Find the mass of the atomic nucleus kg. Atomic nucleus: structure, mass, composition. Communication energy. Nuclear mass defect

Atomic nucleus- this is the central part of the atom, consisting of protons and neutrons (which together are called nucleons).

The nucleus was discovered by E. Rutherford in 1911 while studying the passage α -particles through matter. It turned out that almost all the mass of the atom (99.95%) is concentrated in the nucleus. The size of the atomic nucleus is of the order of 10 -1 3 -10 - 12 cm, which is 10,000 times less than the size of the electron shell.

The planetary model of the atom proposed by E. Rutherford and his experimental observation of hydrogen nuclei knocked out α -particles from the nuclei of other elements (1919-1920), led the scientist to the idea of proton... The term proton was introduced in the early 1920s.

Proton (from the Greek. protons- the first, symbol p) Is a stable elementary particle, the nucleus of a hydrogen atom.

Proton- a positively charged particle, the charge of which is equal in absolute value to the charge of an electron e= 1.6 10 -1 9 Cl. The mass of a proton is 1836 times the mass of an electron. Rest mass of a proton m p= 1.6726231 10 -27 kg = 1.007276470 amu

The second particle in the nucleus is neutron.

Neutron (from lat. neuter- neither the one or the other, the symbol n) Is an elementary particle that has no charge, i.e., neutral.

The mass of the neutron is 1839 times the mass of the electron. The mass of a neutron is almost equal (slightly more) to the mass of a proton: the rest mass of a free neutron m n= 1.6749286 10 -27 kg = 1.0008664902 amu and exceeds the mass of a proton by 2.5 times the mass of an electron. Neutron, along with a proton under the general name nucleon is part of atomic nuclei.

The neutron was discovered in 1932 by E. Rutherford's student D. Chadwig during the bombardment of beryllium α -particles. The resulting radiation with a high penetrating ability (overcoming the barrier of a lead plate 10-20 cm thick) intensified its effect when passing through the paraffin plate (see figure). The estimation of the energy of these particles from the tracks in the Wilson chamber, made by the Joliot-Curies, and additional observations made it possible to exclude the initial assumption that this γ -quants. The great penetrating ability of new particles, called neutrons, was explained by their electroneutrality. After all, charged particles actively interact with matter and quickly lose their energy. The existence of neutrons was predicted by E. Rutherford 10 years before D. Chadwig's experiments. On hit α -particles in the beryllium nucleus, the following reaction occurs:

Here is the symbol of the neutron; its charge is equal to zero, and the relative atomic mass is approximately equal to one. A neutron is an unstable particle: a free neutron in a time of ~ 15 min. decays into a proton, an electron and a neutrino - a particle devoid of rest mass.

After the discovery of the neutron by J. Chadwick in 1932, D. Ivanenko and V. Heisenberg independently proposed proton-neutron (nucleon) nuclear model... According to this model, the nucleus consists of protons and neutrons. Number of protons Z coincides with the ordinal number of the element in the table of D. I. Mendeleev.

Core charge Q determined by the number of protons Z constituting the nucleus, and is a multiple of the absolute value of the electron charge e:

Q = + Ze.

Number Z called the charge number of the nucleus or atomic number.

Mass number of the core A called the total number of nucleons, that is, protons and neutrons, contained in it. The number of neutrons in the nucleus is denoted by the letter N... Thus, the mass number is:

A = Z + N.

Nucleons (proton and neutron) are assigned a mass number equal to one, electron - zero.

The idea of ​​the composition of the nucleus was also facilitated by the discovery isotopes.

Isotopes (from the Greek. isos- equal, the same and topoa- place) are varieties of atoms of the same chemical element, the atomic nuclei of which have the same number of protons ( Z) and different numbers of neutrons ( N).

The nuclei of such atoms are also called isotopes. Isotopes are nuclides one element. Nuclide (from lat. nucleus- nucleus) - any atomic nucleus (respectively, atom) with given numbers Z and N... The general designation of nuclides is ……. where X- symbol of a chemical element, A = Z + N- mass number.

Isotopes occupy the same place in the Periodic Table of the Elements, which is where their name comes from. Isotopes, as a rule, differ significantly in their nuclear properties (for example, in their ability to enter into nuclear reactions). The chemical (b almost to the same extent physical) properties of the isotopes are the same. This is due to the fact that the chemical properties of an element are determined by the charge of the nucleus, since it is he who affects the structure of the electron shell of the atom.

The exception is isotopes of light elements. Isotopes of hydrogen 1 N — protium, 2 N— deuterium, 3 N — tritium so strongly differ in mass that their physical and chemical properties are different. Deuterium is stable (i.e. not radioactive) and is included as a small impurity (1: 4500) in ordinary hydrogen. When deuterium combines with oxygen, heavy water is formed. It boils at 101.2 ° C at normal atmospheric pressure and freezes at +3.8 ° C. Tritium β -Radioactive with a half-life of about 12 years.

All chemical elements have isotopes. Some elements only have unstable (radioactive) isotopes. For all elements, radioactive isotopes were artificially obtained.

Uranium isotopes. The element uranium has two isotopes - with mass numbers 235 and 238. The isotope is only 1/140 of the more common.

Isogons. The nucleus of a hydrogen atom - a proton (p) - is the simplest nucleus. Its positive charge is equal in absolute value to the charge of an electron. The mass of the proton is 1.6726-10'2 kg. The proton as a particle that is part of atomic nuclei was discovered by Rutherford in 1919.

For the experimental determination of the masses of atomic nuclei, mass spectrometers. The principle of mass spectrometry, first proposed by Thomson (1907), is to use the focusing properties of electric and magnetic fields in relation to beams of charged particles. The first mass spectrometers with a sufficiently high resolution were designed in 1919 by F.W. Aston and A. Dempstsrom. The principle of operation of the mass spectrometer is shown in Fig. 1.3.

Since atoms and molecules are electrically neutral, they must first be ionized. Ions are created in an ion source by bombarding the vapors of the test substance with fast electrons and then, after acceleration in an electric field (potential difference V) go out into the vacuum chamber, falling into the region of a uniform magnetic field B. Under its action, the ions begin to move in a circle, the radius of which G can be found from the equality of the Lorentz force and centrifugal force:

where M- the mass of the ion. The ion velocity v is determined by the relation

Rice. 1.3.

Accelerating potential difference Or magnetic field strength V can be chosen so that ions with the same masses fall into the same place d on a photographic plate or another position-sensitive detector. Then, finding the maximum of the mass-spectrum signal and using formula (1.7), it is possible to determine the mass of the ion M. 1

Excluding speed v from (1.5) and (1.6), we find that

The development of mass spectrometry technology made it possible to confirm the assumption made back in 1910 by Frederick Soddy that the fractional (in units of the mass of the hydrogen atom) atomic masses of chemical elements are explained by the existence isotopes- atoms with the same nuclear charge, but different masses. Through pioneering research by Aston, it was established that most elements are indeed composed of a mixture of two or more natural isotopes. The exception is the relatively few elements (F, Na, Al, P, Au, etc.), called monoisotopic. The number of natural isotopes in one element can reach 10 (Sn). In addition, as it turned out later, all elements without exception have isotopes that have the property of radioactivity. Most radioactive isotopes do not occur in nature; they can only be obtained artificially. Elements with atomic numbers 43 (Tc), 61 (Pm), 84 (Po) and above have only radioactive isotopes.

The international atomic mass unit (amu) accepted today in physics and chemistry is 1/12 of the mass of the most widespread carbon isotope in nature: 1 amu. = 1.66053873 * 10 “kg. It is close to the atomic mass of hydrogen, although not equal to it. The mass of an electron is approximately 1/1800 amu. In modern mass spectrometry, the relative error of mass measurement

AMfM= 10 -10, which makes it possible to measure mass differences at the level of 10 -10 amu.

The atomic masses of isotopes, expressed in amu, are almost exactly integer. Thus, each atomic nucleus can be attributed to it mass number A(whole), for example H-1, H-2, H-C, C-12, 0-16, Cl-35, C1-37 and the like. The latter circumstance revived, on a new basis, interest in the hypothesis of W. Prout (1816), according to which all elements are built of hydrogen.

with parameters b v, b s b k, k v, k s, k k, B s B k C1. which is unusual in that it contains a term with Z in a positive fractional power.
On the other hand, attempts have been made to arrive at mass formulas based on the theory of nuclear matter or on the basis of the use of effective nuclear potentials. In particular, effective Skyrme potentials were used in works, where not only spherically symmetric nuclei were considered, but axial deformations were also taken into account. However, the accuracy of the results of calculations for nuclear masses is usually lower than in the macro-macroscopic method.
All the works discussed above and the mass formulas proposed in them were oriented towards a global description of the entire system of nuclei by means of smooth functions of nuclear variables (A, Z, etc.) with an eye on predicting the properties of nuclei in distant regions (near and beyond the nucleon stability boundary, and also superheavy nuclei). The global formulas also include shell corrections and sometimes contain a significant number of parameters, but despite this, their accuracy is relatively low (about 1 MeV), and the question arises as to how optimally they, and especially their macroscopic (liquid-droplet) part, reflect the requirements of the experiment.
In this regard, in the work of Kolesnikov and Vymyatnin, the inverse problem of finding the optimal mass formula was solved, proceeding from the requirement that the structure and parameters of the formula provide the least root-mean-square deviation from the experiment and that this be achieved with the minimum number of parameters n, i.e. so that both the quality index of the formula Q = (n + 1) are minimal. As a result of selection among a fairly wide class of considered functions (including those used in the published mass formulas), the formula (in MeV) was proposed as the optimal option for the binding energy:

where S (Z, N) is the simplest (two-parameter) shell correction, and P (A) is the parity correction (see (6)) The optimal formula (12) with 9 free parameters provides the root-mean-square deviation from the experimental values ​​= 1.07 MeV with a maximum deviation of ~ 2.5 MeV (according to the tables). At the same time, it gives a better (in comparison with other formulas of the global type) description of isobars remote from the beta-stability line and the course of the Z * (A) line, and the Coulomb energy term is consistent with the sizes of nuclei from electron scattering experiments. Instead of the usual term proportional to A 2/3 (usually identified with the “surface” energy), the formula contains a term proportional to A 1/3 (present, by the way, under the name of the “curvature” term in many mass formulas, for example, in). The accuracy of calculations of B (A, Z) can be increased by introducing a larger number of parameters, but the quality of the formula deteriorates (Q increases). This may mean that the class of functions used in was not complete enough, or that a different (not global) approach should be used to describe the masses of nuclei.

4. Local description of the binding energies of nuclei

Another way of constructing mass formulas is based on a local description of the nuclear energy surface. First of all, we note the difference relations that relate the masses of several (usually six) neighboring nuclei with the numbers of neutrons and protons Z, Z + 1, N, N + 1. They were originally proposed by Harvey and Kelson and were further refined in the works of other authors (for example, in). The use of difference relations makes it possible to calculate the masses of unknown, but close to known, nuclei with a high accuracy of the order of 0.1 - 0.3 MeV. However, a large number of parameters have to be entered. For example, to calculate the masses of 1241 nuclei with an accuracy of 0.2 MeV, it was necessary to enter 535 parameters. The disadvantage is that when magic numbers are crossed, the accuracy is significantly reduced, which means that the predictive power of such formulas for any distant extrapolations is small.
Another version of the local description of the nuclear energy surface is based on the idea of ​​nuclear shells. According to the many-particle model of nuclear shells, the interaction between nucleons is not entirely reduced to the creation of a certain mean field in the nucleus. In addition to it, one should also take into account additional (residual) interaction, which manifests itself in particular in the form of spin interaction and in the effect of parity. As de Chalit, Talmy and Tyberger showed, within the limits of filling the same neutron (sub) shell, the binding energy of the neutron (B n) and similarly (within the filling of the proton (sub) shell), the binding energy of the proton (B p) changes linearly depending on the number of neutrons and protons, and the total binding energy is a quadratic function of Z and N. An analysis of experimental data on the binding energies of nuclei in works leads to a similar conclusion. Moreover, it turned out that this is true not only for spherical nuclei (as suggested by de Chalite et al.), But also for regions of deformed nuclei.
By simply dividing the system of nuclei into regions between magic numbers, it is possible (as Levy showed) to describe the binding energies by quadratic functions of Z and N at least no worse than using global mass formulas. A more theoretical work-based approach was taken by Zeldes. He also divided the system of nuclei into regions between the magic numbers 2, 8, 20, 28, 50, 82, 126, but the interaction energy in each of these regions included not only the pairwise interaction of nucleons quadratic in Z and N and the Coulomb interaction, but so called deformation interaction, containing symmetric polynomials in Z and N degrees higher than the second.
This made it possible to significantly improve the description of the binding energies of nuclei, although it led to an increase in the number of parameters. So, to describe 1280 nuclei with = 0.278 MeV, it was necessary to introduce 178 parameters. Nevertheless, the neglect of subshells led to rather significant deviations near Z = 40 (~ 1.5 MeV), near N = 50 (~ 0.6 MeV) and in the region of heavy nuclei (> 0.8 MeV). In addition, difficulties arise when one wishes to match the values ​​of the parameters of the formula in different regions from the condition of the continuity of the energy surface at the boundaries.
In this regard, it seems obvious that it is necessary to take into account the subshell effect. However, at a time when the main magic numbers are reliably established both theoretically and experimentally, the question of submagic numbers turns out to be very confusing. In fact, there are no reliably established generally accepted submagic numbers (although irregularities in some properties of nuclei were noted in the literature for nucleon numbers 40, 56.64, and others). The reasons for relatively small violations of the regularities can be different.For example, as noted by Goeppert-Mayer and Jensen, the reason for the violation of the normal order of filling of neighboring levels can be the difference in the magnitude of their angular momenta and, as a consequence, in the pairing energies. Another reason is the deformation of the nucleus. Kolesnikov combined the problem of taking into account the subshell effect with the simultaneous finding of submagic numbers based on dividing the region of nuclei between neighboring magic numbers into parts such that within each of them the nucleon binding energies (B n and B p) could be described by linear functions of Z and N, and provided that the total binding energy is a continuous function everywhere, including at the boundaries of the regions. Taking subshells into account made it possible to reduce the root-mean-square deviation from the experimental values ​​of the binding energies to = 0.1 MeV, i.e., to the level of experimental errors. Partitioning the system of nuclei into smaller (submagic) regions between the main magic numbers leads to an increase in the number of intermagic regions and, accordingly, to the introduction of a larger number of parameters, but the values ​​of the latter in different regions can be matched from the conditions of the continuity of the energy surface at the boundaries of the regions and thereby reducing the number of free parameters.
For example, in the region of the heaviest nuclei (Z> 82, N> 126), when describing ~ 800 nuclei with = 0.1 MeV, due to taking into account the conditions of energy continuity at the boundaries, the number of parameters decreased by more than one third (now 136 instead of 226).
In accordance with this, the binding energy of a proton - the energy of attachment of a proton to a nucleus (Z, N) - within the same intermagic region can be written as:

where the index i determines the parity of the nucleus by the number of protons: i = 2 means Z is even, and i = 1 - Z is odd, a i and b i are constants common for nuclei with different indices j, which determine the parity by the number of neutrons. In this case, where pp is the energy of pairing of protons, and, where Δ pn is the energy of pn — interaction.
Similarly, the binding (attachment) energy of a neutron is written as:

where c i and d i are constants, where δ nn is the neutron pairing energy, a, Z k and N l are the smallest of the (sub) magic numbers of protons and, accordingly, neutrons that limit the region (k, l).
In (13) and (14), the difference between the kernels of all four types of parity is taken into account: hh, hn, nh, and nn. Ultimately, with such a description of the binding energies of nuclei, the energy surface for each type of parity is divided into relatively small pieces connected to each other, i.e. becomes like a mosaic surface.

5. Line beta - stability and binding energies of nuclei

Another possibility of describing the binding energies of nuclei in the regions between the main magic numbers is based on the dependence of the energies of beta decay of nuclei on their distance from the beta stability line. It follows from the Bethe-Weizsacker formula that the isobaric cross sections of the energy surface are parabolas (see (9), (10)), and the beta stability line, leaving the origin at large A, deviates more and more towards neutron-rich nuclei. However, the real beta stability curve represents straight line segments (see Figure 3) with discontinuities at the intersection of the magic numbers of neutrons and protons. The linear dependence of Z * on A also follows from the many-particle model of nuclear shells by de Chalite et al. Experimentally, the most significant breaks in the beta stability line (Δ Z * 0.5-0.7) occur at the intersection of the magic numbers N, Z = 20, N = 28, 50, Z = 50, N and Z = 82, N = 126 ). Submagic numbers are much weaker. In the interval between the main magic numbers, the values ​​of Z * for the minimum energy of isobars lie with a fairly good accuracy on the linearly averaged (straight) line Z * (A). For the region of the heaviest nuclei (Z> 82, N> 136) Z * is expressed by the formula (see)

As shown in, in each of the intermagic regions (i.e., between the main magic numbers), the energies of beta-plus and beta-minus decay with good accuracy turn out to be a linear function of Z - Z * (A). This is demonstrated in Fig. 5 for the region Z> 82, N> 126, where the dependence of + D on Z - Z * (A) is plotted; for convenience, nuclei with even Z are selected; D is a parity correction equal to 1.9 MeV for nuclei with even N (and Z) and 0.75 MeV for nuclei with odd N (and even Z). Considering that for an isobar with odd Z, the energy of beta-minus decay - is equal to the minus energy of beta-plus decay of an isobar with an even charge Z + 1, and (A, Z) = - (A, Z + 1), the graph in Fig. 5 covers without exception all the cores of the region Z> 82, N> 126 with both even and odd values ​​of Z and N. In accordance with what has been said

where k and D are constants for the region enclosed between the main magic numbers. In addition to the region Z> 82, N> 126, as shown in, similar linear dependences (15) and (16) are valid for other regions distinguished by the main magic numbers.
Using formulas (15) and (16), one can estimate the beta decay energy of any (even so far inaccessible for experimental study) nucleus of the considered submagic region, knowing only its charge Z and mass number A. In this case, the calculation accuracy for the region Z> 82, N> 126, as a comparison with ~ 200 experimental values ​​of the table shows, ranges from = 0.3 MeV for odd A and up to 0.4 MeV for even A with maximum deviations of the order of 0.6 MeV, i.e., higher than when using mass formulas of the global type. And this is achieved using the minimum number of parameters (four in formula (16) and two more in formula (15) for the beta stability curve). Unfortunately, for superheavy nuclei, it is currently impossible to make a similar comparison due to the lack of experimental data.
Knowing the energies of beta decay and plus to this the alpha decay energy for only one isobar (A, Z) makes it possible to calculate the alpha decay energies of other nuclei with the same mass number A, including those far enough from the beta stability line. This is especially important for the region of the heaviest nuclei, where alpha decay is the main source of information on nuclear energies. In the region Z> 82, the beta stability line deviates from the N = Z line along which alpha decay occurs so that the nucleus formed after the alpha particle escapes approaches the beta stability line. For the line of beta stability of the region Z> 82 (see (15)) Z * / A = 0.356, while for alpha decay Z / A = 0.5. As a result, the nucleus (A-4, Z-2), as compared to the nucleus (A, Z), is closer to the beta stability line by an amount (0.5 - 0.356). 4 = 0.576, and its beta decay energy becomes 0.576. k = 0.576. 1.13 = 0.65 MeV less compared to the nucleus (A, Z). Hence, from the energy (,) cycle, which includes the nuclei (A, Z), (A, Z + 1), (A-4, Z-2), (A-4, Z-1), it follows that the energy of alpha decay Q a of the nucleus (A, Z + 1) should be 0.65 MeV more than the isobar (A, Z). Thus, on going from isobar (A, Z) to isobar (A, Z + 1), the alpha decay energy increases by 0.65 MeV. For Z> 82, N> 126, this is, on average, very well justified for all nuclei (regardless of the parity). The root-mean-square deviation of the calculated Q a for 200 nuclei of the considered region is only 0.15 MeV (and the maximum is about 0.4 MeV), despite the fact that the submagic numbers N = 152 for neutrons and Z = 100 for protons intersect.

To complete the overall picture of the change in the energies of alpha decay of nuclei in the region of heavy elements, on the basis of experimental data on alpha decay energies, the value of the alpha decay energy for fictitious nuclei lying on the beta stability line, Q * a, was calculated. The results are shown in Fig. 6. As seen from Fig. 6, the overall stability of nuclei with respect to alpha decay after lead increases rapidly (Q * a falls) to A235 (uranium region), after which Q * a gradually begins to grow. In this case, 5 areas of approximately linear change in Q * a can be distinguished:

Calculation of Q a by the formula

6. Heavy nuclei, superheavy elements

In recent years, significant progress has been made in the study of superheavy nuclei; Isotopes of elements with serial numbers from Z = 110 to Z = 118 were synthesized. In this case, a special role was played by the experiments carried out at JINR in Dubna, where the 48 Ca isotope, containing a large excess of neutrons, was used as a bombarding particle.This made it possible to synthesize nuclides closer to the beta-stability line and therefore more long-lived and decaying with lower energy. The difficulties, however, are that the alpha decay chain of the nuclei formed as a result of irradiation does not end at the known nuclei, and therefore the identification of the resulting reaction products, especially their mass number, is not unambiguous. In this regard, as well as to understand the properties of superheavy nuclei located on the border of the existence of elements, it is necessary to compare the results of experimental measurements with theoretical models.
The orientation could be given by the systematics of energies - and - decay, taking into account new data on transfermium elements. However, the papers published so far have been based on fairly old experimental data of almost twenty years ago and therefore turn out to be of little use.
As for theoretical works, it should be admitted that their conclusions are far from unambiguous. First of all, it depends on which theoretical model of the nucleus is chosen (for the region of transfermium nuclei, the macro-micro model, the Skyrme-Hartree-Fock method and the relativistic mean field model are considered the most acceptable). But even within the framework of the same model, the results depend on the choice of parameters and on the inclusion of certain correction terms. Accordingly, increased stability is predicted for (and near) different magic numbers of protons and neutrons.

So Möller and some other theorists came to the conclusion that in addition to the well-known magic numbers (Z, N = 2, 8, 20, 28, 50, 82 and N = 126), the magic number Z = 114 should also appear in the area of ​​transfermium elements, and near Z = 114 and N = 184 there should be an island of relatively stable nuclei (some exalted popularizers hastened to fantasize about new supposedly stable superheavy nuclei and new sources of energy associated with them). However, in fact, in the works of other authors, the magic of Z = 114 is rejected and instead, the magic numbers of protons are declared Z = 126 or 124.
On the other hand, in the works, it is argued that the magic numbers are N = 162 and Z = 108. However, the authors of the work disagree with this. Opinions of theorists also differ as to whether nuclei with numbers Z = 114, N = 184 and with numbers Z = 108, N = 162 should be spherically symmetric or whether they can be deformed.
As for the experimental verification of theoretical predictions about the magicity of the number of protons Z = 114, then in the experimentally achieved region with neutron numbers from 170 to 176, the isolation of isotopes of element 114 (in the sense of their greater stability) is not visually observed in comparison with isotopes of other elements.

The above is illustrated at 7, 8 and 9. In Figs 7, 8 and 9, in addition to the experimental values ​​of the alpha-decay energies Q a of transfermium nuclei, plotted by dots, the results of theoretical calculations are shown in the form of curved lines. Figure 7 shows the results of calculations according to the macro-micro model of work, for elements with even Z, found taking into account the multipolarity of deformations up to the eighth order.
In fig. 8 and 9 show the results of calculations of Q a according to the optimal formula for, respectively, even and odd elements. Note that the parameterization was carried out taking into account the experiments performed 5-10 years ago, while the parameters have not been adjusted since the publication of the work.
The general character of the description of transfermium nuclei (with Z > 100) in and is approximately the same - the root-mean-square deviation is 0.3 MeV, however, in for nuclei with N> 170 the behavior of the Q a (N) curve differs from the experimental one, while in full agreement is achieved if we take into account the existence of the subshell N = 170.
It should be noted that the mass formulas in a number of papers published in recent years also give a fairly good description of the energies Q a for nuclei in the transfermium region (0.3-0.5 MeV), and in this paper, the discrepancy in Q a for the chain of the heaviest nuclei 294 118 290 116 286 114 turns out to be within the experimental errors (although for the entire region of transfermium nuclei 0.5 MeV, that is, worse than, for example, c).
Above, in Section 5, a simple method was described for calculating the alpha decay energies of nuclei with Z> 82, based on the use of the dependence of the alpha decay energy Q a of a nucleus (A, Z) on the distance from the beta stability line ZZ *, which is expressed by the formulas ( The values ​​of Z * required for calculating Q a (A, Z) are found by formula (15), and Q a * from Fig. 6 or by formulas (17-21). For all nuclei with Z> 82, N> 126, the accuracy of calculating the alpha decay energies turns out to be 0.2 MeV, i.e. at least not worse than for mass formulas of the global type. This is illustrated in table. 1, where the results of calculating Q a by formulas (22, 23) are compared with the experimental data contained in the isotope tables. In addition, in table. 2 shows the results of calculations of Q a for nuclei with Z> 104, the discrepancy of which with recent experiments remains within the same 0.2 MeV.
As for the magicity of the number Z = 108, then, as can be seen from Figs. 7, 8, and 9, there is no significant increase in stability with this number of protons. It is difficult to judge at present how significant the effect of the N = 162 shell is due to the lack of reliable experimental data. True, in the work of Dvorak et al., Using the radiochemical method, a product was isolated, which decays by emitting alpha particles with a rather long lifetime and a relatively low decay energy, which was identified with a 270 Hs nucleus with a number of neutrons N = 162 (the corresponding value of Q a per (see fig. 7 and 8 marked with a cross). However, the results of this work disagree with the conclusions of other authors.
Thus, we can state that so far there are no serious grounds to assert the existence of new magic numbers in the region of heavy and superheavy nuclei and the associated increase in the stability of nuclei, in addition to the previously established subshells N = 152 and Z = 100. As for the magic number Z = 114, then, of course, it cannot be completely ruled out (although this does not seem very likely) that the effect of the shell Z = 114 near the center of the island of stability (i.e., near N = 184) could turn out to be significant, however this area is not yet available for experimental study.
To find the submagic numbers and the associated subshell filling effects, the method described in Section 4 seems logical. As was shown in (see above, Section 4), it is possible to single out the regions of the system of nuclei, within which the binding energies of neutrons B n and the binding energies of protons B p vary linearly depending on the number of neutrons N and the number of protons Z, and the entire system of nuclei is divided into intermagic regions, within which formulas (13) and (14) are valid. The (sub) magic number can be called the boundary between two regions of regular (linear) variation of B n and B p, and the effect of filling the neutron (proton) shell is understood as the difference in energies B n (B p) during the transition from one region to another. The submagic numbers are not specified in advance, but are found as a result of agreement with the experimental data of linear formulas (11) and (12) for B n and B p when dividing the system of nuclei into regions, see Section 4, and also.

As can be seen from formulas (11) and (12), B n and B p are functions of Z and N. To get an idea of ​​how B n changes depending on the number of neutrons and what effect of filling various neutron (sub) shells is convenient to bring the binding energies of neutrons to the line of beta-stability. For this, for each fixed value of N, B n * B n (N, Z * (N)) was found, where (according to (15)) Z * (N) = 0.5528Z + 14.1. The dependence of B n * on N for nuclei of all four types of parity is shown in Fig. 10 for nuclei with N> 126. Each of the points in Fig. 10 corresponds to the average value of B n * values ​​shown on the beta stability line for nuclei of the same parity with the same N.
As can be seen from Fig. 10, B n * undergoes jumps not only at the well-known magic number N = 126 (drop by 2 MeV) and at the submagic number N = 152 (drop by 0.4 MeV for nuclei of all parity types), but also at N = 132, 136, 140, 144, 158, 162, 170.The nature of these subshells turns out to be different. The point is that the magnitude and even the sign of the shell effect turns out to be different for nuclei of different parity types. So when passing through N = 132 B n * decreases by 0.2 MeV for nuclei with odd N, but increases by the same amount for nuclei with even N. The energy C averaged over all types of parity (line C in Fig. 10) does not undergo discontinuity. Rice. 10 allows you to trace what happens when the other submagic numbers listed above are crossed. It is essential that the average energy C either does not experience discontinuity, or changes by ~ 0.1 MeV in the direction of decreasing (at N = 162) or increasing (at N = 158 and N = 170).
The general trend in the change in energies B n * is as follows: after filling the shell with N = 126, the binding energies of neutrons increase to N = 140, so that the average energy C reaches 6 MeV, after which it decreases by about 1 MeV for the heaviest nuclei.

In a similar way, the energies of protons reduced to the beta-stability line B p * B p (Z, N * (Z)) were found taking into account (following from (15)) the formula N * (Z) = 1.809N - 25.6. The dependence of B p * on Z is shown in Fig. 11. Compared to neutrons, the binding energies of protons experience sharper oscillations with a change in the number of protons As can be seen from Fig. 11, the binding energies of protons B p * experience a rupture apart from the main magic number Z = 82 (a decrease in B p * by 1.6 MeV) at Z = 100 and also at submagic numbers 88, 92, 104, 110. As in the case of neutrons, the intersection of proton submagic numbers leads to shell effects of different magnitude and sign. The average value of the energy C does not change when crossing the number Z = 104, but decreases by 0.25 MeV at the intersection of the numbers Z = 100 and 92 and by 0.15 MeV at Z = 88 and increases by the same amount at Z = 110.
Figure 11 shows a general tendency for B p * to change after filling the proton shell with Z = 82 - this is an increase to uranium (Z = 92) and a gradual decrease with shell vibrations in the region of the heaviest elements. In this case, the average energy value changes from 5 MeV in the uranium region to 4 MeV for the heaviest elements, and at the same time the proton pairing energy decreases,

As follows from Figs. 10 and 11, in the region of the heaviest elements, in addition to a general decrease in binding energies, there is a weakening of the bond of external nucleons with each other, which manifests itself in a decrease in the pairing energy of neutrons and the pairing energy of protons, as well as in the neutron-proton interaction. This is demonstrated explicitly in Figure 12.
For nuclei lying on the beta-stability line, the neutron pairing energy nn was determined as the difference between the energy of the even (Z)-odd (N) nucleus B n * (N) and the half-sum
(B n * (N-1) + B n * (N + 1)) / 2 for even-even nuclei; similarly, the pairing energy pp of protons was found as the difference between the energy of the odd-even nucleus B p * (Z) and the half-sum (B p * (Z-1) + B p * (Z + 1)) / 2 for even-even nuclei. Finally, the np interaction energy np was found as the difference between B n * (N) of an even-odd nucleus and B n * (N) of an even-even nucleus.
Figures 10, 11 and 12 do not give, however, a complete idea of ​​how the binding energies of nucleons B n and B p (and everything connected with them) change depending on the ratio between the numbers of neutrons and protons. With this in mind, in addition to fig. 10, 11 and 12 for the sake of clarity, Fig. 13 is given (in accordance with formulas (13) and (14)), which shows the spatial picture of the binding energies of neutrons B n as a function of the number of neutrons N and protons Z, Let us note some general regularities, manifested in the analysis of the binding energies of nuclei of the region Z> 82, N> 126, including in Fig. 13 The energy surface B (Z, N) is continuous everywhere, including at the boundaries of the regions. The binding energy of neutrons B n (Z, N), which varies linearly in each of the intermagic regions, experiences a rupture only when crossing the neutron (sub) shell boundary, whereas when crossing the proton (sub) shell, only the slope B n / Z can change.
On the contrary, B p (Z, N) experiences a rupture only at the boundary of the proton (sub) shell, and at the boundary of the neutron (sub) shell, the slope of B p / N can only change. Within the intermagic region, B n increases with increasing Z and slowly decreases with increasing N; similarly, B p increases with increasing N and decreases with increasing Z. In this case, the change in B p is much faster than B n.
The numerical values ​​of B p and B n are given in table. 3, and the values ​​of the parameters defining them (see formulas (13) and (14)) are in Table 4. The values ​​of n 0 np n 0 nn, as well as p 0 pn and p 0 nn, are not shown in Table 1, but they are found as the differences B * n for odd-even and even-even nuclei and, respectively, even-even and odd-odd nuclei in Fig. 10 and as the differences B * p for even-odd and even-even and, accordingly, odd-even and odd-odd nuclei in Fig. 11.
The analysis of shell effects, the results of which are presented in Fig. 10-13, depend on the input experimental data - mainly on the energies of alpha decay Q a and a change in the latter could lead to a correction of the results of this analysis. This is especially true for the region Z> 110, N> 160, where sometimes conclusions were made on the basis of a single alpha decay energy. Regarding the area Z< 110, N < 160, где результаты экспериментальных измерений за последние годы практически стабилизировались, то результаты анализа, приведенные на рис. 10 и 11 практически совпадают с теми, которые были получены в двадцать и более лет назад.
This work is a review of various approaches to the problem of nuclear binding energies with an assessment of their advantages and disadvantages. The work contains a fairly large amount of information about the work of various authors. Additional information can be obtained by reading the original works, many of which are cited in the bibliography of this review, as well as in the proceedings of conferences on nuclear masses, in particular the AF and MS conferences (publications in ADNDT Nos. 13 and 17, etc.) and conferences on nuclear spectroscopy and nuclear structure conducted in Russia. The tables of this paper contain the results of the author's own estimates related to the problem of superheavy elements (SHE).
The author is deeply grateful to B.S. Ishkhanov, at whose suggestion this work was prepared, and also to Yu.Ts. Oganesyan and V.K. Utenkov for the latest information on the experimental work carried out at FLNR JINR on the problem of STE.

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Studying the composition of matter, scientists have come to the conclusion that all matter consists of molecules and atoms. For a long time, the atom (translated from the Greek "indivisible") was considered the smallest structural unit of matter. However, further research showed that the atom has a complex structure and, in turn, includes smaller particles.

What is an atom made of?

In 1911, the scientist Rutherford suggested that the atom has a central part with a positive charge. This is how the concept of an atomic nucleus appeared for the first time.

According to Rutherford's scheme, called the planetary model, an atom consists of a nucleus and elementary particles with a negative charge - electrons moving around the nucleus, just as the planets revolve around the Sun.

In 1932, another scientist, Chadwick, discovered the neutron, a particle that has no electrical charge.

According to modern concepts, the nuclei correspond to the planetary model proposed by Rutherford. The nucleus carries most of the atomic mass. It also has a positive charge. The atomic nucleus contains protons - positively charged particles and neutrons - particles that do not carry a charge. Protons and neutrons are called nucleons. Negatively charged particles - electrons - orbit around the nucleus.

The number of protons in the nucleus is equal to those moving in orbit. Consequently, the atom itself is a particle that does not carry a charge. If an atom captures other people's electrons or loses its own, then it becomes positive or negative and is called an ion.

Electrons, protons and neutrons are collectively referred to as subatomic particles.

Nuclear charge

The nucleus has a charge number Z. It is determined by the number of protons that make up the atomic nucleus. It is easy to find out this amount: just refer to the periodic system of Mendeleev. The ordinal number of the element to which the atom belongs is equal to the number of protons in the nucleus. Thus, if the serial number 8 corresponds to the chemical element oxygen, then the number of protons will also be equal to eight. Since the number of protons and electrons in an atom is the same, then there will also be eight electrons.

The number of neutrons is called the isotopic number and is denoted by the letter N. Their number may differ in an atom of the same chemical element.

The sum of protons and electrons in the nucleus is called the mass number of the atom and is denoted by the letter A. Thus, the formula for calculating the mass number looks like this: A = Z + N.

Isotopes

In the case when elements have an equal number of protons and electrons, but a different number of neutrons, they are called isotopes of a chemical element. There can be one or several isotopes. They are placed in the same cell of the periodic table.

Isotopes are of great importance in chemistry and physics. For example, the isotope of hydrogen - deuterium - combines with oxygen to form a completely new substance called heavy water. It has a different boiling and freezing point than usual. And the combination of deuterium with another hydrogen isotope, tritium, leads to a thermonuclear fusion reaction and can be used to generate a huge amount of energy.

Mass of the nucleus and subatomic particles

The dimensions and mass of atoms are negligible in the minds of man. The size of the nuclei is approximately 10 -12 cm. The mass of an atomic nucleus is measured in physics in the so-called atomic mass units - amu.

For one amu take one twelfth of the mass of a carbon atom. Using the usual units of measurement (kilograms and grams), the mass can be expressed by the following equation: 1 amu. = 1.660540 · 10 -24 g. Expressed in this way, it is called the absolute atomic mass.

Despite the fact that the atomic nucleus is the most massive component of the atom, its dimensions relative to the electron cloud surrounding it are extremely small.

Nuclear forces

Atomic nuclei are extremely resilient. This means that protons and neutrons are held in the nucleus by some kind of force. These cannot be electromagnetic forces, since protons are like charged particles, and it is known that particles with the same charge repel each other. The gravitational forces are too weak to hold the nucleons together. Consequently, the particles are held in the nucleus by another interaction - nuclear forces.

Nuclear interaction is considered to be the strongest of all existing in nature. Therefore, this type of interaction between the elements of the atomic nucleus is called strong. It is present in many elementary particles, as well as electromagnetic forces.

Features of nuclear forces

1. Short acting. Nuclear forces, in contrast to electromagnetic ones, manifest themselves only at very small distances, comparable to the size of the nucleus.
2. Charge independence. This feature is manifested in the fact that nuclear forces act in the same way on protons and neutrons.
3. Saturation. Nucleons of the nucleus interact only with a certain number of other nucleons.

Core binding energy

Another closely related concept is the binding energy of nuclei. The energy of a nuclear bond is understood as the amount of energy that is required to divide an atomic nucleus into its constituent nucleons. It equals the energy required to form a nucleus from individual particles.

To calculate the binding energy of a nucleus, it is necessary to know the mass of subatomic particles. Calculations show that the mass of a nucleus is always less than the sum of its constituent nucleons. A mass defect is the difference between the mass of a nucleus and the sum of its protons and electrons. With the help of the relationship between mass and energy (E = mc 2), you can calculate the energy generated during the formation of the nucleus.

The strength of the binding energy of the nucleus can be judged by the following example: when several grams of helium are formed, the same amount of energy is generated as when several tons of coal are burned.

Nuclear reactions

The nuclei of atoms can interact with the nuclei of other atoms. Such interactions are called nuclear reactions. There are two types of reactions.

1. Fission reactions. They occur when heavier nuclei disintegrate into lighter ones as a result of interaction.
2. Synthesis reactions. The reverse process of fission: the nuclei collide, thereby forming heavier elements.

All nuclear reactions are accompanied by the release of energy, which is subsequently used in industry, in the military, in the energy sector, and so on.

After reviewing the composition of the atomic nucleus, the following conclusions can be drawn.

1. An atom consists of a nucleus containing protons and neutrons and electrons around it.
2. The mass number of an atom is equal to the sum of the nucleons of its nucleus.
3. Nucleons are held together by strong interactions.
4. The enormous forces that give stability to the atomic nucleus are called nucleus binding energies.

Investigating the passage of an α-particle through a thin gold foil (see Section 6.2), E. Rutherford came to the conclusion that an atom consists of a heavy positive charged nucleus and electrons surrounding it.

Core called the central part of the atom,in which almost all the mass of the atom and its positive charge are concentrated.

V atomic composition elementary particles : protons and neutrons (nucleons from the Latin word nucleus- core). This proton-neutron model of the nucleus was proposed by a Soviet physicist in 1932 by D.D. Ivanenko. The proton has a positive charge e + = 1.06 · 10 -19 C and rest mass m p= 1.673 · 10 -27 kg = 1836 m e... Neutron ( n) Is a neutral particle with rest mass m n= 1.675 · 10 -27 kg = 1839 m e(where the electron mass m e, is equal to 0.91 · 10 –31 kg). In fig. 9.1 shows the structure of the helium atom according to the concepts of the late XX - early XXI century.

Core charge is equal to Ze, where e Is the proton charge, Z- charge number equal to ordinal number chemical element in the periodic table of elements of Mendeleev, i.e. the number of protons in the nucleus. The number of neutrons in the nucleus is denoted N... Usually Z > N.

Currently known kernels with Z= 1 to Z = 107 – 118.

The number of nucleons in the nucleus A = Z + N called massive number ... Kernels with the same Z but different A are called isotopes... Kernels that, with the same A have different Z are called isobars.

The nucleus is denoted by the same symbol as the neutral atom, where X- symbol of a chemical element. For example: hydrogen Z= 1 has three isotopes: - protium ( Z = 1, N= 0), - deuterium ( Z = 1, N= 1), - tritium ( Z = 1, N= 2), tin has 10 isotopes, etc. In the overwhelming majority, isotopes of one chemical element have the same chemical and similar physical properties. In total, about 300 stable isotopes are known and more than 2000 natural and artificially obtained radioactive isotopes.

The size of the nucleus is characterized by the radius of the nucleus, which has a conventional meaning due to the blurring of the boundary of the nucleus. Even E. Rutherford, analyzing his experiments, showed that the size of the nucleus is approximately equal to 10 -15 m (the size of an atom is 10 -10 m). There is an empirical formula for calculating the radius of the kernel:

where R 0 = (1.3 - 1.7) · 10 -15 m. From this it is seen that the volume of the nucleus is proportional to the number of nucleons.

The density of nuclear matter is, in order of magnitude, 10 17 kg / m 3 and is constant for all nuclei. It greatly exceeds the density of the most dense ordinary substances.

Protons and neutrons are fermions since have spin ħ /2.

The nucleus of an atom has proper angular momentum – nucleus spin :

,

(9.1.2)

where I – internal(complete)spin quantum number.

Number I takes integer or half-integer values ​​0, 1/2, 1, 3/2, 2, etc. Kernels with even A have integer spin(in units ħ ) and are subject to statistics Bose–Einstein(bosons). Kernels with odd A have half-integer spin(in units ħ ) and are subject to statistics Fermi–Dirac(those. nuclei - fermions).

Nuclear particles have their own magnetic moments, which determine the magnetic moment of the nucleus as a whole. The unit for measuring the magnetic moments of nuclei is nuclear magneton μ poison:

Here e- the absolute value of the electron charge, m p Is the mass of the proton.

Nuclear magneton in m p/m e= 1836.5 times less than Bohr's magneton, it follows that the magnetic properties of atoms are determined by the magnetic properties of its electrons .

There is a relation between the spin of the nucleus and its magnetic moment:

where γ poison - nuclear gyromagnetic ratio.

The neutron has a negative magnetic moment μ n≈ - 1.913μ poison since the direction of the spin of the neutron and its magnetic moment are opposite. The magnetic moment of the proton is positive and equal to μ R≈ 2.793μ poison. Its direction coincides with the direction of the proton's spin.

The distribution of the electric charge of protons over the nucleus is generally asymmetric. A measure of the deviation of this distribution from a spherically symmetric distribution is quadrupole electric moment of the nucleus Q... If the charge density is considered the same everywhere, then Q is determined only by the shape of the nucleus. So, for an ellipsoid of revolution

,

(9.1.5)

where b- the semiaxis of the ellipsoid along the spin direction, a- semiaxis in the perpendicular direction. For a nucleus elongated along the spin direction, b > a and Q> 0. For a core flattened in this direction, b < a and Q < 0. Для сферического распределения заряда в ядре b = a and Q= 0. This is true for nuclei with spin equal to 0 or ħ /2.

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