Elements of physics of the atomic nucleus and elementary particles. Penetrating power of beta particles

2.3 Patternsα - Andβ -decay

ActivityAnuclidein a radioactive source, the number of decays occurring with the nuclei of a sample in 1 s is called:

Activity unit — becquerel (Bq): 1Bq - activity of a nuclide, at which one decay event occurs in 1 s.Non-system unit of activitynuclide in a radioactive source -curie (Ku): 1 Ku=3.7·1010 Bk.

Alpha decay. Alpha decay is the spontaneous transformation of an atomic nucleus with the number of protons Z and neutrons N into another (daughter) nucleus containing the number of protons Z – 2 and neutrons N – 2. In this case, an alpha particle is emitted - the nucleus of a helium atom. An example of such a process is the α-decay of radium:

Alpha particles emitted by the nuclei of radium atoms were used by Rutherford in experiments on scattering by the nuclei of heavy elements. The speed of α-particles emitted during the α-decay of radium nuclei, measured from the curvature of the trajectory in a magnetic field, is approximately equal to 1.5 107 m/s, and the corresponding kinetic energy is about 7.5 10–13 J (approximately 4.8 MeV). This value can be easily determined from the known values ​​of the masses of the mother and daughter nuclei and the helium nucleus. Although the speed of the escaping α-particle is enormous, it is still only 5% of the speed of light, so when calculating, you can use a non-relativistic expression for kinetic energy.

Research has shown that a radioactive substance can emit alpha particles with several discrete energies. This is explained by the fact that nuclei can be, like atoms, in different excited states. The daughter nucleus may end up in one of these excited states during α decay. During the subsequent transition of this nucleus to the ground state, a γ-quantum is emitted. A diagram of the α-decay of radium with the emission of α-particles with two values ​​of kinetic energies is shown in Figure 2.4.

Thus, α-decay of nuclei is in many cases accompanied by γ-radiation.

In the theory of α-decay, it is assumed that groups consisting of two protons and two neutrons, i.e., an α particle, can be formed inside nuclei. The mother nucleus is a potential well for α particles, which is limited by a potential barrier. The energy of the α particle in the nucleus is not sufficient to overcome this barrier (Figure 2.5). The escape of an alpha particle from the nucleus is possible only due to a quantum mechanical phenomenon called the tunneling effect. According to quantum mechanics, there is a non-zero probability of a particle passing under a potential barrier. The phenomenon of tunneling is probabilistic in nature.

Beta decay. During beta decay, an electron is ejected from the nucleus. Electrons cannot exist inside nuclei (see § 1.2); they arise during beta decay as a result of the transformation of a neutron into a proton. This process can occur not only inside the nucleus, but also with free neutrons. The average lifetime of a free neutron is about 15 minutes. When a neutron decaysturns into a protonand electron

Measurements have shown that in this process there is an apparent violation of the law of conservation of energy, since the total energy of the proton and electron resulting from the decay of a neutron is less than the energy of the neutron. In 1931, W. Pauli suggested that during the decay of a neutron, another particle with zero mass and charge is released, which takes away part of the energy. The new particle is namedneutrino(small neutron). Due to the lack of charge and mass of a neutrino, this particle interacts very weakly with the atoms of matter, so it is extremely difficult to detect in experiment. The ionizing ability of neutrinos is so small that one ionization event in the air occurs approximately 500 km of the way. This particle was discovered only in 1953. It is now known that there are several types of neutrinos. During the decay of a neutron, a particle is created, which is called an electronantineutrino. It is indicated by the symbolTherefore, the neutron decay reaction is written in the form

A similar process occurs inside nuclei during β-decay. An electron formed as a result of the decay of one of the nuclear neutrons is immediately ejected from the “parental home” (nucleus) at enormous speed, which can differ from the speed of light by only a fraction of a percent. Since the distribution of energy released during β-decay between the electron, neutrino and daughter nucleus is random, β-electrons can have different velocities over a wide range of values.

During β-decay, the charge number Z increases by one, but the mass number A remains unchanged. The daughter nucleus turns out to be the nucleus of one of the isotopes of the element, the serial number of which in the periodic table is one higher than the serial number of the original nucleus. A typical example of β-decay is the transformation of thorium isotonearising from the α-decay of uraniumto palladium

Along with electronic β decay, the so-called positron β decay was discovered+ -decay in which a positron is emitted from the nucleusand neutrinos. A positron is a particle twin of an electron, differing from it only in the sign of its charge. The existence of the positron was predicted by the outstanding physicist P. Dirac in 1928. A few years later, the positron was discovered in cosmic rays. Positrons arise as a result of the reaction of converting a proton into a neutron according to the following scheme:

Gamma decay. Unlike α- and β-radioactivity, γ-radioactivity of nuclei is not associated with a change in the internal structure of the nucleus and is not accompanied by a change in charge or mass numbers. Both during α- and β-decay, the daughter nucleus may find itself in some excited state and have an excess of energy. The transition of a nucleus from an excited state to a ground state is accompanied by the emission of one or more γ quanta, the energy of which can reach several MeV.

1.3. Alpha decays, beta decays and gamma emissions of radioactive nuclei

Alpha decay is the spontaneous emission of alpha particles, representing the nuclei of a helium atom, by a radioactive nucleus. The decay proceeds according to the scheme

IN In expression (1.13), the letter X denotes the chemical symbol of the decaying (mother) nucleus, and the letter Y denotes the chemical symbol of the resulting (daughter) nucleus. As can be seen from diagram (1.13), the atomic number of the daughter nucleus is two and the mass number is four units less than that of the original nucleus.

The alpha particle has a positive charge. Alpha particles characterize two-

by basic parameters: travel length (in air up to 9 cm, in biological tissue up to 10-3 cm) and kinetic energy in the range of 2...9 MeV.

Alpha decay is observed only in heavy nuclei with Am>200 and charge number Z>82. Inside such nuclei, the formation of isolated particles of two protons and two neutrons occurs. The separation of this group of nucleons is facilitated by the saturation of nuclear forces, so that the formed alpha particle is subject to less nuclear attractive forces than individual nucleons. At the same time, the alpha particle experiences greater Coulomb repulsion forces from the protons of the nucleus than individual protons. This explains the emission of alpha particles from the nucleus, and not individual nucleons.

IN In most cases, a radioactive substance emits several groups alpha particles of similar but different energies, i.e. groups have a spectrum of energy. This is due to the fact that a daughter nucleus can arise not only in the ground state, but also in excited states with different energy levels.

The lifetime of excited states for most nuclei lies within

affairs from 10 - 8 to 10 - 15 s. During this time, the daughter nucleus passes into the ground or lower excited state, emitting a gamma quantum of the corresponding energy equal to the difference between the energies of the previous and subsequent states. An excited nucleus can also emit any particle: a proton, neutron, electron or alpha particle. It can also transfer excess energy to one of the electrons in the inner layer surrounding the nucleus. The transfer of energy from the nucleus to the closest electron of the K-layer occurs without the emission of a gamma quantum. The electron that receives energy flies out of the atom. This process is called internal conversion. The resulting vacant position is filled with electrons from higher energy levels. Electronic transitions in the inner layers of the atom lead to the emission of X-rays having a discrete energy spectrum (characteristic X-rays). In total, about 25 natural and about 100 artificial alpha radioactive isotopes are known.

Beta decay combines three types of nuclear transformations: electronic (β−)

and positron (β+ ) decays, as well as electron capture or K-capture. The first two types of transformations consist in the fact that the nucleus emits an electron and an antineutrino (during β− decay) or a positron and neutrino (during β+ decay). Elek-

tron (positron) and antineutrino (neutrino) do not exist in atomic nuclei. These processes occur by converting one type of nucleon in the nucleus into another - a neutron into a proton or a proton into a neutron. The result of these transformations is β-decays, the schemes of which have the form:

where − 1 e0 and + 1 e0 are the designation of electron and positron,

0 ν0 and 0 ~ ν0 – designation of neutrinos and antineutrinos.

With negative beta decay, the charge number of the radionuclide increases by one, and with positive beta decay, it decreases by one.

Electronic decay (β − decay) can be experienced by both natural and artificial radionuclides. It is this type of decay that is characteristic of the overwhelming number of environmentally most dangerous radionuclides released into the environment as a result of the Chernobyl accident. Among them

134 55 Cs, 137 55 Cs, 90 38 Sr, 131 53 I, etc.

Positron decay (β + – decay) is characteristic mainly of artificial radionuclides.

Since during beta decay two particles are emitted from the nucleus, and the distribution

between them the total energy occurs statistically, then the energy spectrum of electrons (positrons) is continuous from zero to the maximum value Emax called the upper limit of the beta spectrum. For beta radioactive nuclei, the Emax value lies in the energy region from 15 keV to 15 MeV. The path length of a beta particle in air is up to 20 m, and in biological tissue up to 1.5 cm.

Beta decay is usually accompanied by the emission of gamma rays. The reason for their occurrence is the same as in the case of alpha decay: the daughter nucleus appears not only in the ground (stable) state, but also in an excited state. Then passing into a state of lower energy, the nucleus emits a gamma photon.

During electron capture, one of the protons of the nucleus is converted into a neutron:

1 p 1+ − 1 e 0 → 0 n 1+ 0 ν 0 .

With this transformation, one of the electrons closest to the nucleus (the electron of the K-layer of the atom) disappears. A proton, turning into a neutron, “captures” an electron. This is where the term "electronic capture" comes from. Feature

This type of β-decay is the emission of one particle from the nucleus - a neutrino. The electronic capture circuit looks like

Am Z X+ − 1 e0 → Am Z − 1 Y+ 0 ν 0 . (1.16)

Electronic capture, in contrast to β± decays, is always accompanied by charac-

bacterial x-ray radiation. The latter occurs when an electron more distant from the nucleus moves to an emerging vacant place in

K-layer. The wavelength of X-rays is in the range from 10 − 7 to 10 − 11 m. Thus, during beta decay, the mass number of the nucleus is conserved, and its

the charge changes by one. Half-lives of beta radioactive nuclei

lie in a wide time range from 10 − 2 s to 2 1015 years.

To date, about 900 beta radioactive isotopes are known. Of these, only about 20 are natural, the rest are obtained artificially. The vast majority of these isotopes experience

β− -decay, i.e. with the emission of electrons.

All types of radioactive decay are accompanied by gamma radiation. Gamma rays are short-wave electromagnetic radiation, which is not an independent type of radioactivity. It has been experimentally established that gamma rays are emitted by a daughter nucleus during nuclear transitions from excited energy states to the ground or less excited state. The energy of gamma rays is equal to the difference between the energies of the initial and final energy levels of the nucleus. The wavelength of gamma rays does not exceed 0.2 nanometers.

The process of gamma radiation is not an independent type of radioactivity, since it occurs without changing the Z and Am of the nucleus.

Control questions:

1. What is meant by mass and charge numbers in the periodic table of Mendeleev?

2. The concept of “isotopes” and “isobars”. What is the difference between these terms?

3. Nuclear forces of the nucleus and their most important features.

4. Why is the mass of a nucleus less than the sum of the masses of its constituent nuclides?

5. What substances are called radioactive?

6. What characterizes and shows the radioactive decay constant?

7. Define the half-life of a substance.

8. List the units of measurement for volumetric, surface and specific activity.

9. The main types of radiation from radioactive nuclei and their parameters.

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 R αα-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 Mev

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

(Mev)

T α min = 1.83 Mev (), Tαmax = 11.65 Mev(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 Mev at (4< T α <7 Mev) (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 Mev < Е β < 13,4 Mev ().

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 .

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 - the 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 the 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 roughness of the estimate of the pre-exponential factor is not very significant, because the decay constant depends on it incomparably less 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 the centrifugal energy decreases with distance much faster than the 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.

Decay condition. Alpha decay is characteristic of heavy nuclei, in which a growth A a decrease in binding energy per nucleon is observed. In this region of mass numbers, a decrease in the number of nucleons in the nucleus leads to the formation of a more tightly bound nucleus. At the same time, the gain in energy with a decrease A one is much less than the binding energy of one nucleon in the nucleus; therefore, the emission of a proton or neutron, which has a binding energy equal to zero outside the nucleus, is impossible. The emission of the 4 Ne nucleus turns out to be energetically favorable, since the specific binding energy of a nucleon in a given nucleus is about 7.1 MeV. Alpha decay is possible if the total binding energy of the product nucleus and the alpha particle is greater than the binding energy of the original nucleus. Or in mass units:

M(A,Z)>M(A-4, Z-2) + M α (3.12)

An increase in the binding energy of nucleons means a decrease in the rest energy precisely by the amount of energy released during alpha decay E α. For this reason, if we imagine the alpha particle as a whole within the product nucleus, then it should occupy a level with positive energy equal to E α(Fig. 3.5).

Rice. 3.5. Diagram of the energy level of an alpha particle in a heavy nucleus

When an alpha particle leaves the nucleus, this energy is released in free form, as the kinetic energy of the decay products: the alpha particle and the new nucleus. Kinetic energy is distributed between these decay products in inverse proportion to their masses and, since the mass of the alpha particle is much less than the mass of the newly formed nucleus, almost all of the decay energy is carried away by the alpha particle.. ᴏϬᴩᴀᴈᴏᴍ, with great accuracy E α is the kinetic energy of the alpha particle after decay.

At the same time, the release of energy is prevented by the Coulomb potential barrier Uk(see Figure 3.5), the probability of passage of which by an alpha particle is small and falls very quickly with decreasing E α. For this reason, relation (3.12) is not a sufficient condition for alpha decay.

The height of the Coulomb barrier for a charged particle penetrating into or leaving the nucleus increases in proportion to its charge. For this reason, the Coulomb barrier constitutes an even greater obstacle to the escape of other tightly bound light nuclei from a heavy nucleus, such as 12 C or 16 O. The average binding energy of a nucleon in these nuclei is even higher than in the nucleus 4 Not, in connection with this, in a number of cases, the emission of a nucleus 16 O instead of sequentially emitting four alpha particles, it would be energetically more favorable. In this case, the emission of nuclei heavier than the nucleus 4 Not, not visible.

Explanation of the collapse. The mechanism of alpha decay is explained by quantum mechanics, because within the framework of classical physics this process is impossible. Only a particle with wave properties can appear outside the potential well when E α . Moreover, it turns out that only a potential barrier of infinite width, with a probability equal to one, limits the presence of a particle within the potential well. If the width of the barrier is finite, then the probability of moving beyond the potential barrier is fundamentally always different from zero. True, this probability quickly decreases with increasing width and height of the barrier. The apparatus of quantum mechanics leads to the following expression for the barrier transparency or probability ω for a particle to be outside the potential barrier when colliding with its wall: