VL mat .  2

2

1 

, (2) where 0.5



_²is the kinetic term, and V

  

_{is the} potential energy of the scalar field. This Lagrangian has a canonical form. However, at present, its generalizations have been proposed, known as the k-essence model [15, 16]. The Lagrange function of such a field L(,X) depends on the variables  _{and X , where}







 

x g x

X 





  2

1 .

Action and equations of motion

In this work, we will investigate the model of a flat, homogeneous Universe in the theory of Einstein and k-essence. That is, in action (1), in the role of the matter field, consider the special case of the Lagrange function for the essence.

We obtain the corresponding equations of motion, as well as their particular solutions. Let us compare the results obtained with modern observational data.

As mentioned above, we will consider here the cosmological model of a flat Universe in the framework of the general theory of relativity and kessence, where the gravitational field does not interact minimally with the scalar field. The action for such a model is written in the following form [17]:

 



^{ }_^{  }_^

 d x g M f R P X

S ^P ( ) ,

2

4 2   , (3)

where u() is the connection function and



X



K



, is the Lagrange function for the k - essence. Also here we consider the Friedman- Roberson-Walker metric, which describes a flat, homogeneous and isotropic four-dimensional space-time, namely



^{2 2 2}



2 2

2 dt a(t) dx dy dz

ds     , (4)

where a(t) is a scale factor that depends on time.

This metric is in good agreement with modern

observational data. For this metric, you can write the following expressions

2 2

3 2

2 , 1

6

, ^{ }  



_

 



 





 X

a a a R a a

g .

Hereinafter, the dot above the letter will denote the time derivative t. Now it will be possible to write the Lagrange function in action (3) and taking into account the metric (4) as



X



P a a a f M a fa M

L3 _P² ² 3 _P²  ² ³



, . (5) Here and below, the stroke above the letter will denote the derivative with respect to the field.

Next, using the Euler-Lagrange equations and the zero energy condition, we define the equations of motion for the considered model

0 3

3 ² ₂²  ²  P ² P a

f a a M

f a

M_P ^ _P



_ ^ _X



_{ , (6)}

2 2 2

2

2 2

2

2 0,

P P

P P

a a

M f M f

a a

M f M f a P

a

 

   

 

   (7)

2

2 2 2

3

3 0.

X XX X

P

P P aP

a

a a

P M f

a a

   

 

 

    

 

    

  . (8)

Also, the system of equations (6) – (8) can be written through the Hubble parameter

a a H  / :







 M fH fH

M_P^{2 2} 3 _P² 

3 , (9)



H H



M f M fH p

f

M_P² 3 ²2   _P² 2 _P²   , (10)

 

 

2 2

2 6

3 2 0,

X XX X

P

P P X X HP X

P M f H H

  

 

   



 (11)

89 K.R. Myrzakulov et al.

International Journal of Mathematics and Physics 12, №2, 87 (2021) Int. j. math. phys. (Online)

where  2XP_X P and p_ P



,X



are the energy density and the k-essence pressure.

Hereinafter, the stroke above the letter will denote the derivative with respect to the field φ.

The equation of state parameter for the k- essence can be written in the form

P XP p P

X 



 _ 2



 

. (12) The square of the speed of sound is

X XX

X X

s X XP P

P c p

 

 2

2

 . (13)

The system of equations (6)-(8) or (9)-(11) are nonlinear partial differential equations, for the solution of which it is necessary to determine the explicit form of the functions a(t), f() and



X



P



, . Below we will consider particular solutions of these functions.

Cosmological solutions

We start with the case when _f

  

1and



 X



 V

 



P  ²

2

, 1  , then the system of equations (9)-(11) can be rewritten as

 2

2 1

3

MP

H  , (14)

p

H M H

P2

2 2 1

3    , (15)

0

3  

 H



V



_{ } . (16) Here

 





_  ² _V 2

1  и _p  ²_V

 

 2

1 

The system of equations (14)-(16) is a standard cosmological model with a scalar field, where the gravitational fields interact non minimally with the scalar field .

Now consider the case when

   

, P

 

,X



K(X) V(



)

f    . (17)

Then equations (9) – (11) can be rewritten as

2 2 2

3 3

2 ( ) ( ) 0,

P P

X

M H M H

XK K X V

 



 

   

 (18)

 

2 2 2

2

3 2

2 ( ) ( ) 0,

P P

P

M H H M

M H K X V

 

 

  

   





 (19)

 

 

2 2

2 6

3 2 0.

X XX X

P

K XK X HK X V

M H H

   

  



 (20)

Let's suppose



2



0

3 ^{2 2}  

 M H H

V _P  .

Where do we get

n H d H

dV

M_P2 2 ²    3

1



Here n is a certain constant. Accordingly, we obtain a system of differential equations

d



nM dV 3 _P² ,

0

2 2

2   



 



 na

dt da dt

a

ad .

Integrating them, we find

 

3nM² C₁

V



 _P



 , (21)

 

t e^nt

a  . (22) where C1 is a certain constant of integration. The particular solution we obtained for the scale factor (22) is the de Sitter solution, which describes the modern dynamics of the expanding Universe. The equation of state parameter for such a solution is equal to



1, which corresponds to the dark energy model. Figure 1 shows the dependence of the scale factor a(t) on

90 On one integrable cosmological model of the flat universe in k-essence time, at. Figure 2 also shows the dependence of

the potential energy on the scalar field, at, and.

Figure 1 shows the dependence of the scale

factor a(t) on time t, at n = 1. Figure 2 also shows the dependence of the potential energy V(φ) on the scalar field n1, M_P 1 and C1 = 1.

Figure 1 – Dependence of the scale factor

a(t) on time t Figure 2– Dependence of the potential energy

V(φ) on the scalar field φ

Now equating equations (18) and (19), we obtain

2 0

2 



 _X

P

M XK n

  . (23)

Equation (20) can be written as



K_X 2XK_XX



X 6nXK_X 0. (24) Here we consider the kinetic Lagrange term for the scalar field K

 

X as K

 

X 



_iX_{, where} the



_i constant can take values



₁1 or

2 1



, which correspond to cosmological models of quintessence and phantom field. Then equations (23) and (24) take the form

0

2

2 



   

   MP

n .

0 3 







 n . Equating these equations, we find

0

4 ² 

 n M_P dt

d



 . (25)

By integrating which, we get

 

t 4n M_P²tC₁

  . (26) Next, consider the case when

   

²

2 , 1

,   



 P X X m

f    . (27)

Here

 

²

2

1 

 _m

V  is the potential energy of the scalar field. Then equations (8)-(11) can be rewritten as

2 0 1 2

3 1

3M_P²H² M_P²H ² m²  , (28)

2 2 2 2

2 2 2

3 2

1 1

2 0,

2 2

P P P

P

M H M H M

M H m

  

  

  

   

 

  (29)

91 K.R. Myrzakulov et al.

International Journal of Mathematics and Physics 12, №2, 87 (2021) Int. j. math. phys. (Online)



2



0

3

3 ²   ^{2 2} 

  H m M_P H H





   





_{. (30)}

Figure 3 shows the dependence of the potential energy V() on the scalar field , for the case

 

²

2

1 

 _m

V  , where n1 and m1.

Figure 3 – Dependence of the potential energy V(φ) on the scalar field φ

From equations (28) and (29), we obtain the equation

0

2  ₂ ² 



    

   

MP

H

H . (31)

Substituting solutions (22) into equations (30) and (31), we determine

0

2

2 



   

_{  } MP

n . (32)

Integrating this equation, we get

   

_



 



 

 ² ln ₂ C₁e C₂ M

t M ^nt

P

P



 

, (33)

where С₁ and С₂ are the constants of integration.

Conclusion

In this work, we have considered the cosmological model of the Universe in the framework of the classical theory of gravity and

k-essence, where the gravitational field interacts non minimally with the scalar field. Particular solutions are obtained for the scale factor )a(t in the form of the de Sitter solution, and two particular solutions are obtained for the scalar field  and potential energy V(). It was found that both are more realistic and are able to describe the modern dynamics of the expansion of the Universe. It was found that

   

_



 



 

 ² ln ₂ C₁e C₂ M

t M ^nt

P

P



 

_and

 

²

2

1 

 _m

V  are more realistic and are able to describe the modern dynamics of the expansion of the Universe. The analytical solutions obtained here are solutions of the considered integrable systems.

Acknowledgments. These studies were carried out within the framework of the grant project funded by the Ministry of Education and Science of the Republic of Kazakhstan AP08052034 "Investigation of integrable models of strong gravitational fields in the framework of the theory of solitons".

References

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2 Myrzakul, S.R., Imankul, M., Arzimbetova, M., Myrzakul, T.R. “Gravity with scalar field viscous fluid”. Journal of Physics: Conference Series, 1730, 1 (2021): 012021.

3 Saridakis, E.N., Myrzakul, S., Myrzakulov, K., Yerzhanov, K. “Cosmological applications of F (R,T) gravity with dynamical curvature and torsion”.

Physical Review D, 102, 2 (2020): 023525

4 Arzimbetova, M.B., Myrzakul, S.R., Myrzakul, T.R., Imankul, M., Yar-Mukhamedova. “G.Noe–

ther’s symmetry in horava-lifshitz cosmology”.

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5 Bekov S., Myrzakulov K., Myrzakulov R., Gomez D.S.-C. “General slow-roll inflation in f(R) gravity under the Palatini approach”. Symmetry, 12, 12 (2020): 1-13, 1958.

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6 Somnath Mukherjee, Debashis Gangopadhyay.

“An accelerated universe with negative equation of state parameter in Inhomogeneous Cosmology with k-essence scalar field”. Physics of the Dark Universe, Volume 32, (2021): 100800.

7 J. Bayron Orjuela-Quintana, César A.

Valenzuela-Toledo. “Anisotropic k-essence”. Phys.

Dark Univ. 33, (2021): 100857.

8 Anirban Chatterjee, Saddam Hussain, Kaushik Bhattacharya. “Dynamical stability of K- essence field interacting non-minimally with a perfect fluid”. Phys. Rev. D (2021): 104.

9 S. X. Tian, Zong-Hong Zhu. “Early dark energy in k-essence”. Phys. Rev. D, 103 (2021): 043518.

10 Vinod Kumar Bhardwaj, Anirudh Pradhan, Archana Dixit. “Compatibility between the scalar field models of tachyon, k-essence and quintessence in f(R,T) gravity”. New Astronomy, Vol. 83, Issue Feb. (2021): 101478.

11 John Kehayias, Robert J. Scherrer. “A new generic evolution for k-essence dark energy with w≈−1”. Phys. Rev. D, 100 (2019): 023525.

12 Joel S. Perlmutter. et al. “Measurements of omega and lambda from 42 high-redshift surenovae”.

The Astrophysical Journal, Vol. 517, 2 (1999): 565- 586.

13 Adam G. Riess. “Observational evidence from supernovae for an accelerating universe and a cosmological constant”, The Astrophysical Journal, Vol. 116, No 3. (1998): 1009-1038.

14 Bolotin Yu.L., Erokhin D.A., Lemets O.A.

“Expanding Universe: Deceleration or Acceleration?”, Advances in physical sciences, Volume 182, No. 9. (2012): 941-986.

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“Kinetically drive quintessence”, Physical Review D, Vol. 62. (2000): 023511.

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© 2021 al-Farabi Kazakh National University Int. j. math. phys. (Online) International Journal of Mathematics and Physics 12, №2, 93 (2021)

IRSTI 29.15.35; 34.49.23; 87.15.03; 87.26.25; 87.24.37 https://doi.org/10.26577/ijmph.2021.v12.i2.011

V.V. Dyachkov^1* , Yu.A. Zaripova¹ , M.G. Ahmadieva¹ , M.T. Bigeldiyeva¹ , A.V. Yushkov^1,2

1Al-Farabi Kazakh National University, Almaty, Kazakhstan

2Science Research Institute of Experimental and Theoretical Physics, Almaty, Kazakhstan

* e-mail: slava_kpss@mail.ru

Study of the natural radioactivity of ore deposits

IRSTI 29.15.35; 34.49.23; 87.15.03; 87.26.25; 87.24.37 https://doi.org/10.26577/ijmph.2021.v12.i2.011

V.V. Dyachkov^*1 , Yu.A. Zaripova¹ , M.G. Ahmadieva¹ , M.T. Bigeldiyeva¹ , A.V.

Yushkov^1,2

1Al-Farabi Kazakh National University, Almaty, Kazakhstan

2Science Research Institute of Experimental and Theoretical Physics, Almaty, Kazakhstan

* e-mail: slava_kpss@mail.ru

Study of the natural radioactivity of ore deposits

Abstract. In the article, the authors present experimental data on the specific power equivalent dose (EDR) of radiation gamma, beta, and alpha radiation in samples containing copper, zinc and lead of pyrite-polymetallic ores, which were mined at the Zhezkent mining and processing plant (The East Kazakhstan region, Borodulikhinsky district).

The measurements were carried out by dosimeters and radiometers "RKS-01-SOLO" with alpha, beta and gamma scintillation detectors. For ores, the dependences of the specific power of the equivalent dose of gamma radiation on the content of various concentrations of copper, zinc and lead were revealed. The analysis of natural decay chains, the daughter products of which are stable isotopes of copper and zinc, is carried out. A relationship has been proposed between the concentrations of nickel, copper, lead and EDR, which gives prospects for further spectrometric studies of these samples to identify the corresponding lines of accompanying gamma radiation during decays of radionuclides contained in the samples under study and radiation conversion of stable isotopes. The results of this work will make it possible to build a model for studying the radiation of ores, the distribution of natural radionuclides in the earth's crust, which will undoubtedly provide prerequisites for the verification and clarification of the sources and mechanisms of emanation and coagulation of radon isotopes, which form the natural radiation background of the surface atmospheric layer.

Key words: equivalent dose rate; pyrite-polymetallic ore; radioactivity of minerals; geology of the Earth.

Introduction

The study of natural radioactivity is extremely important due to the direct effect of radiation from natural radionuclides on human health [1-21]. From the very beginning of its formation, the Earth's crust contains natural radioactive elements [22-23], which create a natural background radiation. The radioactive isotopes of potassium-40, rubidium-87 and members of three radioactive families originating from uranium-238, uranium-235 and thorium-232 are present in rocks, soil, atmosphere, waters, plants and tissues of living organisms. Studying the own radiation of rocks, various ores and minerals, minerals will help to supplement the existing geological models on the formation and geological structure of the earth's surface with experimental data. It is of great interest to study the content of various radionuclides in these terrestrial samples. In this work, an attempt has been made to determine the relationship between the decays of radionuclides included in chains, which lead to the current concentration of certain impurities in rocks, ores and minerals, by radiometric measurement of gamma radiation.

In addition, in the geological structure of the Earth, in addition to the elements of the three main radioactive families, the existence of other chemical elements contained in minerals in various geological layers of the Earth, there is a basic hypothesis for the formation of the latter during the formation of planets from stellar material by accretion from a protoplanetary disk, a disk-like mass of gas , dust left over from the formation of the Sun. The study of natural radiation of ore rocks will explain these concentrations in deposits from the standpoint of nuclear-physical mechanisms. Such prerequisites follow from the fact that the formation of light nuclei occurs due to fusion reactions. The formation of medium and heavy occurs due to the capture of neutrons and further beta decay or other nuclear reactions occurring in the evolution of Stars.

Material and Methods

Samples of pyrometallic ore were taken at the Zhezkent mining and processing plant (East Kazakhstan region, Borodulikhinsky district), Figure 1. The main ore bodies of the deposits are confined to zones of interlayer disruption and are characterized

94 Study of the natural radioactivity of ore deposits

by ores close in material composition, differing mainly in the ratios of the main components (copper:

lead : zinc) and the presence of pyrite in varying

amounts. Rocks containing ore deposits are volcanic- sedimentary formations of the Middle and Upper Devonian [24].

Figure 1 – Geological map and location of the Zhezkent mining and processing plant [25]

The measurements were carried out with RKS- 01-SOLO dosimeters and radiometers with alpha, beta and gamma scintillation detectors in contact with the sample surface. These devices are designed for radiation monitoring of the environment and various surfaces. The sensitivity of devices for measuring the equivalent dose rate from 0.05 to 10²μSv/h with a relative measurement error limit of

15%.

The measurement technique for colche – polymetallic ores was as follows. The maximum possible surface was chosen on the sample to cover the working sensitive part of the detector. Within ten days, with a step of two days, a series of measurements of the gamma background and gamma

radiation of the surface of the samples were carried out. The statistical error in measuring the gamma background and gamma radiation of the samples did not exceed 10%. Measurements of alpha and beta radiation were carried out during the day, while fluctuations in the background and self-radiation reached 50%, but on average did not exceed the background value. This error is explained by the relatively low values, which leads to a corresponding uncertainty in the measurement results.

Fig. 2 shows the selected samples of pyrite – polymetallic ore. Samples were taken from various parts of the mine. On average, the depth of mining ranges from 200 to 500 m.The chemical composition of ore samples is given in Table 1.

Table 1 – Composition of samples of pyrite – polymetallic ore

samples Plot Cu, % kg Pb, % kg Zn, % kg Fe, S % kg m, kg Cu, % Pb, % Zn, %

1 1 5.08 0.048 0.165 94.707 0.865 4.39 4.15 0.143

9 1 1.215 0.93 4.29 97.426 0.534 0.65 0.497 2.29

10 1 1.215 0.93 4.29 97.426 0.458 0.55 0.426 0.196

3 2 2.08 1.83 5.26 90.83 1.056 2.2 1.93 5.55

4 2 2.08 1.83 5.26 90.83 0.256 0.53 0.46 1.35

6 2 2.08 1.83 5.26 90.83 0.25 0.52 0.458 1.32

7 2 2.08 1.83 5.26 90.83 0.309 0.64 0.565 1.63

2 3 4.72 0.11 0.58 94.59 0.592 2.79 0.028 0.343

5 3 4.72 0.11 0.58 94.59 0.613 2.89 0.067 0.356

8 3 4.72 0.11 0.58 94.59 0.648 3.06 0.071 0.376

95 V.V. Dyachkov et al.

International Journal of Mathematics and Physics 12, №2, 93 (2021) Int. j. math. phys. (Online)

Figure 2 – Appearance of samples of pyrite – polymetallic ore

96 Study of the natural radioactivity of ore deposits

Results and Discussion

Fluctuations in the background EDR values over the entire measurement period ranged from 0.107 μSv/h to 0.113 μSv/h. Figure 3 shows the

results of measurements of the intrinsic gamma radiation of all samples. Figures 4-6 show the dependences of the specific EDR measurement results on the percentage of lead, copper and zinc.

Figure 3 – Values of specific EDR in all studied samples

Figure 4 – Dependence of the specific EDR on the percentage of lead in the samples.

From left to right, sample numbers: No.1, No.9, No.8, No.2, No.5, No.10, No.6, No.4, No.7, No.3

Figure 5 – Dependence of the specific EDR on the percentage of zinc in the samples.

From left to right, sample numbers: No.1, No.2, No.8, No.5, No.6, No.4, No.7, No.10, No.9, No.3 0

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

1 2 3 4 5 6 7 8 9 10

Samples

Dose, uZv/h kg

0 0,2 0,4 0,6 0,8 1 1,2 1,4

0,04 0,058 0,06 0,06 0,07 0,426 0,458 0,46 0,56 1,93 percentage of lead

Dose, uZv/h kg

0 0,2 0,4 0,6 0,8 1 1,2

0 0,5 1 1,5 2

percentage of lead

Dose, uZv/h kg

0 0,2 0,4 0,6 0,8 1 1,2 1,4

0,143 0,343 0,356 0,376 1,32 1,35 1,63 1,96 2,29 5,55 percentage of zinc

Dose, uZv/h kg

0 0,2 0,4 0,6 0,8 1 1,2 1,4

0 1 2 3 4 5 6

percentage of zinc

Dose, uZv/h kg

97 V.V. Dyachkov et al.

International Journal of Mathematics and Physics 12, №2, 93 (2021) Int. j. math. phys. (Online) Figure 6 – Dependence of the specific EDR on the percentage of copper in the samples.

From left to right, sample numbers: No.6, No.4, No.10, No.7, No.9, No.3, No.2, No.8, No.5, No.1

From the experimental dependences it can be seen (Fig. 4-6) that the values of the specific EDR in ore samples 3, 4, 6, 7, a stable excess of the gamma background is observed. Figure 4 shows the dependence of the specific EDR on the percentage of lead in ore samples. It can be seen that the relationship between the increase in the concentration of lead and the increase in the specific EDR is traced quite well in the ore samples, the correlation coefficient is 0.97.

Figure 5 shows that the relationship between an increase in zinc concentration and an increase in specific EDR is not entirely unambiguous in ore samples, while the correlation coefficient is 0.88.

Figure 6 shows the dependence of the specific EDR on

the percentage of copper in ore samples, which is practically absent, the correlation coefficient is -0.17.

Figure 7 clearly shows the impurities of lead, zinc and copper in the studied ores and their specific EDR values. It can be seen that the relationship between the content of lead and zinc and the specific EDR for the corresponding ore is well traced. As a result of the decays of three natural radioactive families, stable lead isotopes are ultimately formed. This can explain the high correlation coefficient between the concentration of lead and EDR in the samples.

Figures 8, 9 show the results of radiometric measurements of beta and alpha radiation of the samples under study.

Figure 7 – Relation of specific EDR with the concentration of lead, zinc and copper in ore samples

0 0,2 0,4 0,6 0,8 1 1,2 1,4

0,52 0,53 0,56 0,643 0,649 2,2 2,79 2,89 3,06 4,39 percentage of copper

Dose, uZv/h kg

0 0,2 0,4 0,6 0,8 1 1,2 1,4

0 1 2 3 4 5

percentage of copper

Dose, uZv/h kg

0,01 0,1 1 10

0 1 2 3 4 5 6 7 8 9 10 11

Samples lead, zinc, copper, % Dose, uZv/h kg

lead copper

zinc Dose

98 Study of the natural radioactivity of ore deposits

Figure 8 – Values of surface beta radiation in all tested samples

Figure 9 – Values of surface alpha radiation in all tested samples

The figures show that there is no excess over the background level of alpha and beta radiation from the samples under study, obtained by radiometric methods, and is within the measurement error. The effect on the EDR of the samples is indirectly exerted by the concentration of zinc. It can be assumed that, possibly, in the geological structure of the Earth, in addition to the elements of the three main radioactive families, the existence of some chemical elements takes place due to the radiation transformation from one to another. As you know, the nature of the

formation of all chemical elements, and as a result, their presence in the chemical composition of the Earth, is the result of the evolution of stars, from the substance of which, subsequently, the planets are formed. But it is worth noting that the formation of nuclei up to A<60 "iron maximum" occurs due to fusion reactions. The formation of nuclei with A>60 occurs due to the capture of neutrons and further beta decay. Such a transformation of the latter is quite possible in the conditions of the formed planets. In addition, the reactions of radiation capture by

4 6 8 10 12 14 16 18 20 22

0 1 2 3 4 5 6 7 8 9 10 11

Samples beta, 1/(min*cm2)

fon maximum value of fon minimum value of fon samples average value of fon

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1

0 1 2 3 4 5 6 7 8 9 10 11

Samples alpha, 1/(min*cm2)

fon maximum value of fon minimum value of fon samples average value of fon

99 V.V. Dyachkov et al.

International Journal of Mathematics and Physics 12, №2, 93 (2021) Int. j. math. phys. (Online) elements of high-energy protons in cosmic ray fluxes

also make it possible to perform such a transformation. Within the framework of this work, the authors propose a model of the radiation origin of chemical elements of ore rocks, as applied to copper and zinc, not during the birth and formation of the planet, but during its entire life cycle.

Consider a process of radiation origin ⁶⁴Zn from

63Cu. In nature, the content of the stable isotope ⁶³Cu is 69.1%. In the process of radiation capture of a neutron, ⁶³Cu

 

n,



⁶⁴Cu (where En≈0.6 MeV, the reaction cross section σ≈20 mb [26]) a radioactive isotope ⁶⁴Cu is formed. In turn, ⁶⁴Cu, with a half-life of 12.7 hours, decays through β + -decay, ε-capture and β-decay into the corresponding decay products of

64Ni ^{64 64}

1/2

(61,5%)

Cu Ni

T 12,7h

^ 

  

   

 , which is

0.91% in nature, and 64Zn

64 64

1/2

(38,5%)

Cu Zn

T 12,7h

^

 

   

 , which in nature 48.6%.

On the other hand, in the process of radioactive capture of a proton ⁶³Cu

 

p,



⁶⁴Zn, (where Ep = (1.46-3.21) MeV, the reaction cross section σ = (1.2- 15.6) μb [27]) a stable isotope 64Zn is formed.

The process of radiation origin of 66Zn from 65Cu, the content in nature is 30.9%, can be described as follows. 1) in the process of radiation capture of a neutron ⁶⁵Cu

 

n,



⁶⁶Cu, (where En≈0.6 MeV, the reaction cross section σ≈10 mb [26]), a radioactive isotope 66Cu is formed. In turn,

66Cu, with a half-life of 5.12 min, decays through β-

decay into ⁶⁶Zn ^{66 66}

1/2

(100%)

Cu Zn

T 5,12 min

^

 

   

 ,

which is 27.9% in nature. 2 on the other hand, in the process of radioactive capture of a proton

 

p, Zn Cu ⁶⁶

65



, (where Ep = (1.3-3.0) MeV, the reaction cross section σ = (1.0-3.8) μb [28]), a stable isotope ⁶⁶Zn is also formed.

Within the framework of this work, we have limited ourselves to considering only two isotopes of radioactive transformation as an example.

Undoubtedly, such an analysis requires a more detailed study with the ability to trace all stable isotopes of copper and zinc.

This process of radiation origin of Zn from Cu can explain the anticorrelation (-0.34) of the content of zinc and copper in the studied ore samples.

However, the correlation coefficient of DER from the

percentage of copper in ore samples is -0.17, while the percentage of zinc is 0.88.

Conclusion

Thus, in this work, the specific power of the equivalent dose of radiation gamma, beta, and alpha radiation was measured in samples containing copper, zinc and lead of pyrite-polymetallic ores, which were mined at the Zhezkent mining and pro- cessing plant (The East Kazakhstan region, Boro- dulikhinsky district). The measurements were carried out by dosimeters and radiometers "RKS-01-SOLO"

with alpha, beta and gamma scintillation detectors.

For ores, the dependences of the specific power of the equivalent dose of gamma radiation on the content of various concentrations of copper, zinc and lead were revealed. The analysis of natural decay chains, the daughter products of which are stable isotopes of copper and zinc, is carried out. A relationship has been proposed between the concentrations of nickel, copper, lead and EDR, which gives prospects for further spectrometric studies of these samples to identify the corresponding lines of accompanying gamma radiation during decays of radionuclides contained in the samples under study and radiation conversion of stable isotopes. The results of this work will make it possible to build a model for studying the radiation of ores, the distribution of natural radionuclides in the earth's crust, which will undoubtedly provide prerequisites for the verification and clarification of the sources and mechanisms of emanation and coagulation of radon isotopes, which form the natural radiation background of the surface atmospheric layer.

Acknowledgments. This research is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP09258978).

References

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2 Smith H., ed. Headington Hill Hall: Elsetsier Science Ltd, 1987.

3 Yarmoshenko I.V., Kirdin I.A., Zhukovsky M.V., Astrakhantseva S.Yu. Meta-analysis of epidemiological studies of the risk of lung cancer during irradiation with radon in dwellings. Medical Radiology and Radiation Safety. 48, 5. (2003): 33-43.