Physics of the atomic nucleus. Nuclear reactions

And the ability to use nuclear energy, both for creative (nuclear energy) and destructive (atomic bomb) purposes, became, perhaps, one of the most significant inventions of the last twentieth century. Well, at the heart of all that formidable power that lurks in the depths of a tiny atom are nuclear reactions.

What are nuclear reactions

Nuclear reactions in physics mean the process of interaction of an atomic nucleus with another similar nucleus or with different elementary particles, resulting in changes in the composition and structure of the nucleus.

A little history of nuclear reactions

The first nuclear reaction in history was made by the great scientist Rutherford back in 1919 during experiments to detect protons in nuclear decay products. The scientist bombarded nitrogen atoms with alpha particles, and when the particles collided, a nuclear reaction occurred.

And this is what the equation for this nuclear reaction looked like. It was Rutherford who was credited with the discovery of nuclear reactions.

This was followed by numerous experiments by scientists in carrying out various types of nuclear reactions, for example, a very interesting and significant for science was the nuclear reaction caused by the bombardment of atomic nuclei with neutrons, which was carried out by the outstanding Italian physicist E. Fermi. In particular, Fermi discovered that nuclear transformations can be caused not only by fast neutrons, but also by slow ones, which move at thermal speeds. By the way, nuclear reactions caused by exposure to temperature are called thermonuclear reactions. As for nuclear reactions under the influence of neutrons, they very quickly gained their development in science, and what kind of reactions, read about it further.

Typical formula for a nuclear reaction.

What nuclear reactions are there in physics?

In general, nuclear reactions known today can be divided into:

fission of atomic nuclei
thermonuclear reactions

Below we will write in detail about each of them.

Nuclear fission

The fission reaction of atomic nuclei involves the disintegration of the actual nucleus of an atom into two parts. In 1939, German scientists O. Hahn and F. Strassmann discovered the fission of atomic nuclei, continuing the research of their scientific predecessors, they established that when uranium is bombarded with neutrons, elements of the middle part of the periodic table arise, namely radioactive isotopes of barium, krypton and some others elements. Unfortunately, this knowledge was initially used for horrific, destructive purposes, because the Second World War began and German, and on the other hand, American and Soviet scientists raced to develop nuclear weapons (which were based on the nuclear reaction of uranium), which ended in the infamous “ nuclear mushrooms" over the Japanese cities of Hiroshima and Nagasaki.

But back to physics, the nuclear reaction of uranium during the splitting of its nucleus simply has colossal energy, which science has been able to put to its service. How does such a nuclear reaction occur? As we wrote above, it occurs as a result of the bombardment of the nucleus of a uranium atom by neutrons, which causes the nucleus to split, creating a huge kinetic energy of the order of 200 MeV. But what is most interesting is that as a product of the nuclear fission reaction of a uranium nucleus from a collision with a neutron, several free new neutrons appear, which, in turn, collide with new nuclei, split them, and so on. As a result, there are even more neutrons and even more uranium nuclei are split from collisions with them - a real nuclear chain reaction occurs.

This is how it looks on the diagram.

In this case, the neutron multiplication factor must be greater than unity; this is a necessary condition for a nuclear reaction of this type. In other words, in each subsequent generation of neutrons formed after the decay of nuclei, there should be more of them than in the previous one.

It is worth noting that, according to a similar principle, nuclear reactions during bombardment can also take place during the fission of the nuclei of atoms of some other elements, with the nuances that the nuclei can be bombarded by a variety of elementary particles, and the products of such nuclear reactions will vary, so we can describe them in more detail , we need a whole scientific monograph

Thermonuclear reactions

Thermonuclear reactions are based on fusion reactions, that is, in fact, the process opposite to fission occurs, the nuclei of atoms do not split into parts, but rather merge with each other. This also releases a large amount of energy.

Thermonuclear reactions, as the name suggests (thermo - temperature), can occur exclusively at very high temperatures. After all, in order for two atomic nuclei to merge, they must approach a very close distance to each other, while overcoming the electrical repulsion of their positive charges; this is possible with the existence of high kinetic energy, which, in turn, is possible at high temperatures. It should be noted that thermonuclear reactions of hydrogen do not occur, however, not only on it, but also on other stars; one can even say that it lies at the very basis of their nature of any star.

Nuclear reactions, video

And finally, an educational video on the topic of our article, nuclear reactions.

At low (< 1 МэВ), средних (1-100 МэВ) и высоких (>100 MeV) energies. Distinctions are made on light nuclei (target nuclei A< 50), ядрах ср. массы (50 < А < 100) и тяжелых ядрах (А > 100).
I nuclear can occur if the two particles involved in it approach at a distance less than the diameter of the nucleus (approx. 10 -13 cm), i.e. at a distance at which the forces of intranuclear interaction act. between the constituent nucleons of the nucleus. If both nuclear particles involved - the bombarding one and the target nucleus - are positively charged, then the approach of the particles is prevented by the repulsive force of the two positive ones. charges, and the bombarding particle must overcome the so-called. Coulomb potential barrier. The height of this barrier depends on the charge of the bombarding particle and the charge of the target nucleus. For kernels responding with avg. values of , and bombarding particles with charge +1, the barrier height is approx. 10 MeV. If particles that do not have a charge () participate in the nuclear process, there is no Coulomb potential barrier, and nuclear reactions can proceed with the participation of particles having thermal energy (i.e., energy corresponding to thermal vibrations).
The possibility of nuclear nuclei occurring not as a result of bombardment of target nuclei by incident particles, but due to ultra-strong convergence of nuclei (i.e., approaching at distances comparable to the diameter of the nucleus) located in a solid or on a surface (for example, with the participation of nuclei, dissolved in); So far (1995) there is no reliable data on the implementation of such nuclear ("cold thermonuclear fusion").
I nuclear are subject to the same general laws of nature as ordinary chem. r-tion (and energy, conservation of charge, momentum). In addition, during the course of nuclear reactions, certain specific effects also occur. laws that do not appear in chemistry. p-tions, for example, the law of conservation of baryon charge (baryons are heavy).
Nuclear nuclei can be written as shown in the example of the transformation of Pu nuclei into Ku nuclei when a plutonium target is irradiated with nuclei:

From this record it is clear that the sums of charges on the left and right (94 + 10 = 104) and the sums (242 + 22 = 259 + 5) are equal to each other. Because the chemical symbol element clearly indicates its at. number (nuclear charge), then when writing nuclear values of the charge of particles, they are usually not indicated. More often, nuclear ones are written shorter. Thus, the nuclear formation of 14 C during irradiation of 14 N nuclei is recorded as follows. way: 14 N(n, p) 14 C.
In parentheses indicate first the bombarding particle or quanta, then, separated by commas, the resulting light particles or quanta. In accordance with this recording method, (n, p), (d, p), (n, 2n) and other nuclear ones are distinguished.
When the same particles collide, nuclear particles can separate. ways. For example, when an aluminum target is irradiated, a trace may occur. nuclear: 27 А1(n,) 28 А1, 27 А1(n, n) 27 А1, 27 А1(n, 2n) 26 А1, 27 А1(n, p) 27 Mg, 27 Al(n,) 24 Na and etc. The collection of colliding particles is called. the nuclear input channel, and the particles born as a result of the nuclear one form the output channel.
I nuclear can occur with the release and absorption of energy Q. If in general we write nuclear as A(a, b)B, then for such nuclear energy it is equal to: Q = [(MA + M a) - (M b + M b) ] x с 2 , where M is the mass of the nuclear particles involved; c is the speed of light. In practice, it is more convenient to use deltaM values (see), then the expression for calculating Q has the form: and for reasons of convenience, it is usually expressed in kiloelectronvolts (keV, 1 amu = 931501.59 keV = 1.492443 x 10 -7 kJ).
The change in energy that is accompanied by nuclear energy can be 10 6 times or more greater than the energy released or absorbed during chemical reactions. r-tions. Therefore, during a nuclear one, a change in the masses of interacting nuclei becomes noticeable: the energy released or absorbed is equal to the difference in the sums of the masses of particles before and after the nuclear one. The possibility of releasing huge amounts of energy during the implementation of nuclear lies at the basis of nuclear (see). The study of the relationships between the energies of particles participating in nuclear reactions, as well as the relationships between the angles at which the resulting particles fly apart, constitutes a branch of nuclear physics - the kinematics of nuclear reactions.

Nuclear outputs, i.e., the ratio of the number of nuclear particles to the number of particles falling per unit area (1 cm 2) of the target usually does not exceed 10 -6 -10 -3. For thin targets (simply, a thin target can be called a target, when passing through it the flow of bombarding particles does not noticeably weaken), the nuclear yield is proportional to the number of particles falling on 1 cm 2 of the target surface, the number of nuclei contained in 1 cm 2 of the target, and also the value of the effective nuclear cross section. Even when using such a powerful source of incident particles as a nuclear reactor, within 1 hour, as a rule, it is possible to obtain no more than a few. mg containing new nuclei. Usually, the mass of a substance obtained in one or another nuclear facility is significantly less.

Bombarding particles. To carry out nuclear reactions, n, p, deuterons d, tritons t, particles, heavy (12 C, 22 Ne, 40 Ar, etc.), e quanta are used. Sources (see) when carrying out nuclear are: mixtures of metallic. Be and a suitable emitter, e.g. 226 Ra (so-called ampoule sources), neutron generators, nuclear reactors. Since in most cases, nuclear ones are higher for low energies (thermal), then before directing the flow to the target, they are usually slowed down using, and other materials. In the case of slow fundamentals. the process for almost all nuclei is radiation capture - nuclear type, since the Coulomb barrier of the nucleus prevents the escape of particles. Under the influence, chain flows occur.
If used as bombarding particles, deuterons, etc., carrying positive. charge, the bombarding particle is accelerated to high energies (from tens of MeV to hundreds of GeV), using decomposition. accelerators. This is necessary so that a charged particle can overcome the Coulomb potential barrier and enter the irradiated nucleus. When irradiating targets with positively charged particles, max. Nuclear yields are achieved using deuterons. This is due to the fact that the binding energy in the deuteron is relatively small, and accordingly, the distance between and is large.
When deuterons are used as bombarding particles, only one nucleon often penetrates into the irradiated nucleus - or, the second nucleon of the deuteron nucleus flies further, usually in the same direction as the incident deuteron. High effective cross sections can be achieved by conducting nuclear tests between deuterons and light nuclei at relatively low energies of incident particles (1-10 MeV). Therefore, nuclear nuclei with the participation of deuterons can be carried out not only by using deuterons accelerated at an accelerator, but also by heating a mixture of interacting nuclei to a temperature of approx. 10 7 K. Such nuclear ones are called thermonuclear. Under natural conditions, they occur only in the interior of stars. On Earth, thermonuclear r-tions involving,

Isomeric transition

Mechanisms of nuclear reaction

Compound nucleus

The theory of the reaction mechanism with the formation of a compound nucleus was developed by Niels Bohr in 1936 together with the theory of the droplet model of the nucleus and underlies modern ideas about most nuclear reactions.

According to this theory, the nuclear reaction occurs in two stages. At the beginning, the initial particles form an intermediate (composite) nucleus after nuclear time, that is, the time required for a particle to cross the nucleus, approximately equal to 10 −23 - 10 −21. In this case, a compound nucleus is always formed in an excited state, since it has excess energy brought by the particle into the nucleus in the form of the binding energy of the nucleon in the compound nucleus and part of its kinetic energy, which is equal to the sum of the kinetic energy of the target nucleus with mass number and the particle in the system center of inertia.

Excitation energy

The excitation energy of a compound nucleus formed upon absorption of a free nucleon is equal to the sum of the binding energy of the nucleon and part of its kinetic energy:

Most often, due to the large difference in the masses of the nucleus and the nucleon, it is approximately equal to the kinetic energy of the nucleon bombarding the nucleus.

On average, the binding energy is 8 MeV, varying depending on the characteristics of the resulting compound nucleus, but for the given target nucleus and nucleon this value is a constant. The kinetic energy of the bombarding particle can be anything, for example, when excitation of nuclear reactions by neutrons, the potential of which does not have a Coulomb barrier, the value can be close to zero. Thus, the binding energy is the minimum excitation energy of a compound nucleus.

Reaction channels

The transition to a non-excited state can be carried out in various ways, called reaction channels. The types and quantum state of incident particles and nuclei before the start of the reaction are determined by input channel reactions. After completion of the reaction, the totality of the resulting reaction products and their quantum states determines output channel reactions. The reaction is completely characterized by input and output channels.

The reaction channels do not depend on the method of formation of the compound nucleus, which can be explained by the long lifetime of the compound nucleus; it seems to “forget” how it was formed, therefore, the formation and decay of the compound nucleus can be considered as independent events. For example, it can be formed as a compound nucleus in an excited state in one of the following reactions:

Subsequently, provided that the excitation energy is the same, this compound nucleus can decay in the opposite way to any of these reactions, with a certain probability that does not depend on the history of the appearance of this nucleus. The probability of the formation of a compound nucleus depends on the energy and on the type of target nucleus.

Direct nuclear reactions

The course of nuclear reactions is also possible through the mechanism of direct interaction; basically, such a mechanism manifests itself at very high energies of bombarding particles, when the nucleons of the nucleus can be considered as free. Direct reactions differ from the compound nucleus mechanism primarily in the distribution of the momentum vectors of the product particles relative to the momentum of the bombarding particles. In contrast to the spherical symmetry of the compound nucleus mechanism, direct interaction is characterized by the predominant direction of flight of the reaction products forward relative to the direction of movement of the incident particles. The energy distributions of product particles in these cases are also different. Direct interaction is characterized by an excess of high-energy particles. In collisions with the nuclei of complex particles (that is, other nuclei), processes of nucleon transfer from nucleus to nucleus or nucleon exchange are possible. Such reactions occur without the formation of a compound nucleus and they have all the features of direct interaction.

Nuclear reaction cross section

The probability of a reaction is determined by the so-called nuclear reaction cross section. In a laboratory frame of reference (where the target nucleus is at rest), the probability of interaction per unit time is equal to the product of the cross section (expressed in units of area) and the flux of incident particles (expressed in the number of particles crossing a unit area per unit time). If several output channels can be implemented for one input channel, then the ratio of the probabilities of the output reaction channels is equal to the ratio of their cross sections. In nuclear physics, reaction cross sections are usually expressed in special units - barns, equal to 10 −24 cm².

Reaction output

The number of reaction cases divided by the number of particles bombarding the target is called the output of a nuclear reaction. This value is determined experimentally through quantitative measurements. Since the yield is directly related to the reaction cross section, measuring the yield is essentially a measurement of the reaction cross section.

Conservation laws in nuclear reactions

In nuclear reactions, all conservation laws of classical physics are satisfied. These laws place restrictions on the possibility of a nuclear reaction. Even an energetically favorable process always turns out to be impossible if it is accompanied by a violation of any conservation law. In addition, there are conservation laws specific to the microworld; some of them are always fulfilled, as far as is known (law of conservation of baryon number, lepton number); other conservation laws (isospin, parity, strangeness) only suppress certain reactions, since they are not satisfied for some of the fundamental interactions. The consequences of conservation laws are the so-called selection rules, indicating the possibility or prohibition of certain reactions.

Law of energy conservation

If , , , are the total energies of two particles before and after the reaction, then based on the law of conservation of energy:

When more than two particles are formed, the number of terms on the right side of this expression should accordingly be greater. The total energy of a particle is equal to its rest energy Mc 2 and kinetic energy E, That's why:

The difference between the total kinetic energies of particles at the “output” and “input” of the reaction Q = (E 3 + E 4) − (E 1 + E 2) called reaction energy(or energy yield of the reaction). It satisfies the condition:

Multiplier 1/ c 2 is usually omitted when calculating the energy balance, expressing particle masses in energy units (or sometimes energy in mass units).

If Q> 0, then the reaction is accompanied by the release of free energy and is called exoenergetic , If Q < 0, то реакция сопровождается поглощением свободной энергии и называется endoenergetic .

It's easy to see that Q> 0 when the sum of the masses of the product particles is less than the sum of the masses of the initial particles, that is, the release of free energy is possible only by reducing the masses of the reacting particles. And vice versa, if the sum of the masses of secondary particles exceeds the sum of the masses of the initial ones, then such a reaction is possible only if a certain amount of kinetic energy is spent to increase the rest energy, that is, the masses of new particles. The minimum value of the kinetic energy of an incident particle at which an endoenergetic reaction is possible is called threshold reaction energy. Endoenergetic reactions are also called threshold reactions, since they do not occur at particle energies below the threshold.

Law of conservation of momentum

The total momentum of the particles before the reaction is equal to the total momentum of the reaction product particles. If , , , are the momentum vectors of two particles before and after the reaction, then

Each of the vectors can be independently measured experimentally, for example, with a magnetic spectrometer. Experimental data indicate that the law of conservation of momentum is valid both in nuclear reactions and in the processes of scattering of microparticles.

Law of conservation of angular momentum

Nuclear fusion reaction

Nuclear fusion reaction- the process of fusion of two atomic nuclei to form a new, heavier nucleus.

In addition to the new nucleus, during the fusion reaction, as a rule, various elementary particles and (or) quanta of electromagnetic radiation are also formed.

Without the supply of external energy, fusion of nuclei is impossible, since positively charged nuclei experience electrostatic repulsion forces - this is the so-called “Coulomb barrier”. To synthesize nuclei, it is necessary to bring them closer to a distance of about 10–15 m, at which the action of strong interaction will exceed the forces of electrostatic repulsion. This is possible if the kinetic energy of approaching nuclei exceeds the Coulomb barrier.

Such conditions can arise in two cases:

If matter is heated to extremely high temperatures in a star or fusion reactor. According to kinetic theory, the kinetic energy of moving microparticles of a substance (atoms, molecules or ions) can be represented as temperature, and, therefore, by heating a substance, a nuclear fusion reaction can be achieved. In this case, they talk about thermonuclear fusion or thermonuclear reaction.

Thermonuclear reaction

Thermonuclear reaction- the fusion of two atomic nuclei to form a new, heavier nucleus, due to the kinetic energy of their thermal motion.

For a nuclear fusion reaction, the initial nuclei must have relatively high kinetic energy, since they experience electrostatic repulsion, since they are positively charged.

First of all, among them it should be noted the reaction between two isotopes (deuterium and tritium) of hydrogen, which is very common on Earth, as a result of which helium is formed and a neutron is released. The reaction can be written as:

+ energy (17.6 MeV).

The released energy (arising from the fact that helium-4 has very strong nuclear bonds) turns into kinetic energy, most of which, 14.1 MeV, is carried away by the neutron as a lighter particle. The resulting nucleus is tightly bound, which is why the reaction is so highly exoenergetic. This reaction is characterized by the lowest Coulomb barrier and high yield, so it is of particular interest for controlled thermonuclear fusion.

Photonuclear reaction

When a gamma quantum is absorbed, the nucleus receives excess energy without changing its nucleon composition, and a nucleus with excess energy is a compound nucleus. Like other nuclear reactions, absorption of a gamma quantum by a nucleus is possible only if the necessary energy and spin relationships are met. If the energy transferred to the nucleus exceeds the binding energy of a nucleon in the nucleus, then the decay of the resulting compound nucleus occurs most often with the emission of nucleons, mainly neutrons. Such decay leads to nuclear reactions and, which are called photonuclear, and the phenomenon of nucleon emission in these reactions is nuclear photoelectric effect.

Other

Recording nuclear reactions

Nuclear reactions are written in the form of special formulas in which the designations of atomic nuclei and elementary particles are found.

First way writing formulas for nuclear reactions is similar to writing formulas for chemical reactions, that is, the sum of the original particles is written on the left, the sum of the resulting particles (reaction products) is written on the right, and an arrow is placed between them.

Thus, the reaction of radiative capture of a neutron by a cadmium-113 nucleus is written as follows:

We see that the number of protons and neutrons on the right and left remains the same (the baryon number is conserved). The same applies to electric charges, lepton numbers and other quantities (energy, momentum, angular momentum, ...). In some reactions where the weak interaction is involved, protons can turn into neutrons and vice versa, but their total number does not change.

Second way notation, more convenient for nuclear physics, has the form A (a, bcd...) B, Where A- target core, A- bombarding particle (including the nucleus), b, c, d, …- emitted particles (including nuclei), IN- residual core. Lighter reaction products are written in brackets, heavier ones are written outside. Thus, the above neutron capture reaction can be written in this form.

The theory of relativity says that mass is a special form of energy. From this it follows that it is possible to convert mass into energy and energy into mass. At the intraatomic level, such reactions take place. In particular, a certain amount of mass itself may well be converted into energy. This happens in several ways. First, a nucleus can decay into a number of smaller nuclei, a reaction called “decay.” Secondly, smaller nuclei can easily combine to form a larger one - this is a fusion reaction. Such reactions are very common in the Universe. Suffice it to say that the fusion reaction is a source of energy for stars. But the decay reaction is used by humanity because people have learned to control these complex processes. But what is a nuclear chain reaction? How to manage it?

What happens in the nucleus of an atom

A nuclear chain reaction is a process that occurs when elementary particles or nuclei collide with other nuclei. Why "chain"? This is a set of sequential single nuclear reactions. As a result of this process, a change occurs in the quantum state and nucleonic composition of the original nucleus, and even new particles appear - reaction products. The nuclear chain reaction, the physics of which makes it possible to study the mechanisms of interaction of nuclei with nuclei and with particles, is the main method for obtaining new elements and isotopes. In order to understand the course of a chain reaction, you must first deal with single reactions.

What is needed for a reaction

In order to carry out a process such as a nuclear chain reaction, it is necessary to bring particles (a nucleus and a nucleon, two nuclei) closer to the distance of the strong interaction radius (approximately one Fermi). If the distances are large, then the interaction of charged particles will be purely Coulomb. In a nuclear reaction, all laws are observed: conservation of energy, momentum, momentum, baryon charge. A nuclear chain reaction is denoted by the symbols a, b, c, d. The symbol a denotes the original nucleus, b the incoming particle, c the new emitted particle, and d denotes the resulting nucleus.

Reaction energy

A nuclear chain reaction can occur with both absorption and release of energy, which is equal to the difference in the masses of particles after the reaction and before it. The absorbed energy determines the minimum kinetic energy of the collision, the so-called threshold of a nuclear reaction, at which it can proceed freely. This threshold depends on the particles that participate in the interaction and their characteristics. At the initial stage, all particles are in a predetermined quantum state.

Carrying out the reaction

The main source of charged particles with which the nucleus is bombarded is which produces beams of protons, heavy ions and light nuclei. Slow neutrons are produced through the use of nuclear reactors. To detect incoming charged particles, different types of nuclear reactions can be used - both fusion and decay. Their probability depends on the parameters of the particles that collide. This probability is associated with such a characteristic as the reaction cross section - the value of the effective area, which characterizes the nucleus as a target for incident particles and which is a measure of the probability of the particle and the nucleus entering into interaction. If particles with a non-zero spin value take part in the reaction, then the cross section directly depends on their orientation. Since the spins of the incident particles are not completely chaotically oriented, but more or less ordered, all corpuscles will be polarized. The quantitative characteristic of the oriented beam spins is described by the polarization vector.

Reaction mechanism

What is a nuclear chain reaction? As already mentioned, this is a sequence of simpler reactions. The characteristics of the incident particle and its interaction with the nucleus depend on mass, charge, and kinetic energy. The interaction is determined by the degree of freedom of the nuclei, which are excited during the collision. Gaining control over all these mechanisms allows for a process such as a controlled nuclear chain reaction.

Direct reactions

If a charged particle that strikes a target nucleus only touches it, then the duration of the collision will be equal to that required to cover the radius of the nucleus. This nuclear reaction is called direct. A common characteristic for all reactions of this type is the excitation of a small number of degrees of freedom. In such a process, after the first collision, the particle still has enough energy to overcome nuclear attraction. For example, interactions such as inelastic neutron scattering and charge exchange are classified as direct. The contribution of such processes to the characteristic called “total cross section” is quite negligible. However, the distribution of the products of a direct nuclear reaction makes it possible to determine the probability of escape from the beam direction angle, the selectivity of populated states, and determine their structure.

Pre-equilibrium emission

If the particle does not leave the region of nuclear interaction after the first collision, then it will be involved in a whole cascade of successive collisions. This is actually what is called a nuclear chain reaction. As a result of this situation, the kinetic energy of the particle is distributed among the constituent parts of the nucleus. The state of the nucleus itself will gradually become much more complicated. During this process, energy sufficient for the emission of this nucleon from the nucleus can be concentrated on a certain nucleon or an entire cluster (group of nucleons). Further relaxation will lead to the formation of statistical equilibrium and the formation of a compound nucleus.

Chain reactions

What is a nuclear chain reaction? This is the sequence of its constituent parts. That is, multiple sequential single nuclear reactions caused by charged particles appear as reaction products in previous steps. What is a nuclear chain reaction? For example, the fission of heavy nuclei, when multiple fission events are initiated by neutrons obtained from previous decays.

Features of a nuclear chain reaction

Among all chemical reactions, chain reactions have become widespread. Particles with unused bonds act as free atoms or radicals. In a process such as a nuclear chain reaction, the mechanism for its occurrence is provided by neutrons, which do not have a Coulomb barrier and excite the nucleus upon absorption. If a necessary particle appears in the medium, it causes a chain of subsequent transformations that will continue until the chain breaks due to the loss of the carrier particle.

Why is the media lost?

There are only two reasons for the loss of a carrier particle in a continuous chain of reactions. The first is the absorption of a particle without the process of emitting a secondary one. The second is the departure of a particle beyond the volume limit of the substance that supports the chain process.

Two types of process

If in each period of a chain reaction an exclusively single carrier particle is born, then this process can be called unbranched. It cannot lead to the release of energy on a large scale. If many carrier particles appear, then this is called a branched reaction. What is a branching nuclear chain reaction? One of the secondary particles obtained in the previous act will continue the chain started earlier, but others will create new reactions that will also branch. Processes leading to a break will compete with this process. The resulting situation will give rise to specific critical and limiting phenomena. For example, if there are more breaks than purely new chains, then self-sustaining of the reaction will be impossible. Even if it is excited artificially by introducing the required number of particles into a given environment, the process will still decay over time (usually quite quickly). If the number of new chains exceeds the number of breaks, then the nuclear chain reaction will begin to spread throughout the substance.

Critical condition

The critical state separates the region of the state of a substance with a developed self-sustaining chain reaction, and the region where this reaction is impossible at all. This parameter is characterized by equality between the number of new circuits and the number of possible breaks. Like the presence of a free carrier particle, the critical state is the main item on such a list as “conditions for a nuclear chain reaction.” Achieving this state can be determined by a number of possible factors. of a heavy element is excited by just one neutron. As a result of a process called a nuclear fission chain reaction, more neutrons are produced. Consequently, this process can produce a branched reaction, where neutrons act as carriers. In the case when the rate of neutron capture without fission or emission (loss rate) is compensated by the rate of multiplication of carrier particles, the chain reaction will proceed in a stationary mode. This equality characterizes the reproduction coefficient. In the above case it is equal to one. Thanks to the introduction between the rate of energy release and the multiplication factor, it is possible to control the course of a nuclear reaction. If this coefficient is greater than one, then the reaction will develop exponentially. Uncontrolled chain reactions are used in nuclear weapons.

Nuclear chain reaction in energy

The reactivity of a reactor is determined by a large number of processes that occur in its core. All these influences are determined by the so-called reactivity coefficient. The effect of changes in the temperature of graphite rods, coolants or uranium on the reactivity of the reactor and the intensity of a process such as a nuclear chain reaction is characterized by a temperature coefficient (for coolant, for uranium, for graphite). There are also dependent characteristics for power, barometric indicators, and steam indicators. To maintain a nuclear reaction in a reactor, it is necessary to transform some elements into others. To do this, it is necessary to take into account the conditions for the occurrence of a nuclear chain reaction - the presence of a substance that is capable of dividing and releasing from itself during decay a certain number of elementary particles, which, as a consequence, will cause the fission of other nuclei. Uranium-238, uranium-235, and plutonium-239 are often used as such substances. During a nuclear chain reaction, isotopes of these elements will decay and form two or more other chemicals. During this process, so-called “gamma” rays are emitted, an intense release of energy occurs, and two or three neutrons are formed that are capable of continuing the reaction acts. There are slow and fast neutrons, because in order for the nucleus of an atom to decay, these particles must fly at a certain speed.

For a long time, people have been haunted by dreams of the interconversion of elements - more precisely, of the transformation of different metals into one. After realizing the futility of these attempts, the point of view about the inviolability of chemical elements was established. And only the discovery of the structure of the nucleus at the beginning of the 20th century showed that the transformation of elements into one another is possible - but not by chemical methods, that is, by influencing the outer electron shells of atoms, but by interfering with the structure of the atomic nucleus. This kind of phenomenon (and some others) relate to nuclear reactions, examples of which will be discussed below. But first we need to remember some basic concepts that will be required during this discussion.

General concept of nuclear reactions

There are phenomena in which the nucleus of an atom of one or another element interacts with another nucleus or some elementary particle, that is, it exchanges energy and momentum with them. Such processes are called nuclear reactions. Their result may be a change in the composition of the nucleus or the formation of new nuclei with the emission of certain particles. In this case, the following options are possible:

transformation of one chemical element into another;
synthesis, that is, the fusion of nuclei in which the nucleus of a heavier element is formed.

The initial phase of the reaction, determined by the type and state of the particles entering it, is called the entrance channel. Output channels are possible paths along which a reaction will proceed.

Rules for recording nuclear reactions

The examples given below demonstrate the methods by which it is customary to describe reactions involving nuclei and elementary particles.

The first method is the same as that used in chemistry: the initial particles are placed on the left side, and the reaction products are placed on the right side. For example, the interaction of a beryllium-9 nucleus with an incident alpha particle (the so-called neutron discovery reaction) is written as follows:

9 4 Be + 4 2 He → 12 6 C + 1 0 n.

The upper indices indicate the number of nucleons, that is, the mass numbers of the nuclei, the lower indices indicate the number of protons, that is, the atomic numbers. The sums of both on the left and right sides must coincide.

A shorthand way of writing nuclear reaction equations, often used in physics, looks like this:

9 4 Be (α, n) 12 6 C.

The general form of this notation is: A (a, b 1 b 2 ...) B. Here A is the target nucleus; a - incident particle or nucleus; b 1, b 2 and so on are light reaction products; B is the final core.

Energy of nuclear reactions

In nuclear transformations, the law of conservation of energy is fulfilled (along with other conservation laws). In this case, the kinetic energy of particles in the input and output channels of the reaction can differ due to changes in the rest energy. Since the latter is equivalent to the mass of the particles, the masses will also be different before and after the reaction. But the total energy of the system is always conserved.

The difference in rest energy between the particles entering the reaction and those leaving it is called the energy output and is expressed in the change in their kinetic energy.

In processes involving nuclei, three types of fundamental interactions are involved - electromagnetic, weak and strong. Thanks to the latter, the nucleus has such an important feature as high binding energy between its constituent particles. It is significantly higher than, for example, between the nucleus and atomic electrons or between atoms in molecules. This is evidenced by a noticeable mass defect - the difference between the sum of the nucleon masses and the nuclear mass, which is always less by an amount proportional to the binding energy: Δm = Eb /c 2. The mass defect is calculated using the simple formula Δm = Zm p + Am n - M i, where Z is the nuclear charge, A is the mass number, m p is the proton mass (1.00728 amu), m n is the neutron mass ( 1.00866 amu), M i - core mass.

When describing nuclear reactions, the concept of specific binding energy is used (that is, per nucleon: Δmc 2 /A).

Binding energy and nuclear stability

The greatest stability, that is, the highest specific binding energy, is distinguished by nuclei with a mass number from 50 to 90, for example, iron. This “peak stability” is due to the non-central nature of nuclear forces. Since each nucleon interacts only with its neighbors, it is bound weaker on the surface of the nucleus than inside. The fewer interacting nucleons in a nucleus, the lower the binding energy, so light nuclei are less stable. In turn, as the number of particles in the nucleus increases, the Coulomb repulsive forces between protons increase, so that the binding energy of heavy nuclei also decreases.

Thus, for light nuclei the most probable, that is, energetically favorable, are fusion reactions with the formation of a stable nucleus of average mass, while for heavy nuclei, on the contrary, decay and fission processes (often multi-stage), as a result of which more stable products are also formed. These reactions are characterized by a positive and often very high energy yield, which accompanies an increase in binding energy.

Below we will look at some examples of nuclear reactions.

Decay reactions

Nuclei can undergo spontaneous changes in composition and structure, during which some elementary particles or fragments of the nucleus are emitted, such as alpha particles or heavier clusters.

Thus, during alpha decay, made possible by quantum tunneling, the alpha particle overcomes the potential barrier of nuclear forces and leaves the mother nucleus, which, accordingly, reduces the atomic number by 2 and the mass number by 4. For example, a radium-226 nucleus, emitting alpha particle, turns into radon-222:

226 88 Ra → 222 86 Rn + α (4 2 He).

The decay energy of the radium-226 nucleus is about 4.87 MeV.

Beta decay occurs without a change in the number of nucleons (mass number), but with an increase or decrease in the charge of the nucleus by 1, with the emission of an antineutrino or neutrino, as well as an electron or positron. An example of this type of nuclear reaction is the beta-plus decay of fluorine-18. Here, one of the protons of the nucleus turns into a neutron, a positron and a neutrino are emitted, and fluorine turns into oxygen-18:

18 9 K → 18 8 Ar + e + + ν e .

The beta decay energy of fluorine-18 is about 0.63 MeV.

Nuclear fission

Fission reactions have much greater energy output. This is the name of the process in which the nucleus spontaneously or forcibly disintegrates into fragments of similar mass (usually two, rarely three) and some lighter products. A nucleus divides if its potential energy exceeds the initial value by a certain amount, called the fission barrier. However, the probability of a spontaneous process even for heavy nuclei is low.

It increases significantly when the nucleus receives the corresponding energy from the outside (when a particle hits it). The neutron penetrates the nucleus most easily, since it is not subject to electrostatic repulsion forces. The impact of a neutron leads to an increase in the internal energy of the nucleus, it is deformed with the formation of a waist and divides. The fragments scatter under the influence of Coulomb forces. An example of a nuclear fission reaction is demonstrated by uranium-235 absorbing a neutron:

235 92 U + 1 0 n → 144 56 Ba + 89 36 Kr + 3 1 0 n.

Fission into barium-144 and krypton-89 is only one of the possible fission options for uranium-235. This reaction can be written as 235 92 U + 1 0 n → 236 92 U* → 144 56 Ba + 89 36 Kr + 3 1 0 n, where 236 92 U* is a highly excited compound nucleus with high potential energy. Its excess, along with the difference in binding energies of the mother and daughter nuclei, is released mainly (about 80%) in the form of the kinetic energy of the reaction products, and also partially in the form of the potential energy of fission fragments. The total fission energy of a massive nucleus is approximately 200 MeV. In terms of 1 gram of uranium-235 (assuming that all nuclei have reacted), this amounts to 8.2 ∙ 10 4 megajoules.

Chain reactions

The fission of uranium-235, as well as such nuclei as uranium-233 and plutonium-239, is characterized by one important feature - the presence of free neutrons among the reaction products. These particles, penetrating into other nuclei, in turn, are able to initiate their fission, again with the release of new neutrons, and so on. This process is called a nuclear chain reaction.

The course of the chain reaction depends on how the number of neutrons emitted from the next generation compares with their number in the previous generation. This ratio k = N i /N i -1 (here N is the number of particles, i is the serial number of the generation) is called the neutron multiplication factor. At k< 1 цепная реакция не идет. При k >1 the number of neutrons, and therefore fissile nuclei, increases like an avalanche. An example of a nuclear chain reaction of this type is the explosion of an atomic bomb. At k = 1, the process occurs in a steady state, as exemplified by the reaction controlled by neutron-absorbing rods in nuclear reactors.

Nuclear fusion

The greatest energy release (per nucleon) occurs during the fusion of light nuclei - the so-called fusion reactions. To react, positively charged nuclei must overcome the Coulomb barrier and approach each other to a strong interaction distance not exceeding the size of the nucleus itself. Therefore, they must have extremely high kinetic energy, which means high temperatures (tens of millions of degrees and above). For this reason, fusion reactions are also called thermonuclear reactions.

An example of a nuclear fusion reaction is the formation of helium-4 with the release of a neutron during the fusion of deuterium and tritium nuclei:

2 1 H + 3 1 H → 4 2 He + 1 0 n.

Here, an energy of 17.6 MeV is released, which per nucleon is more than 3 times higher than the fission energy of uranium. Of these, 14.1 MeV is the kinetic energy of the neutron and 3.5 MeV is the kinetic energy of the helium-4 nucleus. Such a significant value is created due to the huge difference in the binding energies of the nuclei of deuterium (2.2246 MeV) and tritium (8.4819 MeV) on the one hand, and helium-4 (28.2956 MeV) on the other.

In nuclear fission reactions, the energy of electrical repulsion is released, while in fusion, energy is released due to the strong interaction - the most powerful in nature. This determines such a significant energy yield of this type of nuclear reactions.

Examples of problem solving

Consider the fission reaction 235 92 U + 1 0 n → 140 54 Xe + 94 38 Sr + 2 1 0 n. What is its energy output? In general, the formula for its calculation, reflecting the difference between the rest energies of particles before and after the reaction, is as follows:

Q = Δmc 2 = (m A + m B - m X - m Y + ...) ∙ c 2.

Instead of multiplying by the square of the speed of light, you can multiply the mass difference by a factor of 931.5 to get the energy value in megaelectronvolts. Substituting the corresponding values of atomic masses into the formula, we obtain:

Q = (235.04393 + 1.00866 - 139.92164 - 93.91536 - 2∙1.00866) ∙ 931.5 ≈ 184.7 MeV.

Another example is the synthesis reaction. This is one of the stages of the proton-proton cycle - the main source of solar energy.

3 2 He + 3 2 He → 4 2 He + 2 1 1 H + γ.

Let's apply the same formula:

Q = (2 ∙ 3.01603 - 4.00260 - 2 ∙ 1.00728) ∙ 931.5 ≈ 13.9 MeV.

The main share of this energy - 12.8 MeV - falls in this case on the gamma photon.

We have considered only the simplest examples of nuclear reactions. The physics of these processes is extremely complex; they are extremely diverse. The study and application of nuclear reactions is of great importance both in the practical field (energy) and in fundamental science.