Professor

I.N.Bekman

NUCLEAR PHYSICS

Lecture 16. NUCLEAR INTERACTIONS

The development of nuclear physics is largely determined by research in the field of nuclear reactions. In this lecture we will consider the modern classification of nuclear interactions, their

thermodynamics and kinetics, as well as some examples of nuclear reactions.

1. CLASSIFICATION OF NUCLEAR REACTIONS

Through action nuclear forces two particles (two nuclei or a nucleus and a nucleon) when approaching to distances of the order of 10 -13 cm enter into intense nuclear interaction, leading to the transformation of the nucleus. This process is called a nuclear reaction. During a nuclear reaction, a redistribution of energy and momentum of both particles occurs, which leads to the formation of several other particles escaping from the place of interaction. When an incident particle collides with an atomic nucleus, an exchange of energy and momentum occurs between them, as a result of which several particles can be formed, flying out in different directions from the interaction region.

Nuclear reactions- transformations of atomic nuclei when interacting with elementary particles, γ-quanta or with each other.

Nuclear reaction is the process of formation of new nuclei or particles in collisions of nuclei or particles. For the first time, E. Rutherford observed a nuclear reaction in 1919, bombarding the nuclei of nitrogen atoms with α-particles; it was recorded by the appearance of secondary ionizing particles with a range in the gas greater than the range of α-particles and identified as protons. Subsequently, photographs of this process were obtained with the help of a Wilson camera.

Rice. 1. Processes occurring in the course of nuclear reactions

(input and output reaction channels are presented).

The first nuclear reaction was carried out by E. Rutherford in 1919: 4 He + 14 N → 17 O + p or 14 N (α, p) 17 O. The source of α -particles was an α-radioactive preparation. Radioactive α-drugs at that time were the only sources of charged particles. The first accelerator specially designed for the study of nuclear reactions was built by Cockcroft and Walton in 1932. This accelerator was the first

a beam of accelerated protons was obtained and the reaction p + 7 Li → α + α was carried out.

Nuclear reactions are the main method for studying the structure and properties of atomic nuclei. In nuclear reactions, the mechanisms of interaction of particles with atomic nuclei, the mechanisms of interaction between atomic nuclei are studied. As a result of nuclear reactions, new isotopes not found in natural conditions are obtained and chemical elements... If, after the collision, the original nuclei and particles are preserved and new ones are not born, then the reaction is elastic scattering in the field of nuclear forces, accompanied only by a redistribution kinetic energy and momentum of the particle and the target nucleus and is called the potential

scattering.

The consequence of the interaction of bombarding particles (nuclei) with target nuclei can be:

1) Elastic scattering, in which neither the composition nor the internal energy changes, but only a redistribution of kinetic energy occurs in accordance with the law of internal impact.

2) Inelastic scattering, in which the composition of the interacting nuclei does not change, but part of the kinetic energy of the bombarding nucleus is spent on exciting the target nucleus.

3) Actually a nuclear reaction, as a result of which the internal properties and composition of interacting nuclei change.

	Rice. 2. Nuclear reaction of lithium-6 with deuterium 6 Li (d, α) α
	Nuclear reactions show strong, electromagnetic and weak
	interactions.
	Many different types of reactions are known. They can be classified into
	reactions under the action of neutrons, under the action of charged particles and under the action
	V general view nuclear interaction can be written in the form
	a1 + a2 → b1 + b2 +…,
	where a 1 and a 2 are particles that enter into the reaction, and b 1, b 2, ... are particles,
resulting from the reaction (reaction products).
	The most common type of reaction is the interaction of a light particle a with a nucleus A, in
as a result of which a light particle b and a nucleus B are formed
	a + A → b + B
	Or shorter
	A (a, b) B.

A and b can be taken as a neutron (n), a proton (p), an α-particle, a deuteron (d) and a γ-quantum.

Example 1. Nuclear reaction

4 He + 14 N → 17 O + 1 H

v abbreviated as 14 N (α, p) 17 O

Example 2. Consider the reaction 59 Co (p, n). What is the product of this reaction? Solution. 1 1 H + 27 59 Co → 0 1 n + X Y Z С

on the left side we have 27 + 1 proton. WITH right side 0 + X protons, where X is the atomic number of the product. Obviously, X = 28 (Ni). On the left side there are 59 + 1 nucleons, and on the right side 1 + Y nucleons, where Y = 59. Thus, the reaction product is 59 Ni.

The reaction can go in several competing ways:

Various possible ways the course of a nuclear reaction in the second stage is called reaction channels. First stage the reaction is called the input channel.

Rice. 3. Channels of interaction of protons with 7 Li.

The last two reaction channels in scheme (6) refer to the cases of inelastic (A * + a) and elastic (A + a) nuclear scattering. These are special cases of nuclear interaction, which differ from others in that the reaction products coincide with particles,

reacting, with elastic scattering retaining not only the type of the nucleus, but also its internal state, while inelastic scattering the internal state of the nucleus changes (the nucleus passes into an excited state). The possibility of different reaction channels is determined by the projectile, its energy, and its nucleus.

When studying a nuclear reaction, it is of interest to identify the reaction channels, the comparative probability of its proceeding through different channels at different energies of the incident particles, the energy and angular distribution of the resulting particles, as well as their internal state (excitation energy, spin, parity, isotopic spin).

Nuclear reactions are transformations of atomic nuclei when interacting with elementary particles (including y-quanta) or with each other. The most common type of nuclear reaction is a reaction, written symbolically as follows:

where X and Y are the initial and final nuclei, a and B- the bombarding and emitted (or emitted) particles in a nuclear reaction.

In any nuclear reaction, the laws of conservation of charge and mass numbers: the sum of the charge (massive) the number of nuclei and particles entering into a nuclear reaction is equal to the sum of the charge (mass) numbers of the final products (nuclei and particles) of the reaction... Also performed laws of conservation of energy, momentum and angular momentum.

Unlike radioactive decay, which always occurs with the release of energy, nuclear reactions can be both exothermic (with the release of energy) and endothermic (with the absorption of energy).

An important role in explaining the mechanism of many nuclear reactions was played by N. Bohr's assumption (1936) that nuclear reactions proceed in two stages according to the following scheme:

The first stage is the capture of a particle a by the X nucleus, which has approached it at a distance of action of nuclear forces (approximately 2 10 15 m), and the formation of an intermediate nucleus C, called a compound (or compound nucleus). The energy of the particle that has flown into the nucleus is quickly distributed between the nucleons of the compound nucleus, as a result of which it appears in an excited state. In the collision of nucleons of a compound nucleus, one of the nucleons (or their combination, for example, a deuteron - the nucleus of a heavy isotope of hydrogen - deuterium, containing one proton and one neutron) or a cx-particle can receive energy sufficient to escape from the nucleus. As a result, the second stage of the nuclear reaction is possible - the decay of a compound nucleus into a Y nucleus and a particle B.

Classification of nuclear reactions

By the nature of the particles participating in the reactions:

• reactions under the influence of neutrons;
• reactions caused by charged particles (e.g. protons, (X-particles).

By the energy of the particles causing the reactions:

• reactions at low energies (on the order of eV), occurring mainly with the participation of neutrons;
• reactions at medium energies (several MeV) involving quanta and charged particles;
• reactions at high energies (hundreds and thousands of MeV), leading to the creation of elementary particles absent in a free state and having great importance to study them.

By the nature of the nuclei involved in the reactions:

• reactions on light nuclei (A 50);
• reactions on medium nuclei (50 A
• reactions on heavy nuclei (A> 150).

By the nature of the ongoing nuclear transformations:

• reactions with emission of neutrons;
• reactions with the emission of charged particles. The first ever nuclear reaction (Rutherford; 1919)

Nuclear reactions are transformations of atomic nuclei when interacting with elementary particles (including γ-quanta) or with each other. Symbolic reactions are written in the form:

X + a → Y + b, or X (a, b) Y

where X and Y are the initial and final nuclei, a and b are the bombarding and emitted (or emitted) particles in a nuclear reaction.

In any nuclear reaction, the laws of conservation of electric charges and mass numbers are fulfilled: the sum of the charges (and mass numbers) of nuclei and particles entering into a nuclear reaction is equal to the sum of the charges (and the sum of mass numbers) of the final products (nuclei and particles) of the reaction. The laws of conservation of energy, momentum and angular momentum are also fulfilled.

Nuclear reactions can be both exothermic (with the release of energy) and endothermic (with the absorption of energy).

Nuclear reactions are classified:

1) by the nature of the particles participating in them - reactions under the influence of neutrons; charged particles; γ-quanta;

2) by the energy of the particles causing them - reactions at low, medium and high energies;

3) by the nature of the nuclei participating in them - reactions on the lungs (A< 50) ; средних (50 < A <100) и тяжелых (A >100) cores;

4) by the nature of the ongoing nuclear transformations - reactions with the emission of neutrons, charged particles; capture reactions (in the case of these reactions, the compound nucleus does not emit any particles, but passes into the ground state, emitting one or more γ-quanta).

The first ever nuclear reaction was carried out by Rutherford

1939 - O. Hahn and F. Strassmann discovered the fission of uranium nuclei: when uranium is bombarded with neutrons, elements of the middle part appear periodic system- radioactive isotopes of barium (Z = 56), krypton (Z = 36) - fission fragments, etc. Fission of a heavy nucleus into two fragments is accompanied by energy release of the order of 1 MeV for each nucleon.

For example, there are two possible scenarios for the fission reaction of uranium nuclei.

The theory of fission of atomic nuclei is based on drop core model... The nucleus is considered as a drop of an electrically charged incompressible liquid (a) with a density equal to the nuclear one and obeying the laws of quantum mechanics. When a neutron is captured, the stability of such a charged droplet is violated, the nucleus comes to hesitation- alternately stretched, then compressed. The probability of nuclear fission is determined by the activation energy - the minimum energy required to carry out the nuclear fission reaction. At excitation energies lower than the fission activation energy, the deformation of the droplet nucleus does not reach critical (b), the nucleus does not fission and returns to the ground energy state by emitting a γ-quantum. At energies of excitation higher than the activation energy of fission, the deformation of the drop reaches a critical value (c), a "waist" in the drop (d) is formed and lengthens, and fission (e) begins.

Each of the prompt neutrons generated in the fission reaction, interacting with neighboring nuclei of fissile matter, causes a fission reaction in them. At the same time avalanche increase in the number of acts of division - begins fission chain reaction - a nuclear reaction in which the particles causing the reaction are formed as products of that reaction. The condition for the occurrence of a chain reaction is the presence of multiplying neutrons.

The neutron multiplication factor k is the ratio of the number of neutrons arising in a certain link of the reaction to the number of such neutrons in the previous link.

A necessary condition for the development of a chain reaction: k> 1. This reaction is called an evolving reaction. When k = 1, a self-sustaining reaction takes place. For k<1 идет затухающая реакция.

The multiplication factor depends on the nature of the fissile substance, and for a given isotope - on its amount, as well as the size and shape of the core - the space where the chain reaction takes place.

The minimum size of the core, at which a chain reaction is possible, is called the critical size.

The minimum mass of fissile material in a system of critical dimensions required for a chain reaction to occur is called the critical mass.

Chain reactions are divided into controlled and uncontrolled. The explosion of an atomic bomb is an example of an uncontrollable reaction. Controlled chain reactions take place in nuclear reactors.

A device in which a controlled nuclear fission reaction is maintained is called a nuclear (or atomic) reactor. Nuclear reactors are used, for example, in nuclear power plants.

Consider the scheme of a slow neutron reactor. Nuclear fuel in such reactors can be:

1) - in natural uranium it contains about 0.7%;

2) is obtained from according to the scheme

3) is obtained from thorium according to the scheme

In the reactor core there are fuel elements made of nuclear fuel (fuel elements) 1 and a moderator 2 (in it neutrons are slowed down to thermal velocities). Fuel elements are blocks of fissile material, enclosed in a hermetically sealed shell that weakly absorbs neutrons. Due to the energy released during nuclear fission, the fuel elements are heated, and therefore, for cooling, they are placed in the coolant flow 3. The core is surrounded by a reflector 4, which reduces the neutron leakage. Maintaining a steady state of the reactor is carried out using control rods 5 made of materials that strongly absorb neutrons, for example

from boron or cadmium. The coolant in the reactor is water, liquid sodium, etc. The coolant in the steam generator gives off its heat to the steam, which enters the steam turbine. The turbine rotates an electric generator, the current from which flows into the electrical network.

Our tasks: to acquaint with the main types of radioactive decay, in virtual experiments to show the chains of radioactive transformations and a method for measuring the decay constant.

Nuclear reaction - forced transformation of an atomic nucleus under the action of other particles (about spontaneous changing atomic nuclei by emitting elementary particles - radioactivity read in another lecture).

If you are in doubt whether you have ever seen a nuclear reaction, take a look at the sky on a clear day. We will talk about reactions to the Sun later.

Most often per core A a relatively light particle swoops in a(for example, neutron, proton, α -particle, etc.), and when approaching at a distance of the order of 10 -15 m as a result of the action of nuclear forces, a nucleus is formed V and a lighter particle b.

The set of particles and nuclei entering into a reaction (in the figure A + a) are called input channel of a nuclear reaction, and the resulting reaction - weekend channels. If the kinetic energy of the incident particle a is small, then two particles are formed: the particle itself and the nucleus.

Elastic and inelastic scattering are special cases of nuclear interaction, when the reaction products coincide with the initial ones.

Classification of nuclear reactions

By the type of particles causing the reaction
1. charged particle reactions
2. neutron reactions
3. reactions under the influence γ - quanta - photonuclear reactions

Conservation laws in nuclear reactions

You can think of a great variety of output channels for any reaction. However, most of them will prove to be impossible. The laws of conservation help to choose the reactions that are feasible in practice:

The last two are true for strong interactions. A whole series of laws are manifested in nuclear reactions, they are essential for reactions with elementary particles, we will name them elsewhere.

The set of conservation laws makes it possible to select possible output reaction channels and obtain important information about the properties of interacting particles and reaction products.

Direct nuclear reactions

In a direct reaction, the particle has time to collide with one (less often with two - three) nucleons. These reactions proceed very quickly - during the flight of a particle through the nucleus (10 -22 - 10 -21 s). Consider, for example, (n, p) -reactions. The momentum of the neutron is transferred mainly to one nucleon, which immediately leaves the nucleus, without having time to exchange energy with the rest of the nucleons. Therefore, nucleons should be ejected from the nucleus mainly in the forward direction. The energy of the ejected nucleon should be close to the energy of the projectile.

The kinetic energy of the incident particle must be large enough (imagine a wall made of cubes. If you hit one of them sharply, you can knock it out, almost without affecting the rest. With a slow impact, the wall will fall apart.)

At low energies, a reaction can occur breakdown(d, p). The deuteron is polarized as it approaches the nucleus, the neutron is captured by the nucleus, and the proton continues to move. For such a process, the interaction must occur at the edge of the nucleus. In a deuteron, a proton and a neutron are weakly bound.

Thus, the distinctive features of direct reactions are:
1. flow time ~ 10 -21 s;
2. the angular distribution of products is elongated in the direction of motion of the incident particle;
3. a particularly large contribution to the cross section of nuclear processes at high energies.

Fig. 2 Scheme of exothermic reaction

Energy scheme of a nuclear reaction

Let's depict a nuclear reaction in the form of an energy diagram (Fig. 2). The left part of the figure refers to the first stage - the formation of a compound nucleus, the right - the decay of this nucleus. T "a- part of the kinetic energy of the incident particle that went into the excitation of the nucleus, ε a- particle binding energy a in the compound core, ε b- particle binding energy b in the same core.

There is an apparent contradiction: the core C is a quantum-mechanical system with discrete energy levels, and the excitation energy, as can be seen from (1), is a continuous quantity (energy T a can be any). This will be dealt with in the next section.

Cross section of a nuclear reaction going through a compound nucleus

Fig. 3 Energy blur of the excited state level

Since there are two independent stages in the course of the reaction, the cross section can be represented as the product of the cross section for the formation of a compound nucleus σ state and the probability of its decay by i-th channel f i

The atomic nucleus is a quantum system. Since each of the excited levels of the spectrum has a finite average lifetime τ , level width Γ is also finite (Fig. 3) and is related to the average lifetime by a relation that is a consequence of the uncertainty relation for energy and time Δt ΔE ≥ ћ:

Let us consider the case when the energy levels of the compound nucleus are separated (the widths of the levels Γ less distance between them ΔE). When the excitation energy coincides with the energy of one of the levels E 0 reaction cross section (a, b) will have a resonant maximum. In quantum mechanics, it is proved that the cross section for the formation of a compound nucleus is described by the Breit-Wigner formula

(6)

where λ a is the de Broglie wavelength of the incident particle, Γ - full width of the level, Γ a- the width of the level relative to elastic scattering (partial, partial width).

Let's figure out the widths of the level. Decay probability of a compound nucleus f i inversely proportional to the lifetime τ i regarding this decay. And the life time τ i in turn, according to (5), is inversely proportional to the width Γ i, called partial (partial). As a result, the probabilities f i proportional to widths Γ i, and they can be represented

Fig. 4 Cross-section of the formation of a compound nucleus

Sum Σf i = 1, a ΣΓ i = Γ... Partial widths are more convenient to deal with than probabilities.

Full level width Γ weakly depends on the speed of the incident particle v a, a Γ a proportional to this speed. De Broglie wavelength is inversely proportional to speed v a... Therefore, far from resonance at low velocities, the cross section grows as 1 / v a(You can explain this to yourself by the fact that a slow particle spends more time at the nucleus, and the probability of its capture increases). At E ~ E 0 the capture cross section increases sharply (Fig. 4). In formula (6) E is the kinetic energy of the incident particle, and E 0 is the energy of the compound nucleus level, measured from bond energy: energy level = ε a + E 0.

Nuclear reactions driven by neutrons

The main reactions under the action of nonrelativistic neutrons are shown in the diagram (Fig. 5). There and in what follows we will denote by the letter A mass number kernel A.

Let's consider them in order.

Elastic scattering

Neutrons in nuclear reactions with charged particles and in nuclear fission are born fast ( T n of the order of several MeV), but are absorbed, as a rule, slowly. The deceleration occurs due to multiple elastic collisions with atomic nuclei.

There are two possibilities: deflection of a neutron by the nuclear field without capture - potential scattering, and the emission of a neutron from a compound nucleus is resonant scattering... So the cross section is the sum σ control = σ sweat + σ res.

Fig. 6 Cross section of elastic scattering of neutrons by uranium nuclei

Then, according to (1), scattering will occur with zero angular momentum ( L = 0, s- scattering). The angular distribution of scattered neutrons in the center of mass is isotropic. In fact, these "small" energies are not so small: in hydrogen ~ 10 MeV, in lead ~ 0.4 MeV. The potential scattering cross section in this case does not depend on the neutron energy and is equal to

In the cross section for resonant scattering

width Γ n is directly proportional to the speed, and the de Broglie wavelength λ is inversely proportional to it. Therefore, depending on the energy, we have only a resonance peak at E = E 0... As a result, for the energy dependence of the cross section for elastic neutron scattering, we have a pedestal with resonance peaks (Fig. 6).

Inelastic scattering

The scatterer nucleus is in an excited state: n + A => (A + 1) * => A * + n... Obviously the reaction has threshold character: the energy of the incident neutron must be sufficient to transfer the target nucleus to an excited state. Studying the spectra of neutrons and accompanying γ - radiation, receive information about the structure of the energy levels of the nucleus.

A few words about how you can measure inelastic scattering cross section... When the kinetic energy of neutrons is greater than about 1 MeV,

the main processes will be elastic and inelastic scattering σ = σ control + σ uncontrolled... Let at a distance L from source S detector placed D(fig. 7). Let's surround the source with a sphere of radius R and wall thickness d... If the scattering pure elastic, it can be shown that the attenuation along the line connecting the source and the detector is compensated for by scattering by the sphere towards the detector from other directions. If a decrease in detector readings is observed, then it is due to inelastic scattering

Here N is the concentration of nuclei in the target. Several measurements with different thicknesses allow you to find the cross section σ uncontrolled.

Radiation capture

Radiative capture - capture of a neutron, the formation of a compound nucleus in an excited state and the subsequent transition to the ground one with emission of γ-radiation n + (A, Z) => (A + 1, Z) * ​​=> (A + 1, Z) + γ... The excitation energy of the compound nucleus (2), and hence the total energy of γ quanta, exceeds the binding energy of the neutron in the nucleus, i.e. 7 - 8 MeV.

How is radiation capture manifested?
• emission of γ-quanta;
• in the radioactivity (emission of β-particles) of the formed nucleus (A + 1, Z)(very often the kernel (A + 1, Z) unstable);
• in weakening the neutron flux N = N 0 exp (-σ β nd) (σ β - cross section of radiation capture, d- target thickness).

Fig.10 Cross-section of radiation capture by indium nuclei.

At low neutron energies, resonance effects and the radiative capture cross section are very strong

For slow neutrons Γ = Γ n + Γ γ and Γ γ ≈ const ~ 0.1 eV... Therefore, the dependence of the cross section for radiative capture on energy repeats the dependence of the cross section for the formation of a compound nucleus. Note the very large value of the capture cross section for indium (Fig. 10) at a neutron energy of 1.46 eV. It is 4 orders of magnitude larger than the geometric cross section of the nucleus. Indium is included in compounds with cadmium for use as absorbent materials in reactors.

As noted, the core (A + 1, Z) resulting from neutron capture is very often radioactive with a short half-life. Radioactive radiation and radioactive decay are well known for each element. Since 1936, neutron-induced radioactivity has been used to identify elements. The method was named "activation analysis"... A sample of about 50 mg is sufficient. Activation analysis can detect up to 74 elements and is used to determine impurities in ultrapure materials (in the reactor building and electronics industry), the content of trace elements in biological objects in environmental and medical research, as well as in archeology and forensics. Activation analysis is also successfully used in the search for minerals, to control technological processes and the quality of products.

Nuclear fission is a phenomenon in which a heavy nucleus is divided into two unequal fragments (very rarely into three). It was discovered in 1939 by German radiochemists Hahn and Strassmann, who proved that irradiation of uranium with neutrons produces an element from the middle of the periodic system barium 56 Ba.

A few days after the news of this, the Italian physicist E. Fermi (who had moved to the USA) set up an experiment to observe fission fragments. Uranium salt was deposited on the inner side of the plates of the pulsed ionization chamber (Fig. 11). When a charged particle enters the volume of the chamber, we have an electric pulse at the exit, the amplitude of which is proportional to the energy of the particle. Uranium is radioactive, α-particles give numerous pulses of small amplitude. When the chamber was irradiated with neutrons, pulses of large amplitude caused by fission fragments were detected. The fragments have a large charge and an energy of ~ 100 MeV. A few days earlier, Otto Frisch had observed the debris in Wilson's chamber.

Distinguish
• forced division- fission under the action of an incident particle (most often a neutron)

  Usually, the kinetic energy of the incident particle T a is small and the reaction proceeds through a compound nucleus: a + A => C * => B 1 + B 2

• spontaneous division (spontaneous)... Discovered by Soviet physicists Flerov and Petrzhak in 1940. Uranium 235 U is fissionable with a half-life of approximately 2 * 10 17 years. There are 10 8 α-decays per fission, and this phenomenon is extremely difficult to detect.

Elementary theory of fission

Let us find out the basic conditions for the possibility of fission using the drop model.

Fission energy

Consider fission of a nucleus C into two pieces C => B 1 + B 2... Energy will be released if the binding energies of the nucleus and fragments are related by the ratio

G osc = G C - G 1 - G 2 Based on the drop model, we find out at what mass numbers A C and serial numbers Z C condition (7) is satisfied.

(8)

We substitute these expressions in (7), while taking for a smaller fragment Z 1 = (2/5) Z C, A 1 = (2/5) A C and for the heavier Z 2 = (3/5) Z C, A 2 = (3/5) A C.

The first and fourth terms in (8) will cancel, because they are linear with respect to A and Z.

The first two terms in (9) are the change in the surface tension energy ΔW pov, and the last two are the change in the Coulomb energy ΔW cool... Inequality (7) now looks like this

G osc = - ΔW sp - ΔW cool = 0.25 ΔW sp - 0.36 ΔW cool

If Z 2 / A> 17 then energy is released. Attitude Z 2 / A are called division parameter.

Condition Z 2 / A> 17 is performed for all cores, starting with silver 47 108 Ag... It will become clear below why expensive uranium is used as fuel in reactors, and not cheaper materials.

Division mechanism

Condition Z 2 / A> 17 is performed for all elements of the second half of the periodic table. However, experience shows that only very heavy nuclei are divided. What's the matter? Let's remember α -decay. Very often it is energetically beneficial, but does not happen, because prevents the Coulomb barrier. Let's see how things stand in the case of division. The possibility of fission depends on the magnitude of the sum of the surface and Coulomb energies of the initial nucleus and fragments. Let us see how these energies change upon deformation of the nucleus - an increase in division parameter ρ .

Surface tension energy W pov increases, then, when the fragments take a spherical shape, remains constant. Coulomb energy W cool only decreases, slowly at first, and then as 1 / ρ... Their sum at Z 2 / A> 17 and Z 2 / A behaves as shown in Figure 13. There is a potential barrier with a height B f preventing division. Spontaneous fission can occur due to the quantum mechanical leakage phenomenon (tunneling effect), but the probability of this is extremely small, so the half-life, as mentioned above, is very large.

If Z 2 / A> 49, then the height of the barrier B f = 0, and the fission of such a nucleus occurs instantaneously (in a nuclear time of the order of 10 -23 with).

For the fission of a nucleus, it is necessary to give it an energy greater than B f... This is possible by capturing a neutron. In this case, formula (2) will look like

(11)

Here ε n- the binding energy of the neutron in the nucleus, obtained during its capture; T n is the kinetic energy of the incident neutron.

Let us summarize the consideration of the interaction of neutrons.

Nuclear reactions under the influence of charged particles

Unlike neutrons, when considering collisions of charged particles with a nucleus, it is necessary to take into account the presence of a Coulomb

barrier. The interaction of a neutron with a nucleus is characterized by a deep (30 - 40 MeV) potential well with a radius R i(Figure 14a). A neutron that comes close to the nucleus experiences a strong attraction. In the case of interaction of charged particles with a nucleus, the potential curve has the form of Fig. 14b. When approaching the nucleus, we first have the Coulomb repulsion (long-range forces), and at a distance of the order of R i a powerful nuclear attraction comes into play. Coulomb Barrier Height B cool approximately equal

For example, for protons colliding with an oxygen nucleus, the barrier height will be 3.5 MeV, and with uranium, 15 MeV. For α -particles, the height of the barriers is 2 times higher. If the kinetic energy of the particle T, there is a possibility that the particle will enter the nucleus due to the tunneling effect. But the transparency of the barrier is extremely low, and elastic scattering is most likely to occur. For the same reason, it is difficult for a charged particle to leave the nucleus. Let's remember α -decay.

The dependence of the cross section for a nuclear reaction for charged particles has a threshold character. But the resonance peaks are poorly expressed or completely absent, because at energies of ~ MeV, the density of nuclear levels is high and they overlap.

In the future, great hopes are associated with thermonuclear fusion reactions of the type 2 H + 2 H => 3 He + p or 2 H + 3 H => 4 He + n, which are distinguished by a very large release of energy. An obstacle for such reactions is the Coulomb barrier. It is necessary to heat the substance to such temperatures that the energy of the particles kT let them react. Temperature 1.16 10 7 corresponds to 1 keV. To obtain a self-sustaining "plasma" reaction, three conditions must be met:

the plasma must be heated to the required temperatures,

the plasma density must be high enough

temperature and density must be maintained over a long period of time.

And then there are continuous problems: the confinement of plasma in magnetic traps, the creation of materials for the reactor that would withstand powerful neutron irradiation, etc. It is still unclear how cost-effective the production of electricity using thermonuclear fusion can be. There has been continuous research progress.

Maximum energy loss (minimum E "n) will be at θ = π : E "min = αE(for hydrogen E "min = 0).

At low energies (see (1)), scattering is isotropic, all values ​​of the angles θ are equally probable. Since between the scattering angle θ and the energy of the scattered neutron E "n the relationship is unambiguous (12), the distribution of neutrons in energy after a single scattering will be uniform (Fig. 15). It can be represented as the formula

(13)

Average logarithmic energy loss. Decelerating ability. Deceleration factor

Let's see how a large number of collisions will affect the neutron energy. In this case, it is convenient to use not the energy scale, but the logarithm scale ε = lnE: we saw (see (12)) that E "/ E does not depend on E, i.e. on average, the percentage of energy loss is the same. On the energy scale, the change in energy looks like this

Those. exactly lnE, but not E changes by a more or less fixed amount.

Average neutron energy after collision

Average energy loss

Average logarithmic energy loss

ξ does not depend on E... Axis movement lnE uniform. You can just calculate the average number of collisions n to slow down from E start to the final E con:

(14)

The table below shows the values ξ and n for a number of nuclei with neutron moderation from 1 MeV energy to 0.025 eV thermal.

				ξΣ s, 1 / cm	ξΣ s / Σ a

Looking at the 4th column, it may seem that hydrogen slows down better than others. But we must also take into account the frequency of collisions. For gaseous and liquid hydrogen ξ = 1, but it is clear that the path taken during deceleration will be different. The 5th column shows the logarithmic loss ξ times the collision rate - retarding ability... And here the best moderator is ordinary water. But a good moderator should absorb neutrons poorly. In the last, 6th column, the mean logarithmic loss is multiplied by the ratio of the macroscopic scattering and absorption cross sections. Comparing the numbers, it is clear why heavy water or graphite is used as a moderator in nuclear reactors.

Average deceleration time

Let us estimate the time required for a neutron to slow down as a result of collisions from the initial energy E 0 to the final E to... We split the energy axis into small segments ΔE... Collisions per segment ΔE near E

Free path length λ s determined by the cross section for elastic scattering σ s and the concentration of the moderator nuclei N

, (15)

where Σ s is a quantity called macroscopic section... Time required to decelerate by ΔE, is defined as the product of a time interval and the passage of the free path by the number of collisions by ΔE

Passing to infinitesimal quantities and integrating, we obtain for the deceleration time t

For example, for beryllium at E 0= 2 MeV, E to= 0.025 eV, λ s= 1.15 cm, ξ = 0.21 we get ~ 3.4 · 10 -5 s. Note that, firstly, this value is much less than the half-life of a free neutron (~ 600 s), and, secondly, it is determined by motion near a finite energy.

Spatial distribution of neutrons

Let the medium have a point isotropic source of fast neutrons with the initial energy E 0... Distance L deputy, by which, on average, neutrons are removed during deceleration to E to is called deceleration length... The real path traversed by the neutron is much larger, because the trajectory of movement is a broken line of segments of length λ s... The quantity L deputy is determined by the parameters of the moderation medium, the initial and final energy of the neutron:

For heavy water with a deceleration from 2 MeV to thermal 0.025 eV L deputy~ 11 cm, for graphite ~ 20 cm.

As a result of deceleration in a volume with a radius of the order of the deceleration length, thermal neutrons with a Maxwellian energy distribution are produced. Thermal neutrons begin to diffuse (move chaotically), spreading through the substance in all directions from the source. This process is described by the diffusion equation taking into account the absorption of neutrons

(16)

In this equation Φ - neutron flux (the number of neutrons crossing a unit area per unit of time), Σ s and Σ a are the macroscopic scattering (see (15)) and absorption cross sections, respectively, D- diffusion coefficient, S- neutron source. In this equation, the first term describes the motion of neutrons in matter, the second - absorption, and the third birth.

The main characteristic of the medium describing the diffusion process is diffusion length L diff

The diffusion length characterizes the average removal of a neutron from the source before absorption. For heavy water L diff~ 160 cm, for graphite ~ 50 cm. Ordinary water strongly absorbs neutrons and L diff only 2.7 cm.How tortuous and long the neutron path during diffusion can be judged by comparing the diffusion length (in graphite 50 cm) with the average neutron path length before absorption λ a = 1 / Σ a(in the same graphite 3300 cm).

In practice, they often deal with the transition of neutrons from one medium to another. For example, the reactor core is surrounded by a reflector. Reflection coefficient β - the fraction of neutrons returning to the source environment from the sourceless environment. Approximately, β ≈ 1 - 4 D / L diff where the parameters refer to a sourceless environment. For example, from a graphite reflector β = 0.935, i.e. 93% of the neutrons will return. Graphite is a great reflector. Better only heavy water, where β = 0.98!

Chain reaction in a medium containing a fissile substance

We have a homogeneous medium containing fissile matter. There are no extraneous sources of neutrons, they can appear only as a result of nuclear fission. We will assume that all processes take place at the same energy (the so-called single speed approximation). The question is: is it possible to make a ball out of this substance, in which a stationary chain reaction would be maintained?

We need:

• macroscopic neutron absorption cross section Σ absorbed, which is made up of the gripping section without dividing Σ capture(radiation capture) and fission cross sections Σ cases: Σ absorbed = Σ capture + Σ cases;
• average number of neutrons υ released in one act of division.

Then the equation for the neutron flux Φ in the stationary case it will look like

with the boundary condition

,

which means that at some distance d from a fissile ball of radius R the thread should go to zero.

If we compare the equation for the flow Φ with (16), it can be seen that the source is the quantity υΣ div Φ- the number of neutrons produced per unit volume per unit time.

Consider three cases

υΣ div - fewer neutrons are produced than absorbed. Obviously, a stationary reaction is impossible.

• υΣ div = Σ absor- the source compensates for the absorption of neutrons. The solution to equation (17) gives Φ = const only for endless environment otherwise, due to neutron leakage through the boundary of the medium, the reaction will damp out.

  υΣ div> Σ absor- it is possible to choose such a size of a ball of fissile matter so that the surplus of neutrons escapes through the boundaries of the ball (to prevent a nuclear explosion).

Let us introduce the notation ω 2 = (Σ absorp - υΣ div) / D> 0... Equation (17) takes the form

(18)

His common decision looks like

(19)

Coefficient B in (19) must be set equal to zero so that the solution does not diverge at r = 0... Finding the final solution is complicated by correctly taking into account the boundary condition, and for a natural mixture of uranium isotopes (235 U - 0.7%, 235 U - 99.3%, Σ absorbed= 0.357 1 / cm, Σ cases= 0.193 1 / cm, υ = 2.46) we obtain as the minimum value of the total R ≈ 5 see How does this task differ from the real one? In fact, neutrons are born fast, and they must be slowed down to thermal energies. The first reactor, built by E. Fermi (1942), had dimensions of about 350 cm.

Chain reaction. Nuclear reactor

Devices in which energy is obtained through a stationary fission chain reaction are called atomic reactors (for example, they say, a nuclear power plant, nuclear power plant), although in fact it is nuclear reactors. The design of nuclear reactors is very complex, but an essential element of any reactor is the core in which the fission reaction takes place.

The core contains fissile material, a moderator, control (regulating) rods, structural elements and is surrounded by a neutron reflector to reduce the losses of the latter. All this is inside the protection against neutron flux, γ - radiation.

The fate of the neutron in the core

capture of uranium by the nucleus with the subsequent fission of this nucleus;

capture of uranium by the nucleus with the subsequent transition of the nucleus to the ground state with the emission γ - quanta (radiation capture);

capture of moderator cores or structural elements;

departure from the core;

absorption by control rods.

Neutrons are emitted during nuclear fission, then absorbed or leave the core. Let us denote by k multiplication factor - the ratio of the number of neutrons of the next generation n i + 1 to the number in the previous n i

If we introduce the lifetime of a generation τ , then the equation for the number of neutrons n and his solution would look like this

(21)

If the coefficient k is different from 1, then the number of neutrons decreases ( k) or increases ( k> 1) exponentially, i.e. very fast.

(Observe the influence of the multiplication factor k and the lifetime of a generation τ on the dynamics of the number of neutrons by simple experience)

Reproduction factor k can be represented as a product of the coefficient k ∞ for infinite environment and probability not leave the active zone χ

The quantity χ depends on the composition of the core, its size, shape, reflector material.

Considering a reactor operating on thermal neutrons, the coefficient k ∞ can be represented as four factors

where

ε - multiplication factor on fast neutrons (for real systems of uranium and graphite ε ~ 1.03);

p- the likelihood of avoiding resonance capture during deceleration. Recall that neutrons are produced fast, and when slowing down to thermal energies, they must overcome the resonance region in the absorption cross section (see Fig. 10);

f- the fraction of neutrons absorbed by uranium nuclei (and not moderator or structural elements). ε p f ≈ 0.8;

η is the average number of neutrons emitted per one act of capture by a uranium nucleus (during capture, nuclear fission can occur, or γ -quants). η ≈ 1.35(compare with ~ 2.5 for the number of neutrons per fission event).

From the given data it follows k ∞ = 1.08 and χ = 0.93, which corresponds to the size of the reactor of the order of 5 - 10 m.

Critical mass- the minimum mass of fissile matter at which a self-sustaining nuclear fission reaction can occur in it. If the mass of the substance is below the critical value, then too many neutrons required for the fission reaction are lost, and the chain reaction does not take place. With a mass greater than the critical one, the chain reaction can accelerate like an avalanche, which will lead to a nuclear explosion.

The critical mass depends on the size and shape of the fissile sample, since they determine the neutron leakage from the sample through its surface. A spherical sample has the minimum critical mass, since its surface area is the smallest. Reflectors and moderators of neutrons surrounding the fissile material can significantly reduce the critical mass. The critical mass also depends on chemical composition sample.

The "grandfather" of domestic nuclear reactors is the first physical reactor F-1, which received the status of a monument of science and technology. It was launched in 1946 under the leadership of I.V. Kurchatov. Purified graphite in the form of bars with holes for uranium rods was used as a moderator. The control was carried out by rods containing cadmium, which strongly absorbs thermal neutrons. The core of the boiler contained 400 tons of graphite and 50 tons of uranium. The reactor power was about 100 W; there was no special heat removal system. During operation, heat was accumulated in a large mass of graphite. Then the graphite masonry was cooled with an air stream from a fan. This reactor is still working properly.

The share of nuclear power in global electricity production was different years 10-20%. The largest percentage (~ 74) of electricity is produced at nuclear power plants in France. In Russia ~ 15%.

How the process of physical start-up of an atomic reactor looks like is shown by a computer model.

If you want to check how the lecture material was learned,

An important role in the development of ideas about the structure of nuclei was played by the study of nuclear reactions, which provided extensive information about the spins and parities of excited states of nuclei, and contributed to the development of the shell model. The study of reactions with the exchange of several nucleons between colliding nuclei made it possible to study nuclear dynamics in a state with large angular momenta. As a result, long rotating strips were discovered, which served as one of the foundations for creating a generalized model of the nucleus. When heavy nuclei collide, nuclei are formed that do not exist in nature. The synthesis of transuranic elements is largely based on the physics of the interaction of heavy nuclei. In reactions with heavy ions, nuclei are formed that are far from the β-stability band. Nuclei distant from the β-stability band differ from stable nuclei by a different ratio between the Coulomb and nuclear interactions, the ratio between the number of protons and the number of neutrons, a significant difference in the binding energies of protons and neutrons, which manifests itself in new types of radioactive decay - proton and neutron radioactivity and a number of other specific features of atomic nuclei.
When analyzing nuclear reactions, it is necessary to take into account the wave nature of particles interacting with nuclei. The wave character of the process of interaction of particles with nuclei is clearly manifested in elastic scattering. Thus, for nucleons with an energy of 10 MeV, the reduced de Broglie wavelength is less than the radius of the nucleus, and a characteristic pattern of diffraction maxima and minima arises during nucleon scattering. For nucleons with an energy of 0.1 MeV, the wavelength is larger than the radius of the nucleus and there is no diffraction. For neutrons with energy<< 0.1 МэВ сечение реакции ~π 2 гораздо больше, чем характерный размер площади ядра πR.
Nuclear reactions are an effective method for studying nuclear dynamics. Nuclear reactions occur when two particles interact. During a nuclear reaction, there is an active exchange of energy and momentum between the particles, as a result of which one or more particles are formed, scattering from the interaction region. As a result of a nuclear reaction, a complex process of restructuring of the atomic nucleus occurs. As in the description of the structure of the nucleus, in the description of nuclear reactions it is practically impossible to obtain an exact solution to the problem. And just as the structure of the nucleus is described by different nuclear models, the course of a nuclear reaction is described by different reaction mechanisms. The mechanism of a nuclear reaction depends on several factors - on the type of the incident particle, the type of target nucleus, the energy of the incident particle, and on a number of other factors. One of the limiting cases of a nuclear reaction is direct nuclear reaction... In this case, the incident particle transfers energy to one or two nucleons of the nucleus, and they leave the nucleus without interacting with other nucleons of the nucleus. The characteristic time of the course of a direct nuclear reaction is 10 -23 s. Direct nuclear reactions occur on all nuclei at any energy of the incident particle. Direct nuclear reactions are used to study single-particle states of atomic nuclei, because the reaction products carry information about the position of the levels from which the nucleon is knocked out. With the help of direct nuclear reactions, detailed information was obtained on the energies and occupation of single-particle states of nuclei, which formed the basis of the shell model of the nucleus. Another limiting case is the reactions going through compound nucleus formation.

The description of the mechanism of nuclear reactions was given in the works of W. Weisskopf.

V. Weisskopf: “What happens when a particle enters the nucleus and collides with one of the nuclear constituents? The figure illustrates some of these possibilities.
1) The falling particle loses part of its energy, raising the nuclear particle to a higher state. This will be the result of inelastic scattering if the incident particle is left with enough energy to leave the core again. This process is called direct inelastic scattering, since it involves scattering only on one constituent part of the nucleus.
2) The falling particle transfers energy to collective motion, as it is symbolically shown in the second diagram of the figure, this is also a direct interaction.
3) In the third scheme of the figure, the transferred energy is large enough to pull out a nucleon from the target. This process also contributes to a direct nuclear reaction. In principle, it does not differ from 1), it corresponds to the "exchange reaction".
4) The falling particle can lose so much energy that it remains bound inside the nucleus, the transferred energy can be received by the low-lying nucleon in such a way that it cannot leave the nucleus. We then get an excited nucleus, which cannot emit a nucleon. This state inevitably leads to further excitations of nucleons by internal collisions, in which the energy per excited particle decreases on average, so that in most cases a nucleon cannot leave the nucleus. Consequently, a state with a very long lifetime will be reached, which can decay only if one particle, in collisions inside the nucleus, accidentally acquires sufficient energy to leave the nucleus. We call this situation the formation of a compound nucleus. Energy can also be lost by radiation, after which the escape of a particle becomes energetically impossible: the incident nucleon will experience radiation capture.
5) The formation of a compound nucleus can be carried out in two or more steps, if after a process of type 1) or 2) the incident nucleon strikes another nucleon on its way and excites it in such a way that escape from the nucleus is impossible for any nucleon.

For the first time, the idea of ​​the progress of a nuclear reaction through the stage of a compound nucleus was expressed by N. Bohr. According to the composite nucleus model, an incident particle, after interacting with one or two nucleons of the nucleus, transfers to the nucleus most of its energy and is captured by the nucleus. The lifetime of a compound nucleus is much longer than the time of flight of an incident particle through the nucleus. The energy introduced by the incident particle into the nucleus is redistributed between the nucleons of the nucleus until a significant part of it is concentrated on one particle, and then it flies out of the nucleus. The formation of a long-lived excited state can, as a result of deformation, lead to its division.

N. Bor: “The phenomenon of neutron capture compels us to assume that a collision between a fast neutron and a heavy nucleus should lead, first of all, to the formation of a complex system characterized by remarkable stability. The possible subsequent decay of this intermediate system with the escape of a material particle or the transition to the final state with the emission of a quantum of radiant energy should be considered as independent processes that are not directly related to the first phase of collision. We meet here with a significant difference, previously unrecognized, between real nuclear reactions - ordinary collisions of fast particles and atomic systems - collisions, which until now have been for us the main source of information regarding the structure of the atom. Indeed, the possibility of counting individual atomic particles by means of such collisions and the study of their properties are due, first of all, to the "openness" of the systems under consideration, which makes the exchange of energy between individual constituent particles very unlikely during the impact. However, due to the close packing of particles in the nucleus, we must be prepared for the fact that it is this energy exchange that plays the main role in typical nuclear reactions. "

Classification of nuclear reactions. Nuclear reactions are an effective means of studying the structure of atomic nuclei. If the wavelength of the incident particle is larger than the size of the nucleus, then in such experiments information about the nucleus as a whole is obtained. If the size of the nucleus is smaller, then information on the distribution of the density of nuclear matter, the structure of the surface of the nucleus, the correlation between nucleons in the nucleus, and the distribution of nucleons over the nuclear shells are extracted from the reaction cross sections.

• Coulomb excitation of nuclei under the action of charged particles of relatively large mass (protons, α-particles and heavy ions of carbon, nitrogen) is used to study low-lying rotational levels of heavy nuclei.
• Reactions with heavy ions on heavy nuclei, leading to the fusion of colliding nuclei, are the main method for producing superheavy atomic nuclei.
• Fusion reactions of light nuclei at relatively low collision energies (the so-called thermonuclear reactions). These reactions are due to quantum mechanical tunneling through the Coulomb barrier. Thermonuclear reactions take place inside stars at temperatures of 10 7 –10 10 K and are the main source of energy for stars.
• Photonuclear and electronuclear reactions occur when colliding with nuclei of γ-quanta and electrons with energies E> 10 MeV.
• Fission reactions of heavy nuclei, accompanied by a deep restructuring of the nucleus.
• Reactions on beams of radioactive nuclei open up the possibility of obtaining and studying nuclei with an unusual ratio of the number of protons and neutrons, far from the stability line.

Nuclear reactions are usually classified according to the type and energy of the incident particle, the type of target nuclei, and the energy of the incident particle.

Slow neutron reactions

“1934 One morning Bruno Pontecorvo and Eduardo Amaldi were testing some metals for radioactivity. These samples were shaped like small hollow cylinders of the same size, inside which a neutron source could be placed. To irradiate such a cylinder, a neutron source was inserted into it, and then everything was placed in a lead box. On this momentous morning, Amaldi and Pontecorvo conducted experiments with silver. And suddenly Pontecorvo noticed that something strange was happening to the silver cylinder: its activity was not always the same, it changed depending on where it was placed, in the middle or in the corner of the lead box. In utter bewilderment, Amaldi and Pontecorvo went to report this miracle to Fermi and Rasetti. Franke was inclined to attribute these oddities to some statistical error or inaccurate measurements. And Enrico, who believed that every phenomenon requires verification, suggested that they try to irradiate this silver cylinder outside the lead box and see what happens. And then absolutely incredible miracles went on for them. It turned out that objects in the vicinity of the cylinder are capable of affecting its activity. If the cylinder was irradiated while it was standing on a wooden table, its activity was higher than when it was placed on a metal plate. Now the whole group was interested in this and everyone took part in the experiments. They placed the neutron source outside the cylinder and placed various objects between it and the cylinder. The lead plate slightly increased the activity. Lead−the substance is heavy. “Well, let's try the easy now!−suggested by Fermi.−Let's say paraffin. " On the morning of October 22nd, the paraffin wax experiment was carried out.
They took a large piece of paraffin, hollowed out a hole in it, and placed a neutron source inside, irradiated a silver cylinder and brought it to a Geiger counter. The counter, as if it had fallen off the chain, just clicked. The whole building thundered with exclamations: “Incredible! Unimaginable! Black magic!" Paraffin increased the artificial radioactivity of silver a hundredfold.
At noon, a group of physicists reluctantly dispersed for their lunch break, which usually lasted two hours ... Enrico took advantage of his loneliness, and when he returned to the laboratory, he already had a theory that explained the strange effect of paraffin. "