Interaction of Electrons with Matter and Comparison of the Obtained Results with Experimental Measurements

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1 Australian Journal of Basic and Applied Sciences, 5(): 83-80, 0 ISSN Interaction of Electrons with Matter and Comparison of the Obtained Results with Experimental Measurements Somayeh Almasi Bigdelo, Laleh Alamsi Department of Physics, Pars Abad Moghan Branch, Islamic Azad University, Pars Abad, Iran. Department of Chemistry, Pars Abad Moghan Branch, Islamic Azad University, Pars Abad, Iran. Abstract: Each charged particle loses its energy while passing through a matter. These charged particles have electrons. Electrons lose their energy as a result of the interaction with the matter in four ways:. Bremsstrahlung,. electron-positron pair annihilation, 3. inelastic collision of electrons and positrons with electrons and 4. elastic collisions with atomic nuclei. The amount of energy drop in terms of length unit is called stopping power and it is called collision stopping power in low energies and radiation stopping power in higher energies. In this thesis, the collision and radiation stopping power and the electrons range were simulated using the MATLAB software. The matters applied in this study included Al, Cu, Ag, Au and Pb and the mathematical models and diagrams related to each of them were provided. The obtained diagrams were compared with the experimental results. According to the graphs obtained from the computer model, the minimum point was obtained for the collision stopping power of the experimented matters. Moreover, as the atomic number of applied matters increased, the radiation stopping power increased noticeably. Considering the results obtained for the electron range, the appropriate matter for being used in the detectors can be determined. MATLAB software is an appropriate tool for modeling the radiation and collision stopping power and electron range as a result of passage of radiation detectors and matters or other matters. Key words: Interaction, Electron, Ionization, Brake radiation INTRODUCTION The word radiation was being applied for describing electromagnetic waves from 879 to 900. At the beginning of the twentieth century, electrons, X-rays and natural radioactivity were discovered and all were considered under the term radiation. In contrast to the electromagnetic radiation which was considered as a wave, the newly discovered radiation showed particle behaviors. In the 90s, De Broglie presented his theory based on the matter duality; after a short while, it was proved by electron diffraction experiments and the importance of the separation between particles and waves was removed. Today, radiation means all the electromagnetic spectrum and all the discovered atomic and sub-atomic particles. One of the ways for categorizing different types of radiations is based on the ionization or non-ionization properties of the radiation. Ionization means the radiation capability for ionizing the gas which passes through it. Non-ionizing radiation is the electromagnetic radiation with about 0 nm or more wavelength ( λ ). This section of the electromagnetic spectrum includes radio waves, micro waves and visible light ( λ = 770nm). Ionizing radiation includes the rest of electromagnetic spectrum, X-rays and Gamma rays with the wavelength shorter than that of X-rays ( λ / 0 0 / 005nm). All the atomic and subatomic particles like electron, positron, proton, alpha, neutron and heavy ions are in this group. The following studies have been done on the interaction of radiation and charged particles with matters: a) One of the conducted studies on the interaction of electrons with matter was by ICRU in 984 which was stated by J. Kenneth and Richard E. Faw in the following way: After going along the S pathway, a particle with the initial kinetic energy of E 0 slowing down to the E(S) energy as the result of Colloni interactions with the electrons (atomic) and losing the energy (brake radiation). While losing the acceleration, the stopping power ( de ) usually increases until the particle energy is low ds enough to create load neutralization or reductive quantum effects in the stopping power. Only for the particles with very low energies, the collision with the atomic nuclei of the stopping matters is important. The stopping power resulted from the Colloni interaction ( de is called the collision stopping power or ionization ds)coll stopping power. Another mechanism which is important for the electrons is the loss of radiation energy identified by the radiation stopping power ( de. Moreover, an exact investigation of the electrons ds)rad slowdown requires considering the possibility of producing delta proton and the continuous deviation of the Corresponding Author: Somayeh Almasi, Department of Physics, Pars Abad Moghan Branch, Islamic Azad University, Pars Abad, Iran. Sanay384@gmail.com 83

2 Aust. J. Basic & Appl. Sci., 5(): 83-80, 0 landing electron from its main direction. Here, the electron range is relate to the average pathway rather than the penetration distance of the straight line. b) Another study on the range was done by R.B. Shields using the Tabata and Ito equation which obtained diagrams for different matters. c) One of the studies conducted on the electrons energy drop and their range was by John Wiley and Sons in 988 which used the relation of radiation and collision stopping power obtained by Beth. d) As far as electrons range in matters is concerned, experimental data are used since it is very complex to integrate the radiation and collision energy drop relations. These relations were obtained by MC Graw Hill in 955 using the experimental relation of the energy range of some diagrams. MATERIALS AND METHODS Interaction of Charged Particles with Matters A charged particle which passes through the neutralized atoms enters an interaction with the electrons of atoms more through the Colloni force. Although, in average, the particle loses more than several electron volts of the kinetic energy due to the collision, the highest amount of energy loss occurs along the particle pathway resulted from the atoms impulse and ionization. The loss of kinetic energy in a nuclear collision is much more; however, compared with atomic collisions, such collisions occurrence is almost rare. Thus, nuclear collisions have a noticeable share in the loss of total energy. For the kinetic energy more than MoC in which Mo is the rest mass of the particle, energy loss by the emission of electromagnetic radiation becomes more important. This kind of radiation is called brake radiation or Bremsstrahlung. The mechanism of this radiation is the same as that of the continuous emission of the X-rays and its main process can be classically understood. According to the Maxwell s equations, each accelerated charge radiates electromagnetic radiations. If a charged particle passes near the nucleus, its speed vector changes immediately (at least, in terms of direction; otherwise, in terms of size) in a way that the particle becomes accelerated and therefore makes radiation. Energy Loss Mechanisms of Charged Particles The charged particles which pass through the matter lose energy as a result of the following processes:. Colloni interactions with electrons and nuclei. Electromagnetic radiation emission (brake radiation) 3. Nuclear interactions 4. Cheronkov radiation emission The nuclear interactions can be ignored in the charged particles with high kinetic energy. The Cheronkov radiation is composed of a very small fraction of the lost energy. The Interaction of Electron with Matters Beta particles (electrons or positrons) lead to the production of electron excitation and ionization while moving through a matter. Most of the interactions are small deviations along with the loss of a small amount of energy. However, because of having the mass equal to that of the matter s electron, beta electrons can be scattered in large angles and produce secondary electrons which have a noticeable amount of backstroke energy. These high-energy secondary electrons (called delta rays) pass through the matter and lead to extra excitation and ionization. Deviations with high angles from the atomic nuclei can also occur by losing a negligible amount of energy. As a result, the pathways of beta particles are far from the straight line because of transferring their energy to the surrounding matters. It can be observed for these pathways that the distances of beta particles which pass through a matter change noticeably. The range of beta particles is defined as the pathway length of the particles; i.e. the distance they pass along the complex pathways. This range is the maximum distance of a beta particle which penetrates although this amount of penetration happens in rare cases because of the curves of the pathways. There are four kinds of interactions of electrons with matters:. Brake radiation. Electron-positron pair annihilation 3. Inelastic collisions of electrons and positrons with electrons 4. Elastic collisions with (elastic) atomic nuclei The first three interactions lead to the loss of electron energy and slow it down. In the second interaction, the electron directly gives its inertia energy to the photons and, in the inelastic collisions, energy is transferred to atomic electrons and leads to the ionization of the atoms along the pathway. Collision Stopping Power A charged particle which moves in a matter enters Colloni energy to many atoms simultaneously. Each atom has a large number of electrons with different excitation and ionization potentials. As a result, a moving charged particle interacts with a large number of electrons (millions of them). Each interaction has its own energy loss and occurrence likelihood. It is impossible to calculate energy loss by investigating each and every 84

3 Aust. J. Basic & Appl. Sci., 5(): 83-80, 0 collision. Instead, the average energy loss per unit of the passed distance is calculated. The average energy loss per unit of distance passed by the particle is given by the following relation: The Stopping Power Caused by Ionization and Excitation for Electrons de MeVcm. mc Na. Z mc 4r. Ln Ln dx g A 8 where Classical electron radius r e m c m Electron rest mass energy = T m c m c β = V / c = 3 C m T= kinetic energy= 0.5MeV 0 8 m / s Z= atomic number z= I= excitation potential N = ρn a / A A= mass number or atomic weight Radiation Stopping Power In contrast to heavy charged particles, brake radiation occurs in higher energies in electrons and positrons and the loss of radiation energy in relativistic speeds is valid for the electrons and is obtained from the following relation: de dx rad ZT de 750 dx coll In fact, this relation has been given in terms of collision stopping power. Electron Range in the Matter Electron and positron behave in similar ways in terms of energy loss, slowing down and penetration in the matter; however, electron range is measured because it is applied more than positron in measuring rays. Electron range is obtained by integrating Relations and : R 0 T 0 dx dt dx Because of the complex behavior of electron in the matter, experimental measurements are used for the electron range. One of these experimental results is the semi-experimental formula formulated by Tabata, Ito and Ekabe which gives up to 973 electron range for the energy range from 0.3 kev to 30 MeV, according to the accessible experimental results. This equation is presented in the following way: Kg Ln R a m where a a3 5 a a a 4 85

4 Aust. J. Basic & Appl. Sci., 5(): 83-80, 0 / 335 A a = / 09 a = / 78 0 Z 4 Z 4 ( ) ( ) a3 = 0 / / 0 0 Z a4 = / 468 / 80 0 Z a = 5 / 3 Z 0 / 09 A= mass number or atomic weight, Z= atomic number of the considered matter Results: Range of electrons and radiation and collision stopping power were simulated for 5 matters (Pb, Au, Ag, Cu and Al) using the MATLAB software and their diagrams were obtained in the following way: Fig. : Collision stopping power of electrons in Pb, Au, Ag, Cu and Al. Considering the obtained figures and using the MATLAB software, a table was prepared for each of the diagrams of electron range and radiation and collision stopping power in the considered five matters. The best curve was introduced for the range, radiation and collision stopping power according to these tables. The correlation coefficient of each energy range indicated the optimization of these relations. 86

5 Aust. J. Basic & Appl. Sci., 5(): 83-80, 0 Fig. : Radiation stopping power of electrons in Pb, Au, Ag, Cu and Al. Fig. 3: Electron range in Pb, Au, Ag, Cu and Al (range and energy are in terms of (g/cm^) and (Mev), respectively). 87

6 Aust. J. Basic & Appl. Sci., 5(): 83-80, 0 Table.. Mathematical model for the collision stopping power of the electron in matters. Matter Name Mathematical model of collision Changes in the energy range T (Mev) stopping power Mev.cm g Aluminum (Al) 0 / 0 T de Copper (Cu) Silver (Ag) Gold (Au) Lead (Pb) = / 53( T ) ρ dx T 00 de = / 398( T ) ρ dx 0 / 0 T de / 087( T ) dx T 00 de / 9( T ) dx 0 / 0 T de / 996( T ) dx T 00 de /0( T ) dx 0 / 0 T de / 799( T ) dx T 00 de / 9598( T ) dx 0 / 0 T de / 8007( T) dx T 00 de / 968( T ) dx Correlation coefficient ( ) R R R R R R R R R R R Table : Mathematical model for the radiation stopping power of the electron in matters. Matter Name Changes in the energy range (Mev) Mathematical model of radiation Auminium (Al) 0 / 00 Copper (Cu) 00 Silver (Ag) 00 Gold (Au) 00 Lead (Pb) 00 Mev. cm stopping power g T de / 099( T ) dx 0 / T de / 0585( T ) dx 0 / T de / 086( T ) dx 0 / T de /9( T ) dx 0 / T de /78( T ) dx Correlation coefficient R R R R R R

7 Aust. J. Basic & Appl. Sci., 5(): 83-80, 0 Table 3: Mathematical model for the range of electron in matters. Matter Name Changes in the energy range T(Mev) Changes in the R range in terms of Auminium (Al) Copper (Cu) Silver (Ag) Presented mathematical equation for the range Correlation coefficient R Mev. cm g 0 / 000 T 0 / 7 8 / 48 0 R 0 / R T / T /0 0 / 03 R 5 / R T T 8 5 /8 R 4 / R T / 000 T 0 / 0 6 R 0 / R 0.304T / T 0 0 / 0 R 4 / R 0.85T T 8 4 / 36 R / R 0.483T / 000 T 0 / 7 8 / 48 0 R 0 / R T / T 0 0 / 0 R 3 / R 0.506T T 8 3 / 90 R 8 / R 0.46T / 000 T 0/ 6 / 680 R 0 / R 0.089T / T 0 0 / 007 R 3 / R 0.434T T 8 3/ 447 R 8 / R 0.434T / 000 T 0 / 6 / 640 R 0 / R T / T 0 0 / 0070 R 3 / R 0.879T T 8 3/ 3 R 8 / R T Gold (Au) Lead (Pb) 0 Conclusions:. The comparison of the diagrams of collision stopping power showed that the collision stopping power logarithmically decreases by increasing the energy and increases again after reaching the minimum point.. In the figures of the stopping power for the considered five matters, a minimum point was observed which occurred for all the minimum points at T= Mev and was almost consistent for It can be concluded from the comparison of the radiation stopping power that by the linear increase of energy. 4. The fourth conclusion is related to the range of electrons in matters. The penetration of electrons in aluminum was more than that of other matters. In fact, the electron range was different from the range of heavy charged particles and was not clearly specified compared with the range of these particles. The reasons for this are as follows: ) the pathway of electrons did not change as a result of collision, ) scattering of electrons was much higher than other heavy particles since the energy transfer of collisions was variable. Considering the obtained results for the range, the appropriate matter used in detectors can be determined. Since the pathway of electrons in the air is long, metal sheets, especially aluminum sheets, are used in electron capture experiments. REFERENCES Ashkbousi, J., 005. Calculating energy loss of charged particles as a result of passing through matters. Supervisor: Dr. Mostajab Daavati. Hamidian, M.R., 99. Detection and Detectors of Rays. Mahtab Publications, Tehran. Kenneth, J., A. Richard, A. Faw., 007. Fundamentals of Nuclear Sciences and Engineering. translated by Mohammad Ghannadi Maraghei, Zolal Kowsar. Knoll, G.F., 989. Radiation Detection and Measurement.Wiley, New York, pp: Koch, H.W., J.W. Motz., 959. Bremsstrahlung Cross-section formulas and related data. Rev. Mod. phys., 3: Krane, K., 00. Introductory Nuclear Physics. Translated by Dr. Mohammad Reza Ebrahim Abukazemi and Dr. Manijeh Rahbar, University Publication Center, Fifth Edition. Kui, R., 99. Measuring and Detecting Nuclear Radiations. Mashhad. Kumakhor, M.A., F.F. Komorov., 989. Radition from charged particles in solids,989. Meyerhof, W., 000. Fundamentals of Nuclear Physics. Tanslated by Dr. Mohammad Reza farhadi Rahimi, Publications of Ferdowsi University, Fifth Edition. 89

8 Aust. J. Basic & Appl. Sci., 5(): 83-80, 0 Nelson, G., D. Reilly. Gamma Ray Interactions with Matter. Segre, E. Nucli and Particles. W.A. Benjamin Inc., pp: 74, 964. Ziaee, F., 00. Designing the Target of High-energy Electron Converter to X-rays and Dosimetry Methods. Doctoral dissertation of Nuclear Sciences and Technology, Faculty of Physics and Engineering Sciences, Amirkabir University of Technology. 80

Lecture 14 (11/1/06) Charged-Particle Interactions: Stopping Power, Collisions and Ionization

22.101 Applied Nuclear Physics (Fall 2006) Lecture 14 (11/1/06) Charged-Particle Interactions: Stopping Power, Collisions and Ionization References: R. D. Evans, The Atomic Nucleus (McGraw-Hill, New York,