Calculation of the characteristics of the interaction of gamma quanta with air. Photoelectric effect (photoelectric absorption)
Study of the geological section of wells (lithological-geological section of the well)
Study of the technical condition of wells
Control over oil and gas field development
Carrying out drilling and blasting operations in wells
Testing of formations and sampling from well walls
8. Interaction of gamma rays with matter, gamma ray logging, problems to be solved
Radioactivity is the ability of some atomic nuclei to spontaneously decay with the emission of α, β, γ rays, and sometimes other particles. Gamma rays are short wavelength electromagnetic radiation. The path length of γ - quanta in rocks reaches tens of centimeters. Due to their high penetrating ability, they are the main type of radiation recorded in the natural radioactivity method. Particle energy is expressed in electron volts (eV). The effect of gamma radiation on the environment is quantified in roentgens. Of the natural radioactive elements, the most common are uranium U238, thorium Th232 and potassium isotope K40. The radioactivity of sedimentary rocks, as a rule, is directly related to the content of clay material. Sandstones, limestones and dolomites have low radioactivity; rock salt, anhydrites and coals have the least radioactivity. To measure the intensity of natural gamma radiation along the wellbore, a downhole instrument containing a γ-radiation indicator is used. Gas-discharge scintillation counters are used as an indicator. Gas discharge meters are a cylinder in which two electrodes are placed. The cylinder is filled with a mixture of inert gas and vapor of a high-molecular compound under low pressure. The meter is connected to a high voltage DC source - about 900 volts. The operation of a gas-discharge counter is based on the fact that γ-quanta, entering it, ionize the molecules of the gas filler. This leads to a discharge in the meter, which will create a current pulse in its power supply circuit. Gamma ray logging. When passing through matter, gamma rays interact with electrons and atomic nuclei. This leads to a weakening of the intensity of γ radiation. The main types of interaction of gamma quanta with matter are the formation of electron-positron pairs, the photoelectric effect, the Compton effect (the γ-quantum transfers part of its energy to the electron and changes the direction of movement). An electron is ejected from an atom. After several acts of scattering, the energy of the quantum will decrease to the value at which it is absorbed due to the photoelectric effect. The photoelectric effect comes down to the fact that a γ-quantum transfers all its energy to one of the electrons of the inner shell and is absorbed, and the electron is ejected outside the atom. The well has a significant influence on the GGC readings. It reduces the density of the medium surrounding the probe and leads to an increase in the GGC reading in proportion to the diameter. To reduce the influence of the well, GGS devices have clamping devices and screens that protect the indicator from scattered γ-radiation of the drilling fluid. Irradiation of the rock and perception of scattered γ-radiation in this case is carried out through small holes in the screens, called collimators. Characteristic feature diagrams of the scattered gamma radiation method is not a direct, but an inverse relationship with density, which is due to the size of the probe. If the indicator were placed near the source, a medium with increased density would also be marked by a high intensity of scattered γ-radiation.
9. Identification of perforation intervals by location of couplings
The method of electromagnetic location of couplings is used:
to establish the position of tool joints of stuck drill pipes;
determining the positions of casing coupling connections;
accurately linking the readings of other instruments to the position of the couplings;
mutual reference of readings from several instruments;
clarification of the depth of descent of pumping and compressor pipes;
determining the current bottom of the well;
V favorable conditions– to determine the perforation interval and identify places of violation (ruptures, cracks) of the casing columns.
Physical basis of the method: The method of electromagnetic location of couplings (LM) is based on recording changes in the magnetic conductivity of the metal of drill pipes, casing and tubing due to a violation of their continuity.
Equipment: The clutch locator detector (sensor) is a differential magnetic system, which consists of a multilayer coil with a core and two permanent magnets that create a constant magnetic field in and around the coil. When the locator moves along the column in places where the continuity of the pipes is broken, the magnetic flux is redistributed and an EMF is induced in the measuring coil.
The active clutch locator contains two coils, each of which has an exciting and receiving winding. Under the influence of an alternating magnetic field generated by applying an alternating voltage to the exciting windings, an alternating voltage appears in the receiving windings, which depends on the magnetic properties environment. An informative parameter is the voltage difference across the receiving windings, which depends on the continuity of the medium.
Ticket 4
10. GIS complex in a well cased with a column, tasks to be solved
A prerequisite for the successful use of logging to study the geological section of a well is the selection of an appropriate complex (program) of geophysical research. The program should provide solutions to the tasks assigned to it with the smallest possible volume of measurements. Taking into account the similarities of geological and technical specifications for carrying out work in different areas, standard GIS complexes are installed. Typical packages include general studies that are performed along the entire wellbore and legal studies of oil and gas promising intervals. In a well cased with a column, all types of logging are carried out except micro-logging and BKZ (since they are used in an uncased well with a column, because these methods determine the thickness of the mud cake).
11. Neutron gamma ray logging, physical basis, curves, solvable problems
Neutron logging is used in open and cased wells and is used to solve the following problems:
for the purpose of lithological division of sections;
determination of the position of the current gas-oil contact (GOC), intervals of gas breakthrough, cross-flow, degassing of oil in the reservoir and gas saturation assessment;
determination of the position of the oil-water contact of the OWC in wells with high salinity of formation waters.
Neutron radiation has the greatest penetrating power. This is due to the fact that neutrons, being uncharged particles, do not interact with the electron shells of atoms and are not repelled by the Coulomb field of the nucleus. Just like gamma rays, neutrons are characterized by energy E, which in this case is related to their speed. There are fast neutrons with an energy of 1-15 MeV, intermediate 1 MeV - 10 eV, slow or suprathermal neutrons 0.1-10 eV and thermal neutrons with an average energy of 0.025 eV. The interaction of neutrons with a substance occurs in an elastic collision with a nucleus with the loss of part of the energy, i.e. in neutron moderation, and neutron capture by the nucleus. The main type of interaction of neutrons with energies from several MeV to 0.1 eV is elastic scattering. In elastic neutron scattering, the amount of energy loss due to collision is determined only by the mass of the nucleus: the smaller the mass of the nucleus, the greater the energy loss. Naib. Energy loss occurs when a neutron collides with the nucleus of a hydrogen atom. One of the main neutron parameters of the medium is the slowdown length L3. This is the average distance from the point where a neutron is released to the point where it slows down to thermal energy. Slowed down neutrons continue to move and collide with the nuclei of elements, but without changing the average energy. This process is called diffusion. The average distance that a neutron travels from the point of moderation to the point of capture is called the diffusion length. The diffusion length is usually much smaller than the retardation length. The final result of the movement of a thermal neutron is its absorption by some atomic nucleus. When a neutron is captured by a nucleus, energy is released in the form of one or more γ quanta. There are the following types of neutron methods: neutron gamma method NGM, neutron method using epithermal neutrons NMN, neutron method using thermal neutrons NMT. They differ from each other in the type of indicators used. Pulsed neutron methods. The essence of pulsed neutron logging lies in the study of non-stationary neutron fields and γ-fields created by a neutron generator. The neutron generator operates in pulse mode with a frequency from 10 to 500 Hz. In pulsed methods, rock is irradiated with short-term fluxes of fast neutrons of duration ∆t, following one after another at time intervals t.
Slide 1
Lecture 8 Processes of interaction of gamma rays Photoelectric effect Characteristics of the cross section of the photoelectric effect Cross section of the photoelectric effect Direction of electron emission Compton effect Cross section of the Compton effect on the electron Compton effect cross section on the proton “Interaction of gamma quanta with matter”Slide 2
E/m interaction of gamma quanta: photoelectric effect; - elastic scattering by electrons (Compton effect); - birth of pairs of particles. The processes occur in the energy range of keV - hundreds of MeV, which are most often used in applied research. Let's consider the dependence on the energy Eγ and the characteristics of the substance. Processes of interaction of gamma quanta. The relationship between the energy of a γ-quantum and its wavelength:
Slide 3
Photoelectric effect Photoeffect is the process of knocking out an electron from a neutral atom under the influence of a gamma quantum. A free electron does not absorb a gamma quantum. Let the reaction proceed, use 4-pulses. Let's square it. Transform. The last equality turns out to be valid if Eγ = 0, i.e. There is no gamma quantum. This means that during the photoelectric effect, the electron receives energy Ii - ionization potential TA - kinetic energy of the ion
Slide 4
Characteristics of the photoelectric effect cross section The photoelectric effect is possible if the energy of the γ-quantum is greater than the ionization potential (K, L, M...-shell) If Eγ< Ik , то выбивание электронов происходит только с внешних оболочек L, M.. Выбивание электронов с внутренних оболочек сопровождается монохроматическим рентгеновским характеристическим излучением, возникающим при переходе атомного электрона на освободившийся уровень. При этом может возникать целый каскад взаимосвязанных переходов. Передача энергии иона одному или нескольким орбитальным электронам, приводит в вылету из атома электронов Оже.
Slide 5
Photoelectric cross section If the energy of the γ-quantum is less than the ionization potential of the outermost shell, then the photoelectric cross section is zero. Another limiting case is if the energy of the γ-quantum is very high (Eγ >> I), then we can assume that the electron is free, and the photoelectric effect is not possible on free electrons. As the energy increases, the cross section asymptotically tends to zero. In the region of energies of shell ionization potentials (Eγ = Ii), the cross section undergoes jumps. In the segment, the cross section on the M-shell decreases, since the connectivity of the electron on this shell decreases in relation to the energy of the gamma quantum, while the photoelectric effect from the L-shell is still energetically prohibited .
Slide 6
The influence of the strong coupling of an electron in an atom on the cross section of the photoelectric effect is reflected in a power-law dependence on the charge of the nucleus. Quantum mechanical calculation requires knowledge of the -functions of atomic electrons on different shells. The effective cross section of the photoelectric effect from the inner K-shell is determined by the relations (cm2/atom): if Eγ > mc2 Where Thomson scattering cross section The cross section decreases rapidly Photoelectric effect cross section
Slide 7
Direction of electron emission If a beam of gamma quanta hits atoms, then the knocked out electrons fly out predominantly in the direction perpendicular to the photon momentum along the vector of the electric field of the wave. That's why. angular distribution of photoelectrons for low energies distribution for high-energy photons Photoelectric effect is the main process of photon absorption at low energies. Absorption on heavy atoms is especially effective.
Slide 8
Compton effect: energy of a scattered photon Elastic scattering of a high-energy γ-quantum on an atomic electron Quantum energy is much greater than the ionization potential Eγ >> I; electron can be considered free In this process, a γ-quantum with energy (wave -) exhibited the properties of a particle when scattered () Let us find out how the energy of a scattered quantum depends on the scattering angle Conservation of 4-momentum We obtain the dependence of the energy of a scattered γ-quantum on an angle in the form
Slide 9
Compton effect: energy of a scattered electron Energy of a scattered electron depending on its scattering angle and the relationship between the angles of scattered particles: electron and γ-quantum At high energies, a simplified expression is obtained for the energy of scattered gamma quanta The energy of a gamma quantum after scattering does not depend on the initial energy For an electron, for example, when scattering back () the energy is always This result is a manifestation of the corpuscular properties of a gamma quantum Slide 11 
Cross section of the Compton effect on a proton Is the Compton effect possible on a proton? Qualitative consideration indicates that in order to interact, a gamma quantum must “hit the electromagnetic area” of the target, which is characterized by the Compton wavelength of the particle. From here we find the relation It can be seen that the Compton effect on protons can be neglected. A similar conclusion is obtained from exact formulas for the cross section by replacing the value with the value in the case of scattering by a proton. When gamma rays interact with matter, the quantum mechanical properties of micro-objects appear
Gamma radiation is characterized by intensity, which is understood as the product of energyγ -quanta by their number falling every second on a unit of surface normal to the flow of gamma quanta.
As with any type electromagnetic radiation the intensity of γ-radiation of a point source decreases in inverse proportion to the square of the distance from the radiation source (if there is no additional absorption in the medium). This is determined by the purely geometric properties of the radiation flux, i.e. its divergence with distance from a point source of radiation. In reality, such a weakening will be observed in an absolute vacuum.
Gamma radiation is a highly penetrating radiation. But when passing through any substance, it will be absorbed by this substance. This absorption can occur due to the interaction of γ-radiation with atoms, electrons and nuclei of matter, manifested in the form of the following effects:
· photoelectric effect– consisting of the γ-quantum knocking out electrons from the internal electron shells of atoms (most often from TO-shell), which leads to its ionization and the appearance of a free electron. This effect predominates at γ-quanta energies below 0.5 MeV;
· Compton effect, which consists in the fact that a γ-quantum excites an electron in the outer shell of an atom, transferring part of its energy to it, as a result of which its energy decreases and its direction changes (Compton scattering);
· pair formation – if a γ-quantum flies directly near the nucleus and its energy exceeds 1.022 MeV, then an electron-positron pair can be formed;
· photonuclear reactions, in which gamma rays, absorbed by the nucleus, excite it, transferring their energy to it, and if this energy is greater than the binding energy of a neutron, proton or alpha particle, then these particles can leave the nucleus. On fissile nuclei (235 U, 239 Pu, etc.), if the energy of the gamma quantum is greater than the nuclear fission threshold, fission will occur.
As a result of all these interactions, when gamma radiation passes through an absorber, its intensity decreases according to the law:
Where I 0 , I– intensity of γ-radiation before and after passing through the absorber;
μ – linear attenuation coefficient;
d– absorber thickness.
In Fig. Figure 3.1 shows a simple design of an attenuation experiment. When gamma radiation with intensity I 0 falls on an absorber of thickness d, intensity I radiation passing through the absorber is described by exponential expression (3.1).
Rice. 3.1. Basic law of gamma radiation attenuation
Transmitted radiation intensity I is a function of gamma radiation energy, composition and thickness of the absorber. Attitude I/I 0 is called the gamma radiation transmittance. Figure 3.2 shows the exponential attenuation for three different gamma ray energies. The figure shows that the transmittance increases with increasing gamma radiation energy and decreases with increasing absorber thickness. The coefficient μ in equation (3.1) is called the linear attenuation coefficient.
Linear attenuation coefficientμ depends on the energy of γ quanta and the properties of the absorbing material. It has a dimension of m -1 and is numerically equal to the fraction of monoenergetic gamma quanta leaving a parallel beam per unit radiation path in the substance. The linear attenuation coefficient depends on the density and serial number of the substance, as well as on the energy of gamma rays. For example, lead has a high density and high atomic number and transmits a much smaller fraction of incident gamma radiation than aluminum or steel of the same thickness.
Rice. 3.2. Dependence of the transmittance of gamma quanta on the thickness of the lead absorber
The values of the linear attenuation coefficient of gamma radiation from the 60 Co source for various materials are presented in Table 3.1, and their dependence on the energy of γ quanta is in Table 3.2.
The thickness of the absorber layer required to reduce the radiation intensity by half is called half-thickness d 1/2.
From the absorption law (3.1) it follows that the half-thickness is equal to
Table 3.1
Linear attenuation coefficient μ of γ-radiation materials Co-60
Table 3.2
Dependence of the linear attenuation coefficient μ of materials
on the energy of γ quanta
| E, MeV | μ, cm -1 | |||||
| Lead | Water | Aluminum | Iron | Graphite | Air | |
| 0,10 | 0,171 | 0,455 | 2,91 | 0,342 | 2.00·10 -4 | |
| 0,15 | 22,8 | 0,151 | 0,371 | 1,55 | 0,304 | 1.76·10 -4 |
| 0,20 | 11,1 | 0,137 | 0,328 | 1,15 | 0,277 | 1.59·10 -4 |
| 0,30 | 4,43 | 0,119 | 0,280 | 0,865 | 0,241 | 1.38·10 -4 |
| 0,40 | 2,62 | 0,106 | 0,249 | 0,740 | 0,214 | 1.23·10 -4 |
| 0,50 | 1,80 | 0,0966 | 0,227 | 0,661 | 0,196 | 1.12·10 -4 |
| 0,80 | 0,999 | 0,0786 | 0,184 | 0,526 | 0,159 | 9.13·10 -5 |
| 1,0 | 0,798 | 0,0279 | 0,165 | 0,471 | 0,143 | 8.21·10 -5 |
| 1,5 | 0,591 | 0,0575 | 0,135 | 0,382 | 0,117 | 6.68·10 -5 |
| 2,0 | 0,518 | 0,0493 | 0,116 | 0,334 | 0,0999 | 5.74·10 -5 |
| 3,0 | 0,475 | 0,0396 | 0,0950 | 0,284 | 0,0801 | 4.63·10 -5 |
| 4,0 | 0,472 | 0,0340 | 0,0834 | 0,260 | 0,0684 | 3.98·10 -5 |
| 5,0 | 0,480 | 0,0302 | 0,0761 | 0,247 | 0,0603 | 3.54·10 -5 |
| 8,0 | 0,519 | 0,0242 | 0,0651 | 0,233 | 0,0482 | 2.87·10 -5 |
| 0,552 | 0,0220 | 0,0619 | 0,233 | 0,0439 | 2.62·10 -5 | |
| 0,628 | 0,0193 | 0,0584 | 0,241 | 0,0380 | 2.31·10 -5 | |
| 0,694 | 0,0180 | 0,0578 | 0,250 | 0,0351 | 2.19·10 -5 | |
| 0,792 | 0,0170 | 0,0584 | 0,269 | 0,0329 | 2.08·10 -5 | |
| 0,863 | 0,0166 | 0,0603 | 0,285 | 0,0320 | 2.06·10 -5 | |
| 0,915 | 0,0166 | 0,0616 | 0,299 | 0,0320 | 2.08·10 -5 |
Linear attenuation coefficient is the simplest attenuation coefficient that can be measured experimentally, but is not usually given in lookup tables due to its dependence on the density of the absorbing material. For example, water, ice and steam have different linear extinction coefficients for the same energy, even though they are composed of the same substance.
Gamma rays interact mainly with atomic electrons, therefore, the attenuation coefficient must be proportional to the electron density P, which is proportional to the volumetric density of the absorbing material. For any given substance, the ratio of the electron density to the volume density of that substance is the constant Z/A, independent of the volume density. The Z/A ratio is almost constant for all elements except the heaviest elements and hydrogen:
P=Zρ / A, (3.3)
Where P- electron density;
Z- atomic number;
ρ - mass density;
A- mass number.
If we divide the linear attenuation coefficient by the density of the substance ρ, we get mass attenuation coefficient, independent of the density of the substance:
The mass attenuation coefficient is measured in cm 2 /g (in the SI system - m 2 /kg) and depends only on the serial number of the substance and the energy of gamma quanta. Judging by the unit of measurement of this coefficient, it can be considered as the effective cross section for the interaction of electrons per unit mass of the absorber. The mass attenuation coefficient can be written in terms of the reaction cross section σ (cm 2):
Where N 0 - Avogadro's number (6.02 10 23);
A- mass number of the absorbing element.
Interaction cross section σ i by their definition are similar to reaction cross sections, i.e. determines the probability of leakage i-th process during the interaction of a gamma quantum with an atom. It is related to the linear attenuation coefficients μ i formula
Where N– number of atoms of a substance in 1 cm3;
i– a short designation for the photoelectric effect (ph), the Compton effect (k) and the effect of the formation of electron-positron pairs (p).
Cross sections are expressed in barns per atom.
Using the mass attenuation coefficient, equation (3.1) can be represented as follows:
, (3.7) where x = ρ d.
The mass attenuation coefficient does not depend on density, but depends on the photon energy and the atomic number of the absorber. Figures 3.3 and 3.4 show the dependence on photon energy in the range from 0.01 to 100 MeV for groups of elements from carbon to lead. This coefficient is more often given in tables than the linear attenuation coefficient, since it quantifies the probability of interaction of gamma rays with a particular element.
Rice. 3.3. Dependence of the total mass absorption coefficient on photon energy for various materials (energy range from 0.01 to 1 MeV)
The reference book contains tables of the dependences of the linear and mass attenuation coefficients and the free path of gamma quanta on their energy in the range from 0.01 to 10 MeV for various substances.
The interaction of gamma radiation with a complex substance is characterized by effective ordinal number Z eff of this substance. It is equal to the ordinal number of such a conventional simple substance, the mass attenuation coefficient of which at any energy of gamma rays coincides with the mass attenuation coefficient of the given complex substance. It is calculated from the ratio:
Where Р 1, Р 2, …, Р n– weight percentage constituent substances in a complex substance;
μ 1 /ρ 1 , μ 2 /ρ 2 , …, μ n/ρ n– mass attenuation coefficients of constituent substances in a complex substance.
Taking into account the above three main effects of interaction of gamma radiation with matter, the total linear attenuation coefficient will consist of three components determined by the photoelectric effect, the Compton effect and the pair generation effect:
Each of them depends in different ways on the serial number of the substance and the energy of gamma rays.
At photoelectric effect The gamma quantum is absorbed by the atom, and an electron escapes from the atom (Figure 3.5).
Rice. 3.5. Photoelectric absorption process diagram
Part of the energy of the gamma quantum, equal to the binding energy ε e, is spent on detaching an electron from the atom, and the rest is converted into the kinetic energy of this electron Her:
The first feature of the photoelectric effect is that it occurs only when the energy of the gamma quantum is greater than the binding energy of the electron in the corresponding shell of the atom. If the energy of a gamma quantum is less than the binding energy of an electron in TO-shell, but larger than in L-shell, then the photoelectric effect can occur on all shells of the atom, except TO-shells, etc.
The second feature is the increase in photoelectric absorption of gamma rays with increasing binding energy of electrons in the atom. The photoelectric effect is practically not observed on weakly bound electrons, and free electrons do not absorb gamma rays at all. The linear attenuation coefficient of the photoelectric effect is proportional to the ratio Z 4/E γ 3 .
This proportionality is only approximate, since the exponent Z varies in the range from 4.0 to 4.8. As the energy of the gamma quantum decreases, the probability of photoelectric absorption increases rapidly (see Fig. 3.6). Photoelectric absorption is the predominant interaction process for low-energy gamma rays, X-rays and bremsstrahlung.
The photoelectric effect is mainly observed on K- And L-shells of heavy atoms at gamma quanta energies up to 10 MeV. The coefficient μf sharply decreases with increasing energy of gamma rays and at an energy of about 10 MeV approaches zero, i.e. photoelectrons do not appear. In Fig. Figure 3.6 shows the photoelectric mass attenuation coefficient for lead. The probability of interaction increases rapidly with decreasing energy, but then decreases sharply at gamma-quantum energies just below the K-electron binding energy. This jump is called K- edge. Below this energy, the gamma quantum does not have enough energy to knock out K-electron. Below K-edge the probability of interaction increases again until the energy becomes lower than the binding energies L-electrons. Such jumps are called L I - , L II - , L III - - edges.
Rice. 3.6. Photoelectric mass attenuation coefficient for lead
Scattering of γ quanta occurs on weakly bound electrons of atoms, called Compton effect . With this interaction, elastic collisions of γ-quanta with an equivalent mass occur m γ = E/c 2 with electrons mass m e. Such a collision is shown schematically in Figure 3.7. In each such collision, the γ quantum transfers part of its energy to the electron, giving it kinetic energy. Therefore, such electrons are called recoil electrons. The kinetic energy of the recoil electron will be equal to
Where v and is the frequency of the γ-quantum before and after the collision;
h– Planck’s constant.
Rice. 3.7. Scheme of interaction of a gamma quantum with matter
with Compton effect
After the collision, the recoil electron and the γ-quantum fly apart at angles θ and φ relative to the initial direction of motion of the γ-quantum. Taking into account the laws of conservation of energy and momentum (momentum), the wavelength of the γ-quantum will change:
In tangential collisions, the γ-quantum is deflected by small angles (φ ~ 0) and its wavelength changes insignificantly. It will be maximum in frontal collisions (φ ~ 180 0), reaching the value
Energy of scattered gamma quantum and recoil electron E e are related to the initial energy of the gamma quantum, with the angles φ and θ by the relations:
Since the interaction of a γ-quantum with any electron is independent, the value μ To proportional to electron density N e, which, in turn, is proportional to the ordinal number Z substances. Dependence of μk on the energy of the γ-quantum h v and Z, obtained by physicists Klein, Nishina and Tamm, has the form:
Where N– the number of atoms in 1 cm 3 of a substance.
The Compton effect occurs mainly on weakly bound electrons in the outer shells of atoms. With increasing energy, the fraction of scattered γ quanta decreases. But the decrease in the linear scattering coefficient μ to happens slower than μ f. Therefore, in the energy field Eγ > 0.5 MeV the Compton effect dominates over the photoelectric effect.
In gamma ray spectrometry the quantity used is dμ k /dE e, called differential Compton scattering coefficientγ -quanta. Its physical meaning is that it determines the number of recoil electrons per unit volume of matter, formed by the flow of gamma quanta Ф with energy Eγ, the energy of which lies in the range from zero to maximum value Her Max. The Klein-Nishina-Tamm theory allows us to obtain an analytical expression for the quantity dμ To / dE e = Nd, Where N– the number of atoms per unit volume of a substance. To illustrate this dependence, we present graphical distributions of recoil electrons for three fixed energies of gamma rays (Fig. 3.8). In the case of high γ-quanta energies (more than 2 MeV), the energy distribution of recoil electrons is almost constant. Deviation from a constant value (increase in the distribution density of recoil electrons) begins as their energy approaches the energy of the γ-quantum, forming the so-called Compton peak. In this case, the energy of recoil electrons in the Compton peak is somewhat lower than the energy of the gamma quanta that generated them (as can be seen from the figure).
Rice. 3.8. Energy distribution of recoil electrons
for γ-quanta of various energies
Since the energy of recoil electrons cannot be higher than the initial energy of γ quanta, after the Compton peak the distribution abruptly ends to zero. As the energy of γ quanta decreases (less than 1.5 MeV), the uniformity of the distribution below the Compton peak is also disrupted. Figure 3.9 shows the dependence of the energy of the Compton edge on the energy of gamma rays. It follows from it that with increasing energy of gamma quanta, the difference in the energies of the photopeak and the Compton edge initially grows rapidly, but, starting from energies of 100-200 keV, this difference tends to a constant value.
Pairing effect occurs when a γ-quantum passes near the nucleus if its energy exceeds the threshold value of 1.022 MeV. Outside the field of the nucleus, a γ-quantum cannot form an electron-positron pair, because in this case the law of conservation of momentum will be violated. Although an energy of 1.022 MeV is enough to generate a pair, then the momentum of the generated particles should be equal to zero, while the γ-quantum has a momentum different from zero and equal to E γ /c. However, in the nuclear field this effect becomes possible, since in this case the energy and momentum of the γ-quantum are distributed between the electron, positron and nucleus without violating the conservation laws. Moreover, since the mass of the nucleus is thousands of times greater than the mass of the electron and positron, it receives an insignificant part of the γ-quantum energy, which is almost completely distributed between the electron and positron. The effect of the creation of an electron-positron pair is shown schematically in Figure 3.10.
Rice. 3.9. Dependence of the energy of the Compton edge on the energy of the gamma quantum
Rice. 3.11. Dependence of linear attenuation coefficients of gamma radiation on the energy of γ-quanta for lead
All three interaction processes described above contribute to the total mass attenuation coefficient. The relative contribution of the three interaction processes depends on the energy of the gamma quantum and the atomic number of the absorber. In Fig. Figure 3.12 shows a set of mass attenuation curves covering a wide range of energies and atomic numbers. The extinction coefficient for all elements except hydrogen has a sharp rise in the low energy region, which indicates that photoelectric absorption is the dominant interaction process in this region. The location of this rise is highly dependent on the atomic number. Above the rise in the low energy region, the value of the mass attenuation coefficient gradually decreases, defining the region in which Compton scattering is the predominant interaction.
Rice. 3.12. Mass attenuation coefficients of some elements
(the energies of gamma rays usually used in
identification of isotopes of uranium and plutonium by gamma radiation)
The mass extinction coefficients for all elements with atomic number less than 25 (iron) are virtually identical in the energy range from 200 to 2000 keV. In the range from 1 to 2 MeV, the extinction curves converge for all elements. The shape of the hydrogen mass attenuation curve shows that the interaction of gamma rays with energies greater than 10 keV occurs almost exclusively through Compton scattering. At energies above 2 MeV for elements with high atomic number Z The process of interaction to form pairs becomes important, and the mass attenuation coefficient begins to increase again.
Interactions of gamma rays with matter
PHYSICAL BASICS OF WELL RADIOMETRY
PART 2. Nuclear physical methods
In nuclear geophysics, only the most penetrating radiation is used - neutrons and gamma rays, which “transparent” the well-reservoir system through the steel casing and cement stone. The reactions caused by neutrons in rocks are much more diverse than the reactions caused by gamma rays. For this reason, stationary and pulsed neutron methods are widely used in oil, gas and other mineral deposits to determine the reservoir properties of rocks, identify productive objects, control field development, elemental analysis of rocks and mineral raw materials, and solve many other important problems .
A measure of the interaction of gamma quanta (as well as other particles) with matter is the effective interaction cross section - microscopic and macroscopic. Microscopic section s determines the probability of interaction of one particle with another target particle (nucleus, electron, atom). Macroscopic section Σ - ϶ᴛᴏ measure of the probability of interaction of a particle with a unit volume of matter; it is equal to the product of the microsection and the number of targets per unit volume. According to historical tradition, the macrocross section for gamma rays is usually called linear attenuation coefficient and denote m (not Σ). The value 1/Σ determines the mean free path for a particular type of interaction.
Gamma radiation is attenuated in matter due to: photoelectric effect; Compton effect; pair formation; photonuclear interactions.
At photoelectric effect (Fig. 7.1a) gamma quanta interact with the electron shell of the atom. The resulting photoelectron carries away part of the gamma radiation energy E=hv-E 0 , where E 0 – binding energy of an electron in an atom. The process occurs at energies of no more than 0.5 MeV. As a result of the photoelectric effect, characteristic X-ray radiation also appears.
The microscopic cross section of the photoelectric effect depends on the energy of the gamma quantum and the serial number Z element
s f =12.1 E –3,15 Z 4.6 [barn/atom].
Strong dependence on Z allows the use of the photoelectric effect for the quantitative determination of the content of heavy elements in rocks (X-ray radiometric and selective gamma-gamma methods).
At Compton effect, gamma radiation interacts with electrons, transferring part of the energy to them, and then propagates through the rock, experiencing multiple scattering with a change in the original direction of movement. This process is possible at any energy of gamma rays and is the main one at 0.2<E<3 МэВ, т. е. именно в области спектра первичного излучения естественно-радиоактивных элементов.
Fig.7.1a,b. The main types of interactions of gamma radiation with matter ( A) and the energy and atomic number ranges in which they appear ( b) (IAEA, 1976 ᴦ.):
1 – photoelectric effect; 2 – Compton scattering; 3 – effect of electron-positron nap formation
The process of formation of electron-positron pairs arising from photons in the field of atomic nuclei is most likely for rocks containing heavy elements (see Fig. 7.1b) at energies of at least 1.02 MeV.
However, at different energies, gamma quanta interact predominantly with various targets: atoms, electrons, atomic nuclei.
In the energy region where the Compton and photo effects are most significant (Fig. 7.1b), the total macroscopic interaction cross section (also called the linear attenuation coefficient)
m=m f +m k =m k (1+m f /m k) (7.1)
where m k = n e s к – macrosection of the Compton effect; n e is the number of electrons per unit volume.
The electron density of media consisting of elements with the ratio Z/A=1/2 is strictly proportional to the bulk density (such media are called “normal”). Due to the presence of hydrogen, for which Z/A=1, rocks differ from “normal” environments; the measure of this difference is the “normalization coefficient”.
The effective atomic number of a medium of complex composition is the serial number of such a monoelement medium, the photoelectric absorption cross section of which is the same as in this multielement medium.
For monocell environment n e=d N A Z/A, Where N A– Avogadro’s number; A And Z– mass number and serial number; d – density. Elements included in the composition of rock-forming minerals Since the condition for the stability of atomic nuclei (the condition for saturation of nuclear forces) requires that A=N+P» N+Z»2 Z, (N» Z) (Where N And R– the number of neutrons and protons in the nucleus), then Z/A=0.5 regardless of element type (the only exception is hydrogen).
However, with Compton scattering, the macrocross-section mk is determined by the density (value 2d Z/A commonly called electron density). This fact serves as a strict physical justification density modification of the gamma-gamma method (GGM) . In the energy region of the Compton effect m»d, and the value
does not depend on density (Fig. 7.2b); this quantity is usually called the “mass attenuation coefficient”.
Fig.7.2a,b. Dependence of the mass attenuation coefficient m/d on the energy of gamma rays ( A) and atomic number Z element ( b). Curve code – energy of gamma rays, MeV
For convenient comparison of the influence of the photoelectric effect and Compton scattering, the photoabsorption cross section per electron is used
s f / Z = P e×10 –2 ( E/132) –3,15 , (7.3)
where is the value R e(“photoelectric absorption index”) is equal to ( Z/10) 3.6. Ratio of sections m f /m to =s f /Z s to " P e/s to. Effective atomic number Z eff is expressed as follows (for a multi-element environment):
where Z i, A i,P i – atomic number, atomic weight and weight (mass) fraction i th element, respectively, and the summation is extended to all elements in the natural mixture.
Attenuation and intensity dJ wide beam of gamma radiation in a flat layer of homogeneous substance of thickness dx is described by a differential equation similar to the law of radioactive decay:
in integral form
J(x) = J 0 exp(–m x). (7.6)
If the density of the medium depends on x(“barrier” geometry), that is, μ = μ (x), That
J(x) = J 0 exp[–Λ( x)], (7.7)
where Λ is the optical thickness of the layer x, or
where T(x) is the mass thickness of the layer x; - mass attenuation coefficient.
For a point isotropic source, the exponential attenuation law (7.7) is superimposed by the law of geometric divergence 1/(4p r 2) in spherical geometry (“inverse square law”):
J(r) = J 0 exp(–m r)/ (4p r 2). (7.9)
This expression describes the spatial distribution of unscattered (neutron or gamma) radiation. The spectrum of multiple scattered radiation (Fig. 7.3) from a monoenergetic source includes scattered radiation, but with decreasing energy, multiple scattered radiation makes an increasingly larger contribution. While the cross section of the photoelectric effect is small, the determining factor is the electron density of the substance, which, in turn, is determined by the density of the medium. With an increase in the photoelectric absorption cross section (in accordance with a decrease in the energy of gamma quanta), the amplitude of the spectrum decreases, and is determined not only by the density, but also by the effective atomic number of the substance (photoelectric absorption index). For this reason, spectrometric recording makes it possible to determine not only the density of a rock, but also its effective atomic number (lithological type of rock). This modification of the HGM is usually called “selective”.
Fig.7.3. Spectrum of multiply scattered gamma radiation in rocks of the same density but different composition (according to I.G. Dyadkin, 1978 ᴦ.; V. Bertozzi, D. Ellis, J. Wall, 1981 ᴦ.):
1 -3 – atomic numbers Z respectively small, medium and large; 4 – region of the photoelectric effect and Compton scattering; 5 – Compton scattering region, S– soft part of the spectrum; H– hard (Compton) part of the spectrum
At selective modification of HGM(GGM-S) uses sources and detectors of soft gamma radiation. GGM-S readings depend both on Compton scattering of gamma quanta (hence, on the density of the medium) and on their absorption, which is determined by the concentration of heavy elements in the rock. The interpretation parameter of the method is the photoelectric absorption cross section - P e [barn/electron]. The macroscopic absorption cross section per unit volume of a substance is denoted by U, usually called photoabsorption parameter [barn/cm 3 ] and is determined by the expression:
where b e is the electron density. The U parameter has a linear petrophysical model. This makes it possible to include GHM-S data in a system of petrophysical equations to determine the lithological composition and porosity of polymineral sediments. For example, for a two-component model of a medium (skeleton and fluid filling the capacitive space), the photoelectric absorption index is determined by the expression:
U=K p ·U fl +(1-K p) ·U sk, (7.10)
where U fl, U sk are the corresponding parameters of the fluid and skeleton, respectively.
The difference in the nature of gamma radiation from alpha and beta radiation (the absence of charge and rest mass in gamma quanta) leads to a fundamentally different mechanism for the interaction of this radiation with matter. Ionization and excitation of the medium occurs due to secondary ionizing particles. The primary interaction of gamma rays with matter comes down to three main processes (mechanisms of interaction):
Photoelectric effect;
Compton scattering;
Formation of an electron-positron pair.
Photo effect lies in the fact that a gamma quantum, interacting with an atom (molecule or ion), knocks out an electron from it. In this case, the gamma quantum itself disappears, and its energy is transferred to the electron, which becomes free (Figure a) and produces ionization and excitation similar to a beta particle.
In progress Compton scattering (Compton effect, elastic scattering) a gamma quantum also knocks out an electron from an atom (molecule or ion), but at the same time transfers only part of its energy to the electron, and itself changes the direction of movement (scatters) - Figure b.
If the energy of a gamma quantum is greater than 1.02 MeV, then the gamma quantum can turn into an electron and a positron.
This transformation occurs only near the atomic nucleus and leads to the disappearance of the gamma quantum (Figure 6c). The resulting positron moves in the substance, slows down and interacts with the electron of the medium. In this case, the electron and positron disappear (annihilate) with the formation of electromagnetic radiation, called annihilation.
The probability of the photoelectric effect decreases rapidly with increasing gamma ray energy. The probability of Compton scattering also decreases with increasing gamma ray energy, but not as sharply as for the photoelectric effect. The probability of pair formation increases with increasing energy, starting at 1.02 MeV. We can assume that in the region of “low” energies of gamma rays, the main mechanism of interaction of gamma radiation with matter will be the photoelectric effect. In the region of “medium” energies - the Compton effect, and in the region of “high” energies - the formation of electron-positron pairs. The concepts of “low”, “medium” and “high” energies depend on the charge of the atoms of the medium Z. For example, for lead these energy ranges are separated by values of approximately 0.5 MeV and 5 MeV.
Thus, when gamma radiation interacts with matter, the following are ultimately formed:
a) high-energy electrons, the further fate of which is not fundamentally different from the fate of beta particles;
b) secondary electromagnetic radiation - scattered gamma quanta and annihilation radiation.
In general, the difference in the physical picture of the interaction of alpha, beta and gamma radiation appears only at the initial stage, lasting billionths of a second. The energy transferred by particles to matter is converted into the energy of secondary particles - electrons, photons - and electronic excitations, which behave in a similar way regardless of which ionizing particle generated them. They “exchange” their energy for the formation of a large number of new electrons, photons and electronic excitations with lower energy (this process is called “energy dissipation”), spreading the action of the primary particle over a certain volume.
The outcome of the interaction depends on the state of aggregation of the substance. For gases (including air), ionization and excitation of molecules is the main result of the action of radiation, although along with this, chemical reactions occur to a greater or lesser extent (in gases they are difficult due to the large distance between the molecules), leading to the formation of new substances. For liquids, chemical reactions of the resulting chemically active particles (ions, radicals) are already the main effect of radiation. The effect of radiation on solids also often leads to chemical transformations and always to defects in their crystal lattice (violations of the electronic structure, vacancies, interstitial atoms, dislocations, etc.), the birth and evolution of which in time and volume of the substance is a rather complex problem .
Chemical transformations that occur in matter as a result of exposure to radiation are studied by radiation chemistry. The influence of radiation on the structure of matter and, accordingly, the modification of its properties is studied by radiation materials science, which, like radiation chemistry, is of high importance from both a fundamental (development of natural sciences) and applied (development of technology) point of view.