The interaction of nuclei with each other indicates that special nuclear forces exist in nuclei, which cannot be reduced to any of the types of forces known in classical physics (gravitational and electromagnetic).

Nuclear forces- these are the forces that hold nucleons in the nucleus and represent a manifestation of the strong interaction.

Properties of nuclear forces:

• 1) they are short-range: at distances of the order of ~1(H 5 m, nuclear forces as attractive forces hold nucleons, despite the Coulomb repulsion between protons; at shorter distances, the attraction of nucleons is replaced by repulsion;
• 2) have charge independence: the attraction between any two nucleons is the same (p-p, p-p, p-p);
• 3) nuclear forces are characterized by saturation: each nucleon in the nucleus interacts only with a limited number of nucleons closest to it;
• 4) nuclear forces depend on the mutual orientation of the spins of interacting nucleons (for example, a proton and a neutron form a deuteron - the nucleus of the deuterium isotope ] N, only if their backs are parallel to each other);
• 5) nuclear forces are not central, i.e. are not directed along the line connecting the centers of interacting nucleons, as evidenced by their dependence on the orientation of the nucleon spins.

Experiments on nucleon-nucleon scattering have shown that the nuclear interaction forces acting between nucleons in the nucleus are of an exchange nature and are caused by the exchange of quanta of the nuclear force field, called n-mesons (pions, see subtopic 32.2). The pion hypothesis, within the framework of a detailed quantum theory of the mechanism of nuclear interaction, was proposed by the Japanese physicist H. Yukawa (Nobel Prize, 1949). The Yukawa particle, the pion, is characterized by a mass of approximately 300 electron masses, and helps explain the short-range nature and large magnitude of nuclear forces.

Models of the atomic nucleus. IN the theory of the atomic nucleus is very important role played by models that describe a certain set of nuclear properties quite well and allow a relatively simple mathematical interpretation. To date, due to the complex nature of nuclear forces and the difficulty of accurately solving the equations of motion of all nucleons in a nucleus, there is still no complete theory of the nucleus that would explain all its properties.

Let's consider the following two core models - droplet and shell.

Drip model put forward by the German scientist M. Born and the Russian scientist J. Frenkel in 1936. In this model, it is assumed that the nucleus behaves like a drop of incompressible charged liquid with a density equal to the nuclear one, and obeying the laws of quantum mechanics. Thus, the nucleus is considered as a continuous medium and the movement of individual nucleons is not distinguished. This analogy between the behavior of molecules in a drop of liquid and nucleons in a nucleus takes into account the short-range nature of nuclear interactions, the property of saturation of nuclear forces, and the same density of nuclear matter in different nuclei. The drop model explained the mechanisms of nuclear reactions, especially nuclear fission reactions, made it possible to obtain a semi-empirical formula for the binding energy of nucleons in a nucleus, and also described the dependence of the radius of the nucleus on the mass number.

Shell model was finally formulated by the American physicist M. Goeppert-Mayer and the German physicist J.H. Jensen in 1949-1950 In this model, nucleons are considered to move independently of each other in the averaged centrally symmetric field of the remaining nucleons of the nucleus. In accordance with this, there are discrete energy levels, filled with nucleons taking into account the Pauli principle. These levels are grouped into shells, each of which can contain a certain number of nucleons. The spin-orbit interaction of nucleons is taken into account. In nuclei, with the exception of the lightest ones, j-/"-connection.

Nuclei with completely filled shells are the most stable. Magical are called atomic nuclei whose number of neutrons N and/or the number of protons Z is equal to one of the magic numbers:

2, 8, 20, 28, 50, 82 and TV = 126. Magic nuclei differ from other nuclei, for example, in increased stability, greater prevalence in nature.

Cores for which both Z and Z are magical N, are called twice magical. Doubly magic nuclei include: helium He, oxygen J> 6 0, calcium joCa, tin jjfSn, lead g^fPb. In particular, the special stability of the He nucleus is manifested in the fact that it is a single particle called a -particle, emitted by heavy nuclei during radioactive decay.

In addition to predicting magic numbers, this model made it possible to find values ​​of the spins of the ground and excited states of nuclei, as well as their magnetic moments. This model is especially suitable for describing light and medium nuclei, as well as for nuclei in the ground state.

Nuclear forces provide attraction- this follows from the very fact of the existence of stable nuclei consisting of protons and neutrons.

Nuclear forces are great in absolute magnitude. Their action at short distances significantly exceeds the action of all forces known in nature, including electromagnetic ones.

So far we know four types of interaction:

a) strong (nuclear) interactions;

b) electromagnetic interactions;

c) weak interactions, especially clearly observed in particles that do not exhibit strong and electromagnetic interactions (neutrinos);

d) gravitational interactions.

A comparison of the forces for these types of interactions can be obtained by using a system of units in which the characteristic interaction constants corresponding to these forces (the squares of the “charges”) are dimensionless.

Thus, for the interaction inside a nucleus of two nucleons possessing all these forces, the interaction constants are of the order:

Nuclear forces ensure the existence of nuclei. Electromagnetic - atoms and molecules. The average binding energy of a nucleon in the nucleus is equal to i.e. where is the rest energy of the nucleon. The binding energy of an electron in a hydrogen atom is only i.e. where is the rest energy of the electron. Therefore, on this scale, binding energies are related as characteristic constants:

Weak interactions are responsible for such subtle effects as mutual transformations through -decay and -capture (see § 19), for various decays of elementary particles, as well as for all processes of interaction of neutrinos with matter.

The stability of cosmic bodies and systems is associated with gravitational interactions.

The interaction forces of the second and fourth types decrease with distance, i.e. quite slowly and, therefore, are long-range. Interactions of the first and third types decrease with distance very quickly and are therefore short-range.

Nuclear forces are short-range. This follows: a) from Rutherford’s experiments on the scattering of -particles by light nuclei (for distances exceeding cm, the experimental results

are explained by the purely Coulomb interaction of -particles with the nucleus, but at smaller distances, deviations from Coulomb’s law occur due to nuclear forces. It follows that the range of action of nuclear forces is in any case less

b) from the study of the decay of heavy nuclei (see § 15);

c) from experiments on the scattering of neutrons by protons and protons by protons.

Let's look at them in a little more detail.

Rice. 17. Particle and scattering target

At low neutron energies, their scattering in the center of inertia system is isotropic. Indeed, a classical particle with momentum will “catch” onto a scattering target with a radius of action of nuclear forces if it flies at distances smaller, i.e., if the component of its angular momentum in the direction perpendicular to the trajectory plane does not exceed mountains (Fig. 17).

But according to de Broglie’s relation for an incident particle, therefore,

However, the maximum value of the projection of the orbital momentum of a particle can only be equal to Therefore

Thus, for a value of a, the wave function describing the state of the system is spherically symmetrical in c. c. i.e., in this system the scattering must be isotropic.

When the scattering will no longer be isotropic. By decreasing the energy of incident neutrons and thereby increasing it, one can find its value at which scattering isotropy is achieved. This provides an estimate of the range of nuclear forces.

The maximum neutron energy at which spherically symmetric scattering was still observed was equal to This made it possible to determine the upper limit of the radius of action of nuclear forces; it turned out to be equal to cm.

Further, when a proton flux is scattered on a proton target, one can calculate the expected value of the effective cross section of the process if only Coulomb forces act. However, when the particles come very close together, nuclear forces begin to dominate

above the Coulomb ones, and the distribution of scattered protons changes.

From such experiments it was found that nuclear forces decrease sharply with increasing distance between protons. The area of ​​their action is extremely small and also on the order of magnitude cm. Unfortunately, the results of experiments on the scattering of low-energy nucleons do not provide information about the law of change of nuclear forces with distance. The detailed shape of the potential well remains uncertain.

Experiments to study the properties of two bound nucleons in a deuteron nucleus also do not allow us to unambiguously establish the law of change in the potential of the nuclear force field with distance. The reason lies in the unusually small radius of action of nuclear forces and their very large magnitude within the radius of action. As a first approximation to the potential that describes the properties of deuteron, we can take a fairly wide range of different functions, which should decrease quite quickly with distance.

The experimental data are roughly satisfied, for example, by the following functions.

Rice. 18. Possible shapes of the deuteron potential well: a - rectangular well; exponential well; c is the shape of the well at the Yukawa potential; -well at a potential with a solid repulsive center

1. Rectangular potential well (Fig. 18a):

where is the radius of action of nuclear forces, the distance between the centers of two interacting nucleons.

2. Exponential function (Fig. 18,b):

3. Yukawa meson potential (Fig. 18c):

4. Potential with a solid repulsive middle (Fig. 18d):

A detailed study of the scattering structure and comparison with theoretical calculations speaks in favor of the latter of these forms. Currently, more complex forms are used for calculations, providing better agreement with experimental data.

In all cases, the depth of the potential well is of the order of several tens. The value in the case of a potential with a repulsive center is of the order of tenths of a Fermi.

Nuclear forces do not depend on the electric charges of interacting particles. The forces of interaction between or are the same. This property follows from the following facts.

In light stable nuclei, when electromagnetic repulsion can still be neglected, the number of protons is equal to the number of neutrons. Therefore, the forces acting between them are equal, otherwise there would be a shift in some direction (either or

Light mirror nuclei (nuclei obtained by replacing neutrons with protons and vice versa, for example, have the same energy levels.

Experiments on the scattering of neutrons by protons and protons by protons show that the magnitude of the nuclear attraction of a proton with a proton and a neutron with a proton is the same.

This property of nuclear forces is fundamental and indicates the deep symmetry that exists between two particles: the proton and the neutron. It was called charge independence (or symmetry) and made it possible to consider the proton and neutron as two states of the same particle - the nucleon.

Thus, the nucleon has some additional internal degree of freedom - charge - in relation to which two states are possible: proton and neutron. This is analogous to the spin properties of particles: spin is also, in addition to the motion in space, the internal degree of freedom of the particle, in relation to which the electron (or nucleon) has only two possible states. Sequential quantum mechanical

the description of these two degrees of freedom: charge and spin - is formally the same. Therefore, accordingly, it is customary to visually describe the charge degree of freedom using a conventional three-dimensional space, which is called isotopic, and the state of a particle (nucleon) in this space is characterized by an isotopic spin, denoted

Let's look at this in a little more detail, returning to the concept of ordinary spin.

Let us assume that there are two electrons, which, as we know, are completely identical. Both of them have their own angular momentum - spin. However, the direction of their rotation cannot be detected. Let us now place them in an external magnetic field. According to the basic postulates of quantum mechanics, the “axis of rotation” of each particle can only occupy strictly defined positions relative to this external field. The spin axis of particles with equal spin can be oriented either along or towards the direction of the field (Fig. 19). A particle with momentum can have states; an electron that has 2 states. The value of spin projections can be This leads to the fact that particles in a magnetic field can now have different energies and it becomes possible to distinguish them from one another. This shows that the state of the electron, due to its magnetic properties, is a doublet.

Without external magnetic field there is no way to separate the two possible states of the electron; states are said to “degenerate” into indiscernible states.

A similar situation occurs in the hydrogen atom. To characterize the states of the atom, an orbital quantum number is introduced, which characterizes the orbital angular momentum of the atoms. An atom with a given I can have states, since in an external field only well-defined values ​​of the projections of I onto the direction of the field can exist (from - I to While there is no external field, the state is multiply degenerate.

The discovery of the neutron led to the idea of ​​the existence of a phenomenon similar to the magnetic degeneracy of the electron.

After all, the charge independence of nuclear forces means that in a strong interaction, a proton and a neutron behave like the same particle. They can only be distinguished if we take into account the electromagnetic interaction. If we imagine that electromagnetic LEDs can somehow be “turned off” (Fig. 20, a), then the proton and neutron will become indistinguishable particles and even their masses will be equal (for more details about the equality of masses; see § 12). Therefore, a cyclone can be considered as a "charge doublet", in which one state represents a proton and the other a neutron. If you include electromagnetic forces, conditionally

presented in Fig. 20b with a dotted line, then electric forces depending on the charge will be added to the previous charge-independent forces.

Rice. 19. Orientation of electron spin in a magnetic field

Rice. 20. The difference between a proton and a neutron due to electromagnetic interaction

The energy of charged particles will differ from the energy of neutral particles and the proton and neutron can be separated. Consequently, their rest masses will not be equal.

In order to characterize the state of a nucleon in a nucleus, Heisenberg introduced a purely formal concept of isotopic spin which, by analogy with quantum numbers, should determine the number of degenerate states of a nucleon equal to The word “isotopic” expresses the fact that the proton and neutron are close in their properties (isotopes - identical in chemical properties atoms that differ in the number of neutrons in the nucleus).

The word “spin” in this concept arose from a purely mathematical analogy with the ordinary spin of a particle.

It is important to note once again that the quantum mechanical vector of isotopic spin is introduced not in ordinary, but in conventional space, called isotopic or charge space. The latter, unlike conventional axes, is specified by conditional axes. In this space, the particle cannot move translationally, but only rotates.

Thus, isotopic spin should be considered as a mathematical characteristic that distinguishes a proton from a neutron; physically they are cast in a different relationship to the electromagnetic field.

The isotopic spin of a nucleon is equal and has components and with respect to the axis. The projection onto this axis is denoted. It was conventionally accepted that for a proton and for a neutron, i.e., a proton transforms into a neutron when the isotopic spin is rotated by 180° in isotopic space.

When using this formal technique, the charge dependence takes the form of a conservation law: during the interaction of nucleons, the total isotopic spin and its projection remain unchanged, i.e.

This conservation law can be formally considered as a consequence of the independence of physical laws from rotation in isotopic space. However, this conservation law is approximate. It is valid to the extent that electromagnetic forces can be neglected and may be slightly violated - to the extent of the ratio of electromagnetic and nuclear forces. Its physical meaning lies in the fact that the nuclear forces in the systems are identical.

We will return to the concept of isotopic spin in the chapter on elementary particles, for which it takes on additional meaning.

Nuclear forces depend on spin. The dependence of nuclear forces on spin follows from the following facts.

The same nucleus in states with different spins has different binding energies. For example, the binding energy of a deuteron, in which the spins are parallel, is equal; with antiparallel spins, there is no stable state at all.

Neutron-proton scattering is sensitive to spin orientation. The probability of interaction between neutrons and protons was theoretically calculated under the assumption that the interaction potential does not depend on spin. It turned out that the experimental results differed from the theoretical ones by a factor of five.

The discrepancy is eliminated if we take into account that the interaction depends on the relative orientation of the spins.

The dependence of nuclear forces on spin orientation is manifested in experiments on neutron scattering on ortho- and para-hydrogen molecules.

The fact is that there are two types of hydrogen molecules: in an ortho-hydrogen molecule, the spins of two protons are parallel to each other, the total spin is 1 and can have three orientations (the so-called triplet state); in a para-hydrogen molecule, the spins are antiparallel, the total spin is zero and a single state is possible (the so-called singlet state),

The ratio between the number of ortho- and para-hydrogen molecules at room temperature is This ratio is determined by the number of possible states.

The energy of the ground para state is lower than the energy of the ground orgo state. At low temperatures, ortho-hydrogen molecules transform into para-hydrogen molecules. In the presence of a catalyst, this transformation proceeds quite quickly and it is possible to obtain liquid hydrogen in the pure state of para-hydrogen. In case

scattering of neutrons on ortho-hydrogen, the spin of the neutron is either parallel to the spins of both protons, or antiparallel to both; i.e. there are configurations:

When scattered by para-hydrogen, the spin of the neutron is always parallel to the spin of one proton and antiparallel to the spin of the other proton; Regardless of the orientation of the para-hydrogen molecule, the configuration has the character

Rice. 21 Neutron scattering on hydrogen molecules

Let us consider scattering as a wave process. If scattering depends on the mutual orientation of the spins, then the observed interference effect of neutron waves scattered by both protons will be significantly different for the processes of scattering on ortho- and para-hydrogen molecules.

What must be the energy of the neutrons in order for a difference in scattering to be noticeable? In a molecule, protons are located at a distance many times greater than the radius of action of nuclear forces. cm. Therefore, due to the wave properties of the neutron, the scattering process can occur simultaneously on both protons if (Fig. 21). The de Broglie wave required for this

for a neutron whose mass is equivalent to energy

Nuclear forces have the property of saturation. As already mentioned in § 4, the property of saturation of nuclear forces is manifested in the fact that the binding energy of a nucleus is proportional to the number of nucleons in the nucleus - A, and not

This feature of nuclear forces also follows from the stability of light nuclei. It is impossible, for example, to add more and more new particles to deuteron; only one such combination with an additional neutron-tritium is known. A proton can thus form bound states with no more than two neutrons.

To explain Heisenberg saturation, it was suggested that nuclear forces are of an exchange nature.

Nuclear forces are of an exchange nature. For the first time, the exchange character was established among the forces chemical bond: A bond is formed by the transfer of electrons from one atom to another. Electromagnetic forces can also be classified as exchange forces: the interaction of charges is explained by the fact that they exchange y-quanta. However, in this case there is no saturation, since the exchange of y-quanta does not change the properties of each particle.

The exchange property of nuclear forces is manifested in the fact that during a collision, nucleons can transfer to each other such characteristics as charge, spin projections, and others.

The exchange nature is confirmed by various experiments, for example, by the results of measurements of the angular distribution of high-energy neutrons when they are scattered by protons. Let's look at this in more detail.

In nuclear physics, energy is called high when the de Broglie wave of the particle satisfies the relation i.e.

For nucleons, the de Broglie wavelength is related to the kinetic energy by the equation

and, therefore, the kinetic energy of a nucleon can be called high if it is significantly greater

Quantum mechanics makes it possible to obtain the dependence of the effective scattering cross section on the energy of incident neutrons and the scattering angle if the interaction potential is known.

Calculations show that for a potential like a rectangular well, the scattering cross section should vary depending on the energy of the particles, as well as the scattering itself should occur within a small angle. Therefore, the angular distribution of scattered neutrons in the center of inertia system should have a maximum in the direction of their movement, and the distribution of recoil protons should have a maximum in the opposite direction.

Experimentally, not only a peak in the angular distribution directed forward, but also a second peak in the backward direction was discovered for neutrons (Fig. 22).

Rice. 22. Dependence of the differential cross section for neutron scattering on protons on the scattering angle

The experimental results can only be explained by assuming that exchange forces act between nucleons and that during the scattering process, neutrons and protons exchange their charges, i.e., scattering occurs with “charge exchange.” In this case, part of the neutrons turns into protons, and protons are observed flying in the direction of the incident neutrons, the so-called charge exchange protons. At the same time, part of the protons turns into neutrons and is recorded as neutrons scattered back into the s.

The relative role of exchange and ordinary forces is determined by the ratio of the number of neutrons flying backward to the number of neutrons flying forward.

Based on quantum mechanics, it can be proven that the existence of exchange forces always leads to the phenomenon of saturation, since a particle cannot interact through exchange with many particles simultaneously.

However, a more detailed study of experiments on nucleon-nucleon scattering shows that although the interaction forces are indeed of an exchange nature, the mixture of the ordinary potential with the exchange one is such that it cannot fully explain the saturation. Another property of nuclear forces is also discovered. It turns out that if at large distances between nucleons predominantly attractive forces act, then when nucleons come close together (at a distance of the order of cm), a sharp repulsion occurs. This can be explained by the presence of cores in nucleons that repel each other.

Calculations show that it is these cores that are primarily responsible for the saturation effect. In this regard, nuclear interaction, apparently, should be characterized by a non-uniform potential like a rectangular well (Fig. complex function with a feature at short distances (Fig. 18d).

In physics, the concept of “force” denotes the measure of interaction of material formations with each other, including the interaction of parts of matter (macroscopic bodies, elementary particles) with each other and with physical fields (electromagnetic, gravitational). In total, four types of interaction in nature are known: strong, weak, electromagnetic and gravitational, and each has its own type of force. The first of them corresponds to nuclear forces acting inside atomic nuclei.

What unites the nuclei?

It is common knowledge that the nucleus of an atom is tiny, its size four to five orders of magnitude smaller than the size of the atom itself. This raises an obvious question: why is it so small? After all, atoms, made of tiny particles, are still much larger than the particles they contain.

In contrast, nuclei are not much different in size from the nucleons (protons and neutrons) from which they are made. Is there a reason for this or is it a coincidence?

Meanwhile, it is known that it is electrical forces that hold negatively charged electrons near atomic nuclei. What force or forces hold the particles of the nucleus together? This task is performed by nuclear forces, which are a measure of strong interactions.

Strong nuclear force

If in nature there were only gravitational and electrical forces, i.e. those we encounter in everyday life, then atomic nuclei, often consisting of many positively charged protons, would be unstable: the electrical forces pushing the protons away from each other would be many millions of times stronger than any gravitational forces, attracting them to each other. Nuclear forces provide an attraction even stronger than electrical repulsion, although only a shadow of their true magnitude is manifested in the structure of the nucleus. When we study the structure of protons and neutrons themselves, we see the true possibilities of what is known as the strong nuclear interaction. Nuclear forces are its manifestation.

The figure above shows that the two opposing forces in the nucleus are the electrical repulsion between positively charged protons and the nuclear force, which attracts protons (and neutrons) together. If the number of protons and neutrons is not too different, then the second forces are superior to the first.

Protons are analogs of atoms, and nuclei are analogs of molecules?

Between what particles do nuclear forces act? First of all, between nucleons (protons and neutrons) in the nucleus. Ultimately, they also act between particles (quarks, gluons, antiquarks) inside a proton or neutron. This is not surprising when we recognize that protons and neutrons are intrinsically complex.

In an atom, the tiny nuclei and even smaller electrons are relatively far apart compared to their size, and the electrical forces that hold them together in the atom are quite simple. But in molecules, the distance between atoms is comparable to the size of the atoms, so the internal complexity of the latter comes into play. The varied and complex situation caused by the partial compensation of intra-atomic electrical forces gives rise to processes in which electrons can actually move from one atom to another. This makes the physics of molecules much richer and more complex than that of atoms. Likewise, the distance between protons and neutrons in a nucleus is comparable to their size - and just as with molecules, the properties of the nuclear forces that hold nuclei together are much more complex than the simple attraction of protons and neutrons.

There is no nucleus without a neutron, except hydrogen

It is known that the nuclei of some chemical elements are stable, while in others they continuously decay, and the range of rates of this decay is very wide. Why do the forces that hold nucleons in nuclei cease to operate? Let's see what we can learn from simple considerations about the properties of nuclear forces.

One is that all nuclei, except the most common isotope hydrogen (which has only one proton), contain neutrons; that is, there is no nucleus with several protons that do not contain neutrons (see figure below). So it's clear that neutrons play an important role in helping protons stick together.

In Fig. Above, light stable or nearly stable nuclei are shown along with a neutron. The latter, like tritium, are shown with a dotted line, indicating that they eventually decay. Other combinations with a small number of protons and neutrons do not form a nucleus at all, or form extremely unstable nuclei. Also shown in italics are the alternative names often given to some of these objects; For example, the helium-4 nucleus is often called an α particle, the name given to it when it was originally discovered in early studies of radioactivity in the 1890s.

Neutrons as proton shepherds

On the contrary, there is no nucleus made of only neutrons without protons; most light nuclei, such as oxygen and silicon, have approximately the same number of neutrons and protons (Figure 2). Large nuclei with large masses, like gold and radium, have slightly more neutrons than protons.

This says two things:

1. Not only are neutrons needed to keep protons together, but protons are also needed to keep neutrons together.

2. If the number of protons and neutrons becomes very large, then the electrical repulsion of the protons must be compensated by adding a few additional neutrons.

The last statement is illustrated in the figure below.

The figure above shows stable and nearly stable atomic nuclei as a function of P (number of protons) and N (number of neutrons). The line shown with black dots indicates stable nuclei. Any shift up or down from the black line means a decrease in the life of nuclei - near it, the life of nuclei is millions of years or more, as you move further into the blue, brown or yellow areas (different colors correspond to different mechanisms of nuclear decay), their life time becomes shorter and shorter, down to a fraction of a second.

Note that stable nuclei have P and N roughly equal for small P and N, but N gradually becomes larger than P by a factor of more than one and a half. Note also that the group of stable and long-lived unstable nuclei remains in a fairly narrow band for all values ​​of P up to 82. At larger numbers, the known nuclei are in principle unstable (although they can exist for millions of years). Apparently, the mechanism noted above for stabilizing protons in nuclei by adding neutrons to them in this region is not 100% effective.

How does the size of an atom depend on the mass of its electrons?

How do the forces under consideration affect the structure of the atomic nucleus? Nuclear forces primarily affect its size. Why are nuclei so small compared to atoms? To find out, let's start with the simplest nucleus, which has both a proton and a neutron: it is the second most common isotope of hydrogen, an atom containing one electron (like all hydrogen isotopes) and a nucleus of one proton and one neutron. This isotope is often called "deuterium," and its nucleus (see Figure 2) is sometimes called the "deuteron." How can we explain what holds the deuteron together? Well, you can imagine that it is not so different from an ordinary hydrogen atom, which also contains two particles (a proton and an electron).

In Fig. It is shown above that in a hydrogen atom, the nucleus and electron are very far apart, in the sense that the atom is much larger than the nucleus (and the electron is even smaller.) But in a deuteron, the distance between the proton and neutron is comparable to their sizes. This partly explains why nuclear forces are much more complex than the forces in an atom.

It is known that electrons have a small mass compared to protons and neutrons. It follows that

• the mass of an atom is essentially close to the mass of its nucleus,
• the size of an atom (essentially the size of the electron cloud) is inversely proportional to the mass of the electrons and inversely proportional to the total electromagnetic force; The uncertainty principle of quantum mechanics plays a decisive role.

What if nuclear forces are similar to electromagnetic ones?

What about deuteron? It, like the atom, is made of two objects, but they are almost the same mass (the masses of the neutron and proton differ only by about one part in 1500), so both particles are equally important in determining the mass of the deuteron and its size . Now suppose that the nuclear force pulls the proton towards the neutron in the same way as electromagnetic forces (this is not exactly true, but imagine for a moment); and then, by analogy with hydrogen, we expect the size of the deuteron to be inversely proportional to the mass of the proton or neutron, and inversely proportional to the magnitude of the nuclear force. If its magnitude were the same (at a certain distance) as the electromagnetic force, then this would mean that since a proton is about 1850 times heavier than an electron, then the deuteron (and indeed any nucleus) must be at least a thousand times smaller than that of hydrogen.

What does taking into account the significant difference between nuclear and electromagnetic forces provide?

But we already guessed that the nuclear force is much greater than the electromagnetic force (at the same distance), because if this were not so, it would not be able to prevent electromagnetic repulsion between protons until the nucleus disintegrates. So the proton and neutron under its influence come together even more tightly. And therefore it is not surprising that the deuteron and other nuclei are not just one thousand, but one hundred thousand times smaller than atoms! Again, this is only because

• protons and neutrons are almost 2000 times heavier than electrons,
• at these distances, the large nuclear force between protons and neutrons in the nucleus is many times greater than the corresponding electromagnetic forces (including electromagnetic repulsion between protons in the nucleus.)

This naive guess gives approximately the correct answer! But this does not fully reflect the complexity of the interaction between proton and neutron. One obvious problem is that a force similar to electromagnetic force, but with greater attractive or repulsive power, should obviously manifest itself in everyday life, but we do not observe anything like this. So something about this force must be different from electrical forces.

Short nuclear force range

What makes them different is that the nuclear forces that keep the atomic nucleus from decaying are very important and strong for protons and neutrons that are at a very short distance from each other, but at a certain distance (the so-called "range" of force), they fall very fast, much faster than electromagnetic ones. The range, it turns out, can also be the size of a moderately large nucleus, only several times larger than a proton. If you place a proton and a neutron at a distance comparable to this range, they will attract each other and form a deuteron; if they are separated by a greater distance, they will hardly feel any attraction at all. In fact, if they are placed too close together to the point where they start to overlap, they will actually repel each other. This reveals the complexity of such a concept as nuclear forces. Physics continues to continuously develop in the direction of explaining the mechanism of their action.

Physical mechanism of nuclear interaction

Every material process, including the interaction between nucleons, must have material carriers. They are nuclear field quanta - pi-mesons (pions), due to the exchange of which attraction between nucleons arises.

According to the principles of quantum mechanics, pi-mesons, constantly appearing and immediately disappearing, form around a “naked” nucleon something like a cloud called a meson coat (remember the electron clouds in atoms). When two nucleons surrounded by such coats find themselves at a distance of about 10 -15 m, an exchange of pions occurs, similar to the exchange of valence electrons in atoms during the formation of molecules, and attraction arises between the nucleons.

If the distances between nucleons become less than 0.7∙10 -15 m, then they begin to exchange new particles - the so-called. ω and ρ-mesons, as a result of which not attraction, but repulsion occurs between nucleons.

Nuclear forces: structure of the nucleus from simplest to largest

Summarizing all of the above, we can note:

• the strong nuclear force is much, much weaker than electromagnetism at distances much larger than the size of a typical nucleus, so we don't encounter it in everyday life; But
• at short distances comparable to the nucleus, it becomes much stronger - the force of attraction (provided that the distance is not too short) is able to overcome the electrical repulsion between protons.

So, this force only matters at distances comparable to the size of the nucleus. The figure below shows its dependence on the distance between nucleons.

Large nuclei are held together by more or less the same force that holds the deuteron together, but the details of the process are so complex that they are not easy to describe. They are also not fully understood. Although the basic outlines of nuclear physics have been well understood for decades, many important details are still under active investigation.

1. Nuclear forces are large in absolute magnitude. They are among the strongest of all known interactions in nature.

So far we have known four types of interaction:

a) strong (nuclear) interactions;

b) electromagnetic interactions;

c) weak interactions, especially clearly observed in particles that do not manifest themselves in strong and electromagnetic interactions (neutrinos);

d) gravitational interactions.

For example, it is enough to say that the binding energy of the simplest nucleus, the deuteron, due to nuclear forces is equal to 2.26 MeV, while the binding energy of the simplest atom, hydrogen, due to electromagnetic forces is 13.6 eV.

2. Nuclear forces have the property of attraction at distances in the region of 10 -13 cm, however, at significantly smaller distances they turn into repulsive forces. This property is explained by the presence of a repulsive core in nuclear forces. It was discovered by analyzing proton-proton scattering at high energies. The property of attraction of nuclear forces follows from the mere existence of atomic nuclei.

3. Nuclear forces are short-acting. The radius of their action is of the order of 10 -13 cm. The short-range property was derived from a comparison of the binding energies of the deuteron and the α particle. However, it already follows from Rutherford’s experiments on the scattering of α-particles by nuclei, where the estimated radius of the nucleus is ~10 -12 cm.

4. Nuclear forces are of an exchange nature. Exchangeability is an essentially quantum property due to which nucleons can transfer their charges, spins and even coordinates to each other during collisions. The existence of exchange forces directly follows from experiments on the scattering of high-energy protons on protons, when other particles - neutrons - are detected in the reverse flow of scattered protons.

5. Nuclear interaction depends not only on distance, but also on the relative orientation of the spins of interacting particles, as well as on the orientation of the spins relative to the axis connecting the particles. This dependence of nuclear forces on spin follows from experiments on the scattering of slow neutrons on ortho and parahydrogen.

The existence of such a dependence also follows from the presence of a quadrupole moment; therefore, the nuclear interaction is not central, but tensor, i.e. it depends on the mutual orientation of the total spin and the spin projection. For example, when the spins are oriented n and p, the binding energy of the deuteron is 2.23 MeV.

6. From the properties of mirror nuclei (mirror nuclei are called nuclei in which neutrons are replaced by protons, and protons by neutrons) it follows that the interaction forces between (p, p), (n, n) or (n, p) are the same. Those. exists property of charge symmetry of nuclear forces. This property of nuclear forces is fundamental and indicates the deep symmetry that exists between two particles: the proton and the neutron. It is called charge independence (or symmetry) or isotopic invariance and made it possible to consider the proton and neutron as two states of the same particle - the nucleon. Isotopic spin was first introduced by Heisenberg purely formally and it is generally accepted that it is equal to T = -1/2 - when the nucleon is in the neutron state, and T = +1/2 when the nucleon is in the proton state. Let us assume that there is some kind of three-dimensional space, called isotopic, which has no relation to ordinary Cartesian space, and each particle is located at the origin of this space, where it cannot move translationally, but only rotates and has, accordingly, in this space own angular momentum (spin). A proton and a neutron are particles oriented differently in isotopic space and a neutron turns into a proton when rotated 180 degrees. Isotopic invariance means that the interaction in any two pairs of nucleons is the same if these pairs are in the same states, i.e. nuclear interaction is invariant with respect to rotations in isotopic space. This property of nuclear forces is called isotopic invariance.

7.Nuclear forces have the property of saturation. The property of saturation of nuclear forces is manifested in the fact that the binding energy of a nucleus is proportional to the number of nucleons in the nucleus - A, and not A 2, i.e. Each particle in the nucleus does not interact with all surrounding nucleons, but only with a limited number of them. This feature of nuclear forces also follows from the stability of light nuclei. It is impossible, for example, to add more and more new particles to the deuteron; only one is known like this combination with an additional neutron – tritium. A proton can thus form bound states with no more than two neutrons

8. Back in 1935 Japanese physicist Yukawa, developing Tamm's ideas, suggested that there must be some other particles responsible for nuclear forces. Yukawa came to the conclusion that there must be a field of a different type, similar to the electromagnetic one, but of a different nature, which predicted the existence of particles of intermediate mass, i.e. mesons, later discovered experimentally.

However, the meson theory has not yet been able to satisfactorily explain nuclear interaction. The meson theory assumes the existence of triple forces, i.e. acting between three bodies and vanishing when one of them moves to infinity. The radius of action of these forces is half that of normal paired forces.

At this stage, meson theory cannot explain everything, and therefore we will consider

1. phenomenological selection of the potential corresponding to the above listed properties of nuclear forces - this is the first approach and remains the second approach.

2. reduction of nuclear forces to the properties of the meson field.

In this case, we will consider the elementary theory of the deuteron along the first path.

An atomic nucleus, consisting of a certain number of protons and neutrons, is a single whole due to specific forces that act between the nucleons of the nucleus and are called nuclear. It has been experimentally proven that nuclear forces have very large values, much greater than the forces of electrostatic repulsion between protons. This is manifested in the fact that the specific binding energy of nucleons in the nucleus is much greater than the work done by the Coulomb repulsion forces. Let's look at the main features of nuclear forces.

1. Nuclear forces are short-range attractive forces . They appear only at very small distances between nucleons in the nucleus of the order of 10 –15 m. A distance of the order of (1.5 – 2.2) 10 –15 m is called range of nuclear forces, with its increase, nuclear forces quickly decrease. At a distance of the order of (2-3) m, nuclear interaction between nucleons is practically absent.

2. Nuclear forces have the property saturation, those. each nucleon interacts only with a certain number of nearest neighbors. This nature of nuclear forces is manifested in the approximate constancy of the specific binding energy of nucleons at charge number A>40. Indeed, if there were no saturation, then the specific binding energy would increase with the number of nucleons in the nucleus.

3. A feature of nuclear forces is also their charge independence , i.e. they do not depend on the charge of the nucleons, so the nuclear interactions between protons and neutrons are the same. The charge independence of nuclear forces is visible from a comparison of binding energies mirror cores . This is the name given to nuclei in which the total number of nucleons is the same, but the number of protons in one is equal to the number of neutrons in the other. For example, the binding energies of helium and heavy hydrogen – tritium nuclei are respectively 7.72 MeV and 8.49 MeV. The difference in binding energies of these nuclei, equal to 0.77 MeV, corresponds to the energy of the Coulomb repulsion of two protons in the nucleus. Assuming this value to be equal to , we can find that the average distance r between protons in the nucleus is 1.9·10 –15 m, which is consistent with the radius of action of nuclear forces.

4. Nuclear forces are not central and depend on the mutual orientation of the spins of interacting nucleons. This is confirmed by the different nature of neutron scattering by ortho- and parahydrogen molecules. In an orthohydrogen molecule, the spins of both protons are parallel to each other, while in a parahydrogen molecule they are antiparallel. Experiments have shown that neutron scattering on parahydrogen is 30 times greater than scattering on orthohydrogen.

The complex nature of nuclear forces does not allow the development of a single, consistent theory of nuclear interaction, although many different approaches have been proposed. According to the hypothesis of the Japanese physicist H. Yukawa (1907-1981), which he proposed in 1935, nuclear forces are caused by exchange - mesons, i.e. elementary particles, whose mass is approximately 7 times less than the mass of nucleons. According to this model, a nucleon in time m- meson mass) emits a meson, which, moving at a speed close to the speed of light, covers a distance , after which it is absorbed by the second nucleon. In turn, the second nucleon also emits a meson, which is absorbed by the first. In H. Yukawa’s model, therefore, the distance at which nucleons interact is determined by the meson path length, which corresponds to a distance of about m and in order of magnitude coincides with the radius of action of nuclear forces.

Let us turn to the consideration of the exchange interaction between nucleons. There are positive, negative and neutral mesons. The modulus of charge - or - mesons is numerically equal to the elementary charge e . The mass of charged mesons is the same and equal to (140 MeV), meson mass is 264 (135 MeV). The spin of both charged and neutral mesons is 0. All three particles are unstable. The lifetime of - and - mesons is 2.6 With, - meson – 0.8·10 -16 With. The interaction between nucleons is carried out according to one of the following schemes:

1. Nucleons exchange mesons: . (22.8)

In this case, the proton emits a meson, turning into a neutron. The meson is absorbed by a neutron, which consequently turns into a proton, then the same process occurs in the opposite direction. Thus, each of the interacting nucleons spends part of the time in a charged state and part in a neutral state.

2. Nucleons exchange - mesons:

3. Nucleons exchange - mesons:

, (22.10)

All these processes have been proven experimentally. In particular, the first process is confirmed when a neutron beam passes through hydrogen. Moving protons appear in the beam, and a corresponding number of practically resting neutrons are detected in the target.

Kernel models. Under kernel model in nuclear physics they understand a set of physical and mathematical assumptions with the help of which it is possible to calculate the characteristics of a nuclear system consisting of A nucleons.

Hydrodynamic (drip) model of the core It is based on the assumption that, due to the high density of nucleons in the nucleus and the extremely strong interaction between them, the independent movement of individual nucleons is impossible and the nucleus is a drop of charged liquid with the density .

Shell model of the kernel It assumes that each nucleon moves independently of the others in some average potential field (potential well created by the remaining nucleons of the nucleus.

Generalized kernel model, combines the main provisions of the creators of hydrodynamic and shell models. In the generalized model, it is assumed that the nucleus consists of an internal stable part - the core, which is formed by the nucleons of filled shells, and external nucleons moving in the field created by the nucleons of the core. In this regard, the motion of the core is described by a hydrodynamic model, and the motion of external nucleons by a shell model. Due to interaction with external nucleons, the core can be deformed, and the core can rotate around an axis perpendicular to the deformation axis.

26. Reactions of fission of atomic nuclei. Nuclear power.

Nuclear reactions are called transformations of atomic nuclei caused by their interaction with each other or with other nuclei or elementary particles. The first message about a nuclear reaction belongs to E. Rutherford. In 1919, he discovered that when particles pass through nitrogen gas, some of them are absorbed, and protons are simultaneously emitted. Rutherford concluded that nitrogen nuclei were converted into oxygen nuclei as a result of a nuclear reaction of the form:

, (22.11)

where − is a particle; − proton (hydrogen).

An important parameter of a nuclear reaction is its energy yield, which is determined by the formula:

(22.12)

Here and are the sums of the rest masses of particles before and after the reaction. When nuclear reactions occur with the absorption of energy, that’s why they are called endothermic, and when - with the release of energy. In this case they are called exothermic.

In any nuclear reaction, the following are always fulfilled: conservation laws :

− electric charge ;

– number of nucleons;

− energy;

− impulse.

The first two laws allow nuclear reactions to be written correctly even in cases where one of the particles participating in the reaction or one of its products is unknown. Using the laws of conservation of energy and momentum, it is possible to determine the kinetic energies of particles that are formed during the reaction process, as well as the directions of their subsequent movement.

To characterize endothermic reactions, the concept is introduced threshold kinetic energy , or nuclear reaction threshold , those. the lowest kinetic energy of an incident particle (in the frame of reference where the target nucleus is at rest) at which a nuclear reaction becomes possible. From the law of conservation of energy and momentum it follows that the threshold energy of a nuclear reaction is calculated by the formula:

. (22.13)

Here is the energy of the nuclear reaction (7.12); -mass of the stationary core – target; is the mass of the particle incident on the nucleus.

Fission reactions. In 1938, German scientists O. Hahn and F. Strassmann discovered that when uranium is bombarded with neutrons, nuclei sometimes appear that are approximately half the size of the original uranium nucleus. This phenomenon was called nuclear fission.

It represents the first experimentally observed nuclear transformation reaction. An example is one of the possible fission reactions of the uranium-235 nucleus:

The process of nuclear fission proceeds very quickly in a time of ~10 -12 s. The energy released during a reaction like (22.14) is approximately 200 MeV per fission event of the uranium-235 nucleus.

In general, the fission reaction of the uranium-235 nucleus can be written as:

+neutrons . (22.15)

The mechanism of the fission reaction can be explained within the framework of the hydrodynamic model of the nucleus. According to this model, when a neutron is absorbed by a uranium nucleus, it goes into an excited state (Fig. 22.2).

The excess energy that the nucleus receives due to the absorption of a neutron causes more intense movement of nucleons. As a result, the nucleus is deformed, which leads to a weakening of the short-range nuclear interaction. If the excitation energy of the nucleus is greater than a certain energy called activation energy , then under the influence of the electrostatic repulsion of protons the nucleus splits into two parts, emitting fission neutrons . If the excitation energy upon absorption of a neutron is less than the activation energy, then the nucleus does not reach

critical stage of fission and, having emitted a quantum, returns to the main