What property of nuclear forces is called charge independence? Properties of nuclear forces

In physics, the concept of "force" denotes the measure of the 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 forces. The first of these corresponds to nuclear forces acting inside atomic nuclei.

What unites the cores?

It is generally known that the nucleus of an atom is tiny, four to five decimal 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 up of tiny particles, are still much larger than the particles they contain.

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

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

Strong nuclear force

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

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

Are protons analogs of atoms, and nuclei analogs of molecules?

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

In an atom, tiny nuclei and even smaller electrons are relatively far apart compared to their size, and the electrical forces that hold them in the atom are simple enough. But in molecules, the distance between atoms is comparable to the size of atoms, so the intrinsic 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 like molecules, the properties of the nuclear forces holding nuclei together are much more complex than simply attracting protons and neutrons.

There is no nucleus without a neutron, except for 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 the nucleons in nuclei cease to act? Let's see what we can learn from simple considerations about the properties of nuclear forces.

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

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

Neutrons as proton shepherds

On the contrary, there is no nucleus made only of neutrons without protons; most light nuclei such as oxygen and silicon have roughly 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 needed to keep neutrons together too.

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 represents stable nuclei. Any shift from the black line up or down means a decrease in the life of the nuclei - near it, the life of the nuclei is millions of years or more, as they move inward the blue, brown or yellow regions (different colors correspond to different mechanisms of nuclear decay), their lifetimes become shorter, down to fractions of a second.

Note that stable kernels have P and N that are approximately equal for small P and N, but N gradually becomes more than 1.5 times larger than P. We also note that the group of stable and long-lived unstable nuclei remains in a rather narrow band for all values \u200b\u200bof P up to 82. With a large number of them, known nuclei are in principle unstable (although they can exist for millions of years). Apparently, the above mechanism of stabilization of protons in nuclei due to the addition of neutrons to them in this region does not have one hundred percent efficiency.

How the size of an atom depends on the mass of its electrons

How do the considered forces 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, whose atom contains 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 "deuteron." How can we explain what holds the deuteron together? Well, you can imagine that it is not that different from an ordinary hydrogen atom, which also contains two particles (a proton and an electron).

In fig. it was shown above that in the hydrogen atom the nucleus and the electron are very far from each other, in the sense that the atom is much larger than the nucleus (and the electron is even smaller.) But in the deuteron the distance between the proton and the neutron is comparable to their size. This partly explains why nuclear forces are much more complex than atomic forces.

It is known that electrons have a small mass compared to protons and neutrons. Hence 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 an electron cloud) is inversely proportional to the mass of electrons and inversely proportional to the total electromagnetic force; the uncertainty principle of quantum mechanics plays a decisive role.

And if nuclear forces are similar to electromagnetic

What about the deuteron? It, like an atom, is made of two objects, but they have almost the same mass (the masses of a neutron and a proton differ only by about one 1500th part), so both particles are equally important in determining the mass of the deuteron and its size ... Now suppose the nuclear force pulls the proton towards the neutron in the same way as the electromagnetic forces (this is not entirely 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 value was 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 a deuteron (and indeed any nucleus) must be at least a thousand times smaller than hydrogen.

What gives taking into account the significant difference between nuclear and electromagnetic forces

But we have already guessed that nuclear force is much greater than electromagnetic (at the same distance), because if it is not, it would not be able to prevent electromagnetic repulsion between protons until the nucleus decays. So the proton and neutron under its action come closer together even more densely. And therefore it is not surprising that the deuteron and other nuclei are not just one thousand, but one hundred thousand times less 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 the electromagnetic repulsion between protons in the nucleus.)

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

Short range nuclear power

What distinguishes them is that the nuclear forces that keep the atomic nucleus from decay are very important and large 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. 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 neutron at a distance comparable to this range, they will be attracted to each other and form a dayton; if they are spread over a greater distance, they will hardly feel any attraction at all. In fact, if you place them too close together so that they start to overlap, then they will actually repel each other. This is where the complexity of such a concept as nuclear forces manifests itself. Physics continues to develop continuously in the direction of explaining the mechanism of their action.

Physical mechanism of nuclear interaction

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

According to the principles of quantum mechanics, pi-mesons, now and then appearing and immediately disappearing, form around the "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 an 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 there is repulsion rather than attraction between the nucleons.

Nuclear forces: the structure of the nucleus from the simplest to the largest

Summarizing all of the above, we can note:

strong nuclear force is much, much weaker than electromagnetism at distances much larger than the size of a typical nucleus, so that we do not 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 the protons.

So, this force matters only at distances comparable to the size of the nucleus. The figure below shows the form of 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 become more complex and difficult to describe. They are also not fully understood. Although the basic outline of nuclear physics has been well studied for decades, many important details are still being actively explored.

The atomic nucleus, consisting of a certain number of protons and neutrons, is a single whole due to the specific forces that act between the nucleons of the nucleus and are called nuclear. It has been experimentally proven that nuclear forces are very large, far exceeding 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 higher than the work of the forces of Coulomb repulsion. Consider the main features of nuclear forces.

1. Nuclear forces are short-range forces of attraction ... They appear only at very small distances between nucleons in the nucleus of the order of 10-15 m. The distance of the order of (1.5-2.2) · 10 -15 m is called range of nuclear forces, with its increase, nuclear forces rapidly decrease. At a distance of the order of (2-3) m, there is practically no nuclear interaction between nucleons.

2. Nuclear forces have the property saturation, those. each nucleon interacts only with a certain number of nearest neighbors. This character of nuclear forces manifests itself in the approximate constancy of the specific binding energy of nucleons at a charge number AND\u003e 40. Indeed, if there were no saturation, then the specific binding energy would increase with an increase in 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 nucleons, therefore the nuclear interactions between protons and neutrons are the same. The charge independence of nuclear forces is seen from a comparison of the binding energies mirror cores ... This is the name of 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 the nuclei of helium and heavy hydrogen - tritium are, respectively, 7.72 MeV and 8.49 MeV... The difference between the 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 equal, we can find that the average distance rbetween the 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 the interacting nucleons. This is confirmed by the different character of neutron scattering by ortho- and parahydrogen molecules. In the orthohydrogen molecule, the spins of both protons are parallel to each other, and in the parahydrogen molecule they are antiparallel. Experiments have shown that the scattering of neutrons on parahydrogen is 30 times higher than the scattering on orthohydrogen.

The complex nature of nuclear forces does not allow the development of a unified 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 due to the exchange - mesons, i.e. elementary particles, the mass of which is approximately 7 times less than the mass of nucleons. According to this model, a nucleon in time mis the mass of the meson) emits a meson, which, moving at a speed close to the speed of light, travels the 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. Thus, in H. Yukawa's model, the distance at which nucleons interact is determined by the meson free path, which corresponds to a distance of about m and coincides in order of magnitude 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 charge modulus - or - of mesons is numerically equal to the elementary charge e ... The mass of charged mesons is the same and equal to (140 MeV), the mass of a meson is 264 (135 MeV). The spin of both charged and neutral mesons is 0. All three particles are unstable. The lifetime of - u - mesons is 2.6 from, - meson - 0.8 10 -16 from... 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, as a result, turns into a proton, then the same process proceeds in the opposite direction. Thus, each of the interacting nucleons spends part of the time in a charged state, and part in a neutral one.

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 the corresponding number of practically resting neutrons is found 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 AND nucleons.

Hydrodynamic (drop) core modelIt 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 a density .

Shell core model It assumes that each nucleon moves independently of the others in a certain average potential field (potential well created by the rest of the nucleons in the nucleus.

Generalized kernel model, combines the main provisions of the creators of the 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 nucleons of the 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 the hydrodynamic model, and the motion of the outer nucleons is described by the shell model. Due to the interaction with external nucleons, the core can be deformed, and the nucleus can rotate around an axis perpendicular to the deformation axis.

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

Nuclear reactions transformations of atomic nuclei caused by their interaction with each other or with other nuclei or elementary particles are called. 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, while the emission of protons occurs simultaneously. 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 the particles before and after the reaction. When nuclear reactions proceed with the absorption of energy, therefore they are called endothermic, and at - with the release of energy. In this case, they are called exothermic.

In any nuclear reaction, always conservation laws :

− electric charge;

- the number of nucleons;

- energy;

- impulse.

The first two laws make it possible to correctly record nuclear reactions 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, as well as the direction of their subsequent motion.

To characterize endothermic reactions, the concept is introduced threshold kinetic energy , or nuclear reaction threshold , those. the smallest kinetic energy of the 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); - the mass of the fixed nucleus - the target; Is the mass of the particle incident on the nucleus.

Fission reactions. In 1938 the 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 has been named fission.

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

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

In the general case, 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 passes into an excited state (Fig. 22.2).

The excess energy that the nucleus receives as a result of the absorption of a neutron causes a 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 electrostatic repulsion of protons, the nucleus splits into two parts, with the emission fission neutrons ... If the excitation energy upon absorption of a neutron is less than the activation energy, then the nucleus does not reach

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

What unites the cores?

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

Strong nuclear force

Are protons analogs of atoms, and nuclei analogs of molecules?

There is no nucleus without a neutron, except for hydrogen

Neutrons as proton shepherds

This says two things:

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

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.

How the size of an atom depends on the mass of its electrons

It is known that electrons have a small mass compared to protons and neutrons. Hence 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 an electron cloud) is inversely proportional to the mass of electrons and inversely proportional to the total electromagnetic force; the uncertainty principle of quantum mechanics plays a decisive role.

And if nuclear forces are similar to electromagnetic

What gives taking into account the significant difference between nuclear and electromagnetic forces

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 the electromagnetic repulsion between protons in the nucleus.)

Short range nuclear power

Physical mechanism of nuclear interaction

Nuclear forces: the structure of the nucleus from the simplest to the largest

Summarizing all of the above, we can note:

strong nuclear force is much, much weaker than electromagnetism at distances much larger than the size of a typical nucleus, so that we do not 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 the protons.

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

1.3.1 ... The nucleus of any atom has a complex structure and consists of particles called nucleons. Two types of nucleons are known - protons and neutrons .
Protons - nucleons with a mass of 1 amu. with a positive charge equal to unit, that is, the elementary charge of an electron.
Neutrons - electrically neutral nucleons with a mass of 1 amu
*) Strictly speaking, the rest masses of protons and neutrons are somewhat different: m p \u003d 1.6726. 10 -24 r , and m n \u003d 1.67439. 10 -24 r ... This difference will be discussed later.

1.3.2. Since the mass of the core practically is equal to A, the charge of the nucleus is z, and the masses of the proton and neutron almost equal with such views, it should be taken for granted that the nucleus of an electrically neutral stable atom consists ofz protons and (A - z ) neutrons.Therefore, the atomic number of an element is nothing more than the proton charge of the nucleus of an atom, expressed in elementary charges of an electron.In other words, z is the number protons in the nucleus of an atom.

1.3.3 . The presence in the nucleus of protons (particles with an electric charge of the same sign) due to the Coulomb repulsive forces between them should lead to the expansion of nucleons. In reality, this does not happen. The existence in nature of many stable nuclei leads to the conclusion about the existence between nucleons of a nucleus more powerful than Coulomb, nuclear forces attraction, which, overcoming the Coulomb repulsion of protons, pull the nucleons into a stable structure - the nucleus.

1.3.4. The sizes of the nuclei of atoms, determined by the formula (1.4), are values \u200b\u200bof the order of 10 -13 cm. Hence the first property of nuclear forces (as opposed to Coulomb, gravitational and others) - short-acting: nuclear forces act only at small distances, comparable in order of magnitude with the size of the nucleons themselves.
Even without knowing exactly what kind of material formation is a proton or neutron, you can estimate them effective dimensions as the diameter of a sphere, on the surface of which the nuclear attraction of two neighboring protons is balanced by their Coulomb repulsion. Experiments at accelerators on electron scattering by nuclei made it possible to estimate the effective nucleon radius R n ≈ 1.21. 10 -13 cm.

1.3.5 ... From the short-range action of nuclear forces follows their second property, briefly referred to as saturation . It means that any nucleon of a nucleus interacts not with all other nucleons, but only with a limited number of nucleons that are its immediate neighbors.

1.3.6. The third property of nuclear forces - their equal action. Since it is assumed that the forces of interaction between nucleons of both types are forces of the same nature, it is thereby postulated that at equal distances of the order of 10 -13 cm two protons, two neutrons or a proton with a neutron interact the same.

1.3.7. Free proton (that is, outside atomic nuclei ) stable . A neutron in a free state cannot exist for a long time: it undergoes decay into a proton, an electron and antineutrino with a half-life T 1/2 \u003d 11.2 min. according to the scheme:
o n 1 → 1 p 1 + - 1 e + n
*) Antineutrino (n) - an electrically neutral particle of matter with zero rest mass.

1.3.8. So, any core is considered completely individualized, if its two main characteristics are known - the number of protons z and the mass number A, since the difference (A - z) determines the number of neutrons in the nucleus. Individualized atomic nuclei are generally called nuclides.
Among the many nuclides (and there are currently more than 2000 known - natural and artificial) there are those in which one of the two mentioned characteristics is the same, and the other differs in magnitude.
Nuclides with the same z (number of protons) are called isotopes. Since the atomic number determines, in accordance with the Periodic Law of D.I. Mendeleev, individuality only chemicalproperties of the atom of the element, isotopes are always spoken of with reference to the corresponding chemical element in the Periodic Table.
For example, 233 U, 234 U, 235 U, 236 U, 238 U, 239 U - all these are isotopes of uranium, which has a serial number z \u003d 92 in the Periodic Table of Elements.
Isotopes any chemical element as we see , have an equal number of protons, but different numbers of neutrons.

Nuclides of equal mass (A ), but with different charges z are called isobars . Isobars, unlike isotopes, are nuclides of various chemical elements.
Examples of... 11 В 5 and 11 С 4 - isobars of boron and carbon nuclides; 7 Li 3 and 7 Be 4 are isobars of lithium and beryllium nuclides; 135 J 53, 135 Xe 54 and 135 Cs 55 are also isobars of iodine, xenon and cesium, respectively.

1.3.9 ... From formula (1.4), one can estimate the density of nucleons in nuclei and the mass density of nuclear matter. Assuming the nucleus to be a sphere with radius R and with the number of nucleons in its volume equal to A, the number of nucleons per unit volume of the nucleus is found as:
N n \u003d A / V i \u003d 3A / 4pR 3 \u003d 3A / 4p (1.21. 10 -13 A 1/3) 3 \u003d 1.348. 10 38 nucleus / cm 3,
a, since the mass of one nucleon is equal to 1 amu. \u003d 1.66056. 10 -24 r , then the density of nuclear matter is found as:
γ jav \u003d Nm n \u003d 1.348. 10 38 .1.66056. 10 -24 ≈ 2.238. 10 14 g / cm 3.= 223 800 000 t / cm 3
The procedure for the above calculation indicates that the density of nuclear matter is the same in the nuclei of all chemical elements.
Volume. per 1 nucleon in the nucleus, V i/ A \u003d 1 / N \u003d 1 / 1.348. 10 38 \u003d 7.421. 10 -39 cm 3
- also the same for all kernels, therefore, the average distance between the centers of neighboring nucleons in any nucleus (which can be conventionally called the average nucleon diameter) will be
D n \u003d (V i) 1/3 \u003d (7.421. 10 -39) 1/3 \u003d 1.951. 10 -13 cm .

1.3.10. Little is known about the density of the arrangement of protons and neutrons in the nucleus of an atom. Since protons, unlike neutrons, are subject not only to nuclear and gravitational attraction, but also to Coulomb repulsion, it can be assumed that the proton charge of a nucleus is more or less uniformly distributed over its surface.

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1. Nuclear forces are short-range forces of attraction ... They manifest themselves only at very small distances between nucleons in the nucleus of the order of 10 -15 m. The distance of the order of (1.5 - 2.2) · 10 -15 m is called the radius of action of nuclear forces, with an increase in nuclear forces rapidly decrease. At a distance of the order of (2-3) m, there is practically no nuclear interaction between nucleons.

The complex nature of nuclear forces does not allow the development of a unified consistent theory of nuclear interaction, although many different approaches have been proposed. According to the hypothesis of the Japanese physicist H. Yukawa, which he proposed in 1935, nuclear forces are due to the exchange - mesons, i.e. elementary particles, the mass of which is approximately 7 times less than the mass of nucleons. According to this model, a nucleon in time mis the mass of the meson) emits a meson, which, moving at a speed close to the speed of light, travels the 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. Thus, in H. Yukawa's model, the distance at which nucleons interact is determined by the meson free path, which corresponds to a distance of about m and coincides in order of magnitude 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 charge modulus - or - of mesons is numerically equal to the elementary charge e... The mass of charged mesons is the same and equal to (140 MeV), the mass of a meson is 264 (135 MeV). The spin of both charged and neutral mesons is 0. All three particles are unstable. The lifetime of - u - mesons is 2.6 from, - meson - 0.8 10 -16 from... The interaction between nucleons is carried out according to one of the following schemes:

(22.7)
1. Nucleons exchange mesons:

2. Nucleons exchange - mesons:

3. Nucleons exchange - mesons:

. (22.10)

Kernel models. The absence of a mathematical law for nuclear forces does not allow the creation of a unified theory of the nucleus. Attempts to create such a theory run into serious difficulties. Here is some of them:

1. Lack of knowledge about the forces acting between nucleons.

2. Extreme cumbersomeness of the quantum many-body problem (a nucleus with a mass number AND is a system of AND tel).

These difficulties force us to go along the path of creating nuclear models that make it possible to describe a certain set of nuclear properties with the help of relatively simple mathematical means. None of these models can give an absolutely accurate description of the kernel. Therefore, you have to use several 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 AND nucleons. Many models of varying degrees of complexity have been proposed and developed. We will consider only the most famous of them.

Hydrodynamic (drop) core modelwas developed in 1939. N. Bohr and the Soviet scientist J. Frenkel. 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 motion of individual nucleons is impossible and the nucleus is a drop of charged liquid with density. As in the case of an ordinary liquid droplet, the surface of the core can vibrate. If the amplitude of the oscillations becomes large enough, the process of nuclear fission occurs. The drop model made it possible to obtain a formula for the binding energy of nucleons in the nucleus, and explained the mechanism of some nuclear reactions. However, this model does not allow explaining most of the excitation spectra of atomic nuclei and the special stability of some of them. This is due to the fact that the hydrodynamic model very approximately reflects the essence of the internal structure of the nucleus.

Shell core model developed in 1940-1950 by the American physicist M. Goeppert - Mayer and the German physicist H. Jensen. It assumes that each nucleon moves independently of the others in some average potential field (potential well created by the rest of the nucleons in the nucleus. Within the framework of the shell model, the function is not calculated, but is selected so that the best agreement with experimental data can be achieved.

The depth of the potential pit is usually ~ (40-50) MeV and does not depend on the number of nucleons in the nucleus. In accordance with quantum theory, nucleons in a field are at certain discrete energy levels. The main assumption of the creators of the shell model about the independent motion of nucleons in the mean potential field is in contradiction with the main provisions of the developers of the hydrodynamic model. Therefore, the characteristics of the nucleus, which are well described by the hydrodynamic model (for example, the value of the binding energy), cannot be explained within the framework of the shell model, and vice versa.

Generalized kernel model , developed in 1950-1953, combines the main provisions of the creators of the 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 nucleons of the 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 the hydrodynamic model, and the motion of the outer nucleons is described by the shell model. Due to the interaction with external nucleons, the core can be deformed, and the nucleus can rotate around an axis perpendicular to the deformation axis. The generalized model made it possible to explain the main features of the rotational and vibrational spectra of atomic nuclei, as well as the high values \u200b\u200bof the quadrupole electric moment in some of them.

We have considered the main phenomenological, i.e. descriptive, kernel models. However, to fully understand the nature of nuclear interactions that determine the properties and structure of the nucleus, it is necessary to create a theory in which the nucleus would be considered as a system of interacting nucleons.