Atomic nucleus. Atomic nucleus: composition, characteristics, models, nuclear forces
Long before the appearance of reliable data about the internal structure of all things, Greek thinkers imagined matter in the form of tiny fiery particles that were in constant motion. Probably this vision of the world order of things was derived from purely logical conclusions. Despite some naivety and the absolute lack of evidence of this statement, it turned out to be true. Although scientists were able to confirm this bold guess only twenty-three centuries later.
Atomic structure
IN late XIX century, the properties of a discharge tube through which current was passed were studied. Observations have shown that two streams of particles are emitted:
The negative particles of cathode rays were called electrons. Subsequently, particles with the same charge-to-mass ratio were discovered in many processes. Electrons seemed to be universal components of various atoms, quite easily separated when bombarded by ions and atoms.
Particles carrying a positive charge were represented as fragments of atoms after they had lost one or more electrons. In fact positive rays were groups of atoms devoid of negative particles and, as a result, having a positive charge.
Thompson model
Based on experiments, it was found that positive and negative particles represented the essence of the atom and were its components. The English scientist J. Thomson proposed his theory. In his opinion, the structure of the atom and the atomic nucleus was a kind of mass in which negative charges were squeezed into a positively charged ball, like raisins into a cupcake. Charge compensation made the “cupcake” electrically neutral.
Rutherford model
The young American scientist Rutherford, analyzing the tracks left behind by alpha particles, came to the conclusion that Thompson’s model was imperfect. Some alpha particles were deflected at small angles - 5-10 o. IN in rare cases alpha particles were deflected at large angles of 60-80 o, and in exceptional cases the angles were very large - 120-150 o. Thompson's model of the atom could not explain the difference.
Rutherford suggests new model, explaining the structure of the atom and the atomic nucleus. The physics of the process states that an atom should be 99% empty, with a tiny nucleus and electrons rotating around it, moving in orbits.
He explains deviations during impacts by the fact that the particles of an atom have their own electrical charges. Under the influence of bombarding charged particles, atomic elements behave like ordinary charged bodies in the macrocosm: particles with the same charges repel each other, and those with opposite charges attract.
State of atoms
At the beginning of the last century, when the first accelerators were launched elementary particles, all theories that explained the structure of the atomic nucleus and the atom itself were awaiting experimental verification. By that time, the interactions of alpha and beta rays with atoms had already been thoroughly studied. Up until 1917, it was believed that atoms were either stable or radioactive. Stable atoms cannot be split, and the decay of radioactive nuclei cannot be controlled. But Rutherford managed to refute this opinion.
First proton
In 1911, E. Rutherford put forward the idea that all nuclei consist of identical elements, the basis for which is the hydrogen atom. The scientist was prompted to this idea by an important conclusion from previous studies of the structure of matter: the masses of all chemical elements are divided without remainder by the mass of hydrogen. The new assumption opened up unprecedented possibilities, allowing us to see the structure of the atomic nucleus in a new way. Nuclear reactions were supposed to confirm or refute the new hypothesis.
Experiments were carried out in 1919 with nitrogen atoms. By bombarding them with alpha particles, Rutherford achieved an amazing result.
The N atom absorbed an alpha particle, then turned into an oxygen atom O 17 and emitted a hydrogen nucleus. This was the first artificial transformation of an atom of one element into another. Such an experience gave hope that the structure of the atomic nucleus and the physics of existing processes make it possible to carry out other nuclear transformations.
The scientist used the scintillation flash method in his experiments. Based on the frequency of flares, he drew conclusions about the composition and structure of the atomic nucleus, the characteristics of the generated particles, their atomic mass and atomic number. The unknown particle was called the proton by Rutherford. It had all the characteristics of a hydrogen atom stripped of its single electron - a single positive charge and corresponding mass. Thus, it was proven that the proton and the hydrogen nucleus are the same particles.
In 1930, when the first large accelerators were built and launched, Rutherford's model of the atom was tested and proven: each hydrogen atom consists of a lone electron, the position of which cannot be determined, and a loose atom with a lone positive proton inside. Since protons, electrons and alpha particles can fly out of an atom during bombardment, scientists thought that these were the components of any atomic nucleus. But such a model of the atom of the nucleus seemed unstable - the electrons were too large to fit in the nucleus, in addition, there were serious difficulties associated with the violation of the law of momentum and conservation of energy. These two laws, like strict accountants, said that momentum and mass during a bombardment disappear in an unknown direction. Since these laws were generally accepted, it was necessary to find explanations for such a leak.
Neutrons
Scientists around the world conducted experiments aimed at discovering new components of atomic nuclei. In the 1930s, German physicists Becker and Bothe bombarded beryllium atoms with alpha particles. At the same time, unknown radiation was recorded, which it was decided to call G-rays. Detailed Research talked about some of the features of the new rays: they could propagate strictly in a straight line, did not interact with electrical and magnetic fields, had high penetrating ability. Later, the particles that form this type of radiation were found during the interaction of alpha particles with other elements - boron, chromium and others.
Chadwick's conjecture
Then James Chadwick, Rutherford's colleague and student, gave a short message in the journal Nature, which later became generally known. Chadwick drew attention to the fact that contradictions in conservation laws can be easily resolved if we assume that the new radiation is a stream of neutral particles, each of which has a mass of approximately equal to mass proton. Considering this assumption, physicists significantly expanded the hypothesis that explains the structure of the atomic nucleus. Briefly, the essence of the additions was reduced to a new particle and its role in the structure of the atom.
Properties of the neutron
The discovered particle was given the name “neutron”. The newly discovered particles did not form electromagnetic fields around themselves and easily passed through matter without losing energy. In rare collisions with light atomic nuclei, a neutron is able to knock the nucleus out of the atom, losing a significant part of its energy. The structure of the atomic nucleus assumed the presence of a different number of neutrons in each substance. Atoms with the same nuclear charge but different numbers of neutrons are called isotopes.
Neutrons served an excellent replacement alpha particles. Currently, they are used to study the structure of the atomic nucleus. It is impossible to briefly describe their significance for science, but it is thanks to neutron bombardment atomic nuclei physicists were able to obtain isotopes of almost all known elements.
Composition of the nucleus of an atom
Currently, the structure of the atomic nucleus is a collection of protons and neutrons held together by nuclear forces. For example, a helium nucleus is a lump of two neutrons and two protons. Light elements have almost equal number protons and neutrons; heavy elements have a much larger number of neutrons.
This picture of the structure of the nucleus is confirmed by experiments at modern large accelerators with fast protons. The electrical repulsive forces of protons are balanced by nuclear forces, which act only in the nucleus itself. Although the nature of nuclear forces has not yet been fully studied, their existence is practically proven and completely explains the structure of the atomic nucleus.
Relationship between mass and energy
In 1932, the Wilson's camera captured an amazing photograph proving the existence of positively charged particles with the mass of an electron.
Prior to this, positive electrons were predicted theoretically by P. Dirac. A real positive electron was also discovered in cosmic radiation. The new particle was called a positron. When colliding with its double - an electron, annihilation occurs - the mutual destruction of two particles. This frees up a certain amount energy.
Thus, the theory developed for the macrocosm was fully suitable for describing the behavior of the smallest elements of matter.
An atom consists of a positively charged nucleus and electrons surrounding it. Atomic nuclei have dimensions of approximately 10 -14 ... 10 -15 m (the linear dimensions of an atom are 10 -10 m).
The atomic nucleus consists of elementary particles - protons and neutrons. The proton-neutron model of the nucleus was proposed by the Russian physicist D. D. Ivanenko, and subsequently developed by W. Heisenberg.
Proton ( r) has a positive charge equal to the electron charge and a rest mass T p =
1.6726∙10 -27 kg 1836 m e, Where m eelectron mass. Neutron ( n) – neutral particle with rest mass m n= 1.6749∙10 -27 kg 
1839T e ,.
The mass of protons and neutrons is often expressed in another unit - atomic mass units (amu, a unit of mass equal to 1/12 the mass of a carbon atom 
). The masses of a proton and a neutron are approximately one atomic mass unit. Protons and neutrons are called nucleons(from lat. nucleuscore). The total number of nucleons in an atomic nucleus is called the mass number A).
The radii of the nuclei increase with increasing mass number according to the ratio R= 1,4A 1/3 10 -13 cm.
Experiments show that nuclei do not have sharp boundaries. At the center of the nucleus there is a certain density of nuclear matter, and it gradually decreases to zero with increasing distance from the center. Due to the lack of a clearly defined boundary of the nucleus, its "radius" is defined as the distance from the center at which the density of nuclear matter is halved. The average matter density distribution for most nuclei turns out to be more than just spherical. Most of the nuclei are deformed. Often the nuclei have the shape of elongated or flattened ellipsoids
The atomic nucleus is characterized chargeZe, Where Zcharge number nucleus, equal to the number of protons in the nucleus and coinciding with the serial number of the chemical element in Mendeleev’s Periodic Table of Elements.
The nucleus is denoted by the same symbol as the neutral atom: 
, Where X- symbol of a chemical element, Zatomic number (number of protons in the nucleus), Amass number (number of nucleons in the nucleus). Mass number A approximately equal to the mass of the nucleus in atomic mass units.
Since the atom is neutral, the nuclear charge is Z determines the number of electrons in an atom. Their distribution among states in an atom depends on the number of electrons. The charge of the nucleus determines the specifics of a given chemical element, i.e. it determines the number of electrons in the atom and their configuration electronic shells, magnitude and nature of the intraatomic electric field.
Nuclei with the same charge numbers Z, but with different mass numbers A(i.e. with different numbers of neutrons N = A – Z), are called isotopes, and nuclei with the same A, but different Z – isobars. For example, hydrogen ( Z= l) has three isotopes: N – protium ( Z= l, N= 0),
N – deuterium ( Z= l, N= 1),
N – tritium ( Z= l, N= 2), tin - ten isotopes, etc. In the vast majority of cases, isotopes of the same chemical element have the same chemical and almost identical physical properties.
E, MeV
Energy levels
and observed transitions for the boron atomic nucleus
Quantum theory strictly limits the energies that the constituent parts of nuclei can possess. Collections of protons and neutrons in nuclei can only be in certain discrete energy states characteristic of a given isotope.When an electron goes from a higher to a lower energy state, the energy difference is emitted as a photon. The energy of these photons is on the order of several electron volts. For nuclei, the level energies lie in the range from approximately 1 to 10 MeV. During transitions between these levels, photons of very high energies (γ quanta) are emitted. To illustrate such transitions in Fig. 6.1 shows the first five levels of nuclear energy 
.Vertical lines indicate observed transitions. For example, a γ-quantum with an energy of 1.43 MeV is emitted when a nucleus transitions from a state with an energy of 3.58 MeV to a state with an energy of 2.15 MeV.
Atomic nucleus
Atomic nucleus
Atomic nucleus
- the central and very compact part of the atom, in which almost all of its mass and all the positive electric charge are concentrated. The nucleus, holding electrons close to itself by Coulomb forces in an amount that compensates for its positive charge, forms a neutral atom. Most nuclei have a shape close to spherical and a diameter of ≈ 10 -12 cm, which is four orders of magnitude smaller than the diameter of an atom (10 -8 cm). The density of the substance in the core is about 230 million tons/cm 3 .
The atomic nucleus was discovered in 1911 as a result of a series of experiments on the scattering of alpha particles by thin gold and platinum foils, carried out in Cambridge (England) under the direction of E. Rutherford. In 1932, after the discovery of the neutron there by J. Chadwick, it became clear that the nucleus consists of protons and neutrons
(V. Heisenberg, D.D. Ivanenko, E. Majorana).
To designate an atomic nucleus, the symbol of the chemical element of the atom that includes the nucleus is used, and the upper left index of this symbol shows the number of nucleons (mass number) in this nucleus, and the lower left index shows the number of protons in it. For example, a nickel nucleus containing 58 nucleons, of which 28 are protons, is designated . This same core can also be designated 58 Ni, or nickel-58.
The nucleus is a system of densely packed protons and neutrons moving at a speed of 10 9 -10 10 cm/sec and held by powerful and short-range nuclear forces of mutual attraction (their area of action is limited to distances of ≈ 10 -13 cm). Protons and neutrons are about 10 -13 cm in size and are considered two different states of a single particle called a nucleon. The radius of the nucleus can be approximately estimated by the formula R ≈ (1.0-1.1)·10 -13 A 1/3 cm, where A is the number of nucleons (the total number of protons and neutrons) in the nucleus. In Fig. Figure 1 shows how the density of matter changes (in units of 10 14 g/cm 3) inside a nickel nucleus, consisting of 28 protons and 30 neutrons, depending on the distance r (in units of 10 -13 cm) to the center of the nucleus.
Nuclear interaction(interaction between nucleons in the nucleus) arises due to the fact that nucleons exchange mesons. This interaction is a manifestation of the more fundamental strong interaction between the quarks that make up nucleons and mesons ( in a similar way chemical bonding forces in molecules are a manifestation of more fundamental electromagnetic forces).
The world of nuclei is very diverse. About 3000 nuclei are known, differing from each other either in the number of protons, or in the number of neutrons, or both. Most of them are obtained artificially.
Only 264 cores are stable, i.e. do not experience any spontaneous transformations over time, called decays. Others experience various shapes decay – alpha decay (emission of an alpha particle, i.e. the nucleus of a helium atom); beta decay (simultaneous emission of an electron and an antineutrino or a positron and a neutrino, as well as the absorption of an atomic electron with the emission of a neutrino); gamma decay (photon emission) and others.
Various types nuclei are often called nuclides. Nuclides with the same number of protons and different numbers neutrons are called isotopes. Nuclides with the same number nucleons, but different ratios of protons and neutrons are called isobars. Light nuclei contain approximately equal numbers of protons and neutrons. In heavy nuclei, the number of neutrons is approximately 1.5 times greater than the number of protons. The lightest nucleus is the nucleus of the hydrogen atom, consisting of one proton. The heaviest known nuclei (they are obtained artificially) have a number of nucleons of ≈290. Of these, 116-118 are protons.
Different combinations of the number of protons Z and neutrons correspond to different atomic nuclei. Atomic nuclei exist (i.e. their lifetime t > 10 -23 s) in a rather narrow range of changes in the numbers Z and N. In this case, all atomic nuclei are divided into two large groups- stable and radioactive (unstable). Stable nuclei are grouped near the line of stability, which is determined by the equation
|
Rice. 2. NZ diagram of atomic nuclei. |
In Fig. Figure 2 shows the NZ diagram of atomic nuclei. Black dots indicate stable nuclei. The region where stable nuclei are located is usually called the valley of stability. On the left side of stable nuclei there are nuclei overloaded with protons (proton-rich nuclei), on the right - nuclei overloaded with neutrons (neutron-rich nuclei). Currently discovered atomic nuclei are highlighted in color. There are about 3.5 thousand of them. It is believed that there should be 7–7.5 thousand in total. Proton-rich nuclei (raspberry color) are radioactive and turn into stable ones mainly as a result of β + decays; the proton included in the nucleus is converted into a neutron. Neutron-rich nuclei (blue color) are also radioactive and turn into stable ones as a result of - - decays, with the transformation of the neutron of the nucleus into a proton.
The heaviest stable isotopes are those of lead (Z = 82) and bismuth (Z = 83). Heavy nuclei, along with the processes of β + and β - decay, are also subject to α-decay ( yellow) and spontaneous fission, which become their main decay channels. The dotted line in Fig. 2 outlines the region of possible existence of atomic nuclei. The line B p = 0 (B p is the energy of proton separation) limits the region of existence of atomic nuclei on the left (proton drip-line). Line B n = 0 (B n – neutron separation energy) – on the right (neutron drip-line). Outside these boundaries, atomic nuclei cannot exist, since they decay during the characteristic nuclear time (~10 -23 – 10 -22 s) with the emission of nucleons.
When two light nuclei combine (synthesis) and divide a heavy nucleus into two lighter fragments, large amounts of energy are released. These two methods of obtaining energy are the most effective of all known. So 1 gram of nuclear fuel is equivalent to 10 tons of chemical fuel. Nuclear fusion (thermonuclear reactions) is the source of energy for stars. Uncontrolled (explosive) fusion occurs when a thermonuclear (or so-called “hydrogen”) bomb is detonated. Controlled (slow) fusion underlies a promising energy source under development - a thermonuclear reactor.
Uncontrolled (explosive) fission occurs when an atomic bomb explodes. Controlled division is carried out in nuclear reactors, which are energy sources in nuclear power plants.
Quantum mechanics and various models are used to theoretically describe atomic nuclei.
The nucleus can behave both as a gas (quantum gas) and as a liquid (quantum liquid). Cold nuclear liquid has superfluid properties. In a highly heated nucleus, nucleons decay into their constituent quarks. These quarks interact by exchanging gluons. As a result of this decay, the collection of nucleons inside the nucleus turns into a new state of matter - quark-gluon plasma
Core charge
The nucleus of any atom is positively charged. The carrier of positive charge is the proton. Since the charge of a proton is numerically equal to the charge of an electron $e$, we can write that the charge of the nucleus is equal to $+Ze$ ($Z$ is an integer that indicates the serial number of a chemical element in D. I. Mendeleev’s periodic system of chemical elements). The number $Z$ also determines the number of protons in the nucleus and the number of electrons in the atom. Therefore it is called the atomic number of the nucleus. Electric charge is one of the main characteristics of the atomic nucleus, on which the optical, chemical and other properties of atoms depend.
Core mass
Another important characteristic the nucleus is its mass. The mass of atoms and nuclei is usually expressed in atomic mass units (amu). for atomic unit The mass is usually considered to be $1/12$ of the mass of the carbon nuclide $^(12)_6C$:
where $N_A=6.022\cdot 10^(23)\ mol^-1$ is Avogadro's number.
According to Einstein's relation $E=mc^2$, the mass of atoms is also expressed in energy units. Because:
- proton mass $m_p=1.00728\ amu=938.28\ MeV$,
- neutron mass $m_n=1.00866\ amu=939.57\ MeV$,
- electron mass $m_e=5.49\cdot 10^(-4)\ amu=0.511\ MeV$,
As you can see, the mass of the electron is negligibly small in comparison with the mass of the nucleus, then the mass of the nucleus almost coincides with the mass of the atom.
Mass is different from whole numbers. Nuclear mass, expressed in amu. and rounded to a whole number is called the mass number, denoted by the letter $A$ and determines the number of nucleons in the nucleus. The number of neutrons in the nucleus is $N=A-Z$.
To designate nuclei, the symbol $^A_ZX$ is used, where $X$ means the chemical symbol of a given element. Atomic nuclei with the same number of protons but different mass numbers are called isotopes. In some elements, the number of stable and unstable isotopes reaches tens, for example, uranium has $14$ isotopes: from $^(227)_(92)U\ $ to $^(240)_(92)U$.
Most chemical elements existing in nature are a mixture of several isotopes. It is the presence of isotopes that explains the fact that some natural elements have masses that differ from whole numbers. For example, natural chlorine consists of $75\%$ $^(35)_(17)Cl$ and $24\%$ $^(37)_(17)Cl$, and its atomic mass equal to $35.5$ a.m.u. in most atoms, except hydrogen, the isotopes have almost the same physical and chemical properties. But behind their exclusively nuclear properties, isotopes differ significantly. Some of them can be stable, others - radioactive.
Nuclei with the same mass numbers, but different meanings$Z$ are called isobars, for example, $^(40)_(18)Ar$, $^(40)_(20)Ca$. Nuclei with the same number of neutrons are called isotones. Among light nuclei there are so-called “mirror” pairs of nuclei. These are pairs of nuclei in which the numbers $Z$ and $A-Z$ are swapped. Examples of such nuclei can be $^(13)_6C\ $ and $^(13_7)N$ or $^3_1H$ and $^3_2He$.
Atomic nucleus size
Assuming the atomic nucleus to be approximately spherical, we can introduce the concept of its radius $R$. Note that in some nuclei there is a slight deviation from symmetry in the distribution electric charge. In addition, atomic nuclei are not static, but dynamic systems, and the concept of core radius cannot be represented as the radius of a ball. For this reason, the size of the nucleus must be taken as the area in which nuclear forces manifest themselves.
When creating the quantitative theory of scattering of $\alpha $ - particles, E. Rutherford proceeded from the assumptions that the atomic nucleus and $\alpha $ - particle interact according to Coulomb's law, i.e. What electric field around the core has spherical symmetry. The scattering of an $\alpha $ particle occurs in full accordance with Rutherford's formula:
This occurs for $\alpha $ - particles whose energy $E$ is quite small. In this case, the particle is not able to overcome the Coulomb potential barrier and subsequently does not reach the region of action of nuclear forces. As the particle energy increases to a certain boundary value $E_(gr)$ $\alpha $ -- the particle reaches this boundary. Then in the scattering of $\alpha $ - particles there is a deviation from the Rutherford formula. From the relation
Experiments show that the radius $R$ of the nucleus depends on the number of nucleons that enter the nucleus. This dependence can be expressed by the empirical formula:
where $R_0$ is a constant, $A$ is a mass number.
The sizes of nuclei are determined experimentally by proton scattering, fast neutrons or high energy electrons. There are a number of other indirect methods for determining the size of nuclei. They are based on the connection between the lifetime of $\alpha $ -- radioactive nuclei and the energy of $\alpha $ -- particles released by them; on the optical properties of so-called mesoatoms, in which one electron is temporarily captured by a muon; by comparing the binding energy of a pair of mirror atoms. These methods confirm the empirical dependence $R=R_0A^(1/3)$, and using these measurements the value of the constant $R_0=\left(1.2-1.5\right)\cdot 10^(-15) was established \ m$.
Note also that the unit of distance in atomic physics and particle physics is taken as the “Fermi” unit of measurement, which is equal to $(10)^(-15)\ m$ (1 f=$(10)^(-15)\ m )$.
The radii of atomic nuclei depend on their mass number and are in the range from $2\cdot 10^(-15)\ m\ to\\ 10^(-14)\ m$. if we express $R_0$ from the formula $R=R_0A^(1/3)$ and write it in the form $\left(\frac(4\pi R^3)(3A)\right)=const$, then we can see that each nucleon contains approximately the same volume. This means that the density of nuclear matter is approximately the same for all nuclei. Based on the existing data on the sizes of atomic nuclei, we find the average value of the density of nuclear matter:
As we can see, the density of nuclear matter is very high. This is due to the action of nuclear forces.
Energy of communication. Nuclear mass defect
When comparing the sum of the rest masses of the nucleons that form the nucleus with the mass of the nucleus, it was noticed that for all chemical elements the following inequality is true:
where $m_p$ is the mass of the proton, $m_n$ is the mass of the neutron, $m_я$ is the mass of the nucleus. The value $\triangle m$, which expresses the mass difference between the mass of nucleons that form the nucleus and the mass of the nucleus, is called the nuclear mass defect
Important information about the properties of the nucleus can be obtained without delving into the details of the interaction between the nucleons of the nucleus, based on the law of conservation of energy and the law of proportionality of mass and energy. Depending on how much as a result of any change in mass $\triangle m$ there is a corresponding change in energy $\triangle E$ ($\triangle E=\triangle mc^2$), then during the formation of a nucleus a certain amount of energy is released. According to the law of conservation of energy, the same amount of energy is needed to divide the nucleus into its constituent particles, i.e. move nucleons one from another at the same distances at which there is no interaction between them. This energy is called the binding energy of the nucleus.
If the nucleus has $Z$ protons and mass number $A$, then the binding energy is equal to:
Note 1
Note that this formula is not entirely convenient to use, because the tables do not list the masses of nuclei, but the masses that determine the masses of neutral atoms. Therefore, for the convenience of calculations, the formula is transformed in such a way that it includes the masses of atoms, not nuclei. For this purpose, on the right side of the formula we add and subtract the mass $Z$ of electrons $(m_e)$. Then
\c^2==\leftc^2.\]
$m_(()^1_1H)$ is the mass of the hydrogen atom, $m_a$ is the mass of the atom.
In nuclear physics, energy is often expressed in megaelectron volts (MeV). If we're talking about O practical application nuclear energy, it is measured in joules. In the case of comparing the energy of two nuclei, the mass unit of energy is used - the ratio between mass and energy ($E=mc^2$). A mass unit of energy ($le$) equals energy, which corresponds to a mass of one amu. It is equal to $931,502$ MeV.
Figure 1.
Besides the energy important has a specific binding energy - the binding energy that falls on one nucleon: $w=E_(st)/A$. This value changes relatively slowly compared to the change in the mass number $A$, having an almost constant value of $8.6$ MeV in the middle part of the periodic system and decreases to its edges.
As an example, let us calculate the mass defect, binding energy and specific binding energy of the nucleus of a helium atom.
Mass defect
Binding energy in MeV: $E_(bv)=\triangle m\cdot 931.502=0.030359\cdot 931.502=28.3\ MeV$;
Specific binding energy: $w=\frac(E_(st))(A)=\frac(28.3\ MeV)(4\approx 7.1\ MeV).$
ATOMIC NUCLEUS- the central massive part of an atom, consisting of protons and neutrons (nucleons). In Ya. a. almost the entire mass of the atom is concentrated (more than 99.95%). The dimensions of the kernels are about 10 -13 -10 -12 cm. The kernels have positive. electric , multiple of abs. electron charge value e: Q = Ze. The integer Z matches the ordinal number of the element in periodic table of elements. Ya. a. was discovered by E. Rutherford in 1911 in experiments on the scattering of alpha particles as they passed through matter.
Kernel composition. Soon after the discovery of the neutron, J. Chadwick (1932), D. D. Ivanenko and W. Heisenberg independently expressed the foundation. the assumption that Ya. a. consists of protons (p) and neutrons (n). The total number of nucleons in Ya. a. called mass A, the number of protons in the nucleus is equal to the nuclear charge Z, the number of neutrons N = A - Z. Nuclei with the same charges Z and different numbers of neutrons are called. isotopes, nuclei with different Z and the same N- isotonics, nuclei with the same A and different Z and N- and z o b a r a m i. According to modern In our opinion, a proton and a neutron consist of quarks And gluons and Ya. a.- complex system from a large number of gluon and meson fields interacting with each other. Consistent description of Ya. a. must be achieved within quantum chromodynamics. However, due to its complexity, this problem has not yet been solved.
The composite nature of nucleons manifests itself only in collisions with a large transfer of momentum and energy. At low excitation energies, such collisions in the nucleus are rare. Therefore, when describing Ya. a. And nuclear reactions, occurring at not too high energies (<= 1 ГэВ на нуклон), в первом приближении можно считать, что ядра
состоят из вполне определённого числа нуклонов, движущихся с нерелятивистскими
скоростями (u 2 /c 2 ~0,l). Quarks are “locked” each in their own nucleon. Nucleons do not lose their individuality and have approximately the same properties as in a free state (with some exceptions, see below). Proton-neutron picture of the structure of nuclear a. is approximate and is violated at high excitation energies and in processes with large transfer of momentum and energy.
Under ordinary conditions, deviations from the proton-neutron model associated with the composite nature of nucleons and the quark-gluon structure of nuclear particles are small and are as follows. 1) As a result of the interaction between nucleons, the latter can exist in nuclear a. not only in the main, but also in excited states, called. sloping shapes. The lowest of them in terms of energy is the so-called. D-isobar (see Resonances).Part of the time (~ 1%) nucleons in the nucleus can reside in the form of nucleon isobars. 2) The locking of quarks in nucleons is not absolute; clumps of quark-gluon matter can form in the nucleus for a short time ( fluctons), consisting of 6, 9, etc. quarks (see. Quark-gluon plasma).3) The properties of nucleons bound in a nucleus may differ from the properties of free nucleons. As experiments on deep inelastic scattering show (see Deeply inelastic processes) leptons on nuclei, the structural functions of nucleons in the nucleus, which characterize the distribution of quarks over momentum in a nucleon, differ from the structural functions of free nucleons (EMC effect - European Muon Collaboration, CERN, 1982). One of the possible explanations for the EMC effect is based on the hypothesis that the nucleon radius in the nucleus increases compared to a free nucleon. 4) Periodically appear in the kernels for a period of 10 -23 -10 -24 s (virtual) mesons, incl. pi mesons.Investigation of non-nucleon degrees of freedom of the nucleus - basic. modern subject research in relativistic nuclear physics.
Nuclear forces. Nucleons are hadrons, i.e. they belong to the number of particles experiencing strong interaction. The interaction between nucleons that holds them in the nucleus, i.e. nuclear forces, arises as a result of the interaction between the constituent parts (quarks, glu-ons), which form nucleons. The theory of nuclear forces based on quark concepts is in its infancy and has not yet been completed.
The traditional meson theory of nuclear forces is based on an idea proposed in 1935 by H. Yukawa. According to the meson theory, the interaction between nucleons is carried out through the exchange of mesons. characterized by range; it is determined Compton wavelength mesons, with which nucleons are exchanged, where m is the meson mass. Naib. the radius of action are the forces of attraction due to the exchange of π-mesons. For them l c = 1.41 fm (1 fm = 10 -13 cm). This corresponds to the distance between nucleons in nuclei. The exchange of heavier mesons (r, w, etc.) affects the interaction between nucleons at shorter distances, causing, in particular, repulsion between them at distances<=0,4 Фм.
Kernel sizes depend on the number of nucleons in the nucleus and vary from 10 -13 to 10 -12 cm. Experiment. data shows that avg. nucleons (the number of nucleons per unit volume) is almost the same in all nuclei with A>= 20. This means that the volume of the nucleus is proportional A, and its radius R proportional A 1/3 :
where is the constant A close to the range of nuclear forces. The charge radius of the nucleus is distinguished, i.e. cf. the radius of distribution of protons in the nucleus, and the radius of distribution of nuclear matter (radius of distribution of nucleons, regardless of their type). The first is measured in experiments with electromagnetic interaction(scattering of high-energy electrons on nuclei, study of levels muonic atoms), which gives the value A=1.12 fm; the second - in nuclear reactions involving (scattering of nucleons, a-particles, interaction of p- and K-mesons with nuclei, etc.). In this case, a slightly higher value is obtained a = 1.2-1.4 fm. Wed. the density of nuclear matter is very high and amounts to ~ 10 14 g/cm 3 .
Experiments on the scattering of fast electrons by nuclei made it possible not only to determine the avg. the size of the nucleus, but also to study in detail the charge distribution r( r) in the nucleus. Let's experiment. the results are in better agreement not with a uniform charge distribution in the nucleus, but with the so-called. Fermi distribution:
Where R 0
= 1,1 A 1/3 fm. This distribution shows that the charge density is almost constant in the interior. areas ( r
Binding energy and nuclear mass. The binding energy of the nucleus is called. energy that must be expended to split the nucleus into parts. nucleons. It is equal to multiplied by With 2 differences between the total mass of all nucleons that make up the nucleus and the mass M the kernel itself:
Here T p, T n - masses of proton and neutron. The binding energy of the nucleus is approximately proportional. number of nucleons in the nucleus, and beat. binding energy /A almost constant (for most kernels / A~ 6-8 MeV). This property, called saturation of nuclear forces, means that a nucleon in a nucleus effectively interacts not with all nucleons of the nucleus, but only with a certain limited number of them (otherwise case, the binding energy would be proportional. A).
Constancy of density and beat. the binding energy of the nucleus brings the properties of the nucleus closer to the properties of the liquid. This similarity formed the basis for the model of the nucleus as a liquid drop ( droplet model of the nucleus), based on the cut of K. F. von Weizsacker (S. F. von Weizsacker) in 1935 proposed a semi-empirical. f-lu ( Weizsäcker formula) for the binding energy of the nucleus:
Here the first term describes the volumetric energy of the “drop”, the second characterizes the weakening of the bond for nucleons located on the surface of the nucleus, the third term describes the contribution of the Coulomb energy of a drop with a radius R~A 1/3 and with charge Z. The fourth term (the so-called energy symmetry) does not have a classical analogue and reflects the fact that the attraction between nucleons of different types in avg. stronger than for identical nucleons. This is along with Pauli principle makes it energetically unfavorable. deviation N from Z. The fifth member is called ENERGY OF SPARING:
It reproduces the experimental fact that even-even nuclei ( Z And N even) are connected more strongly than neighboring even-odd ones, and the latter, in turn, are more stable than odd-even nuclei.
Modern Weizsäcker parameter values: b 1 =
15.75 MeV, b 2 = 17.8 MeV, b 3 = 0.71 MeV, b 4 = 23.7 MeV. F-la (4) on Wed. describes the binding energies of nuclei well, limits the value Z 2 /A~ 46 region of existence of nuclei that are resistant to fission. However, it does not take into account the individual characteristics of the shell structure of the nucleus. These effects can be taken into account by the Strutinsky shell correction method, which predicts the possibility of the existence of the so-called. Island of stability of superheavy nuclei at Z~114 (see Transuranic elements).
Quantum characteristics of nuclear levels. Ya. a. at energies below the decay threshold (with the emission of a nucleon, a-particle, etc.) can only be in discrete states with a certain definition. energy, characterized by a set of quantum numbers that specify the values of conserved quantities (integrals of motion) in these states. Above the nuclear decay threshold, discrete states become nonstationary and appear in nuclear reactions as resonances of finite width.
Naib. important characteristics of nuclear states are the spin of the nucleus (or the angular momentum of the nucleus, also called the angular momentum of the nucleus) I and parity p = +
1. Spin / is measured in units and takes half-integer values ( I= 1 / 2, 3 / 2, ...) Odd kernels also have integer values ( I=0, 1, 2, ....) for even nuclei. Parity p indicates the symmetry of the wave function y of the nuclear state relative to the mirror reflection of space R(cm. Spatial inversion): P y = py. In this regard, a combined characteristic is indicated for nuclear states I p. It has been empirically established that the main states of even-even nuclei have the characteristic 0 + . The spins and parities of odd nuclei are usually explained by the shell model (see below). Strictly speaking, parity is not an exact quantum number, since it is not conserved when weak interaction. Due to strength electroweak interaction between nucleons there is a mixing of states with the same spin I and opposite parities. However, due to the smallness of the forces violating parity, this mixing is small and can be neglected when considering the spectra of nuclear levels of various nuclear reactions and transitions, with the exception of processes aimed specifically at studying the phenomenon non-conservation of parity in kernels.
Another important, although approximate, nuclear characteristic is isotopic spin(or isobaric spin) T, which is made up of isospins dept. nucleons according to the same rules as ordinary spin. The conservation of this value is associated with isotopic invariance nuclear forces, the edge is that nuclear interactions between two nucleons in identical spaces. and spin states do not depend on the type of nucleons, i.e. they are the same in pairs pp, pp and pp. Isotopic spin (isospin) can take values T>=(N-Z)/ 2, integers for even kernels and half-integers for odd ones. Like a regular spin, it also has a fixed projection onto one of the formal isospin axes. space T Z = (A - 2Z)/2. It is related to the charge of the nucleus and is therefore a strictly conserved quantity in all nuclear states. In contrast, isospin T is an approximate quantum number. Isospin violation (i.e. mixing of components with different values T in the wave function of the nuclear state) is due to the difference in the masses of the proton and neutron, as well as the Coulomb interaction between protons. In light nuclei with Z<=20 эти эффекты малы и изоспин T is a fairly accurate quantum number. As a result, nuclear states can be characterized by quantum numbers T And TZ,a states with the same values I p, T in neighboring isobar nuclei, combine into isotopic mul tiplets. Since the projection of isoepin takes on the values T Z =T, T-1, ...., - T, then in isotopic multi-pleth included 2 T+ 1 levels.
It has been experimentally established that the higher the isospin, the higher the excitation energy of the nuclear state. Therefore, basically kernel state T= T Z and for even-even nuclei with Z=N T= 0. Cores with T= 1/2 and T Z = b 1/2 form isodoublet (for example, 3 H - 3 He). An example of an isotriplet is basic. state 0 + ( T=1, T Z = 1) nuclei 6 He, excited state 0 + ( T= 1, T Z = 0
)nuclei 6 Li
(excitation energy 3.56 MeV) and basic. state of the 6 Be nucleus ( T= 1, T Z =-1)
. In nuclear physics it is customary to assign isospin to the nucleon T= 1/2 and values T Z = 1/2 neutron, T Z =- 1/2 to a proton, in contrast to particle physics, where opposite signs of nucleon isospin projections are used. This is done for reasons of convenience so that the values T Z were positive for stable nuclei, in which N>Z.
States of nuclei that make up one isotopic. multiplet, called analog states. Due to the isotopic invariance of nuclear forces, the structure (purely nuclear) of these states is the same, and all differences in their properties are due to el-magn. interaction. For example, the binding energies of analog states are identical up to the difference in the Coulomb energies in the nuclei of a given multiplet. As Z increases, the role of the Coulomb interaction increases. Therefore, in heavy nuclei, the accuracy of isoepine as a quantum number decreases. Nevertheless, traces of isospin symmetry are manifested in the fact that in decomp. In nuclear reactions, states discovered in 1961 are observed that are unstable with respect to the emission of a nucleon, which are analogues of the ground or lower stable excited states of a neighboring nucleus with a lower Z (analog resonance s). For example, when protons are scattered on a stable nucleus A with numbers of neutrons and protons N And Z(T 0 = T Z = (N-Z)/ 2
)resonances are observed corresponding to the formation compound nucleus A+ 1 (Z+l, N)in an excited state with quantum numbers T=T 0 +
1 / 2 , T Z =T 0 - 1/2, included in the same isotopic. multiplet as the main one. state of the neighboring nucleus A+ 1(N+ 1, Z), T=T Z =T 0 +
1/2. However, experiments have shown that analog resonances have a fine structure, indicating that mixing of the analog state characterized by isospin takes place T 0 + 1 / 2 with other excited states of the compound nucleus corresponding to isospin T=T 0
- 1 / 2 .
Electric and magnetic moments of nuclei. In each of the possible states of Ya. a. has a certain magnetic values dipole moment and quadrupole electric moment (see. Quadrupole moment of the nucleus). Static mag. the moment can be different from 0 only in the case when the spin of the nuclear state I 0, and static. The quadrupole moment can have a non-zero value only when I> 1/2. Nuclear state with definition. parity cannot have a non-zero electric. dipole moment ( E 1)
, as well as other electrical moments E l odd multipole l and static. mag. moments M l even multipole l. The existence of a non-zero electric dipole moment E 1 is also prohibited by invariance under time reversal ( T-invariance). Since the effects of parity nonconservation and violation T-invariances are very small, then dipole electric. the moments of the nuclei are either equal to 0 or very small and are not yet available for measurement.
Magn. nuclear moments ( M 1) have the order of magnitude of nuclear magneton.Electric. quadrupole moments eQ vary from e 10 -27 cm 2 in some light nuclei up to e 10 -24 cm 2 in heavy deformed nuclei. Systematic information about magnet. and quadrupole moments are available only for the main. states of nuclei. They can be measured by radio spectroscopic measurements. methods (see Nuclear magnetic resonance).Specialist. Methods (method of distorted angle correlations) can also measure static. mag. and quadrupole moments of excited states of nuclei. Magnetic data and quadrupole moments of nuclei contain important information about the structure and shape of nuclei and are used to build and test nuclear models. There is some data on higher multipole moments of nuclei (for example, hexadec-pole - E 4)
.
Structure and models of nuclei
Ya. a. is a quantum system of many. bodies that interact strongly with each other. Theoretical describing the properties of such a system (spectra of energy levels, decays, nuclear reactions and quantum transitions) is a difficult task. Number of nucleons A in the core is not so large that it is possible to use statistical methods without reservations. mechanics (see Gibbs distribution), successfully used in condenser physics. media (liquids, solids). At the same time, an exact solution in quantum mechanics is possible only for the two-body problem ( deuteron).The progress achieved in solving the problem 3-4 bodies ch. arr. using the equations of Faddeev and Faddeev-Yakubovsky, they allow one to obtain strict quantities. results only for the lightest nuclei 3 H, 3 He, 4 He. The situation is complicated by the insufficient certainty of our knowledge about nuclear forces. Finally, the establishment of the composite nature of nucleons transforms the system A nucleons per system, at least 3 A quarks, which further complicates the task of describing the structure and properties of nuclei. A consistent solution to this problem can only be achieved within the framework of the (non-perturbative) quantum chromodynamics, but it is still far from being resolved.
Understanding the structure of the kernel is based on the use of various. nuclear models, each of which aims to describe a definition. set of nuclear properties and characteristics. Some models, at first glance, are mutually exclusive. Therefore, microscopic ones are important. approaches in nuclear theory that make it possible to establish the limits of applicability of dec. models, the degree of their compatibility with each other, as well as evaluate or calculate, based on first principles, the values of the parameters, which are used in the models as phenomenological and are extracted from experimental data.
Shell model of the kernel assumes that as a result of the interaction of nucleons with each other in the nucleus, a common average (self-consistent) field is formed, described by the shell potential V o6 ( r), in which nucleons move as independent (to a first approximation) particles. Each of the nucleons fills one of the orbits, characterized by orbital momentum l(in the case of a spherically symmetric average field), full angle. moment j=l+
1/2 and parity p = (- 1) l. Energy of a nucleon in orbit lj independent of projection T total angular momentum of a nucleon j(-j<=m<=j)
. Therefore, in accordance with the Pauli principle, at each level with energy( nlj)can be 2 j+1 nucleons of the same type, forming a proton (or neutron) subshell ( nlj), Where n= 1, 2,... - Ch. quantum number (radial).
Several subshells of similar energy are grouped into shells separated from each other by large energy values. at intervals. Full moment I
For k nucleons in the shell is obtained by adding the moments j
dept. nucleons. In a filled shell, the moments of all nucleons cancel each other out and only one value of the total moment is allowed I= 0. Like noble gas atoms with filled electron shells, nuclei consisting of filled nucleon shells are also characterized by special stability (high specific binding energy). In the ground and low-lying excited states of nuclei, the lowest single-particle orbits are filled and form an “inert” core of the nucleus, in addition to which there is a certain number of nucleons in the nearest unfilled shell. Just as valence electrons determine chemical properties of atoms, spectra of lower levels and their properties in most nuclei are determined by “valence” nucleons from unfilled shells.
The simplest version of the shell model (single-particle model) represents the odd nucleus as a combination of an even-even core in the 0 + state and an odd nucleon in orbit nlj. Then the spin of the odd nucleus is fundamental. state is equal j, and parity p = (- 1) l. The systematics of spins and parities of odd nuclei makes it possible to determine the sequence of filling orbits in nuclei, as well as the energies of these orbits. This made it possible to establish the basic characteristics and shape of the shell potential V o6 ( r). In particular, M. Goeppert-Mayer (USA) and J. H. Jensen (Germany) in 1949-50 established the need to include spin-orbit interaction in the shell potential V co( r) (ls). Only by taking into account the strong spin-orbit splitting of single-particle states is it possible to explain the systematics of nuclear spins and the sequence of filling orbits, as well as magic. numbers of protons or neutrons corresponding to filled shells (see. Magic cores).Magic numbers (2, 8, 20, 28, 50, 82, 126) correspond to sequential. filling shells with nucleons of the same type:
The set of single-particle states that are close in energy and form one shell is indicated in parentheses. The shells are separated from each other energetically. a gap that significantly exceeds the distance between levels within one shell (Fig. 1).
Center. part of the shell potential is potential. a hole of finite depth, the shape of the cut repeats the distribution of nuclear density. Most often, the so-called shell potential is used. Saxon-Woods potential:
With V 0 50 MeV. When describing the bound states of nucleons, it can be approximately replaced by the harmonic potential. oscillator or rectangular well and use the wave functions of nucleons for these simple shell potentials when describing the properties of nuclear states.
Rice. 1. Scheme of filling nuclear shells with protons (left) and neutrons (right). To the right of the levels are the total angular momenta of the nucleus; on the left - spectroscopic symbols: the letter corresponds to a certain meaning l [l=0 (s), 1(p), 2(d),
3(f), 4(g), 5(h), 6(i)]; digit is the main quantum number. The dotted line marks the magic numbers for filling shells.
The shell model satisfactorily describes the magnetic field. moments of odd nuclei, which, according to experimental data, lie between the so-called. Schmidt lines. Schmidt lines are called. magnetic dependencies nucleon dipole moments M from angle moment j given l=jb 1/2 (Fig. 2). The electric ones are described somewhat worse. quadrupole moments of nuclear states. The latter is due to the fact that the potential V o6 ( r) was originally assumed to be spherically symmetrical.
Rice. 2. Schmidt lines for nuclei with an odd number protons Z.
Nonsphericity of nuclei. Rotary model. The quadrupole moments are especially large Q cores with I> 1/2 in the field of rare earths (150<A<190)
и актинидов (A> 200
). They exceed the values predicted by the spherical shell model. potential V about 10-100 times. The energies of the lower levels of these nuclei satisfy the “rotation law”:
which describes the rotation spectrum. levels of a rigid symmetrical top with a moment of inertia J(cm. Rotational motion of the core).The state of such a top with angle. moments I=K, K+ 1, K+ 2, ... form a rotating band characterized by a certain angle projection value moment on the axis of symmetry of the top I 3
= TO. The exception is stripes with K= 0, for which only even or only odd angle values are allowed. moment I. In particular, on the basis states of even-even nuclei are based on rotation. stripes with K= 0 and values I p = 0 + , 2 + , 4 + , ... Rotate between adjacent levels. bands there are strong electric currents. quadrupole ( E 2
)g-transitions.
These facts served as the basis for the construction of a collective model of the nucleus, proposed in the 50s. J. Rainwater, A. Bohr, B. R. Mottelson. According to this model, the nuclei in the above regions have the shape of an ellipsoid of revolution with semi-axes
where the deformation parameter P characterizes the degree of nonsphericity of the nucleus. It determines the values of static quadrupole moments of nuclei, the probability of el-magn. E 2 transitions between rotations. levels and values of the moment of inertia of the core (see. Deformed kernels). According to experimental data, the value of b for most deformed nuclei is in the range of 0.1-0.3 (normal deformation). Excited rotators were discovered using nuclear reactions with heavy ions. states of certain nuclei (152 Dy) with large angles. moments I~40-60 (high-spin states of nuclei), which are characterized by extremely large deformation when the ratio of the semi-axes of the core A 1 : A 2 = 2:1 or 3:2 (super distortion-world band). Some deformed nuclei (Os, Pt isotopes) do not have axial symmetry. Their lower levels represent rotation. states of an asymmetric top (model of a non-axial Davydov-Filippov rotator). The scale is rotated. energies ( 2 /
2J~= 100 keV) in heavy deformations. nuclei is such that the moment of inertia of the nucleus in states with normal deformation J~10 -27 g cm 2. It is 2-3 times less than the moment of inertia of a solid ellipsoid of the corresponding shape. This means that not all the mass of the nucleus is involved in rotation. movement. In super deformed. In strips, the moment of inertia is close to that of a solid body.
Int. structure deformed cores are described by a model of shells with deformable potential V about ( r)(Nilsson model). A study of the dependence of the energy of single-particle nucleon orbits on deformation in this model shows that in certain regions it is periodic. systems of elements, it is energetically favorable for nuclei to be deformed rather than spherical. The magnitude of deformation predicted by theory is generally consistent with experiment. On the basis of oscillatory excitations, deform. kernels (see Vibrational excitations of nuclei) new rotations arise. bands (b-band with K= 0 and g-band with K= 2)
. Reorganization of the filling of single-particle orbits into deformed ones. potential generates excited rotations. stripes. As a result, in the spectra of a number of nuclei it is possible to distinguish rotation number bands (up to 9 in the 235 U core). Dept. the bands are traced to very high angle values. moment I~ 25-30. Means. deformation, as well as rotation. the spectra have certain relatively light nuclei (for example, 20 Ne, 4 Mg). When the core deformation parameter b changes, the structure of the shells changes. For large b ( a 1 :a 2
=
2:1
) single-particle orbits are grouped into shells differently than during normal deformations, new magic particles appear. numbers. Nuclei close to magic (for example, 152 Dy) with such deformation are relatively stable and can generate rotations. stripes. They were discovered experimentally in the form of superdeforms. stripes
The structure is rotated. spectra of real nuclei deviate from the ideal rotation. law (
5
)due to centrifugal effects (increasing the moment of inertia of the core with increasing torque), as well as due to Coriolis forces and others nonadiabatic. amendments Movement communication dep. nucleons with the rotation of the nucleus as a whole affects the structure of the rotation. states of odd nuclei already at small values of b and TO, leading to the fact that their energies, instead of (5), are described by f-loy
Here d K,1/2 =0 at TO 1/2 and d TO, 1/2 =1 at K= 1/2, constant A-empirically selected “decoupling parameter” characterizing the connection angle. moment of the nucleon and rotate. moment of the core.
Superfluid core model. Pair correlations of the superconducting type arise in the nucleus due to the so-called. The residual interaction between nucleons, that part of the real nucleon-nucleon interaction, is not included in the self-consistent potential cf. fields V about ( r). Empirically noted energetic. benefit to two nucleons in orbit nlj form a pair with compen-sir. backs, i.e. with full torque I= 0. Such a pair is similar to a Cooper pair of electrons with opposite momenta in superconductor. The attraction between nucleons in the indicated states near the Fermi surface determines superfluidity of atomic nuclei.
A detailed superfluid model of the nucleus was developed independently by S. T. Belyaev and V. G. Solovyov using methods similar to those of the theory of superconductivity. One of the manifestations of superfluidity of nuclear matter can be the presence of energy. gaps D between the superfluid and normal states of nuclear matter. It is determined by the energy of destruction of the Cooper pair and is ~ 1 MeV in heavy nuclei. The superfluidity of nuclear matter is also associated with the difference between the moments of inertia of nuclei and solid-state values. The superfluid model of the nucleus satisfactorily describes the moments of inertia of nuclei and the change in the nuclear deformation parameter b as the valence shell is filled with nucleons. Superfluidity of nuclear matter, leading to blurring of the Fermi surface, significantly affects the electron magnet. transitions, probabilities of one-nucleon (break, pick-up) and two-nucleon transfer reactions (see. Direct nuclear reactions).
The superfluid model predicts the destruction of pair correlations in the nucleus at sufficiently large spins ( I>>1). This phenomenon is similar to the destruction of superconductivity by strong magnetic fields. field, manifests itself in a sudden increase in the moment of inertia J in this rotation. band at some critical point. spin value I cr ~60. This has not yet been clearly discovered, however, when studying high-spin states of nuclei ( I<=20-30),
возбуждаемых в реакциях с тяжёлыми ионами, наблюдалось немонотонное изменение
J with increasing I(reverse z ag and b). In the region of spin values I B (~12-16) increase in angle. moment I does not lead to an increase in angle. rotation speed w, but to its decrease due to the fact that the moment of inertia of the core sharply increases J. This change is due to the fact that near the point I B there is an intersection of the main rotation. core stripes ( K= 0 +
) with an excited stripe built on the inside. state of the nucleus, in which one of the Cooper pairs in neutron orbit h 11/2 is destroyed and the spins of these two nucleons no longer compensate each other, but both line up parallel and rotate. moment. In this case, the deformation of the core changes, the moment of inertia increases, and the magnetic field changes. core characteristics.
The destruction of a pair is caused by Coriolis forces, the effect of which is maximum for nucleons in shells with large nucleon moments j. Alignment of protons in orbit discovered h 11/2 and neutrons in orbit i 13/2. The alignment of two pairs of nucleons leads to a second reverse bend, etc. The question of the nature of superfluidity of nuclear matter into superdeformation. states is under investigation.
Other kernel models. Along with the main Kernel models use more specialized ones. models. The cluster model interprets the structure of certain nuclei as a kind of molecule consisting of a-particles, deuterons (d), newts(t) etc. For example, l2 C = 3a, 16 O = 4a, 6 Li = a+d, 7 Li = a + t, etc. (cm. Nucleon association model). Statistical model of the kernel describes the properties and characteristics of highly excited states of nuclei, such as level density, temperature, etc.
In the model of interaction between bosons, it is assumed that in the lowest states of the even-even nucleus, nucleons combine into S- And D-pairs (with moments 0 and 2), which can approximately be interpreted as ideal s- And d-bosons. The number of these bosons is equal to half the number of valence nucleons. In this model, the spectrum of the lowest collective states of the nucleus is formed as a result of interactions between bosons. More refined versions of this model include s-, d-, g-,... bosons, and also compare different bosons to proton and neutron pairs. The model of interacting bosons allows us to describe, along with rotation. and oscillation The spectra also include spectra of a more complex structure, characteristic of nuclei transitioning from spherical to deformed nuclei. Justification of nuclear models and more detailed calculations of the properties of nuclei are carried out using the so-called. microscopic methods (Hartri-Foka method, random phase method, theory of finite Fermi systems, etc.).
Lit.: Davydov A.S., Theory of the atomic nucleus, M., 1958; Mukhin K.N., Experimental nuclear physics, 5th ed., book. 1-2, M., 1993; Migdal A. B., Theory of finite Fermi systems and properties of atomic nuclei, 2nd ed., M., 1983; Bohr O., Mottelson B., Structure of the atomic nucleus, trans. from English, vol. 1-2, M., 1971-77; Sitenko A.G., Tartakovsky V.K., Lectures on nuclear theory, M., 1972; Shirokov Yu. M., Yudin N. P., Nuclear Physics, 2nd ed., M., 1980; Eisenberg I., Greiner V., Models of nuclei, collective and single-particle phenomena, trans. from English, M., 1975; them, Microscopic theory of the nucleus, trans. from English, M., 1976; Rhinewater J., How the model of spheroidal nuclei arose, trans. from English, "UFN", 1976, vol. 120, v. 4, p. 529; Bohr O., Rotational motion in nuclei, trans. from English, in the same place, p. 543; Mottelson B., Elementary types of excitation in nuclei, trans. from English, in the same place, p. 563; Soloviev V.G., Theory of the atomic nucleus. Nuclear Models, M., 1981; Mikhailov V.M., Kraft O.E., Nuclear Physics, Leningrad, 1988; Nemets O.F. et al., Nucleon associations in atomic nuclei and nuclear reactions of multinucleon transfers, K., 1988.
Yu. F. Smirnov.
