→A – 4 ; Z→Z- 2) during β-decay ( A→A; Z→Z+1).Since the mass number A during α-decay it changes to 4, and during β-decay A does not change, then members of different radioactive families do not “get confused” with each other. They form separate radioactive series (chains of nuclei), which end with their stable isotopes.

The mass numbers of members of each radioactive family are characterized by the formula

a=0 for the thorium family, a=1 for the neptunia family, a=2 for the uranium family, a=3 for the actinouranium family. n- an integer. see table 1.2

Table 1.2

From a comparison of the half-lives of the ancestors of the families with the geological lifetime of the Earth (4.5 billion years), it is clear that almost all of the thorium-232 was preserved in the Earth’s substance, uranium-238 decayed by about half, uranium-235 for the most part, and almost all of neptunium-237 .

In this type of decay, a nucleus with atomic number Z and mass number A decays by emitting an alpha particle, which leads to the formation of a nucleus with atomic number Z-2 and mass number A-4:

Currently, more than 200 alpha-emitting nuclides are known, among which light and medium nuclei are almost absent. Among light nuclei, the exception is 8 Be; in addition, about 20 alpha-emitting nuclides of rare earth elements are known. The vast majority of a-emitting isotopes belong to radioactive elements, i.e. to elements with Z> 83, a significant part of which are artificial nuclides. Among natural nuclides, there are about 30 alpha-active nuclei belonging to three radioactive families (uranium, actinium, and thorium series), which are discussed above. The half-lives of known alpha radioactive nuclides range from 0.298 μs for 212 Po to >10 15 years for 144 Nd, 174 Hf. The energy of alpha particles emitted by heavy nuclei from ground states is 4-9 MeV, and by nuclei of rare earth elements 2-4.5 MeV.

That the probability of alpha decay increases with increasing Z, due to the fact that this type of nuclear transformation is associated with Coulomb repulsion, which, as the size of the nuclei increases, increases proportionally Z 2, while nuclear attractive forces grow linearly with increasing mass number A.

As was shown earlier, the nucleus will be unstable with respect to a-decay if the inequality holds:

where and are the rest masses of the initial and final nuclei, respectively;

– mass of the a-particle.

Energy of α-decay of nuclei ( Eα) consists of the kinetic energy of the alpha particle emitted by the mother nucleus Tα, and the kinetic energy that the daughter nucleus acquires as a result of the emission of an alpha particle (recoil energy) T department:

Using the laws of conservation of energy and momentum, we can obtain the relation:

Where M department = – recoil core mass;

Mα is the mass of the alpha particle.

Solving equations (4.3) and (4.4) together, we obtain:

. (4.5)

And correspondingly,

. (4.6)

From equations (4.5 and 4.6) it is clear that the bulk of the alpha decay energy (about 98%) is carried away by alpha particles. The kinetic energy of the recoil nucleus is ≈100 keV (with an alpha decay energy of ≈5 MeV). It should be noted that even such seemingly small values ​​of the kinetic energy of recoil atoms are very significant and lead to the high reactivity of atoms having similar nuclei. For comparison, note that the energy of thermal motion of molecules at room temperature is approximately 0.04 eV, and the energy of chemical bonds is usually less than 2 eV. Therefore, the recoil nucleus not only breaks the chemical bond in the molecule, but also partially loses the electron shell (electrons simply cannot keep up with the recoil nucleus) with the formation of ions.

When considering different types of radioactive decay, including alpha decay, energy diagrams are used. The simplest energy diagram is shown in Fig. 4.1.

Rice. 4.1. The simplest alpha decay scheme.

The energy state of the system before and after decay is depicted by horizontal lines. An alpha particle is represented by an arrow (bold or double) going down from right to left. The arrow indicates the energy of the emitted alpha particles.

It should be borne in mind that the one shown in Fig. 4.1 diagram is the simplest case when the alpha particles emitted by the nucleus have one specific energy. Typically, the alpha spectrum has a fine structure, i.e. nuclei of the same nuclide emit alpha particles with energies that are quite close, but still differ in magnitude. It was found that if an alpha transition occurs in the excited state of the daughter nucleus, then the energy of the alpha particles will be, accordingly, less than the energy inherent in the transition between the ground states of the original and daughter nuclei of radionuclides. And if there are several such excited states, then there will be several possible alpha transitions. In this case, daughter nuclei with different energies are formed, which, upon transition to the ground or more stable state, emit gamma rays.

Knowing the energy of all alpha particles and gamma quanta, we can construct an energy decay diagram.

Example. Construct a decay diagram using the following data:

· the energy of α-particles is: 4.46; 4.48; 4.61; and 4.68 MeV,

· energy of γ-quanta – 0.07; 0.13; 0.20; and 0.22 MeV.

The total decay energy is 4.68 MeV.

Solution. From the energy level of the original nucleus we draw four arrows, each of which indicates the emission of α-particles of a certain energy. By calculating the differences between the energies of individual groups of α-particles and comparing these differences with the energies of γ-quanta, we find which transitions correspond to the emission of γ-quanta of each energy

4.48 – 4.46 = 0.02 MeV there are no corresponding γ-quanta

4.61 – 4.46 = 0.15 MeV

4.61 – 4.48 = 0.13 MeV energies correspond to energies

4.68 – 4.46 = 0.22 MeV of γ quanta emitted during decay

4.68 – 4.48 = 0.20 MeV 230 Th

4.68 – 4.61 = 0.07 MeV

Rice. 4.2 – Scheme of the decay of 230 Th.

At the same time, a second case is also possible, when an alpha transition occurs from the excited state of the parent nucleus to the ground state of the daughter nucleus. These cases are usually classified as the appearance of long-range alpha particles, the emission of which arises from excited nuclei formed as a result of complex β-decay. So, as an example, Figure 4.3 shows a diagram of the emission of long-range α particles by the polonium-212 nucleus, formed as a result of the β-decay of the bismuth-212 nucleus. It can be seen that, depending on the nature of the β transition, the polonium-212 nucleus can be formed in the ground and excited states. Alpha particles emitted from excited states of the polonium-212 nucleus are long-range. However, it should be borne in mind that for alpha-active nuclei generated in this way, a transition from an excited state is more likely by emitting a γ-quantum rather than a long-range alpha particle. Therefore, long-range alpha particles are very rare.

Further, scientists have established a very important pattern: when small increasing the energy of a-particles, the half-lives change by several orders of magnitude. So for 232 Th T a = 4.08 MeV, T 1/2 = 1.41×10 10 years, and for 230 Th – T a = 4.76 MeV, T 1/2 = 1.7∙10 4 years.

Rice. 4.3. Sequential decay pattern: 212 Bi – 212 Po – 208 Pb

It can be seen that a decrease in the energy of alpha particles by approximately 0.7 MeV is accompanied by an increase in the half-life by 6 orders of magnitude. At T α < 2 МэВ период полураспада становится настолько большим, что экспериментально обнаружить альфа-активность практически невозможно. Разброс в значениях периодов полураспада, характерных для альфа-распада, весьма велик:

10 16 years ≥ T 1/2 ≥ 10 –7 sec,

and at the same time, there is a very narrow range of energies of alpha particles emitted by radioactive nuclei:

2 MeV ≤ Tα ≤ 9 MeV.

The relationship between the half-life and the energy of an alpha particle was established experimentally by Geiger and Nattall in 1911-1912. They showed that the dependence lg T 1/2 of lg Tα is well approximated by a straight line:

. (4.7)

This law holds well for even-even nuclei. Whereas for odd-odd nuclei a very significant deviation from the law is observed.

The strong dependence of the probability of alpha decay, and therefore the half-life, on energy was explained by G. Gamow and E. Condon in 1928 using the theory of a single-particle model of the nucleus. In this model, it is assumed that the alpha particle constantly exists in the nucleus, i.e. The mother nucleus consists of a daughter nucleus and an alpha particle. It is assumed that the alpha particle moves in a spherical region of radius R (R– radius of the nucleus) and is held in the nucleus by short-range Coulomb nuclear forces. At distances r greater than the radius of the daughter nucleus R, Coulomb repulsion forces act.

In Fig. Figure 4.4 shows the dependence of the potential energy between the alpha particle and the recoil nucleus on the distance between their centers.

The abscissa axis shows the distance between the daughter nucleus and the alpha particle, and the ordinate axis shows the energy of the system. Coulomb potential is cut off at a distance R, which is approximately equal to the radius of the daughter nucleus. The height of the Coulomb barrier B, which an alpha particle must overcome in order to leave the nucleus, is determined by the relation:

Where Z And z are the charges of the daughter nucleus and the alpha particle, respectively.

Rice. 4.4. Change in the potential energy of the system with the distance between the daughter nucleus and the alpha particle.

The magnitude of the potential barrier significantly exceeds the energy of alpha particles emitted by radioactive nuclei, and according to the laws of classical mechanics, an alpha particle cannot leave the nucleus. But for elementary particles whose behavior is described by the laws of quantum mechanics, it is possible for these particles to pass through a potential barrier, which is called a tunnel transition.

In accordance with the theory of alpha decay, the beginnings of which were laid by G. Gamow and E. Condon, the state of a particle is described by the wave function ψ, which, according to the normalization conditions, at any point in space is nonzero, and thus there is a finite probability of detecting an alpha particle both inside and outside the barrier. That is, the process of the so-called tunneling transition of an alpha particle through a potential barrier is possible.

Barrier permeability has been shown to be a function of atomic number, atomic mass, core radius, and potential barrier characteristics.

It has been established that alpha transitions of even-even nuclei from the main level of mother nuclides to the main level of daughter nuclides are characterized by the smallest half-lives. For odd-even, even-odd and odd-odd nuclei the general trend remains, but their half-lives are 2-1000 times longer than for even-even nuclei with given Z and Tα. It is useful to remember: the energy of alpha particles emitted by radionuclides with the same mass number increases with increasing nuclear charge.