Empty of elementary particles and thermal energy. Nuclear RIA can be accompanied by both energy release and its absorption. Coupling of energy is called the energy of the energy of the masses of the initial and end nuclei. Track classifications Features: L By energy Element of particles Participate in nuclear rods: at low energies of 1 Evria on slow neutrons: Rhines on the emission of medium-energy particles with the charge of particles of electron of protons of datonene ions \u003d 1MEV; On high-energy particles, 103mave Space rays of particles are obtained in accelerators ...

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45. Nuclear reactions and their classification

Nuclear reactions are the process of intensive interaction of the atomic nucleus with an elementary particle or with another core, leading to the transformation of the nuclei. Empty of elementary particles and thermal energy. The interaction of reacting particles occurs when they are rapprocial to the distance of about 10 ~13 see thanks to the action of nuclear forces. The most propagation nuclear reaction is, the light particles interact, and with the kernelX. in the resulting image of an email particleb. And the kernel of H. Nuclear R-AI may be accompanied by both energy release and its absorption. The number of energy is called the energy of the R-AI - this is the difference between the masses of the initial and end nuclei. Charter classification featured:L. by energy, the particle element, participate in nuclear rods: at low energies of 1EV - P epic on slow neutrons: P-α to email particles with charges of particles -electrons, protons, ions, datonev\u003e \u003d 1MEV; on high energy particles (~ 103 MeV - Space rays, particles are obtained in accelerators) by nature the element of the neutron particle is involved; on charged particles; caused by y - quanta, by nature (mass) nuclei participate in the number: on the lungs (and<50);средних (50<А<100);тяжелых(А>100). Po. the nature of the transformations: P-radioactivity; division of heavy nuclei, chain division; Synthesis of light nuclei into heavy, thermonuclear R-α.

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In general, nuclear interaction can be written in the form:

The most common type of nuclear reaction is the interaction of light particles a. with kernel X., as a result of which a particle is formed b. and kernel Y.. It is written symbolically like this:

The role of particles a. and b. Most often neutron n., Proton p., deuteron d., α-particle and γ-quantum.

The process (4.2) is usually ambiguous, since the reaction can go several competing methods, i.e. Particles born as a result of a nuclear reaction (4.2) may be different:

.

Different possibilities of nuclear reaction in the second stage are sometimes called reaction channels. The initial stage of the reaction is called the input channel.

The two recent reaction channels refer to cases of inelastic ( A 1. + a.) and elastic ( A. + a.) Nuclear scattering. These particular cases of nuclear interaction differ from other facts that the reaction products coincide with the reaction particles, and with elastic scattering, not only the type of kernel is maintained, but also its inner state, and with inelastic scattering the inner state of the kernel changes (the kernel goes into an excited state).

Figure 4.1. Qualitative addiction The probability of the decay of the nucleus of energy.

When studying a nuclear reaction, the identification of the reaction channels is of interest, the comparative probability of it in different channels at various energies of incident particles. Kernels may be in various energy states. The state of a stable or radioactive nucleus that corresponds to minimal energy (mass) E 0 called basic. From quantum mechanics it is known that between the state of the state and its time of life takes place gaisenberg's ratio: ΔE \u003d ћ / Δt,

Excited kernels are experiencing various types of energy transitions. The excitation energy can be discharged along various channels (translating the kernel to the ground state): the emission of γ-quanta, the division of the nucleus, etc. For this reason, the concept of partial level width is introduced Γ I. . Partial width of the resonance level is the probability of decay by i.- Channel. Then the probability of decay per unit time ω May be presented in the form:

.

It is also of great interest is the energy and angular distribution of the resulting particles, and their inner state (excitation energy, spin, parity, isotopic spin).

Many of nuclear reactions can be obtained as a result of the application of conservation laws.

For more information on this section, you can see.

Our tasks: To introduce the main types of radioactive decay, in virtual experiments, show chains of radioactive transformations and a method for measuring the constant decay.

Nuclear reaction - forced transformation of the atomic nucleus under the action of other particles (about spontaneous Changes in atomic nuclei by emissing elementary particles - radioactivity Read in another lecture).

If you doubt whether you have seen a natural reaction, take a look at a clear day on the sky. We'll talk about reactions in the sun later.

Most often on the kernel BUT relatively light particle flies but (for example, neutron, proton, α -caster, etc.), and when approaching the distance of about 10 -15 m as a result of the actions of the nuclear force, the kernel is formed IN and easier particle b..

A combination of particles and reaction kernels (in the figure BUT + but), called input the channel of the nuclear reaction, and the resulting reaction - output channels. If the kinetic energy of the flutter particle but It is small, then two particles are formed: a particle and core actually.

Elastic and inelastic scattering is special cases of nuclear interaction when the reaction products coincide with the original.

Classification of nuclear reactions

By the type of particles causing the reaction
1. reactions under the action of charged particles
2. neutron reactions
3. reactions under action γ -Kvanta - Photonuclear Reactions

Laws of preservation in nuclear reactions

You can come up with a great set of output channels for any reaction. However, most of them will be impossible. Choose the reaction in fact helps the laws of preservation:

The last two are true for strong interaction. In nuclear reactions, another number of laws are manifested, they are significant for reactions with elementary particles, they will be called them elsewhere.

The set of conservation laws allows you to select possible output reaction channels and obtain important information about the properties of interacting particles and reaction products.

Direct nuclear reactions

In a direct reaction, the particle time has time to face one (less often with two - -trees) nucleons. These reactions proceed very quickly - during the span of particles through the kernel (10 -22 - 10 -21 s). Consider for example (n, p) -ring. The neutron pulse is transmitted mainly to one nucleon, which immediately flies out of the kernel, without having time to exchange energy with the rest of the nucleons. Therefore, nucleons should fly out of the nucleus mainly in the front direction. The energy of the fleering nucleon should be close to the energy of the flying.

The kinetic energy of the flutter particle must be large enough (imagine the wall folded from cubes. If you have to sharply hit one of them, it can be disappeared, almost not affected by the rest. With slow exposure, the wall will fall apart.)

With low energies can go reaction sharp (D, P). Deuteron polarizes when approaching the kernel, neutron is captured by the kernel, and the proton continues to move. For such a process, the interaction should occur at the edge of the kernel. In Deuteron, Proton and Neutron are linked weakly.

Thus, the distinctive features of direct reactions are:
1. the flow time is ~ 10 -21 C;
2. the angular distribution of products is stretched in the direction of movement of the flutter particle;
3. especially great contribution to the cross section of nuclear processes at high energies.

Fig.2 Exothermic reaction scheme

Nuclear reaction energy scheme

I will depict a nuclear reaction in the form of an energy chart (Fig. 2). The left part of the figure refers to the first stage - the formation of the composite core, the right - the decay of this nucleus. T "A. - part of the kinetic energy of the flutter particle, which went to the excitation of the nucleus, ε A. - particle binding energy a. In the compound core, ε B. - particle binding energy b. In the same kernel.

There is an apparent contradiction: kernel C. - quantum mechanical system with discrete energy levels, and excitation energy, as seen from (1), continuous value (energy T A. Maybe any). To deal with this will allow the next section.

The cross section of a nuclear reaction going through the composite core

Fig.3 Blur energy of the level of excited state

Since there are two independent stages during the reaction, the cross section can be represented as a piece of section of the formation of an composite nucleus σ Sost and probability of decay it i.- Channel f I.

Atomic core is a quantum system. Since each of the excited spectrum levels has a finite average lifetime. τ , width level Γ It is also finite (Fig. 3) and is associated with average life time by the relationship that is a consequence of the ratio of uncertainty for energy and time Δt · ΔE ≥ ћ:

Consider the case when the energy levels of the composite kernel are separated (level widths Γ less distances between them ΔE.). With the coincidence of the excitation energy with the energy of one of the levels E 0 Reaction section (A, B) will have a resonance maximum. In quantum mechanics, it is proved that the section of the formation of a compound kernel is described by Brete-Wigner's formula

(6)

where λ A. - De Brogly's wavelength of the falling particle, Γ - full level width, Γ A. - The width of the level relative to elastic scattering (partial, partial width).

We will deal with the widths of the level. The probability of decay of the composite kernel f I. inversely proportional to the lifetime τ I. relative to this decay. And the time of life τ I. In turn, according to (5) inversely proportional to the width Γ I., called partial (partial). As a result, probabilities f I. proportional to widths Γ I., and they can be represented

Fig.4 Section of the formation of a compound kernel

Sum ΣF i \u003d 1, but Σγ i \u003d γ. With partial widths, it is more convenient to deal with the probabilities.

Full level width Γ weakly depends on the speed of the flutter particle v A., but Γ A. proportional to this speed. De Brogly wavelength is inversely proportional to speed v A.. Therefore, away from the resonance at low speeds the cross section is growing like 1 / v a (You can explain this by the fact that the slow particle spends more time at the nucleus, and the probability of capture increases). For E ~ E 0 The seizure cross section increases sharply (Fig. 4). In formula (6) E. - kinetic energy of the flutter particle, and E 0 - Energy of the level of the compound kernel, energy Curved: Energy level \u003d ε a + E 0.

Nuclear reactions under the action of neutrons

The main reactions under the action of nonrelativistic neutrons are shown in the diagram (Fig. 5). There and in the future we will denote the letter A. core with a massive number A..

Consider them in order.

Elastic scattering

Neutrons in nuclear reactions with charged particles and when dividing nuclei is born rapid ( T N. About a few MeV), but absorbed, as a rule, slow. The slowdown occurs due to multiple elastic collisions with the nuclei of atoms.

There are two possibilities: Neutron deviation of the core field without capture - potential scattering, and departure neutron from the composite nucleus - resonant scattering. So the cross section is the amount σ Ex \u003d Σ Pot + Σ.

Fig.6 Section of elastic neutron scattering on uranium nuclei

Then according to (1), the scattering will occur with the zero moment of the pulse ( L \u003d 0, s - scattering). The angular distribution of scattered neutrons in the system of the inertia isotropic. In fact, these "small" energies are not so small: in hydrogen ~ 10 MeV, in lead ~ 0.4 MeV. The cross section of potential scattering in this case does not depend on the neutron energy and equal

In cross section of resonant scattering

width Γ N. Directly proportional to the speed, and the wavelength of de Broglie λ inversely proportional to her. Therefore, depending on the energy we only have a resonant peak when E \u003d E 0. As a result, for the dependence of the cross section of elastic scattering neutrons from energy, we have a pedestal with resonant peaks (Fig. 6).

Incomplete scattering

The core diffuser is in the excited state: n + a \u003d\u003e (a + 1) * \u003d\u003e a * + n. Obviously, the reaction has threshold Character: The energy of the flutter neutron should be sufficient to translate the target nucleus into the excited state. Studying the spectra of neutrons and accompanying γ - Radiation, receive information about the structure of the energy levels of the kernel.

A few words about how measure the cross section of inelastic scattering. With the kinetic neutron energy, more than 1 MeV,

The main processes will be elastic and inelastic scattering. σ \u003d σ UPR + Σ NEUPRO. Let be at a distance L. from source S. placed detector D. (Fig. 7). Surrounding the source of the radius sphere R. and wall thickness d.. If scattering purely elasticYou can show, weakening along the line connecting the source and detector compensated by scattering the sphere towards the detector from other directions. If there is a decrease in the detector testimony, then it is due to inelastic scattering

Here N. - Concentration of nuclei in the target. Several dimensions with different thicknesses allow you to find a section Σ NEUPR.

Radiation Capture

Radiation capture - neutron capture, the formation of the composite core in the excited state and the subsequent transition to the main one with the emission of γ-radiation n + (a, z) \u003d\u003e (a + 1, z) * \u003d\u003e (a + 1, z) + γ. The excitation energy of the composite nucleus (2), which means the total energy of γ-quanta exceeds the neutron binding energy in the nucleus, i.e. 7 - 8 MeV.

How does radiation capture manifest?
• emitting γ-quanta;
• in radioactivity (departure of β-particles) the formed kernel (A + 1, Z) (very often kernel (A + 1, Z) unstable);
• in the weakening of the neutron flow N \u003d n 0 exp (-σ β nd) (σ β - cross section of radiation capture, d. - target thickness).

Fig.10 The cross section of radiation capture with india cores.

With low neutron energies, resonant effects and a radiation grip cross section are very strong.

For slow neutrons Γ \u003d γ n + γ γ and Γ γ ≈ const ~ 0.1 eV. Therefore, the dependence of the cross section of radiation capture on energy repeats the dependence of the cross section of the formation of the composite nucleus. We note the very large value of the cross section of the capture of India (Fig. 10) at neutron energy of 1.46 eV. It is 4 orders of magnitude greater than the geometric cross section of the kernel. Indines include cadmium compounds for use as absorbing materials in reactors.

As noted, the kernel (A + 1, Z)The resulting neutron capture is very often radioactively with a short half-life. Radioactive radiation and radioactive decay are well known for each element. Since 1936, radioactivity induced neutron is used to identify elements. The method was called "Activated Analysis". There are enough sample about 50 mg. Activational analysis can detect up to 74 elements and is used to determine impurities in ultrapure materials (in reactor construction and electronics), the content of trace elements in biological objects in environmental and medical studies, as well as in archeology and forensic. Activation analysis is also successfully used when searching for minerals, to control technological processes and quality products.

The division of the nucleus is a phenomenon in which the heavy core is divided into two unequal fragments (very rarely for three). It was open in 1939 by the German radiochemists with Gan and Stresman, who proved that during the irradiation of uranium neutrons, an element from the middle of the periodic barium system is formed 56 BA..

A few days after the news of this, the Italian physicist E.Phermi (who moved to the United States) put experience in observing the fragments of division. Salt uranium was applied to the inner side of the plates of the pulsed ionization chamber (Fig.11). If the charged particle is hit to the volume of the chamber at the outlet, we have an electrical impulse, the amplitude of which is proportional to the particle energy. Uranium radioactive, α-particles give numerous impulses with small amplitude. When the camera is irradiated with neutrons, a large amplitude pulses caused by fragments of division were detected. Shardings have a large charge and energy of ~ 100 MeV. A few days earlier, Otto Frish watched fragments in Wilson's chamber.

Distinguish
• forced division - division under the action of a flutter particle (most often neutron)

  Usually the kinetic energy of the flutter particle T a is small and the reaction is through the composite core: a + a \u003d\u003e c * \u003d\u003e b 1 + b 2

• spontaneous division (spontaneous). Opened by Soviet physicists Flerov and Petrzhak in 1940. Uranium 235 U is divided with a half-life of about 2 * 10 17 years. On 1 division accounts for 10 8 α-decays, and it is extremely difficult to detect this phenomenon.

Elementary division theory

With the help of a drip model, we find out the main conditions of the possibility of division.

Energy division

Consider the division of the nucleus C. on two fragments C \u003d\u003e B 1 + b 2. Energy will stand out if the binding energies of the core and fragments are associated with the relation

G OSC \u003d G C - G 1 - G 2 based on the drip model, we find out at what mass numbers A C. and ordinal numbers Z C. Condition (7) is performed.

(8)

Substitute these expressions in (7), and we will take for a smaller fragment Z 1 \u003d (2/5) z c, A 1 \u003d (2/5) a C And for heavier Z 2 \u003d (3/5) z c, A 2 \u003d (3/5) a c.

The first and fourth terms in (8) will be reduced, because They are linear about A. and Z..

The first two terms in (9) - the change in the energy of the surface tension Δw pov, and the last two - a change in Coulomb energy Δw Kul. Inequality (7) now looks like

G osk \u003d - Δw pov - Δw kul \u003d 0.25 · Δw pov - 0.36 · Δw kul

If a Z 2 / a\u003e 17, the energy is allocated. Attitude Z 2 / a Call the division parameter.

Condition Z 2 / a\u003e 17 Performed for all cores, starting with silver 47 108 AG. Below it becomes clear why in reactors is used as a fuel dear uranium, and not cheaper materials.

Section mechanism

Condition Z 2 / a\u003e 17 Performed for all elements of the second half of the Mendeleev table. However, experience says that only very heavy kernels are divided. What's the matter? Remember α -Spad. Very often it is energetically beneficial, and does not happen, because Prevents the Coulomb barrier. Let's see how it is in the case of division. The possibility of dividing depends on the amount of the sum of the surface and Coulomb energy of the source kernel and fragments. Let's see how these energies change during core deformation - increasing parameter division ρ .

Surface tension energy W pov It increases, then when the fragments take a spherical shape, remains constant. Coulomb energy W Cul only decreases, first slowly and then 1 / ρ.. The sum of them Z 2 / a\u003e 17 and Z 2 / A behaves as shown in Figure 13. There is a potential barrier height B F.preventing division. Spontaneous division can occur due to a quantum-mechanical phenomenon of seepage (tunnel effect), but the probability of this is extremely small, so the half-life period, as mentioned above, is very large.

If a Z 2 / a\u003e 49, then the height of the barrier B f \u003d 0, and the division of such a nucleus happens instantly (for the nuclear time order 10 -23 from).

To divide the kernel, you must inform him the energy greater B F.. This is possible when capturing neutron. In this case, Formula (2) will look like

(11)

Here ε N. - Neutron binding energy in the kernel, obtained when capturing it; T N. - the kinetic energy of the flutter neutron.

Let's summarize the consideration of the interaction of neutrons.

Nuclear reactions under the action of charged particles

Unlike neutrons, when considering the collisions of charged particles with the nucleus, it is necessary to take into account the presence of Coulomb

Barrier. Neutron interaction with the kernel is characterized by deep (30 - 40 MeV) by a potential replacement R J. (Fig.14a). Neutron, close to the kernel, is experiencing a strong attraction. In the case of interaction of charged particles with the kernel, the potential curve has the form of Rice14b. When approaching the kernel, we first have a Coulomb repulsion (long-range forces), and at a distance of order R J. Powerful nuclear attraction comes into effect. Height of the Coulomb Barrier B Cul Approximately equal

For example, for protons when a collision with a core of oxygen, the height of the barrier will be 3.5 MeV, and with uranium - 15 MeV. For α - The height of the barriers is 2 times higher. If the kinetic particles T, there is a chance that the particle falls into the core due to the tunnel effect. But the transparency of the barrier is extremely small, most likely there will be elastic scattering. For the same reason, a charged particle is difficult to leave the kernel. Remember α -Spad.

The dependence of the cross section of a nuclear reaction for charged particles has a threshold. But resonant peaks are weakly pronounced or there are no no, because With energies ~ MeV, the density of the kernel levels is large and they overlap.

In the future, high hopes are related to thermonuclear synthesis reactions of type 2 H + 2 H \u003d\u003e 3 He + P or 2 H + 3 H \u003d\u003e 4 He + Nwhich differ in very large energy release. An obstacle to the implementation of such reactions is the Coulomb barrier. It is necessary to warm up the substance to such temperatures to the particle energy kt. allowed them to join the reaction. Temperature 1.16 · 10 7 corresponds to 1 keV. To obtain a self-sustaining "plasma" reaction, three conditions must be performed:

plasma should be heated to the required temperatures,

plasma density should be high enough

temperature and density must be maintained for a long time interval.

And there are solid problems: retention of plasma in magnetic traps, creating materials for a reactor that would withstand powerful neutron irradiation, etc. It is still unclear even how much electricity production can be cost-effective using the thermalide synthesis. There is constant progress in research.

Maximum energy loss (minimum E "N.) will be at θ = π : E "Min \u003d αe (for hydrogen E "Min \u003d 0).

At low energies (see (1)) scattering isotropic, all angles values θ Easily it. Because between the scattering angle θ and scattered neutron E "N. The connection is unambiguous (12), the distribution of neutrons by energy after one-time scattering will be uniform (Fig. 15). It can be represented as a formula

(13)

The average logarithmic loss of energy. Slowing ability. Slow coefficient

Let's see how a large number of collisions will affect the neutron energies. It is convenient to use no energy scale, but the scale of logarithms ε \u003d lne.: We have seen (see (12)) that E "/ E does not depend on E.. On average, the percentage of energy loss. On the energy scale, the change in energy looks like

Those. exactly lNE, but not E. Changes on a more or less fixed value.

The average neutron energy after a collision

Average energy loss

Middle Logarithmic Energy Loss

ξ does not depend on E.. Movement along the axis lNE uniform. You can simply calculate the average number of collisions n. To slow down OT. E NCH Understand E Kon.:

(14)

The table below shows the values ξ and n. For a number of nuclei when slowing the neutron from energy 1 MeV to thermal 0.025 eV.

				ξς s, 1 / cm	ξς S / Σ A

Watching the 4th column, it may seem that the hydrogen slows down better. But it is necessary to take into account the frequency of collisions. For gaseous and liquid hydrogen ξ \u003d 1.But it is clear that the path passing during deceleration will be different. In the 5th column there are logarithmic losses ξ multiplied by collision frequency - slowing ability. And here is the best retarder - ordinary water. But a good retarder must absorb neutrons. In the last, 6th column, the average logarithmic loss is multiplied by the ratio of macroscopic scattering and absorption sections. Comparing numbers, it is clear why heavy water or graphite use in atomic reactors as a retarder.

Average deceleration

We estimate the time required by the neutron to slow down as a result of collisions from the initial energy E 0 Understand E K.. We break the axis of energies on small segments ΔE.. Number of collisions ΔE. near E.

Free Male Length λ S. determined by the cross section of elastic scattering Σ S. and concentration of moderator kernels N.

, (15)

where Σ S. - the value called macroscopic cross section. The time required for slowing on ΔE., we define as a product of a segment of time to pass the length of the free run by the number of collisions on ΔE.

Turning to infinitely low values \u200b\u200band integrating, we get to slow down t.

For example, for beryllium when E 0 \u003d 2 MeV, E K. \u003d 0.025 eV, λ S. \u003d 1.15 cm, ξ \u003d 0.21 We get ~ 3.4 · 10 -5 s. Note that, firstly, this value is much less than the half-life of the free neutron (~ 600 s), and, secondly, it is determined by the movement near the final energy.

Spatial distribution of neutrons

Suppose in the medium there is a point isotropic source of fast neutrons with initial energy E 0. Distance L Zam.which is on average neutrons are removed when slowing to E K., called long slowdown. The real pathway passing by neutron is significantly more, because The trajectory of movement is a broken line of segments length λ S.. Value L Zam. Determined by the parameters of the deceleration medium, initial and final neutron energy:

For heavy water when slowing from 2 MeV to thermal 0.025 eV L Zam. ~ 11 cm, for graphite ~ 20 cm.

As a result of a slowdown in the amount with a radius of the length of the slowdown, thermal neutrons with Maxwell energy distribution are born. Thermal neutrons begin to diffuse (chaotically move), spreading through the substance in all directions from the source. This process is described by the diffusion equation with an obligatory accounting of neutron absorption.

(16)

In this equation Φ - the flow of neutrons (the number of neutrons crossing the unit platform per unit time), Σ S. and Σ A. - macroscopic scattering cross sections (see (15)) and absorption, respectively, D. - diffusion coefficient, S. - source of neutrons. In this equation, the first term describes the movement of neutrons in the substance, the second - absorption, and the third birth.

The main characteristic of the medium describing the diffusion process is diffusion length L Diff

The diffusion length characterizes the average removal of neutron from the source before absorption. For heavy water L Diff ~ 160 cm, for graphite ~ 50 cm. Ordinary water absorbs neutrons and L Diff A total of 2.7 cm. As far as the neutron is long and the path of the neutron during diffusion can be judged, if you compare the length of the diffusion (in graphite 50 cm) with the average length of the neutron path before absorption λ a \u003d 1 / σ a (in the same graphite 3300 cm).

In practice, it is often dealing with the transition of neutrons from one environment to another. For example, the active zone of the reactor is surrounded by reflector. Reflection coefficient β - The proportion of neutrons returning to Wednesday having sources from the environment without sources. Approximately, β ≈ 1 - 4 · d / l Diffwhere parameters relate to the environment without sources. For example, from a graphite reflector β \u003d 0.935, i.e. 93% neutrons will return. Graphite is an excellent reflector. It is only hard water, where β = 0.98!

Chain reaction in a medium containing a fideling substance

We have a homogeneous medium containing the dividing substance. There are no extraneous neutron sources, they can only appear as a result of core division. We assume that all processes go at one energy (the so-called single speed approximation). Question: Is it possible to make a ball in which a stationary chain reaction would be supported in this substance?

We will need:

• macroscopic neutron absorption section Σ Lakewhich folds from the sequence of capture without division Σ ZAZHV (radiation capture) and division sections Σ business: Σ Lake = Σ ZAZHV + Σ business;
• the average number of neutrons υ released in one share of division.

Then the neutron stream equation Φ in the inpatient case will look like

with boundary condition

,

which denotes that at some distance d. From a bowl with a substance of radius R. The flow should contact it in zero.

If you compare the equation for the stream Φ C (16), it can be seen that the value of the source ςς deeds Φ. - The number of neutrons born in a unit of volume per unit of time.

Consider three cases

ςς cases - neutrons are born less than absorbed. Obviously, the stationary reaction is impossible.

• ςς deed \u003d Σ - The source compensates for neutron absorption. The solution of equation (17) gives Φ \u003d const. only for endless environmentOtherwise, due to neutron leakage through the boundary of the medium, the reaction will fall.

  ςς cases\u003e Σ - You can choose such sizes of a bowl of the dividing substance so that the surplus of neutrons go through the borders of the ball (preventing a nuclear explosion).

We introduce the designation ω 2 \u003d (σ melted - ςς deeds) / d\u003e 0. Equation (17) will take a view

(18)

His general solution looks like

(19)

Coefficient B. in (19) must be put equal to zero so that the decision does not disperse when r \u003d 0. Finding the final solution is complicated by correct accounting of the boundary condition, and for the natural mixture of uranium isotopes (235 U - 0.7%, 235 U - 99.3%, Σ Lake \u003d 0.357 1 / cm, Σ business \u003d 0.193 1 / cm, υ \u003d 2.46) We get as the minimum value of all R ≈ 5.see what this task is different from real? In reality, neutrons are born rapidly, and they must be slowed down to heat energies. The first reactor, built by E. Fermi (1942), had a size of about 350 cm.

Chain reaction. Nuclear reactor

Devices in which energy is obtained by the stationary chain fission reaction, called atomic reactors (for example, they say nuclear power plant, nuclear power plant), although in essence it nuclear Reactors. The design of atomic reactors is very complex, but the necessary element of any reactor is the active zone in which the division reaction occurs.

The active zone contains a dividing substance, a moderator, controlling (regulating) rods, structural elements and is surrounded by a neutron reflector to reduce the losses of the latter. All this is inside protection against neutron flux, γ - emission.

Neutron's fate in the active zone

capture the uranium core with the subsequent division of this nucleus;

capture the uranium core with the subsequent transition of the kernel to the ground state with emission γ -banks (radiation capture);

capture kernels of a moderator or structural elements;

departure from the active zone;

absorption by regulating rods.

Neutrons are emitted when dividing nuclei, then absorbed or leaving the active zone. Denote by k. The coefficient of reproduction is the ratio of the number of neutrons of the subsequent generation n i + 1 to the number in the previous n I.

If you enter the lifetime of the generation τ , then the equation for the number of neutrons n. and his decision will look like

(21)

If the coefficient k. Detained from 1, the number of neutrons decreases ( k) or increases ( k\u003e 1.) According to the exponential law, i.e. very quickly.

(Follow the effect of reproduction coefficient k. and generation life τ on the dynamics of the number of neutrons on simple experience)

Reproduction coefficient k. can be represented as a product of the coefficient k ∞. For an infinite environment and probability not Leave an active zone χ

Value χ Depends on the composition of the active zone, its size, form, reflector material.

Considering the reactor operating on thermal neutrons, coefficient k ∞. can be represented in the form of four factors

where

ε - reproduction coefficient on fast neutrons (for real systems from uranium and graphite ε ~ 1.03);

p. - The probability of avoiding resonant capture during a slowdown. Recall that neutrons are born rapidly, and when slowing down to heat energies, they need to overcome the region of resonances in the absorption section (see Fig. 10);

f. - The proportion of neutrons absorbed by the uranium nuclei (and not a moderator or design elements). ε · p · f ≈ 0.8;

η - The average number of neutrons emitted to one act of capturing the uranium core (the core can occur when capturing, and maybe emissions γ -Kvanta). η ≈ 1.35 (Compare with ~ 2.5 for the number of neutrons per act of division).

From the given data follows k ∞ \u003d 1.08 and χ \u003d 0.93, which corresponds to the size of the reactor of about 5 - 10 m.

Critical mass - The minimum mass of the dividing substance in which the self-sustaining nuclear reaction can occur in it. If the mass of the substance is below the critical, then too many neutrons necessary for the fission reaction is lost, and the chain reaction does not go. When mass is more critical, the chain reaction may be avalanchely accelerated, which will lead to a nuclear explosion.

The critical mass depends on the size and shape of the sample dividing, as they determine the leakage of neutrons from the sample through its surface. The minimum critical mass has a sample of a spherical form, since the area of \u200b\u200bits surface is the smallest. The neutron reflectors and retarders surrounding the divided substance can significantly reduce the critical mass. Critical mass depends on the chemical composition of the sample.

The "grandfather" of domestic nuclear reactors is the first physical reactor F-1, which received the status of a monument of science and technology. It was launched in 1946 under the leadership of I.V. Kurchatov. As a retarder used purified graphite in the form of bars with holes for uranium rods. Management was carried out by rods containing cadmium, strongly absorbing thermal neutrons. In the active zone of the boiler there were 400 tons of graphite and 50 tons of uranium. The reactor power was about 100 W, there was no special heat sink system. When working, the heat was accumulated in a large mass of graphite. Then the graphite masonry was cooled by a jet of air from the fan. This reactor works regularly and so far.

The share of nuclear power in global electricity production was 10-20% in different years. The greatest percentage (~ 74) of electricity is made at NPP in France. In Russia, ~ 15%.

What does the physical starting process of the atomic reactor looks like a computer model.

If you want to check how the lecture material is learned,

Professor

I.N.Bekman

NUCLEAR PHYSICS

Lecture 16. Nuclear interactions

The development of nuclear physics is largely determined by research in the field of nuclear reactions. In this lecture, we will consider the modern classification of nuclear interactions, their

thermodynamics and kinetics, as well as give separate examples of nuclear reactions.

1. Classification of nuclear reactions

Due to the action of nuclear forces, two particles (two kernels or core and nucleon) when approaching up to the distance distance10 -13 cm re-enter into intensive nuclear interaction, leading to the conversion of the kernel. This process is called a nuclear reaction. During the nuclear reaction, the redistribution of energy and the pulse of both particles occurs, which leads to the formation of several other particles departing from the interaction site.In the collision of the flutter particles with the atomic core between them, the exchange of energy and pulse occurs, as a result of which several particles flying out in various directions from the interaction area can be formed.

Nuclear reactions - transformations of atomic nuclei when interacting with elementary particles, γ -qvants or with each other.

The nuclear reaction is the process of forming new cores or particles in the collisions of cores or particles. For the first time, the nuclear reaction was observed by E. Rutherford in 1919, bombarding α-particles of nucleus atoms of nitrogen, it was recorded by the emergence of secondary ionizing particles having a gas mileage greater than the α-particles and identified as protons. Subsequently, with the help of the Wilson cameras, photos of this process were obtained.

Fig. 1. Processes occurring during nuclear reactions

(The reaction input and output channels are presented).

The first nuclear reaction was carried out by E. Rutherford in 1919: 4 HE + 14 N → 17 O + P or 14 N (α, p) 17 O. The source of α-particles was an α-radioactive drug. Radioactive α-preparations at the time were the only sources of charged particles. The first accelerator, specially created to study nuclear reactions, was built by Cockrift and Walton in 1932. At this accelerator first was

a beam of accelerated protons was obtained and the P + 7 Li → α + α reaction was carried out.

Nuclear reactions are the main method of studying the structure and properties of atomic nuclei. In nuclear reactions, mechanisms of interaction of particles with atomic nuclei are studied, mechanisms of interaction between atomic nuclei. As a result of nuclear reactions, new isotopes and chemical elements are obtained in natural conditions. If, after the collision, the initial kernels and particles are preserved and new ones are not born, the reaction is elastic scattering in the field of nuclear forces, is accompanied only by the redistribution of kinetic energy and the pulse of the particle and the target nucleus and is called potential

scattering.

The consequence of the interaction of bombarding particles (cores) with the target nuclei can be:

1) Elastic scattering, in which no composition nor internal energy changes, and only the redistribution of kinetic energy occurs in accordance with the law of internal impact.

2) Incomplete scattering, in which the composition of the interacting nuclei does not change, but part of the kinetic energy of the bombing nucleus is spent on the excitation of the target kernel.

3) Actually nuclear reaction, as a result of which the internal properties and the composition of the interacting nuclei are changing.

	Fig. 2. Lithium-6 nuclear reaction with deuterium 6 Li (D, α) α
	In nuclear reactions, strong, electromagnetic and weak
	interaction.
	Many different types of reactions are known. They can be classified on
	reactions under the action of neutrons, under the action of charged particles and under the action
	In general, nuclear interaction can be written in the form
	a1 + A2 → B1 + B2 + ...
	where and 1 and a 2 are particles reacting, and b 1, b 2, ... - particles,
resulting as a result of the reaction (reaction products).
	The most common type of reaction is the interaction of a light particle A with a kernel A, in
the result of which the lung particle B and the kernel in
	a + A → B + B
	Or shorter
	A (a, b) b.

Neutron (N), Proton (P), α - particle, deton (d) and γ-kart can be taken as a and b.

Example 1. Nuclear reaction

4 HE + 14 N → 17 O + 1 H

in abbreviated form is written as14 N (α, p) 17 o

Example 2. Consider the reaction 59 CO (P, N). What is the product of this reaction? Decision. 1 1 H + 27 59 CO → 0 1 n + x y z with

the left side we have 27 + 1 proton. On the right side of 0 + X protons, where X is the nuclear number of the product. Obviously, x \u003d 28 (ni). On the left side of 59 + 1 of nucleons, and with the right 1 + y of nucleons, where y \u003d 59. Thus, the 59 Ni reaction product.

The reaction can go several competing paths:

Different possible paths of the nuclear reaction in the second stage are called reaction channels. The initial stage of the reaction is called the input channel.

Fig. 3. Channels for the interaction of protons with 7 Li.

The two recent reaction channels in Scheme (6) refer to cases of inelastic (A * + A) and elastic (a + a) nuclear scattering. These are special cases of nuclear interaction, differing from other fact that the reaction products coincide with particles,

with the reaction, and with elastic scattering, not only the type of kernel is maintained, but also its internal state, and with inelastic scattering the inner state of the kernel changes (the kernel goes into an excited state). The possibility of various reaction channels is determined by the inclusive particle, its energy and the core.

When studying the nuclear reaction, the identification of the reaction channels is of interest to the comparative probability of it in different channels at various energies of incident particles, the energy and angular distribution of the resulting particles, as well as their inner state (excitation energy, spin, readiness, isotopic spin).

Nuclear reaction is a complex process of restructuring atomic nucleus. As with the description of the structure of the kernel, it is almost impossible to obtain an accurate solution to the problem. And just as the structure of the nucleus is described by various nuclear models, the course of nuclear reactions is described by various mechanisms of reactions.

There are many different reaction mechanisms. We will consider only the main of them. Initially, the classification of reaction mechanisms will be given, and then the most important of them will be considered in more detail.

We will classify the reactions by the flow time. As a temporary scale, it is convenient to use nuclear time - the time of the span of particles through the kernel: T I \u003d 2R / V≈10 -22 p. (9.11)

We will use the following classification of nuclear reactions in terms of flowing:

1. If the T P ≈T reaction time is, then this is a direct reaction (reactive time).

2. If T P \u003e\u003e T I, then the reaction goes through the composite core.

In the first case (direct reaction)the particle A transmits the energy to one or two nucleons of the nucleus, without affecting the rest, and they immediately leave the kernel, without having time to exchange energy with the rest of the nucleons. For example, the reaction (P, N) may occur as a result of a collision of the proton with one nuclear neutron. The processes should include a breaking reaction (D, P), (D, N) and the reaction of pickup reactions (P, D), (N, D), the fragmentation reaction, in which the high energy nucleon, facing the kernel, knocks out of It is a fragment consisting of several nucleons.

In the second case (composite core) A particle A and the nucleon she passed the energy, "confused" in the kernel. Energy is distributed among many nucleons, and each nucleon has insufficient for departure from the kernel. Only after a relatively large time as a result of random redistributions, it is concentrated in sufficient quantity on one of the nucleons (or object from several connected nucleons) and it leaves the kernel. The mechanism of the composite nucleus was introduced by Niels Bohr in 1936

The intermediate position between the reaction mechanism through the composite core and the mechanism of direct reaction occupies mechanism of foresightest nuclear reactions.

The time of nuclear reactions can be determined by analyzing the widths of the excited nuclear states.

To describe elastic scattering averaged on nuclear resonance, used optical modelin which the core is interpreted as a solid medium capable of refracting and absorbing sebroil waves of particles falling on it.

Nuclear reaction nature depends on a number of factors: type of a mextile particle, type of target nucleus, the energy of their collision and some others, which makes any classification of nuclear reactions quite conditional. The easiest is classification of the type of particle-projectile. As part of such a classification, the following main types of nuclear reactions can be distinguished:

Reactions under the action of protons, deuterons, α-particles and other light nuclei. It was these reactions that were given the first information about the structure of atomic nuclei and the spectra of their excited states.

Reactions with heavy ions on heavy nuclei, leading to the merging of encountered nuclei. These reactions are the main method of obtaining superheavy atomic nuclei.

Reactions of the merge of light nuclei at relatively low collision energies ( so-called thermonuclear reactions). These reactions occur at the expense of quantum-mechanical tunnation through the Coulomb barrier. Thermonuclear reactions proceed inside the stars at temperatures of 10,7 -10 10 K and are the main source of stars.

Coulomb excitation of cores under the action of protons, α-particles and especially repeatedly ionized heavy ions of elements such as carbon, nitrogen, argon, etc. These reactions are used to study low-laying rotational levels of heavy nuclei.

The reactions under the action of neutrons, first of all (N, N), (N, γ) and the reaction of the core division (N, F).

Many specific properties have photonuclear and electrical reactions that occur when a collision with nuclei of γ-quanta and electrons with energy E\u003e 10 MeV.

Reactions on the beams of radioactive cores. Modern technical means allow you to generate fairly intense bundles of such cores, which opens up the possibilities of obtaining and studying nuclei with an unusual ratio of the number of protons and neutrons, distant from the stability line.