RU2602769C1 - Method of creating population inversion of nuclear levels in material of active medium and initiation of single-pass coherent gamma-radiation - Google Patents

Abstract

FIELD: chemistry.

SUBSTANCE: invention relates to production of coherent sources of gamma-radiation and can be used in various physical applications. Method of creating inverted population of nuclear levels in material of active medium and initiation of coherent single-pass gamma-radiation includes transfer of some portion of nuclei to excited metastable state and consists in fact that used material of active medium is radionuclide, wherein transfer of nuclei of excited metastable state is performed through gamma-radiation, material of active medium is represented by radionuclide, where beta decay of nuclei of type X(A,Z)→Y(A,Z-1) is performed, while maintaining parity of initial and intermediate excited conditions; radionuclide is placed into longitudinal uniform magnetic field such, that energy levels of maternal and daughter radionuclide nuclei acquire in magnetic field super-thin energy structure with quantum characteristics of sublevels, characterizing selective acceleration of beta-decay for part of maternal nuclei, and maintaining stability of intermediate excited state of daughter nuclei, for period not exceeding lifetime of metastable state of working intermediate energy level of daughter nuclei but sufficient for creation of required population inversion of this level; radio pulses of cross magnetic excitation are injected in material of active medium in following sequence: supply π/2-radio pulse of low amplitude, after action of π/2-radio pulse quarter period of phase relaxation follows, after quarter period of phase relaxation π-low-amplitude radio pulse is supplied after action of π-radio pulse half-period of phase relaxation follows, after half-period of phase relaxation short radio pulse of high amplitude is supplied.

EFFECT: technical result is increased efficiency of using material of active medium for generation of single-pass coherent gamma-radiation.

1 cl, 4 dwg

Description

The invention relates to the field of creating sources of coherent gamma radiation and can be used in various physical applications.

As is known [1], gamma lasers operating on nuclear transitions in solids, as compared to other sources of coherent radiation, could have a higher output power, reaching 10 ²¹ W. In most cases, in order to create a gamma laser, stimulated emission is used at the transition from the metastable state of the isomer nucleus. However, despite the ongoing theoretical and experimental efforts over the past few years, the current state of affairs in the field of gamma-ray lasers is still at the stage of developing ideas and creating concepts. The main subject of research is the search for the optimal substance of the active medium and the pump mechanism, i.e. a method of creating an inverse population of nuclear levels in the material of the active medium.

A method and system for realizing a gamma laser [2] is known, in which Mossbauer isotopes, for example ⁵⁷ Co, ⁵⁷ Fe, ¹¹⁹ Sn, etc., with resonant (without recoil) excitation and absorption of gamma quanta are used as the material of the active medium isomer nuclei. In this method, in the absence of population inversion in the active medium material of the initial gamma source, the generation of stimulated gamma radiation is achieved due to the "illumination" of its active medium by an auxiliary gamma source identical to the original one. In this case, the beneficial effect of using the second source is manifested after a sharp ("stepwise") phase shift of auxiliary gamma radiation by π relative to the gamma radiation of the original source. This causes the “gamma echo” effect in the active medium of the initial gamma source, which results in the suppression of resonance absorption of monoenergetic gamma quanta corresponding to a given nuclear transition, i.e. there is an abrupt increase in the transparency of the active medium and thereby the creation of conditions for a stimulated output of coherent gamma radiation even in the absence of inversion of resonantly excited isomer nuclei.

The disadvantage of this method of creating a gamma laser is the technological complexity of its implementation and the low efficiency of using the material of the active medium.

The closest in physical essence to the proposed (prototype) is a method of creating an inversion of the population of nuclear levels in the material of the active medium of a gamma laser [3], which consists in using the isotope osmium-187 as a material in the active medium, transferring a certain fraction of osmium-187 nuclei to excited metastable state, the transition of which to the final stable state is through an intermediate energy level, and the level with a higher excitation energy decays through gamma radiation into more short the current level, which has a lifetime sufficient to create gamma resonance conditions in the material of the active medium, as applied to the gamma-radiation transition used.

To create gamma resonance conditions in the active medium material, the prototype uses the osmium-187 single crystal isotope, in addition, it is proposed to pump the ¹⁸⁷ Os isomer level with an energy of about 257 keV and a lifetime of about 230 μs, and use the transition as a gamma resonance transition ¹⁸⁷ Os isomer nuclei per level with an energy of about 101 keV and a lifetime of about 110 ns. In this case, the inverse population of the indicated isomeric energy levels is automatically ensured (due to the difference in the lifetime), and the intensity of pumping the material of the active medium should ensure that the probability of emission of stimulated gamma radiation exceeds the probability of interaction of this gamma radiation with the electron shell of ¹⁸⁷ Os atoms.

The effectiveness of using the material of the active medium in the prototype is evaluated through the proportion of the interaction processes occurring in single-crystal osmium ¹⁸⁷ Os without recoil. For this, we determine the value of the Debye – Waller factor f _D , which is described by the expression [4], which is valid for monatomic crystals

- среднее значение энергии отдачи для связанного ядра;Where

- the average value of the recoil energy for the bound nucleus;

k is the Boltzmann constant;

θ _D is the Debye temperature characterizing the elastic properties of the crystal and corresponding to the limiting frequency of elastic vibrations of the crystal lattice;

T is the temperature of the environment surrounding the crystal.

From [5] it is known that the equality

,

,

- кинетическая энергия свободного ядра;Where

- kinetic energy of the free nucleus;

E _γ , M _poison - the energy of the γ transition and the mass of the nucleus;

c is the speed of light in free space,

имеемwhence for the γ transition of the nucleus

we have

.

.

, зависящая от его констант упругости, может быть определена в соответствии с общепринятой формулой [6]Debye crystal temperature

depending on its elastic constants can be determined in accordance with the generally accepted formula [6]

,

,

- приведенная постоянная Планка;Where

- reduced Planck constant;

- средняя скорость упругих волн в кристалле Os;

is the average velocity of elastic waves in the Os crystal;

N _A is the Avogadro number;

V ^Os is the molar volume of Os;

- модуль упругости Os;

- elastic modulus Os;

ρ ^Os is the specific gravity of Os.

и удельному весу

средняя скорость упругих волн в гексагональном кристалле осмия равнаGiven the reference data on the modulus of elasticity

and specific gravity

the average speed of elastic waves in an osmium hexagonal crystal is

.

.

After which the Debye temperature of osmium is estimated as

.

.

Calculation of the Debye-Waller factor for crystalline osmium according to formula (1) at normal ambient temperature (T = 300 K) and the indicated values of the constants estimated above gives the value

f _D ≈ 0.06.

в дочернее ядро осмия

, вероятность перехода γ₁₆ (с уровня 257 кэВ на уровень 101 кэВ) ядра

через K и L₁ - электронные уровни составляет в сумме у(се - K₁L₁)=3,9·10^-3 с^-1 на один распад иридия

. В то же время вероятность выхода γ-излучения с энергией квантов Е(γ₁₆)=156 кэВ с учетом замечания, сделанного в [9], относительно того, что все явно в численном виде не представленные там γ-переходы ядра

(в том числе и γ₁₆) по своему вкладу в суммарное γ-излучение не превышают 0,1%, можно считатьAnother factor leading to a decrease in the generation of γ-radiation is the possibility of removing the excitation of the nucleus due to the conversion of the energy of the nuclear transition into the energy of atomic electrons. In accordance with the data of [9], where the β-decay scheme of the maternal iridium nucleus is presented

in the daughter core of osmium

, probability of transition of γ ₁₆ (from the level of 257 keV to the level of 101 keV) of the nucleus

through K and L ₁ - the electronic levels total y (ce - K ₁ L ₁ ) = 3.9 · 10 ^-3 s ^-1 per iridium decay

. At the same time, the probability of the yield of γ radiation with quantum energy E (γ ₁₆ ) = 156 keV, taking into account the remark made in [9], regarding the fact that all the γ transitions of the nucleus that are not represented there explicitly in numerical form

(including γ ₁₆ ) do not exceed 0.1% in their contribution to the total γ-radiation, we can assume

,

,

which is approximately an order of magnitude less than the probability of energy conversion of the 257 keV level through the electronic component.

After that, the probability of the resonant transition in the material of the active medium from crystalline osmium in the material under normal conditions does not exceed

,

,

ядер

только

смогут принять участие в процессе формирования стимулированного излучения γ-квантов с энергией 156 кэВ.those. for each daughter

cores

only

will be able to take part in the formation of stimulated emission of γ-rays with an energy of 156 keV.

Thus, the disadvantage of the prototype is the low efficiency of using the material of the active medium for the generation of single-pass coherent gamma radiation.

The technical result of the method is to increase the efficiency of using the material of the active medium to generate single-pass coherent gamma radiation.

The technical result is achieved by the fact that in the method of creating an inverse population of nuclear levels in the material of the active medium and initiating single-pass coherent gamma radiation, which involves transferring a certain fraction of the nuclei to an excited metastable state and consisting in the use of a radionuclide as the material of the active medium, moreover, the transition of nuclei from an excited metastable state is carried out through gamma radiation, a radionuclide is used as the material of the active medium, in which there is beta decay of nuclei of the form X (A, Z) → Y (A, Z-1) with the parity of the initial and intermediate excited states being preserved, the radionuclide is placed in a strong longitudinal uniform magnetic field such that the energy levels of the parent and daughter nuclei of the radionuclide become This magnetic field has an ultrathin energy structure with quantum characteristics of sublevels that determine the selective acceleration of the beta decay process for part of the mother nuclei and maintain the stability of intermediate excited states of the daughter x nuclei, for a time not exceeding the lifetime of the metastable state of the working intermediate energy level of daughter nuclei, but sufficient to create the necessary population inversion of this level, the radio pulses of transverse magnetic excitation are injected into the material of the active medium in the following sequence: a small amplitude π / 2 radio pulse is applied , after the end of the action of the π / 2 radio pulse, a quarter-period of phase relaxation follows, after a quarter-period of the phase relaxation, a small-amplitude π-radio pulse is fed, according le closure action π-rf pulse should be half the phase relaxation time, after the half cycle of the phase relaxation fed short RF pulse of large amplitude.

во внешнем сильном однородном магнитном поле напряженностью Н₀, а на фиг. 2 - условная схема бета-распада ядра вида X(A,Z)→Y(A,Z-1) через промежуточные возбужденные уровни энергии, например Е1 и Е₂.The invention is illustrated in FIG. 1. In FIG. 1 schematically depicts a family of energy sublevels formed by splitting the main energy level E _{0 of the} mother nucleus, for example, the polonium radionuclide

in an external strong uniform magnetic field with intensity H ₀ , and in FIG. 2 - conventional beta-decay scheme core type X (A, Z) → Y (A, Z- 1) through intermediate excited energy levels, e.g. E1 and _E2.

In FIG. 1, 2 the following notation is introduced:

,

- векторы квантово-механического момента ядра и внешнего магнитного поля соответственно;

,

are the vectors of the quantum-mechanical moment of the nucleus and the external magnetic field, respectively;

- ядерное гиромагнитное отношение;

- nuclear gyromagnetic ratio;

в сильном однородном магнитном поле

;ε ₁ ... ε ₆ - allowed energy sublevels, derivatives of the main energy level E ₀ , nuclei

in a strong uniform magnetic field

;

ядра

на направление вектора магнитного поля

;I ₁ ... I ₆ - allowed projections of the quantum-mechanical moment

the cores

in the direction of the magnetic field vector

;

"0.0" is the index of the ground state of the mother and daughter nucleus;

γ ₁ ... γ ₃ - gamma-radiation energy transitions;

β ⁺ , EC - positron or electron-capture beta decay, respectively.

In FIG. Figure 3 shows a schematic representation of a gamma laser device using a radionuclide as an active medium material in which beta decay of nuclei of the form X (A, Z) → Y (A, Z-1) takes place. In FIG. 3 adopted the following notation:

1 - solenoid to create a strong uniform longitudinal magnetic field H ₀ ;

2 - power supply solenoid;

3 - open strip field-forming systems for creating a transverse magnetic field H ₁ ;

4 - a source of radio frequency signals;

5 - a balancing device;

6 - hollow dielectric cylinder;

7 - material of the active medium;

8 - matching loads of open strip field-forming systems;

9 - a stub.

In FIG. 4 shows a timing diagram of a sequence of transverse excitation pulses in the material of the active medium and the appearance of a pulse of output gamma radiation when using this technology in the proposed device. All pulse amplitudes in FIG. 4 are given in relative units, and all time intervals are correlated with each other and the characteristic times of the physical processes occurring in the material of the active medium in each phase of the formation of a gamma-ray pulse.

The proposed method of creating an inverse population of nuclear levels in the material of the active medium and initiating single-pass coherent gamma radiation is as follows:

1) using reference data on the physical parameters of substances and decay schemes of radionuclides select a radionuclide having a crystalline structure with a high atomic packing density, i.e. with a high density of mother nuclei in the crystalline cell, and a large gyromagnetic ratio of daughter nuclei, moreover, the decay scheme of the radionuclide should correspond to the isobar series with decreasing nuclear charge, i.e. beta decay of maternal nuclei X into daughter nuclei Y of the form X (A, Z) → Y (A, Z-1);

2) a sample of the required, for example cylindrical, shape is formed from the material of the selected radionuclide;

3) this sample is placed in a strong uniform longitudinal magnetic field H ₀ , acting along the axis of the sample, such that the energy levels of the mother and daughter nuclei of the radionuclide acquire an ultrathin structure in it, selectively accelerating the beta decay process of part of the mother nuclei having superresolved quantum-mechanical beta decay status, and supporting stability of intermediate excited states of daughter nuclei due to systemic spin interaction of nuclei in a strong uniform longitudinal magnetic field ;

4) the sample is held in a strong uniform longitudinal magnetic field for a time not exceeding the lifetime of the metastable state of the working intermediate energy level of daughter nuclei, but sufficient to create the necessary population inversion of this level, as a result of which one or several intermediate metastable energy levels are formed in the sample with population inversion with respect to gamma-radiative transitions of daughter nuclei to the final stable state;

5) inject the radio pulses of transverse magnetic excitation into the material of the active medium 7 in the following sequence:

a) a π / 2 radio pulse of a transverse magnetic field H _{1 of} small amplitude is supplied that satisfies the conditions

,

,

where t _and - pulse duration;

,

,

- величина неоднородного уширения спектра прецессирующих дочерних ядер;Where

- the value of the inhomogeneous broadening of the spectrum of precessing daughter nuclei;

- средняя круговая частота процессии дочерних ядер в сильном не идеально однородном магнитном поле Н₀, с частотой заполнения ω₀, равной средней частоте прецессии

дочерних ядер;

- the average circular frequency of the procession of daughter nuclei in a strong not perfectly uniform magnetic field H ₀ , with a filling frequency ω ₀ equal to the average precession frequency

daughter cores;

in this case, the magnetic moments of the daughter nuclei of the upper and lower sublevels of the working energy level by the end of this pulse will be in planes coplanar to the transverse plane xy, precessing around the longitudinal axis z; moreover, at the time when the magnetic moments of the nuclei are in the xy plane, the nuclei have minimal energy coupling with the longitudinal magnetic force field H ₀ directed along the z axis, and their magnetic quantum number m is zero;

b) after the end of the action of the π / 2 radio pulse of transverse magnetic excitation, a quarter-period of phase relaxation Δt ₂ = π / 4Δω follows, during which the system of sector-localized (conditionally in the transverse xy plane) magnetic moments corresponding to the upper and lower initial sublevels of energy and now rotate in planes coplanar to the xy plane, due to the difference in the precession frequencies (ω ₀ -Δω) ← ω ₀ → (ω ₀ + Δω) it will start to run up, trying to uniformly fill the entire plane of rotation xy, and the fan-shaped scatter of moments from the first the second conditional half-plane bounded by the x axis to the second and vice versa will occur both clockwise and counterclockwise;

c) after the time interval Δt _{1 has} elapsed since the start of the phase relaxation, a π-radio pulse of a transverse magnetic field H _{1x of} small amplitude is fed, which mirrors magnetic moments located in opposite half-planes bounded by the x axis, xy plane with respect to the xz plane;

; при этом два результирующих момента М_y и -М_y будут расти, стремясь к своим максимальным значениям; в максимуме результирующих моментов индивидуально сфазированные две подсистемы спинов получают возможность излучать в противоположенные стороны - каждая как самостоятельное целое, т.к. в этот момент для каждой из подсистем обеспечивается выполнение условия когерентного излучения (r=IN>>m);d) after the end of the action of the π-radio pulse of transverse magnetic excitation, the time interval Δt ₂ = π / 2Δω is equal to the half-period of phase relaxation, during which the magnetic moments of the nuclei, continuing their circular motion around the z axis, now, however, after turning around the x axis will change its direction of rotation is reversed, and divided in a time Δt ₁ into two conditional sectoral half will move in their conventional plane bounded by the axis x, towards each other, gradually gathering around the magnetic m ments which are directed to one of these half-planes of y-axis, and the other on the -y axis and having a circumferential speed

; while the two resulting moments M _y and -M _y will grow, striving for their maximum values; at the maximum of the resulting moments, the individually phased two subsystems of spins are able to radiate in opposite directions - each as an independent whole, because at this moment, for each of the subsystems, the coherent radiation condition is satisfied (r = IN >>m);

d) after the time interval Δt ₂ expires at the time of reaching the maximum, the resulting magnetic moments of the subsystems M _y and -M _y give a short radio pulse of a transverse magnetic field H _{1x of} large amplitude, which, quickly rotating the resulting vectors of magnetic moments of the nuclei M _y and -M _y around the axis x, creates in the region of small values of the magnetic moment M _z arising during this rotation, a significant value of the derivative dM _z / dt, stimulating (due to its value) the gamma radiation of the working transition under conditions of minimal recoil of nuclei, i.e. In the regime of radiation from the resonance plane xy of coherent gamma rays in a very narrow spectral band, an ultrashort gamma pulse with a narrow radiation pattern due to the axial geometry of the system and the coaxiality of the material sample is formed at the output of the device during the action of a powerful short stimulating radio pulse of transverse magnetic x-excitation active medium 7 and solenoid 1.

Consider the implementation of the proposed method for creating an inverse population of nuclear levels in the material of the active medium and the initiation of single-pass coherent gamma radiation.

In order to ensure the parametric stability of the gamma laser to create its active medium, the initial radioactive material can be used that during the formation of population inversion in this medium does not emit energetic particles with a non-zero rest mass, such as electrons and alpha particles, because, As is known [10], collisional ionization and atom excitation caused by these particles are not selective and poorly controlled. Beta-radioactive materials are more stable when the positron exits the mother nucleus and then annihilates it on the electron shell of the atom or captures the electron from the lower orbit of the atom, i.e. materials in which isobaric beta decay of nuclei of the form X (A, Z) → Y (A, Z-1) takes place, where A is the total number of protons and neutrons in the nucleus, Z is the number of protons.

. На основании данных [11] полоний

испытывает распад вследствие захвата электрона (в основном с K и L электронных уровней) или испускания позитрона.In accordance with the Periodic system of elements and decay schemes of radionuclides, we choose one of the elements from the edge of the region of β ⁺ -radioactivity, for example, polonium

. Based on the data of [11] polonium

undergoes decay due to capture of an electron (mainly from K and L electronic levels) or emission of a positron.

сильное однородное поле

такое, что энергия его взаимодействия с электронными оболочками атомов

много больше энергии взаимодействия электронных оболочек с магнитными моментами их ядер [12]We put on the substance of the radionuclide

strong uniform field

such that the energy of its interaction with the electron shells of atoms

much more energy of interaction of electron shells with magnetic moments of their nuclei [12]

,

- полный магнитный момент электронов и магнитный момент ядра

соответственно;Where

,

- the total magnetic moment of electrons and the magnetic moment of the nucleus

respectively;

- магнитное поле, создаваемое электронами атома Ро.

is the magnetic field created by the electrons of the Po atom.

и H_e≈10⁶ Э (µ_N, М_B - ядерный и электронный магнетоны соответственно), из (2) для величины внешнего однородного магнитного поля получаемTaking appraisingly

and H _e ≈10 ⁶ Oe (μ _N , M _B are the nuclear and electron magnetons, respectively), from (2) for the value of the external uniform magnetic field we obtain

связь магнитного момента ядра

с магнитным полем электронов

нарушается, и магнитные моменты электронной оболочки

и ядра

ориентируются относительно внешнего магнитного поля

независимо друг от друга в соответствии с собственным квантово-механическими моментами

и

.As a result of the action of a strong uniform magnetic field

relationship of the magnetic moment of the nucleus

with electron magnetic field

broken and magnetic moments of the electron shell

and cores

oriented relative to the external magnetic field

independently from each other in accordance with their own quantum-mechanical moments

and

.

с внешним магнитным полем

определяется скалярным произведениемSince the energy U is the interaction of nuclei

with external magnetic field

defined by a scalar product

,

,

с произвольными направлениями

после наложения на нее магнитного поля

, удовлетворяющего по величине условию (3), начинают различаться в зависимости от взаимной ориентации

и

, образуя сверхтонкую структуру энергетических подуровней. Как известно из квантовой механики, количество проекций

вектора квантово-механического момента ядра

на внешнее магнитное поле

ограничено, дискретно и равно (2I+1), где I - положительное целое или полуцелое число, которым выражается квантово-механический момент ядра (спин) через приведенную постоянную Планка

, причем модуль вектора

равен

.then the previously coincided (in the absence of force impact on the microparticle system) values of the nuclear energy

with arbitrary directions

after applying a magnetic field to it

satisfying condition (3) in magnitude, begin to differ depending on the relative orientation

and

forming the hyperfine structure of energy sublevels. As is known from quantum mechanics, the number of projections

vectors of the quantum mechanical moment of the nucleus

to an external magnetic field

bounded, discrete, and equal to (2I + 1), where I is a positive integer or half-integer that expresses the quantum-mechanical moment of the nucleus (spin) through the reduced Planck constant

, and the module of the vector

is equal to

.

в основном (невозбужденном) состоянии имеет спин I=5/2 и четность Р=-1. Это означает, что все ядра

, находящиеся под действием поля

, распределятся в пространстве по 6-ти разрешенным ориентациям вектора

, имеющим проекции

из следующего рядаIt follows from [13] that the kernel

in the ground (unexcited) state, it has spin I = 5/2 and parity P = -1. This means that all cores

under the influence of the field

are distributed in space according to 6 allowed orientations of the vector

having projection

from the next row

I, I-1, I-2, - (I-2), - (I-1), -I.

расщепляется на 6 подуровней, снимая кратность его вырождения.In this case, the initial energy level of the nucleus

splits into 6 sublevels, removing the multiplicity of its degeneracy.

Under conditions of thermodynamic equilibrium in the absence of exchange interaction between microparticles located at different quantum sublevels, the distribution of a system of microparticles among sublevels obeys Boltzmann statistics, which is valid for nondegenerate systems of microparticles that meet the criterion

where d is the distance between the microparticles;

λ _B is the de Broglie wavelength for homogeneous microparticles in the system.

In the case of the crystalline structure of the substance (this also applies to polonium), the distance between adjacent microparticles approximately corresponds to two atomic radii, i.e.

d≈2 · r _at ≈10 ^-10 m,

, где

, c - средняя скорость микрочастиц, колеблющихся вокруг своего положения равновесия в кристалле, и скорость света в свободном пространстве соответственно, определяется формулойand the de Broglie wavelength for microparticles bound in the crystal at

where

, c is the average speed of microparticles oscillating around their equilibrium position in the crystal, and the speed of light in free space, respectively, is determined by the formula

,

,

where m is the mass of microparticles;

k is the Boltzmann constant;

T is the absolute temperature.

имеем λ_Б≈2·10^-12 м, что с учетом оценки d отвечает выполнению критерия (4) и следовательно правомерности использования статистики Больцмана при количественной оценке распределения ядер

по энергетическим подуровням.As a result, at normal temperature for nuclei

λ _B have ≈2 · 10 ^-12 m, which is based on an assessment d corresponds to satisfying the criterion (4) and hence the legitimacy of using Boltzmann statistics in quantitative estimate of the distribution of nuclei

on energy sublevels.

As follows from [14], the probability of ω ₁ according to Boltzmann of one microparticle to be in the ith quantum state is

,

,

where µ _chemical is the chemical potential that determines the average number of microparticles in the subsystem included in the Gibbs large statistical ensemble;

ε _i - ie quantum energy state.

There are six different quantum states in our case, and the index i takes the values i = 1, 2 ... 6. The energy interval Δε between neighboring states is the same and equal

.

.

в основном состоянии по данным [15] имеет величинуMagnetic moment µ _I cores

in the ground state according to [15] has the value

.

.

, исходя из условия (3), принимаем равным Н₀=10⁴ Э.To specify further estimates, the value of the external uniform magnetic field

based on condition (3), we take equal to H ₀ = 10 ⁴ E.

выражается в общепринятых единицахAfter which the interval of splitting the core level of nuclei

expressed in conventional units

.

.

The chemical potential μ _chem can be found from the normalization condition

,

,

whence the corresponding value of the chemical potential taking into account the energy series ε ₁ = 0 eV, ε ₂ = 3.4 · 10 ^-9 eV, ... ε ₆ = 1.7 · 10 ^-8 eV is

μ _chem ≈ -4.2 · 10 ^-2 eV.

в каждом состоянии в подсистеме равноAs a result, all six quantum states are almost equally probable and the average relative number of nuclei

in each state in the subsystem is equal

.

.

, распределение ядер по энергетическим состояниям-подуровням будет равномернымTherefore, in the entire system of microparticles, occupying the volume V and including N _∑ nuclei

, the distribution of nuclei in energy sublevels will be uniform

and quantum as shown in FIG. 1a.

Due to the fact that the β-decay process depends on the quantum characteristics of the initial and subsequent states of the nucleus, spatial quantization of the nuclei after superposition of the H ₀ field on the system leads to the fact that for its nuclei having different spin projections the course of the β-decay process will be vary.

The parametric probability of a λ _β transition per unit time is characterized by the relation [16]

- постоянная β-распада;Where

- constant β-decay;

B is a dimensionless quantity that varies depending on the influence of the structure of the nucleus on β decay;

f (E _β , Z) is the integral function of the energy spectrum of β-decay and the Coulomb interaction of the nucleus.

It follows from (5) that the product τ _β · f (E _β , Z) = 1 / B is a constant, which is a generalized parameter for each of the types of β-decay nuclei, due to the features of the β-decay process. In [16], a general classification of all known β transitions depending on the value of log (f · τ _β ) is also given. In accordance with this classification and generalized data presented in [17], the minimum value of log (f · τ _β ) ≈3 is associated with superresolved β transitions.

по справочным данным [11] период полураспада и соответственно его постоянная равны

мин и τ_β=350/ln2≈500 мин, а численное значение интегральной функции f(E_β,Z), оцениваемое суммой вероятностей выхода всего спектра γ-излучения и конверсионных электронов на один β-распад ядер

, имеет величинуFor cores

according to reference data [11], the half-life and, accordingly, its constant are equal

min and τ _β = 350 / ln2≈500 min, and the numerical value of the integral function f (E _β , Z), estimated by the sum of the probabilities of the output of the whole spectrum of γ-radiation and conversion electrons to one β-decay of nuclei

has the value

,

,

therefore, the logarithm of their product is

.

.

относятся к переходам нормально разрешенным.It follows that, according to the classification adopted in [16], β-transitions of nuclei

refer to transitions normally allowed.

является электронный захват, а вероятность позитронного канала распада в сравнении с электронным захватом мала (y_β+≈5·10^-3 с^-1). Это позволяет упростить поиск предполагаемого рабочего уровня, пригодного для формирования активной среды, среди общей картины возбуждения промежуточных энергетических уровней дочерних ядер

.The main β-process in the decay of maternal nuclei

is electron capture, and the probability of a positron decay channel in comparison with electron capture is small (y _β + ≈5 · 10 ^-3 s ^-1 ). This allows us to simplify the search for the estimated working level suitable for the formation of an active medium among the general picture of the excitation of intermediate energy levels of daughter nuclei

.

выделим промежуточный уровень, в общем вероятностном потоке β-превращений заполняемый с наибольшей вероятностью.Based on the concept of ensuring the inversion of the population of nuclear levels directly in the process of β-decay, in the energy picture of the excitation of daughter nuclei

we select an intermediate level that is most likely to be filled in the general probabilistic flow of β-transformations.

из своего начального состояния со спином I=5/2 и четностью Р=-1 являются возбужденные разновероятные состояния дочерних ядер

в диапазоне энергий от Е₁=0,66 МэВ до Е₁₅=2,4 МэВ. Спины этих промежуточных состояний имеют значения от 3/2 до 7/2. При этом заведомо менее вероятные состояния, отвечающие β-переходам с изменением четности, с уровнями энергий возбуждения ядер

Е₁₃=2,0 МэВ и Е₁₅=2,4 МэВ, обусловленные электронными захватами ЕС₂ и ЕС₁ соответственно, составляют примерно пятую часть всех переходов исходных ядер

In accordance with [11], the sought intermediate states of the β-transition of mother nuclei

from their initial state with spin I = 5/2 and parity P = -1 are excited unlikely states of daughter nuclei

in the energy range from E ₁ = 0.66 MeV to E ₁₅ = 2.4 MeV. The spins of these intermediate states have values from 3/2 to 7/2. In this case, obviously less probable states corresponding to β transitions with a change in parity, with levels of nuclear excitation energies

E ₁₃ = 2.0 MeV and E ₁₅ = 2.4 MeV, due to electron captures of EC ₂ and EC _1, respectively, make up about a fifth of all transitions of the source nuclei

.

.

совершаются на промежуточные уровни Е₂=0,74 МэВ и Е₄=0,99 МэВ после электронных захватов ЕС₄ и ЕС₃ соответственно и доминируют над остальными, составляя четыре пятых всех переходов исходных ядер

The most likely β transitions of nuclei

occur at intermediate levels E ₂ = 0.74 MeV and E ₄ = 0.99 MeV after electron captures of EU ₄ and EU _3, respectively, and dominate the rest, making up four fifths of all transitions of the source nuclei

.

.

после наложения на исходную систему материнских ядер

однородного магнитного поля напряженностью Н₀ остается неизменной. Однако в силу появления у ядер в магнитном поле Н₀ дополнительной квантовой характеристики - проекции спина

для части материнских ядер

β-переходы будут осуществляться с большими вероятностями.Due to the independence of the weak (determining β-radioactivity) and strong (determining the structure of the nucleus) interactions from a magnetic field of the level of 10 ⁴ G, the concept of excited intermediate states and energy transitions of daughter nuclei

after superimposing on the original system of mother cores

homogeneous magnetic field strength H ₀ remains unchanged. However, due to the appearance of nuclei in a magnetic field H ₀ an additional quantum characteristic - spin projection

for part of the mother cores

β-transitions will occur with high probability.

относятся те, которые в результате β-перехода выходят на промежуточные уровни

со спином 5/2 и четностью - 1. Среди возбужденных состояний дочерних ядер

имеются три промежуточных энергетических уровня с требуемыми квантовыми характеристиками: Е₅=1,1 МэВ, Е₈=1,3 МэВ и Е₁₁=1,7 МэВ. Из них уровни Е₈ и Е₁₁ можно не принимать в расчет, поскольку вероятности их реализации много меньше, чем уровня Е₅ Naturally, to such kernels

include those that, as a result of the β-transition, go to intermediate levels

with spin 5/2 and parity - 1. Among the excited states of daughter nuclei

There are three intermediate energy levels with the required quantum characteristics: E ₅ = 1.1 MeV, E ₈ = 1.3 MeV and E ₁₁ = 1.7 MeV. Of these, the levels of E ₈ and E ₁₁ can not be taken into account, since the probability of their implementation is much less than the level of E ₅

.

.

, приемлемого для формирования активной среды гамма-лазера, больше других подходит уровень Е₅.As a result, it can be seen that, to a first approximation, as a working intermediate energy level of nuclei

acceptable for the formation of the active medium of a gamma laser, the level E _{5 is} most suitable.

позволяет считать, что за среднее время β-перехода (τ_β≈500 мин), а также в предположении метастабильности уровня Е₅, рабочий энергетический уровень дочернего ядра по аналогии с начальным уровнем материнского успевает в процессе пространственного квантования дочерних ядер в магнитном поле Н₀ расщепиться на подуровни.Slow nature of β-transitions of nuclei

allows us to assume that for the average time of the β-transition (τ _β ≈500 min), and also assuming metastability of the E ₅ level, the working energy level of the daughter nucleus, by analogy with the initial level of the mother nucleus, is in time during the spatial quantization of daughter nuclei in a magnetic field of H ₀ split into sublevels.

на соответствующие подуровни уровня Е₅ дочерних ядер

остаются неизменными. Это дает возможность отнести данные β-переходы к фермиевским [18], совершающимся с максимальной вероятностью. Как уже отмечалось в [16, 17], максимальная вероятность по факту соответствует β-переходам, для которых значение lg(f·τ_β)≈3. При неизменности энергетического спектра β-распада - в случае электронного захвата в качестве опорного может рассматриваться спектр сопровождающих захват электронных нейтрино, вылетающих из материнского ядра - функция f в произведении f·τ_β также постоянна. Следовательно, в условиях, реализуемых для β-переходов на уровень Е₅ ядер

, изменение величины lg(f·τ_β) связано с изменением постоянной времени рассматриваемого канала β-распада. Отмечаемое здесь уменьшение величины lg(f·τ_β) со значения ≈4,6 характерного для β-распада ядер

в невозмущенном состоянии, до значения ≈3, соответствующего β-распаду ядер

на уровень Е₅ ядер

в магнитном поле Н₀, означает уменьшение постоянной распада τ_β(Е₅) и ускорении распада соответствующих материнских ядер

примерно в 40 раз.As a result, such quantum characteristics as the quantum-mechanical angular momentum, its projection on the direction of the magnetic field H ₀ , as well as parity, in the process of β-transitions from the sublevel of the parent nuclei

to the corresponding sublevels of level E of ₅ daughter cores

remain unchanged. This makes it possible to attribute these β transitions to Fermi transitions [18], which occur with maximum probability. As already noted in [16, 17], the maximum probability in fact corresponds to β transitions for which the value log (f · τ _β ) ≈3. If the energy spectrum of β decay remains unchanged — in the case of electron capture, the spectrum of electron neutrinos accompanying capture from the mother nucleus can be considered as a reference — the function f in the product f · τ _{β is} also constant. Therefore, under the conditions realized for β-transitions to the level of E ₅ nuclei

, a change in lg (f · τ _β ) is associated with a change in the time constant of the β-decay channel under consideration. The decrease in the value of log (f · τ _β ) noted here from ≈4.6 characteristic of β-decay of nuclei

in an unperturbed state, to a value of ≈3, corresponding to β-decay of nuclei

to level E ₅ cores

in a magnetic field H ₀ , means a decrease in the decay constant τ _β (E ₅ ) and an acceleration of the decay of the corresponding mother nuclei

about 40 times.

в магнитном поле Н₀ имеем ветви с различными постоянными распада ядер

Taking into account the fact that the considered β-decay channel also admits Gamma-Teller [18] normally allowed β-transitions with ΔI = (0, ± 1), for β-transitions to the level of E ₅ cores

in a magnetic field H ₀ we have branches with different decay constants of nuclei

для обычных нормально разрешенных β-переходов;one)

for ordinary normally allowed β-transitions;

для ускоренных сверхразрешенных β-переходов.2)

for accelerated superresolved β transitions.

уровня

дочерних ядер

, устанавливающуюся к моменту времени t в процессе β-распада материнских ядер

, можно предварительно - в предположении, что время жизни уровня

велико

- оценивать из выраженияAfter which the maximum possible population

level

daughter cores

established at time t in the process of β-decay of mother nuclei

, it is possible preliminary - under the assumption that the lifetime of the level

great

- evaluate from expression

- исходное количество ядер

;Where

- initial number of cores

;

- суммарная (подсчитанная по всем возможным гамма- и конверсионным переходам) вероятность реализации уровня

ядер

при β-распаде ядер

.

- total (calculated for all possible gamma and conversion transitions) probability of level realization

cores

with β decay of nuclei

.

заселенность уровня Е₅ составляет

, а к моменту

.From (6), for example, it follows that by the time

the population of level E ₅ is

, and by the time

.

может быть проведена, если обратиться к формулам Вайскопфа [19] для вероятностей излучения электрического и магнитного мультиполей Y_E и Y_M, полученным на основе одночастичной модели ядраFor an isolated core, the estimate of the lifetime of the γ level is E ₅ -τ _γ (E ₅ ), neglecting the contribution of conversion electrons to this level of unloading

can be carried out if we turn to the Weisskopf formulas [19] for the radiation probabilities of the electric and magnetic multipoles Y _E and Y _M obtained on the basis of a single-particle model of the nucleus

и

- электрический и магнитный мультипольные моменты соответственно;Where

and

- electric and magnetic multipole moments, respectively;

и

- электрический и магнитный моменты, обусловленные намагничиванием системы;

and

- electric and magnetic moments due to the magnetization of the system;

;l is the order of the multipole moment equal to the angular momentum ΔI carried away by γ-quanta during radiation, in units

;

m is the order of projection of the multipole moment (in units of Q or M) on the axis of symmetry of the system z, i.e. in the direction of the field H ₀ applied to the system;

- волновое число;

- wave number;

(2l + 1) !! = 1 · 3 · 5 ... (2l + 1).

The set of possible values of 1 and m is determined by the selection rules [20, 21] according to the moment of momentum and parity

where l _E and l _M are the order of the electric and magnetic multipoles, respectively.

осуществляются на уровни Е₂ и Е₀ As follows from [11], possible γ-transitions (γ ₂₁ , γ ₃₆ ) from the excitation level E _{5 of the} nucleus

carried out at levels E ₂ and E ₀

,

,

,

,

occur without changing parity and carry away in the case of γ ₂₁ → | ΔI | = 1, and in the case of γ ₃₆ → | ΔI | = 2. In accordance with [21, tab. 18] the transition γ ₂₁ , obeying the selection rules (8), can be carried out as the radiation of a magnetic quasidipole (M1) or an electric quasiquadrupole (E2). The data [15] on the magnetic and electric moments of ²⁰⁷ Po and ²⁰⁷ Bi in the ground states contribute to certainty.

,

,

,

,

,

,

,

,

- ядерный магнетон;Where

- nuclear magneton;

- собственный (внутренний) электрический квадрупольный момент ядра, отнесенный к единичному заряду 4,8·10^-10 СГСЭ.

- intrinsic (internal) electric quadrupole moment of the nucleus, attributed to a unit charge of 4.8 · 10 ^-10 SGSE.

Taking into account the magnitudes of the magnetic and electric moments of ²⁰⁷ Po and ²⁰⁷ Bi and relations (7), we can write

,

,

при его β-переходе в ядро

. Этот вывод подтверждает также смена знака электрического квадруполя с положительного на отрицательный, что говорит о приобретаемой в распределении заряда дочернего ядра поперечной направлению спина эллипсности. Тогда в соответствии с магнитным характером диполя (Е₅-γ₂₁) и его набором квантовых чисел l=l_M=1 вычислим значение Y_M(γ₂₁) из (7), предположив, что магнитные моменты различных состояний ядра

соотносятся друг с другом так же, как их квантово-механические моменты, после чего допустимо считатьwhich indicates the magnetic nature of the rearrangement of the nucleus

during its β-transition to the nucleus

. This conclusion also confirms the change in the sign of the electric quadrupole from positive to negative, which indicates the transverse direction of the ellipse spin acquired in the charge distribution of the daughter nucleus. Then, in accordance with the magnetic nature of the dipole (E ₅ -γ ₂₁ ) and its set of quantum numbers l = l _M = 1, we calculate the value Y _M (γ ₂₁ ) from (7), assuming that the magnetic moments of different states of the nucleus

relate to each other in the same way as their quantum-mechanical moments, after which it is permissible to consider

and therefore

.

.

, наведенное внешним магнитным полем Н₀, аналогично прецессирующим электронам, определим через прецессию момента

вокруг направления

, руководствуясь изложенным в [22]. Согласно [22] вектор

направлен встречно вектору

и по величине в единицах СГС равенValue

induced by an external magnetic field H ₀ , similarly to precessing electrons, we define through the precession of the moment

around the direction

guided by the above [22]. According to [22], the vector

directed counter to vector

and in terms of units of GHS equal

в единичных зарядах;where Z ^Bi = 83 is the charge of the nucleus

in unit charges;

e is the unit charge;

- Ларморова круговая частота прецессии ядер

вокруг

;

- Larmorov circular frequency of nuclear precession

around

;

- гиромагнитное отношение магнитного и механического моментов ядер

;

- gyromagnetic ratio of the magnetic and mechanical moments of the nuclei

;

- проекция эффективной площади спинового тока ядра

на плоскость, перпендикулярную направлению

.

- projection of the effective area of the nuclear spin current

to a plane perpendicular to the direction

.

можно выразить через электрический момент

, используя соотношение [23]Value

can be expressed in terms of electric moment

using the relation [23]

.where a and b are the semiaxes of the ellipse in the cross section of the charge distribution over the core

.

а>b, выражение для оценки

приобретает видTaking into account (10) and the fact that for the core

a> b, expression for evaluation

takes on the form

его выражением (11), получаемReplacing in (9)

by its expression (11), we obtain

where k is the dimensionless coefficient.

, то с учетом (12) справедливо такжеSubstitution of the numerical values of the physical quantities included in the coefficient k gives its value equal to k = 2 · 10 ^-12 . Because, as already noted,

, then, taking into account (12),

вокруг собственной оси (спиновая частота). Т.е. выполняется

, что, как известно из динамики вращательного движения [24], свидетельствует об устойчивом псевдорегулярном характере прецессии ядер

, охваченных магнитным полем H₀.where Ω ^Bi is the circular core rotation frequency

around its own axis (spin frequency). Those. performed

, which, as is known from the dynamics of rotational motion [24], indicates a stable pseudo-regular nature of nuclear precession

covered by a magnetic field H ₀ .

As a result, taking into account the negligible smallness of k, expression (7) is simplified and takes the form for the magnetic nature of the radiation

, равнуюand substituting the physical quantities for the γ-transition γ ₂₁ with energy E _γ21 = 0.40 MeV into it, we have the individual probability of spontaneous emission of an isolated nucleus

equal to

,

,

and accordingly the lifetime of level E ₅

.

.

At the same time, for the γ transition γ ₃₆ with energy E _γ36 = 1.14 MeV corresponding to electric quadrupole radiation, this probability is expressed from (7) as

and numerically equal

,

,

which corresponds

.

.

.However, in an external magnetic field H ₀ with a stable nature of the precession around the H ₀ direction of the system of microparticles with spin, a group interaction of these microparticles arises, which noticeably changes the initial estimate of the lifetime

.

ядер

), как псевдодиполя, на приложенное извне возмущающее поле описывается уравнением Лиувилля [25], которое идентично уравнению Блоха для магнитного резонанса ядерного магнитного диполя, т.е. двухуровневую систему можно рассматривать как псевдоспиновую. Излучение спиновой системы, отождествляемой с магнитным псевдодиполем, в случае приложенного извне стационарного магнитного поля Н₀ может происходить только при изменении во времени составляющей магнитного момента прецессирующих элементов спиновой системы, направленной вдоль поля Н₀, т.е. в процессе изменения угла прецессии спинов. Изменения угла прецессии отдельных ядерных спинов возможны как за счет взаимодействия между соседними ядерными моментами, так и за счет взаимодействия ядерных спинов с "решеткой", как следствие теплового движения [26]. При этом под "решеткой" понимают все другие степени свободы микрочастиц вещества, кроме спина.Dynamic response characterizing the adaptive ability of a two-level system (for example,

cores

), as a pseudodipole, to a disturbing field applied externally, is described by the Liouville equation [25], which is identical to the Bloch equation for the magnetic resonance of a nuclear magnetic dipole, i.e. a two-level system can be considered as a pseudospin. Radiation of a spin system identified with a magnetic pseudo-dipole in the case of a stationary magnetic field H ₀ applied externally can occur only when the magnetic moment component of the precessing elements of the spin system directed along the field H ₀ changes, i.e. in the process of changing the angle of precession of the spins. Changes in the precession angle of individual nuclear spins are possible both due to the interaction between neighboring nuclear moments, and due to the interaction of nuclear spins with the "lattice", as a result of thermal motion [26]. Moreover, by "lattice" is meant all other degrees of freedom of microparticles of a substance, except for spin.

зависит также от спин-спинового взаимодействия и от неоднородности поля Н₀.If we assume that the perturbing magnetic field H _{1 is} small in comparison with the field H ₀ , then the energy of the precessing spin system is determined mainly by the orientation of the nuclear magnetic moments relative to the field H ₀ . Therefore, a pure spin-spin interaction cannot change this energy, i.e. it does not affect the resulting magnetization M _z in the direction of the z axis, corresponding to the direction of the magnetic field H ₀ . To change the magnetization M _z , an energy exchange with the lattice is necessary; only in the interaction of nuclear moments with other (translational, vibrational, and rotational, except spin) degrees of freedom can an equilibrium be established corresponding to the temperature of the substance. The process of establishing equilibrium depends on relaxation mechanisms and is characterized by the longitudinal (along the z axis) relaxation time T ₁ and the transverse relaxation time T ₂ [27]. The longitudinal relaxation time T ₁ is mainly determined by the spin-lattice interaction, while the time

also depends on the spin-spin interaction and on the inhomogeneity of the field H ₀ .

The reciprocal of the relaxation time T ₁ can be considered as a measure of the probability of a change in the value of M _z [28] and considered for longitudinal relaxation

,

,

similar for lateral relaxation

,

,

where p and q * are weights.

In the case of an ideally uniform field H ₀

where the probability W ₂ is responsible for the resulting spin-lattice and spin-spin interactions without taking into account the factors of field non-uniformity Н ₀ .

Bearing in mind that the spin – lattice interaction is characterized by the probability W ₁ , we can write

,

,

характеризует спин-спиновое взаимодействие.where is the probability

characterizes spin-spin interaction.

можно связать с вероятностью

через свой весовой коэффициент

Then the spin-spin relaxation time

can be associated with probability

through its weight coefficient

and as a result, for the transverse relaxation time T ₂ to obtain the ratio

If necessary, the heterogeneity of the field H ₀ can be taken into account in (13) through the probability of the nucleus being in a magnetic field other than H ₀ by δH ₀

,

,

which in the case of a transverse (across the z axis) heterogeneity is added linearly with probability W ₂ , so that

,

,

and in the case of longitudinal (along the z axis) heterogeneity - quadratically [28]

.

.

For example, with the dominant contribution of the transverse gradient of the field H ₀ over the longitudinal, expression (13) becomes

with an extended nuclear resonance band of precessing spins.

In principle, produce a dynamic change in the longitudinal magnetization M _z , i.e. It is possible to destabilize the energy state of precessing microparticles that are in equilibrium without resorting to an intense effect on the system, but using the nutation mechanism. Nutation (a change in the angle of precession) is easily excited by applying to the system an additional alternating transverse magnetic field H _⊥ = H ₁ . In the absence of deliberate generation of a disturbing field H _1, its value is determined by possible random manifestations of transverse magnetic fields. Under natural conditions, the source of such fluctuations can be, for example, non-periodic variations of the Earth’s magnetic field ΔH _Zem ; therefore, when evaluating the adaptability of a microparticle system for a field that destabilizes the state of the system, it is acceptable

H ₁ ≈ΔH _land

With such a fluctuation effect on the system under consideration, H _z >> H ₁ and, accordingly, M _z >> M ₁ and the maximum perturbed relative change in the longitudinal magnetization δM _z caused by the perturbation is equal to

,

,

- полная намагниченность.Where

- full magnetization.

In the framework of the relaxation theory, the expression for estimating the M ₁ / M ratio in the case of unsteady excitation by a weak field H _{1 of a} spin system covered by a strong longitudinal field H ₀ follows from consideration [29]

- компонента поперечной намагниченности, отвечающая за поглощение энергии возбуждения;Where

- the component of the transverse magnetization, responsible for the absorption of excitation energy;

τ = γH ₁ Δt, α = 1 / (γH ₁ T ₁ ), β = 1 / (γH ₁ T ₂ ) - dimensionless quantities;

Δt is the duration of the impact on the system of the transverse field H ₁ ;

- коэффициент, характеризующий начальное (до появления поля H₁) значение продольной намагниченности

.

- coefficient characterizing the initial (before the appearance of the field H ₁ ) the value of longitudinal magnetization

.

Note that expression (14) is obtained under the assumption of a relatively short disturbing action, such that

- период нутации.Where

- nutation period.

Taking into account that, with perfect uniformity of the field H _0, relation (13) with an equally probable contribution to the transverse relaxation of the spin-lattice and spin-spin interactions (p≈r) implies the inequality T ₁ > T ₂ , which in practice [30, FIG. . 2.12] is always strong T ₁ >> T ₂ . Further, if, in accordance with the established ratio between T ₁ and T ₂ , for example, we put specifically T ₁ ≈ 4T ₂ and, using the expression for the value of the exciting field H ₁ [31]

,

,

при стационарном возбуждении, для времени поперечной релаксации получаем ориентировочно T₂≈T_N/4π. Подставляя это ориентировочное соотношение между Т₂ и T_N, соответствующее некоторому приближению к максимально эффективному взаимодействию между возбуждающим полем H₁ и системой прецессирующих спинов, в (14), для максимального значения относительного изменения δM_Z получаем предельно простую оценкуcorresponding to the maximum absorption

under stationary excitation, for the transverse relaxation time, we obtain approximately T ₂ ≈T _N / 4π. Substituting this approximate relation between T ₂ and T _N , corresponding to a certain approximation to the maximum effective interaction between the exciting field H ₁ and the system of precessing spins, in (14), for the maximum value of the relative change δM _Z we get an extremely simple estimate

The optimal duration of the disturbing action Δt _opt , simultaneously satisfying condition (15) and corresponding to the upper bound (16), can be chosen approximately in accordance with the relation T ₂ ≈4Δt. With this in mind, (16) goes over to the form

Substituting numerical values in (17)

ϒ ^Bi = 2π · 684.3≈4.3 · 10 ³ Hz / G [32];

ΔH ≈0,1H _{zem zem} ≈0,05 E at mid-latitudes [33];

- среднее значение для протонов в чистых жидкостях [34, табл. Г. 6],

is the average value for protons in pure liquids [34, tab. G. 6],

, находимfor a system of precessing microparticles consisting of nuclei

we find

.

.

раз. Система спиновых микрочастиц как бы "замораживается" в приложенном сильном однородном магнитном поле. Из этого следует, что при групповом взаимодействии ядер

в сильном однородном магнитном поле Н₀=10⁴ Э время жизни их возбужденного уровня Е₅ заметно возрастает. Например, для перехода γ₂₁ вместо

для изолированных ядер актуальное время жизни с учетом группового взаимодействия в рамках релаксационной теории составляетAs can be seen from (7), taking into account the quadratic dependence of the probability of spontaneous emission of a single multipole Y _M (l, m) on the magnetic moment M _{l, m,} we can assume that under conditions of group interaction of spin microparticles in a strong uniform magnetic field, this probability decreases according to the equality M _{l, m} = μ _{l, m} δM _z in

time. The system of spin microparticles is as if “frozen” in an applied strong uniform magnetic field. It follows from this that in the case of group interaction of nuclei

in a strong uniform magnetic field H ₀ = 10 ⁴ Oe, the lifetime of their excited level E ₅ increases markedly. For example, for the transition γ ₂₁ instead

for isolated nuclei, the actual lifetime, taking into account group interaction in the framework of the relaxation theory, is

.

.

However, a more accurate and correct approach to estimating the probability of a gamma transition of nuclei in a strong uniform magnetic field is the estimate made in the quantum-mechanical description of the phenomenon of nuclear induction.

Suppose, as before, that the exciting magnetic field H _{1 is} polarized linearly and transversely to the external uniform magnetic field H ₀ . Due to the spin interaction of the nuclei nearest to each other, the resonance region of the precessing nuclei is smeared out, so that some weighted spectral distribution of resonance frequencies for individual spin groups in the sample of matter g (ν) is introduced, and to calculate the transition probability, the function g (ν) must satisfy the condition normalization

.

.

Then, for the average probability of the energy transition (E ₀ → E _n ) of the spin ensemble per unit time, we can write

,

,

- общая вероятность перехода.Where

- general probability of transition.

For quantum transitions of nuclei having spin I, with magnetic quantum numbers m corresponding to the series m = -I (upper limit), m = - (I + Δm), ... m = I (lower limit), with a quantum increment Δm = -1, the average probability of the transition of the absorption corresponding to the excitation of the system from level m to level m-1, referred to a unit of time, as follows from [35], is

- матричный элемент магнитного возмущения;Where

- matrix element of magnetic disturbance;

- оператор поперечной составляющей магнитного момента спиновой микрочастицы.

- the operator of the transverse component of the magnetic moment of the spin microparticle.

Given the relation [36] for the matrix element

expression (18) for the average probability of the transition of an ensemble of spin microparticles from sublevel m to level m-1 is converted to

. (19)

. (19)

In a system of nuclear spins covered by a strong uniform magnetic field, the energy transition occurs as a result of two successive independent events: the first of them is the transition of the ensemble from one sublevel to another in accordance with probability (19), the second is the emission of a γ-ray in accordance with probability (7). In this case, the total average probability of the γ transition is

.

.

в силу того, что E_γ>>E_Δm, то для общей вероятности этого события справедливоInsofar as

since E _γ >> E _Δm , then for the general probability of this event,

.

.

, инициированного сменой знака проекции магнитного момента при поперечном возбуждении H₁ подуровня m=1/2 уровня Е₅ и последующем переходе ядер

на подуровень m=-1/2 уровня Е₅, имеемTherefore, substituting m = 1/2, I = 5/2 in (19), for the probability of a γ transition from the level E of ₅ cores

initiated by a change in the sign of the projection of the magnetic moment during transverse excitation of H ₁ sublevel m = 1/2 of level E ₅ and the subsequent transition of nuclei

to the sublevel m = -1 / 2 of level E ₅ , we have

The function g (ν) determines the shape and width of the absorption and emission lines of the hyperfine structure of quantization of the energy of the spin system. Assuming that the transverse effects of the spin interaction in a solid lead to g (ν) corresponding to the Gaussian distribution, then, as follows from [37], we can write

where ν ₀ is the resonant frequency of the precessing microparticles.

представлен в виде порошка из кристаллитов, оценим величину функции g(ν), заменив в (21) квадрат отклонения от резонансной частоты (ν-ν₀)² на его среднее значение (второй момент) в жесткой решетке

. Второй момент можно вычислить из соотношения [38]Assuming that the sample of the parent substance is polonium

represented in the form of a powder of crystallites, we estimate the value of the function g (ν), replacing in (21) the square of the deviation from the resonance frequency (ν-ν ₀ ) ² by its average value (second moment) in the rigid lattice

. The second moment can be calculated from the relation [38]

,

,

where K _res - a numerical coefficient depending on the type of crystal lattice;

g _I is the nuclear Land coefficient;

d _res - lattice constant,

выражается черезor otherwise, given the fact that the gyromagnetic ratio

expressed through

,

,

we get

From (22), when substituting the values of K _res and the corresponding physical quantities

- для простой кубической решетки материнского полония [39],

выходим на оценку второго момента для системы микрочастиц, состоящей из дочерних ядер

- for a simple cubic lattice of maternal polonium [39],

we arrive at an estimate of the second moment for a system of microparticles consisting of daughter nuclei

.

.

,Then from (21) the average value of the distribution function follows

,

, взятой для протонов в соответствии с [30].calculated at constant transverse relaxation time

taken for protons in accordance with [30].

Next, from (20) we find the average value of the probability of a γ transition from the level of E ₅ cores

when the magnitude of the disturbing field H ₁ = 0.05 E.

As a result, the quantum-mechanical approach gives an estimate of the metastable level of E ₅ cores induced by nuclear induction

,

,

which is generally consistent with the estimate resulting from the theory of relaxation.

на промежуточный возбужденный уровень Е₅ ядер

с временем жизни уровня

показывает, чтоComparison of nuclear decay constants

to intermediate excited level E ₅ cores

with level lifetime

shows that

,

,

из-за слишком быстрой спонтанной γ-разгрузки уровня Е₅ ядер

.whence the obvious conclusion about the impossibility of nuclear accumulation at the E ₅ level and, accordingly, the impossibility of creating a γ-active medium based on a β-decay pair

due to too fast spontaneous γ-unloading of level E ₅ cores

.

. Из всех сомножителей, входящих в выражение (22) для

, заметно увеличить можно только K_реш и

. Коэффициент K_реш возрастает до значения K_реш=69 для гранецентрированной решетки [40] с более плотной, чем у простой кубической решетки, упаковкой атомов, а гиромагнитное отношение

повышается в β⁺-распадном ряде радионуклидов у таллия до значения

[32].However, an analysis of relations (20), (21), and (22) suggests that the lifetime of a metastable level of a nucleus belonging to an ensemble of similar spin microparticles in a strong uniform magnetic field increases if the average value of the second moment increases

. Of all the factors in expression (22) for

, only K _res and

. The coefficient K _res increases to K _res = 69 for a face-centered lattice [40] with a denser packing of atoms than a simple cubic lattice, and the gyromagnetic ratio

increases in the β ⁺ decay series of thallium radionuclides to a value

[32].

с периодом полураспада метастабильного материнского свинца

Т_1/2=15,8 мин [41].Taking into account the foregoing, as the next iteration of the proposed method for creating an active medium of a gamma laser, we choose, for example, a β ⁺ decay pair

with half-life of metastable maternal lead

T _1/2 = 15.8 min [41].

, необходимый для вычисления вероятности γ-перехода ядер

с промежуточного возбужденного уровня Е₁(3/2+)=0,38 МэВ на основной уровень Е₀(1/2+), в соответствии с (22) численно равенFor this new pair of elements, taking into account the face-centered lead lattice and the high gyromagnetic ratio of thallium nuclei, the second moment

needed to calculate the probability of a gamma transition of nuclei

from the intermediate excited level E ₁ (3/2 +) = 0.38 MeV to the ground level E ₀ (1/2 +), in accordance with (22) it is numerically equal

.with a constant lattice of lead

.

при той же, что и прежде, оценке времени поперечной релаксации

в соответствии с (21) принимает значениеThen the function

with the same estimate of the transverse relaxation time as before

in accordance with (21) takes the value

,

,

в соответствии с (20) становится равнойand the average probability of a γ transition from the level of E ₁ nuclei

in accordance with (20) becomes equal

.

.

, в сильном однородном магнитном поле стабилизирует ее электромагнитное состояние, увеличивая среднее время жизни промежуточного возбужденного метастабильного уровня E₁ ядер

до перспективного значенияThus, the residence of a spin system consisting of nuclei

, in a strong uniform magnetic field stabilizes its electromagnetic state, increasing the average lifetime of an intermediate excited metastable level E _{1 of} nuclei

to promising value

,

,

which far exceeds the β-decay constant of nuclei

.

.

формируется в результате двух противоположных процессов:In general, level population

formed as a result of two opposite processes:

, обусловливающего подпитку данного уровня;1) β decay of lead nuclei

, conditioning the recharge of this level;

, обусловливающего разгрузку данного уровня.2) radiation of γ-quanta (γ ₆ ) from the level E ₁ of thallium nuclei

causing the unloading of this level.

можно, воспользовавшись соотношением [42], при нулевых начальных условиях

Therefore, estimate the desired population

it is possible, using the relation [42], with zero initial conditions

- результирующая постоянная β-распада пространственно квантованных ядер

на уровень E₁ ядер

;Where

- the resulting β-decay constant of spatially quantized nuclei

to level E ₁ cores

;

- постоянная β-распада ядер

на уровень E₁ ядер

со всех других своих подуровней, кроме (±3/2+);

- β-decay constant of nuclei

to level E ₁ cores

from all its other sublevels, except (± 3/2 +);

- постоянная сверхразрешенного β-распада ядер

на уровень Е₁ ядер

с подуровней (±3/2+).

- constant of superresolved β-decay of nuclei

to level E ₁ cores

with sublevels (± 3/2 +).

, а также что запитка уровня E₁ дочерних ядер

осуществляется в основном только с двух подуровней материнских ядер

(±3/2+), выражение (23) преобразуется к видуGiven that

, and also that the power level E ₁ daughter cores

carried out mainly from only two sublevels of the mother nuclei

(± 3/2 +), expression (23) is transformed to the form

- общее количество подуровней, на которое расщепляется основной уровень ядер

(13/2+) в сильном однородном магнитном поле Н₀.Where

- total number of sublevels into which the core level of nuclei is split

(13/2 +) in a strong uniform magnetic field H ₀ .

заселенность уровня E₁ составитAs a result, it follows from (24), for example, that by the time

the population of level E ₁ will be

и находящейся в сильном однородном магнитном поле Н₀, необходимо рассмотреть следующее.Before proceeding to the estimation of the Debye-Waller factor for the proposed material of a γ-active nuclear medium formed as a result of a β-decay process of nuclei

and located in a strong uniform magnetic field H ₀ , it is necessary to consider the following.

при излучении (или поглощении) γ-кванта с уровня E_n может быть уменьшена ее перераспределением между соседними ядрами, охваченными фотонным механизмом взаимодействия.In a solid crystalline substance immersed in a strong uniform magnetic field H ₀ (longitudinal excitation of the medium), the energy in the crystal can be transferred not only using the phonon mechanism according to the Debye model [43], when the wavelength is higher than a certain characteristic temperature θ _d for most phonons has the order of only a few interatomic distances a, while at temperatures well below the Debye distance, the most probable phonon wavelength grows and has the order aθ _d / T, but also using the photon mechanism, having its place is due to the appearance of the hyperfine structure of the energy sublevels of spatially quantized nuclei. Therefore, in such a resonant medium, due to the precession of nuclei around the direction of the field H ₀ , the average recoil energy of the nucleus

upon emission (or absorption) of a γ-quantum from the level of E _{n, it} can be reduced by its redistribution between neighboring nuclei covered by the photon interaction mechanism.

The longitudinal velocity v _pz of the transverse excitation pulse H ₁ (t) of the longitudinal component of the magnetic moment of the nucleus µ _z in the resonant medium under consideration can be estimated by the formula [44]

,Where

,

- период поперечной релаксации,

- period of lateral relaxation,

,

,

,

,

- нормированная поперечная компонента магнитного момента ядра;

- normalized transverse component of the magnetic moment of the nucleus;

z is the longitudinal coordinate along which, for example, an undistorted 2π-excitation pulse propagates, for which the area under the envelope is

;

;

α _N is the nuclear constant of the relative change in the area of the 2π-pulse per unit length as it spreads in the medium;

τ _and is the duration of the 2π pulse;

µ _x is the transverse component of the magnetic moment of the nucleus during transverse x-excitation;

c is the speed of light in free space.

To estimate v _pz, we assume that Δω → 0, then f (Δω) → 1 and, taking into account the normalization

the parameter S associated with the dispersion of the transverse excitation is approximately equal to S≈1. The nuclear constant α _N , due to the magnetic susceptibility of the excited medium, can be found from the relation with the electron constant α _e ≈ 10 ^-2 cm ^-1 , estimated in [44],

,

,

where μ _N and μ _e are the magnetic moments of the nucleus and electron, respectively.

принимается равнойThe duration of the 2π pulse τ _and with the amplitude of the transverse excitation, for example, H ₁ = 0.1 Oe and

taken equal

.

.

, охваченных сильным однородным магнитным полем Н₀, т.е. в продольно напряженной ядерной среде

Substituting the obtained parameter values in (26), we obtain an approximate estimate of the rate of advancement of photon excitation in the medium of nuclei

covered by a strong uniform magnetic field H ₀ , i.e. in a longitudinally stressed nuclear environment

,

,

which is approximately two orders of magnitude higher than the phonon excitation transfer rate.

с энергией

имеет период полураспада

. Поскольку и в этом случае и при распаде уровня

γ-квант уносит один и тот же момент количества движения ΔI=1, то в соответствии с (7) можно считать, что длительность непосредственно акта излучения

(γ₆, 383 кэВ) с уровня

будет примерно равнаAccording to the data presented in [45], the first γ level of iridium

with energy

has a half-life

. Since both in this case and during the decay of the level

γ-quantum carries away the same moment of momentum ΔI = 1, then in accordance with (7) we can assume that the duration of the radiation act itself

(γ ₆ , 383 keV) from level

will be approximately equal

.

.

, успеет пробежать расстояниеDuring the γ-ray emission, the photon excitation wave caused by the recoil of the nucleus

will have time to run a distance

.

.

, провзаимодействовавших с направленной волной фотонного возбуждения за время излучения γ-кванта, будет приблизительно равноAccording to [46], the concentration of mother lead atoms in 1 cm ³ is n ^Pb = 3.3 · 10 ²² cm ^-3 , then the number of nuclei

interacting with a directed wave of photon excitation during the emission of a γ-quantum will be approximately equal to

.

.

в этом случае составитAverage recoil energy of the daughter thallium core

in this case will be

where M ^Tl = 195 is the atomic mass of thallium in amu

и дебаевской температуры материнского свинца [43]

в выражение (1) для фактора Дебая-Уоллера, находим f_D≈0,4.Introducing the value of the recoil energy of the nucleus of a daughter thallium

and Debye temperature of maternal lead [43]

in expression (1) for the Debye-Waller factor, we find f _D ≈0.4.

, излучающих с уровня

резонансно - без отдачи, выделяемых из общего количества ядер, находящихся на уровне E₁, с помощью фактора Дебая-Уоллера, необходимо также определить количество ядер

, которые теряют энергию возбуждения промежуточного уровня

, передавая ее атомным электронам. В соответствии с данными [41] суммарная вероятность внутренней конверсии энергии уровня

через собственные электронные переходы атома равнаIn addition to the share of cores

emitting from a level

resonantly - without the recoil released from the total number of nuclei at the level of E ₁ , using the Debye-Waller factor, it is also necessary to determine the number of nuclei

that lose intermediate level excitation energy

passing it to atomic electrons. In accordance with the data of [41], the total probability of internal energy conversion of the level

through the intrinsic electronic transitions of an atom is equal to

,

,

while the probability of a γ transition γ ₆ is

.

.

определяется исходя из соотношенияThe coefficient K _se electron conversion level

determined from the ratio

.

.

, равному постоянной времени ускоренного β-распада ядер

в магнитном поле Н₀, "резонансная" заселенность

уровня

составитAs a result, taking into account (25), as well as the Debye-Waller factor and the electron conversion coefficient by the time

equal to the time constant of accelerated β-decay of nuclei

in a magnetic field H ₀ , "resonant" population

level

will make

.

.

верхнего уровня энергии

по отношению к нижнему уровню энергии

γ-перехода γ₆ обусловливается разностью между заселенностями этих уровней с учетом их вырожденияInverted resonance population

top level energy

in relation to the lower energy level

γ transition γ ₆ is due to the difference between the populations of these levels, taking into account their degeneracy

,

,

и

- коэффициенты вырождения соответствующих уровней энергии.Where

and

are the degeneracy coefficients of the corresponding energy levels.

If we neglect the “smearing” of the energies of the emitted γ-quanta associated with the hyperfine structure of the levels under consideration, since this “smearing” is relatively small and in this case is

,

,

.then you can take

.

с проекцией спина I=3/2+ на уровень E₁ дочерних ядер

, обладающий теми же спином и четностью, то до момента начала процесса излучения γ-квантов с этого уровня можно положить

и считатьIf we also take into account the advanced β-decay of the mother nuclei

with the projection of the spin I = 3/2 + on the level E _{1 of} daughter nuclei

having the same spin and parity, then before the start of the process of emission of γ-quanta from this level, we can put

and count

,

,

where F ₁ = (1-N ₀ / N ₁ ) is the inversion coefficient.

3·10³ дочерних ядер

смогут принять участие в формировании резонансного стимулированного излучения гамма-квантов с энергией 383 кэВ, т.е. в предлагаемом способе на три порядка эффективнее используется материал активной среды.Thus, in comparison with the prototype in the proposed method for creating an inverse population of nuclear levels, for example, for every 10 ⁵ mother nuclei

3 · 10 ³ daughter cores

will be able to take part in the formation of resonant stimulated emission of gamma rays with an energy of 383 keV, i.e. in the proposed method, the material of the active medium is used three orders of magnitude more efficiently.

To ensure coherent radiation, i.e. in-phase mode of a typically classical group radiation, in such a nuclear-spin quantum generator it is necessary to fulfill the following conditions.

It is known [47] that the radiation intensity J of a quantum system consisting of N spins with I = 1/2 when the system is in the quantum state / r, m> is

where r is the spin quantum number for the total spin of the system;

m is the magnetic quantum number of the system;

J ₀ - the intensity of spontaneous emission of a single spin.

It is seen from (27) that for r = m = r _max = (1/2) N we have the intensity J = NJ ₀ , i.e., despite the presence of a complete inversion of the system, the spins in this case emit incoherently (or spontaneously) . If the system is prepared in such a way that by the moment of radiation it goes into the state / r = r _max = (1/2) N, m>, where | m | << r, then the radiation intensity becomes equal to J≈ (1/4 ) N ² J ₀ , indicating the coherent nature of the radiation.

Noting that the radiation intensity is nothing more than a stream of energy through a unit area

where E _zap = NE _γ is the energy stored in the spin system and radiated through the transition E _γ ;

Δt is the duration of the emitted pulse;

S _n - the projection of the site through which the radiation is output, on the direction of radiation,

then for a single γ-ray it is natural to set J ₀ = Е _γ / (τ _γ · S _n ) and for the coherent radiation regime, relation (28) can be rewritten as

.

.

The last record means that, due to the conservation of the energy balance, the energy NE _γ stored in the system cannot be exceeded in the process of radiation formation at the self-limited transition, and therefore, when the coherent radiation regime is implemented in this system, wave synchronism leads to a compression of the wave packet and a decrease in 1 / N radiation pulse duration.

Based on the proposed method for creating an inverse population of nuclear levels in the material of the active medium and initiating single-pass coherent gamma radiation, a gamma laser having acceptable characteristics can be built.

The proposed gamma laser device (Fig. 3) contains a solenoid 1 for creating a strong uniform longitudinal magnetic field H ₀ connected to a power supply 2, open strip field forming systems 3 for creating a transverse magnetic field H ₁ connected at their inputs through a balancing device 5 creating antiphase signals to the source 4 of the radio frequency signals, and at the outputs to the matching loads 8, a hollow dielectric cylinder 6 filled with the material of the active medium 7 in the form of a beta-radionuclide adnogo types and forms with one of its front end exit window for the generated radiation, and the other end closed the plug 9.

Conceptually, the device is a single-pass gamma laser operating on a self-limiting gamma transition of radionuclide nuclei.

, необходимо стимулировать переходы вообще всех микрочастиц в системе. Этого можно достичь, обеспечив режим условного избыточного усиления, приводящего к насыщению потока излучения на каждом элементе канала усиления общей длиной L, удовлетворив неравенствуWith a resonant gain of radiation power in the amplification channel, in order to guarantee a radiation pulse with an energy close to the energy of all potentially resonant transitions in the output section of the device

, it is necessary to stimulate transitions in general of all microparticles in the system. This can be achieved by providing a conditional conditional excess gain, leading to saturation of the radiation flux on each element of the gain channel with a total length L, satisfying the inequality

where J and J _L are the output and specific per unit length of the channel for amplifying the radiation intensity, respectively;

N _L is the specific number of microparticles per unit length of the amplification channel that are potentially involved in increasing the intensity of the initial radiation;

L is the length of the gain channel in relative units.

It is known from the theory of amplification of spontaneous emission [48] that the analytical expression for the intensity ratio J / J _L , valid for any form of emission lines with a narrow profile, including Doppler, has the form

where G is the peak specific gain corresponding to the center of the spectral line;

L is the length of the gain channel, equal to that part of the length of the cylindrical sample 6, which is filled with the material of the active medium 7.

From [49] it follows that the peak specific gain is approximately equal to

- удельная "резонансная" инверсная заселенность соответствующего уровня энергии;Where

- specific "resonant" inverse population of the corresponding energy level;

σ _stim is the cross section of the forced transition.

The stimulated transition cross section or otherwise the stimulated emission cross section is determined through the spontaneous emission probability Y (γ) according to the formula [49]

where λ _γ is the wavelength at which the transition radiates;

Δλ _γ is the spectral broadening ("smearing") of the carrier wavelength caused by the interaction of microparticles.

Passing to a specific quantitative estimate of the gain and calculating the values of the physical quantities for the γ transition of γ ₆ daughter nuclei

;

;

,

,

- доплеровское уширение при нормальной температуре в соответствии с [50], принимаемое в качестве максимально возможного уширения, вызванного взаимодействием ядер

;Where

- Doppler broadening at normal temperature in accordance with [50], taken as the maximum possible broadening caused by the interaction of nuclei

;

Or, more precisely, given the value mentioned above

and substituting these values in (32), we obtain

.

.

Then, taking into account relation (31), the peak specific gain in the channel with a cross section of 1 cm ² in the first approximation will be

,

,

[46] - концентрация атомов материнского свинца

.Where

[46] - atomic concentration of maternal lead

.

Assuming now L = 10 cm, from (30) we find

,

,

from which it follows that for the initial data used, inequality (29) holds, but not strictly.

с известным в пассивной среде свинца линейным коэффициентом, равным 2,5 см^-1 [51], в материале активной среды не происходит, все же существует некоторая вероятность выбывания резонансных γ-квантов из потока не резонансным способом. Поэтому поднять условный потолок коэффициента усиления до более высокого уровня было бы желательно.In this situation, however, the following must be understood. Although in the resonance medium the classical mechanism of attenuation of the flux of resonant γ-quanta does not work, and the attenuation of the flux of γ-quanta of interest to us with energy

with a linear coefficient of 2.5 cm ⁻¹ known in a passive lead medium [51], the active medium does not occur in the material, but there is still some chance that resonance gamma quanta will be eliminated from the flux in a non-resonant manner. Therefore, raising the conditional gain ceiling to a higher level would be desirable.

и (или) температуры окружающей среды Т. Понижение температуры окружающей среды является известной общетехнической возможностью обеспечить приемлемую работоспособность устройств мессбауэрского типа, поэтому в рассматриваемом случае необходимо приоритетно использовать первую возможность, относящуюся к специфике предлагаемого устройства.The gain can be increased by increasing the cross section of the stimulated emission by reducing the Doppler broadening D, which, ultimately, can be reduced by reducing the recoil energy of the nucleus

and (or) ambient temperature T. Lowering the ambient temperature is a well-known general technical opportunity to ensure acceptable performance of the Mossbauer type devices, therefore, in the case under consideration, it is necessary to use the first opportunity that is specific to the specificity of the proposed device.

через выражение (26) для продольной скорости распространения поперечного радиоимпульса возбуждения материала активной среды связана дисперсионным соотношением с частотой ω в спектре этого радиоимпульса длительностью τ_и Average core recoil energy

through expression (26) for the longitudinal propagation velocity of the transverse radio pulse of excitation of the active medium material, it is related by the dispersion relation with the frequency ω in the spectrum of this radio pulse of duration τ _and

,

,

which, in turn, leads to a dependence on the frequency of the gain G in the form

,

,

wherein _Har ω = (Sα _N c / πg (0)) ^1/2 - characteristic frequency transverse magnetic excitation of nuclear spins, expressed in terms of known physical quantities.

, то для ω_хар имеемIf we use the values of S, α _N and g (0), which appeared in the estimation of the velocity

then for ω _har we have

.

.

и несоизмеримо превышает

t, зависимость G от частоты в этой части спектра отсутствует. Вместе с тем, эта зависимость на частотах нижней части спектра вблизи

практически линейна.Since the upper cutoff frequency ω _in the spectrum of the excitation radio pulse always lies near the longitudinal precession frequency

and disproportionately exceeds

t, the dependence of G on frequency is absent in this part of the spectrum. At the same time, this dependence at the frequencies of the lower part of the spectrum near

almost linear.

Then, in an effort to obtain the necessary high gain with a weakening of its dependence on frequency, we require the deliberate fulfillment of condition (29) by assigning

,

,

and, taking into account that e ^GL >> 1, we write for the second approximation G _{2 the} dimensionless equality following from (30) for dimensionless G ₂ and L

.

.

равно 0,8. При этом амплитуда радиоимпульса поперечного магнитного поля возбуждения материала активной среды H_1max, обеспечивающая этот коэффициент усиления, равнаWhence with L = 10 the required value

equal to 0.8. In this case, the amplitude of the radio pulse of the transverse magnetic field of the excitation of the material of the active medium H _1max , providing this gain, is

.

.

. Для этого будем считать, что первый (инициирующий) единичный элемент канала усиления длиной 1 см осуществляет эмиссию γ-излучения спонтанно и квазиизотропно. Тогда в контексте изложенного выше получимLet us estimate the maximum output intensity J _{max of the} γ-radiation of the amplification channel within the accepted values of the physical parameters of the channel and the material of the active medium based on the radionuclide

. For this, we assume that the first (initiating) unit element of the amplification channel 1 cm long carries out emission of γ-radiation spontaneously and quasi-isotropically. Then in the context of the above we get

,

,

substituting numerical values, we obtain

with total energy per pulse duration

.

.

The initiation of single-pass coherent gamma radiation in the described device (Fig. 4) is based on the principles of generation of a spin or photon echo in a magnetically stressed medium, which are outlined in general [52, 53].

The proposed method using the described device (Fig. 3) is implemented as follows.

The hollow dielectric cylinder 6 is filled with the material of the active medium 7, which is a beta decay radionuclide. The cartridge thus equipped, consisting of a cylinder 6 and active material 7, is installed inside the solenoid 1 along its axis. Turn on the power source 2 and create inside the solenoid 1 a strong uniform magnetic field H ₀ . The material of the active medium 7 is left in the magnetic field H ₀ alone for the time necessary to create, as a result of beta decay of the mother nuclei, a sufficient inversion of the population of the working intermediate energy level of the daughter nuclei. Then turn on the source of 4 radio frequency signals. Feeding from the source 4 into the open strip field-forming systems 3 through the balancing device 5 antiphase radio pulses, the radio pulses of the transverse magnetic field H _{1x are} injected into the material of the active medium 7 in the following sequence:

- serves π / 2-radio pulse of a transverse magnetic field H _1x small amplitude, satisfying the conditions

,

,

where t _and - pulse duration;

,

,

- величина неоднородного уширения спектра прецессирующих дочерних ядер;Where

- the value of the inhomogeneous broadening of the spectrum of precessing daughter nuclei;

- средняя круговая частота процессии дочерних ядер в сильном не идеально однородном магнитном поле Н₀, с частотой заполнения ω₀, равной средней частоте прецессии

дочерних ядер;

- the average circular frequency of the procession of daughter nuclei in a strong not perfectly uniform magnetic field H ₀ , with a filling frequency ω ₀ equal to the average precession frequency

daughter cores;

in this case, the magnetic moments of the daughter nuclei of the upper and lower sublevels of the working energy level by the end of this pulse will be in planes coplanar to the transverse plane xy, precessing around the longitudinal axis z; moreover, at the time when the magnetic moments of the nuclei are in the xy plane, the nuclei have minimal energy coupling with the longitudinal magnetic force field H ₀ directed along the z axis, and their magnetic quantum number m is zero;

- after the end of the action of the π / 2 radio pulse of the transverse magnetic x-excitation, a quarter-period of phase relaxation Δt ₁ = π / 4Δω follows, during which the system of sector-localized (conditionally in the xy plane) magnetic moments corresponding to the upper and lower initial energy sublevels and now rotating in planes coplanar xy plane, due to the difference in the precession frequency (ω ₀ -Δω) ← ω ₀ → (ω ₀ + Δω) begins to disperse, aiming to fill uniformly the whole xy plane of rotation, the fan-shaped divergence of the moments of the first conditional half-plane bounded by the x-axis, the second and vice versa will take place both clockwise and counterclockwise;

- after the time interval Δt _{1 has} elapsed since the start of the phase relaxation, a π-radio pulse of a transverse magnetic field H _{1x of} small amplitude is fed, which mirrors magnetic moments located in opposite half-planes bounded by the x axis, xy plane with respect to the xz plane;

; при этом два результирующих момента M_y и -M_y будут расти, стремясь к своим максимальным значениям; в максимуме результирующих моментов индивидуально сфазированные две подсистемы спинов получают возможность излучать в противоположенные стороны - каждая как самостоятельное целое, т.к. в этот момент для каждой из подсистем обеспечивается выполнение условия когерентного излучения (r=IN>>m);- after the end of the action of the π radio pulse of the transverse magnetic x-excitation, the time interval Δt ₂ = π / 2Δω is equal to the half-period of phase relaxation, during which the magnetic moments of the nuclei, continuing their circular motion around the z axis, now, however, after rotation around the axis x will change the direction of their rotation in the opposite direction, and after dividing during Δt ₁ into two conditional sector halves, they will move in their conditional half-planes bounded by the x axis towards each other, gradually gathering around those magnetic moments that are directed in one of these half-planes along the y axis, and in the other along the -y axis and having a circular rotation frequency

; in this case, the two resulting moments M _y and -M _y will grow, striving for their maximum values; at the maximum of the resulting moments, the individually phased two subsystems of spins are able to radiate in opposite directions - each as an independent whole, because at this moment, for each of the subsystems, the coherent radiation condition is satisfied (r = IN >>m);

- after the time interval Δt ₂ expires at the time of reaching the maximum, the resulting magnetic moments of the subsystems M _y and -M _y give a short radio pulse of a transverse magnetic field H _{1x of} large amplitude, which, quickly rotating the resulting vectors of magnetic moments of the nuclei M _y and -M _y around the x axis , creates in the region of small values of the magnetic moment M _z arising during this rotation, a significant value of the derivative dM _z / dt, stimulating (due to its value) gamma radiation of the working transition under conditions of minimal recoil of nuclei, i.e. in the mode of radiation from the resonance plane xy of coherent gamma rays in a very narrow spectral band;

- at the output of the device during the action of a powerful short stimulating radio pulse of transverse magnetic x-excitation, an ultrashort gamma pulse is formed with a narrow radiation pattern due to the axial geometry of the system and the alignment of the sample material of the active medium 7 and solenoid 1.

Matching loads 8 absorb the energy of the transverse excitation radio pulses remaining after passing along the active medium 7 material zone. The plug 9 intercepts gamma radiation that does not meet the given diagram and is directed in the direction opposite to the output of the device.

If it is necessary to improve the output parameters of the proposed device by reducing, for example, the Doppler broadening of the gamma-ray spectral line and stabilizing the hyperfine structure of the system of quantum sublevels of nuclei, the material of the active medium can be cooled to the temperature of liquid nitrogen or helium or even lower.

To ensure an appropriate level of transverse excitation in the conductive materials of the active medium, it is necessary to take into account the surface electromagnetic effect. Taking into account the skin effect, the penetration depth of the electromagnetic field into the conductor

при удельной проводимости, соответствующей, например, свинцу, равной σ_Pb=0,48·10⁷ См/м [54], и магнитной проницаемости µ=µ₀ составляет δ_s≈0,5·10^-4 м, что предъявляет к материалу активной среды агрегатные требования: он должен представлять собой порошок из кристаллитов с размером частиц не более δ_s либо быть изготовлен в виде пакета пластин соответствующей толщины.at characteristic frequencies of nuclear precession

at a specific conductivity corresponding, for example, to lead equal to σ _Pb = 0.48 · 10 ⁷ S / m [54], and magnetic permeability µ = μ ₀ is δ _s ≈0.5 · 10 ^-4 m, which leads to material of the active medium is aggregate requirements: it must be a powder of crystallites with a particle size of not more than δ _s or be made in the form of a package of plates of the corresponding thickness.

Thus, the proposed method for creating an inverse population of nuclear levels in the material of the active medium and initiating single-pass coherent gamma radiation provides an increase in the efficiency of using the material of the active medium for generating single-pass coherent gamma radiation.

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Claims (1)

The method of creating an inverse population of nuclear levels in the material of the active medium and initiating single-pass coherent gamma radiation, which involves transferring a certain fraction of the nuclei to an excited metastable state and consisting in the use of a radionuclide as the material of the active medium, the transition of nuclei from an excited metastable state carried out through gamma radiation, characterized in that a radionuclide in which beta decay is carried out is used as the material of the active medium hell of the nuclei of the form X (A, Z) → Y (A, Z-1) while maintaining the parity of the initial and intermediate excited states, the radionuclide is placed in a strong longitudinal homogeneous magnetic field such that the energy levels of the parent and daughter nuclei of the radionuclide acquire in this magnetic field the hyperfine energy structure with the quantum characteristics of sublevels, which determine the selective acceleration of the beta decay process for a part of the mother nuclei and maintain the stability of the intermediate excited states of daughter nuclei, for a time, not exceed which reduces the lifetime of the metastable state of the working intermediate energy level of daughter nuclei, but sufficient to create the necessary population inversion of this level, the radio pulses of transverse magnetic excitation are injected into the material of the active medium in the following sequence: a π / 2 radio pulse of small amplitude is supplied, after the action of π / 2 -radio pulse follows a quarter-period of phase relaxation, after a quarter-period of phase relaxation a π-radio pulse of small amplitude is fed, after the end of the action π- the radio pulse follows a half-period of phase relaxation, after a half-period of phase relaxation a short radio pulse of large amplitude is supplied.

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