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 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 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. 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 away from each other would be many millions of times stronger than any gravitational forces pulling them together to a friend. 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 is clear that neutrons play 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 lifespan of nuclei - near it, the lifespan of nuclei is millions of years or more, as you move further into the blue, brown or yellow areas ( different colors corresponds to different mechanisms of nuclear decay) their lifetime becomes increasingly shorter, down to fractions 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 "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; uncertainty principle 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 those who keep them from falling apart atomic nucleus Nuclear forces are very important and large for protons and neutrons that are very close apart, but over a certain distance (called the "range" of force), they fall very quickly, much faster than electromagnetic forces. 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 attractive force (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.
Inside the kernel there are:
1) electrical repulsive forces between protons and
2) nuclear forces between nucleons (repulsion - at small distances and attraction - at large distances).
It has been established that nuclear forces are the same for both types of nucleons. The nuclear attraction between protons significantly exceeds the electrical repulsion, as a result of which the proton is firmly held within the nucleus.
The core is surrounded by a potential barrier caused by nuclear forces. Escape from the nucleus of a nucleon and a system of nucleons (for example, alpha particles) is possible either through the “tunnel effect” or by receiving energy from the outside. In the first case, spontaneous radioactive decay of the nucleus occurs, in the second - a forced nuclear reaction. Both processes allow some judgments to be made about the size of the nucleus. Valuable information about the extent of the potential barrier around nuclei was obtained by studying the scattering of various bombarding particles by nuclei - electrons, protons, neutrons, etc.
Research has shown that the nuclear forces of attraction between nucleons decrease very quickly with increasing distance between them. The average radius of action of nuclear forces, which can be interpreted in the same way as a certain conditional (“effective”) size of the nucleus, based on experimental data is expressed by the evaluation formula
If we assume that nuclei with a large number of nucleons consist of a core, where particles are uniformly distributed throughout the volume, and a spherical shell, in which the particle density decreases to zero towards the boundaries of the nucleus, then in this case
These formulas show that the “effective” volume of a nucleus is directly proportional to the number of nucleons; therefore, nucleons in all nuclei are packed on average with almost the same density.
The density of nuclei is very high; for example, a nucleus with mass has a radius
State of the nucleon in various places inside the nucleus can be characterized by the amount of energy that must be expended to extract this nucleon from the nucleus. It is called the binding energy of a given nucleon in the nucleus. In general, this energy is different for protons and neutrons and may depend on where in the volume of the nucleus a given nucleon is located.
The interaction of nucleons in the nucleus can be compared with a similar interaction of atoms in the crystal lattices of metals, where
Electrons play a significant role as “interaction transmitters.”
The difference is that in nuclei the “transmitters of interaction” between nucleons are heavier particles - pi-mesons (or pions), whose mass is 273 times greater than the mass of the electron. It is believed that nucleons continuously generate and absorb pi mesons according to the scheme
so that each nucleon is surrounded by a cloud of virtual pi mesons. Inside the nucleus, where particles are at relatively small distances from each other, the pi-meson cloud actively participates in nuclear processes, causing interaction and mutual transformations of nucleons.
Introduction
The hydrogen atom is the simplest in structure. As is known, a hydrogen atom has a nucleus consisting of one proton and one electron located in the 1s orbital. Since the proton and electron have opposite charges, the Coulomb force acts between them. It is also known that the nuclei of atoms have their own magnetic moment and therefore their own magnetic field. When charged particles move in a magnetic field, they are subject to the Lorentz force, which is directed perpendicular to the particle velocity vector and the magnetic induction vector. Obviously, the Coulomb force and the Lorentz force are not enough; in order for the electron to remain in its orbital, a repulsion force between the electron and the proton is also necessary. Modern quantum concepts do not give a clear answer as to what exactly causes the quantization of orbitals and, consequently, the energies of an electron in an atom. Within the framework of this article, we will consider the reasons for quantization and obtain equations describing the behavior of an electron in an atom. Let me remind you that according to modern concepts, the position of an electron in an atom is described by the probabilistic Schrödinger equation. We will obtain a purely mechanical equation, which will make it possible to determine the position of the electron at any time, which will show the inconsistency of the Heisenberg principle.
Balance of power
Figure 1 shows all the forces that act in an atom.
Figure 1 – forces acting on an electron in a hydrogen atom
Let's write down Newton's second law for the system of forces shown in the figure.
Let us write down a system of equations for the projections of these forces onto the XYZ coordinate axes.
(2)
Here the angle is the angle between the radius vector r(t) and the XY plane,
angle – the angle between the X axis and the projection of the radius vector r(t) onto the XY plane.
Let us write each force in system (2) through known formulas, taking into account their projections on the axis.
Coulomb force
, (3)
where is the electrical constant equal to
– electron or proton charge modulus
– electron coordinates in the selected coordinate system
Potential strength of gravitational waves
More information about this force can be found in the monograph
(4)
are the masses of the electron and proton, respectively.
X– The proportionality coefficient is numerically equal to the square of the speed of light.
As you know, the Lorentz force is calculated as follows
The vector product (5) can be represented in components on an axis orthogonal to the coordinate system:
(6)
In the system of equations (6), it is necessary to determine the components of the magnetic induction vector 
.
Since the magnetic moment of the nucleus of a hydrogen atom is caused by the ring current of truly elementary particles moving in it, then in accordance with the Biot-Savart-Laplace law obtained for a ring with current, we write down the components of the magnetic induction vector:
(7)
angle is the angle around the circular contour
– proton radius
– current strength in the proton ring circuit
– magnetic constant
As is known, centrifugal force acts normal to the trajectory of a body and depends on the mass of the body, the curvature of the trajectory and the speed of movement.
– instantaneous curvature of the trajectory
– electron speed relative to the origin
– normal vector to the electron trajectory
The instantaneous curvature of the trajectory is determined by the expression
– the first and second derivatives of the radius vector with respect to time.
The speed of an electron is the root of the sum of the squares of its projections on the coordinate axes, which in turn are the first derivatives of the projections of the radius vector with respect to time, i.e.
The unit normal vector to the electron trajectory is determined by the expression
(11)
Expanding the vector products through the vector components on the coordinate axis, writing the radius vector through its components, we substitute expressions (9), (10) and (11) into (8), we obtain the components of the centrifugal force in projections on the coordinate axes:
(12)
Having determined the projections of all forces included in the system of equations (2), it can be rewritten taking into account the following expressions:
The resulting system looks like:
It is not possible to find an analytical solution to this system. The solution can be obtained by numerical methods for solving systems of second-order differential equations. The solution is given in the video below.
The energy levels of an electron are determined by a whole number of resonant standing waves (a train of antinodes behind the electron) that arise along the trajectory of the electron. If the energy of a photon absorbed by an electron corresponds to the energy necessary to form a whole number of standing waves, the movement of the electron in them is repeated, making them resonant, thereby the photon is held by the electron for a certain time and we observe a picture of the electron’s absorption of the photon and then its emission. Photons whose energy does not lead to the appearance of a whole number of antinodes along the trajectory of the electron are not captured, because no resonant wave is formed and no absorption-emission pattern is observed.
