Theoretical Study of Alpha Particles Energy Loss in Human Bones with (6-13)Year Old

Abstract

The Energy loss of light ions, such as alpha particles, was measured in human Bones with different energy. They are very important and useful especially in radiation protection. Using SRIM Computer Programs to calculate the stopping power in bones by considering the tissue mostly composed of 7 elements, the alpha stopping powers and Range were calculated for those elements with the energy interval (0.1–4.5) MeV. In addition the Results of stopping power for alpha in Bones tissues are presented and compared with the latest published data.

Keywords

Alpha particles; Stopping power; Range; Energy loss; SRIM

Introduction

Charged particles are generated in accelerators, nuclear decays, or in the cosmic ray field. All such particles interact with matter through the Lorentz force, primarily the Coulomb force. In addition, the strongly interacting particles, such as protons and alpha particles, interact with nuclei through the short range nuclear force [1].

When fast ion passes through matter, it loss energy principally by scattering electrons in the matter it passes through and more importantly at low energies, by scattering from the nuclei of the atoms. The energy loss by α- particle per unit distance is an important term in radiation physics [2]. Charged particles are often used for radiation therapy because they have a well-defined penetration in tissues, the depth being dependent on the nature of irradiated material and the incident energy of particles. A charge particle (protons, deuterons, alpha particles) has an important effect in radiation therapy as they have the ability to deliver their energies to the target [3].

Material Method

Theory

Over the years, the study of the interaction of alpha particles with matter has evolved into a large research field due to new powerful experimental methods and facilities around the world. The interaction of alpha ions with matter is a unique method to investigate the processes in complex atomic systems, which play a very important role in the development of modern physics.

In calculating the alpha particles ranges and stopping in solid targets, there are numerous techniques and calculation methods [4,5]. Among these techniques, one method was improved by Bier sack for slowing down of ions in matter based on the analysis of the directional angular spread of ion motion as a function of energy [6].

Energy loss mechanisms

In any radiation, energy is transfer from the radiation particle to the electrons of the interacting or absorbing medium. If the energy of radiation is rapidly transfer to the matter with in a short distance of the interacting matter, the number of electric excitations and ionizations of the interacting atoms are very high and hence more damage is done to the interacting matter. At any given time the particle is interacting with many electrons, so the net electric charge is to decrease its velocity continuously until the particle is stopped [7]. A moving α particle penetrates matter; the major interaction is the collision between α particle and the orbiting electron. Very rarely α- particle will collide with the nucleus of an atom due to the extremely small volume occupied by a nucleus in space [8,9].

The energy transfer to the orbiting electron in collision by an α- particle is only a small fraction of the α- particle energy due to the very small mass of an electron compared to that of an α- particle. This can be shown for the maximum energy transfer which occurs when α- particle has a head on collision with an electron [10].

These processes are responsible for the slowing down of alpha particles in matter. Charged particles interact with electrons and nuclei via coulomb interaction. Due to coulomb interaction, α- particles may excite an electron to higher energy state. Ionization and excitation break chemical bond and generate reactive species the cause for further chemical reactions.

The bethe-bloch

Formula Bohrs stopping model was unique for many years. However, Bohr understood the limits of its application. The model didn’t take into account the discrete energy of target electrons. Some years later Bohr pointed out that the binding effects are very important during the slowing-down process. Distant collisions are treated as free-electron scattering by the projectile ion. However, interactions at small distances were considered as electromagnetic excitations of harmonic oscillators and could not be described by means of classical mechanics. Hans Bethe treated the energy loss process by means of the quantum mechanics using the first Born approximation [6]. He used the momentum transfer rather than impact parameter to characterize collisions [11]. Bethe-Bloch expression for the stopping power of an alpha particle derived using relativistic quantum mechanics is given by.

Range

In passing through matter, charged particles ionize and thus loss energy in many steps, until their energy is (almost) zero. The range is the average distance traveled before a particle has lost all of its original kinetic energy. The range R is continuous slowing down approximation is given by.

SRIM

SRIM is a software package concerning the Stopping and Range of Ions in Matter. Since its introduction in 1985, major upgrades are made about every six years. Currently, more than 700 scientific citations are made to SRIM every year. For SRIM- 2010, the following major improvements have been made:

(1) About 2,800 new experimental stopping powers were added to the database, increasing it to over 28,000 stopping values.

(2) Improved corrections were made for the stopping of ions in compounds.

(3) New heavy ion stopping calculations have led to significant improvements on SRIM stopping accuracy.

(4) A self-contained SRIM module has been included to allow SRIM stopping and range values to be controlled and read by other software applications.

(5) Individual interatomic potentials have been included for all ion/atom collisions, and these potentials are now included in the SRIM package [8,9].

Results and Discussion

In this Present work measured the mass stopping and range of alpha particles in the elements of human bones with age (6-13) years old with energy interval (0.1- 4.5) MeV by using SRIM (2013) Computer program code. It is known that the chemical compositions of human tissues are of importance in studying micro-diametric distributions in human irradiated with radiation. Chemical composition of human tissues depends in general on breed, diet, age, sex, health, etc. [9].

Table 1 represent the range of incident alpha particles inside each element of the bones tissue such as P, Mg, Ca, C, N, O, values were ranged from (0.7994, 0.8123, 1.34, 0.4901, 6.16, 1.41) μm to (27.64, 26.36, 33.92, 15.77, 162.49, 36.23) μm respectively, maximum value of range record H and minimum was recorded from C, since the density of H small than C it means the penetration of alpha particles inside H greater C as show in Figure 1, the following results are good agreement with ref [11] were reported by (IAEA), as well as the Figures 2-5 represented the range of incident alpha particles inside C, Ca, P, Mg respectively as a function of energy for that particles, they are shown the range increasing in all element with increasing energy of that particles, its refer to the ref [1], as well as for same energy the range of alpha inside the H atom greater than Ca atom in that medium (bones).

Table 1: The range of α Particle in difference element with difference energy.

Figure 1: The range of Alpha Particles in differences Element as function energy.

Figure 2: The range of Alpha Particles in Carbon with differences of energy.

Figure 3: The range of Alpha Particles in Calcium with differences of energy.

Figure 4: The range of Alpha Particles in Phosphor with differences of energy.

Figure 5: The range of Alpha Particles in Magnesium with differences of energy.

The results of mass electronic and nuclear stopping power were reported in Table 2. The values mass electronic stopping power varied from (0.624, 0.691, 0.626, 0.87, 2.451, and 0.838) Mev/(mg/cm²) to (1.442, 1.420, 1.229, 1.928, 7.679 and 1.909) Mev/(mg/cm²) for individual elements P, Mg, Ca, C, H, N, O respectively, results were agreement with [11]. The maximum value of electronic stopping power at same energy found in H element and minimum value found from C because of H was gaseous molecules in the traversing path of the alpha particle ions and hence the more probability of interaction and more energy loosed refer by [11]. The values mass nuclear stopping power varied from (0.0102, 0.0136, 0.01, 0.0137, 0.0627, and 0.0133) Mev/(mg/cm²) to (0.00048, 0.00052, 0.0005, 0.00057, 0.0025 and 0.0006) Mev/(mg/cm²) for individual element P, Mg, Ca, C, H, N, O respectively, results were agreement with [11]. The maximum value of electronic stopping power at same energy found in H element and minimum value found from C, Figures 6-8 shows a plot of total, nuclear and electronic energy loss in human bones, as a function of projected energy of alpha particles in the energy range of (0.1- 4.5) MeV (Figures 9-12). This graph reveals that as projected energy of the alpha particles increases the nuclear energy loss decreases exponentially at low energy it’s important. This is due to the interaction mechanism by which the ion can lose energy by elastic collision with the nuclei of target atoms of media.

Table 2: The electron S_e (MeV/(mg/cm²)) and Nuclear stopping S_n (MeV/(mg/cm²)) of α Particle in difference element with difference energy.

Figure 6: Represented the Total stopping for Alpha Particles in Human Bones with differences of energy.

Figure 7: Represented the Nuclear stopping for Alpha Particles in Human Bones with differences of energy.

Figure 8: Represented the electronic stopping for Alpha Particles in Human Bones with differences of energy.

Figure 9: The nuclear Stopping power of Alpha Particles in Carbon with differences of energy.

Figure 10: The nuclear Stopping power of Alpha Particles in Calcium with differences of energy.

Figure 11: The Nuclear Stopping power of Alpha Particles in Phosphor with differences of energy.

Figure 12: The Nuclear Stopping power of Alpha Particles in Magnesium with differences of energy.

The electronic stopping power of alpha particles inside C, Ca, P, Mg and all elements were showed in Figures 13-17. On can conclude from these figures that the electronic stopping power of alpha particle increases rapidly as the energy of alpha particle increase nearly at dominates (0.1 to 0.7) MeV. When the energy of the alpha particles increases from (0.7 to 4.5) MeV the behavior of the electronic stopping power is exactly difference. One can conclude that there is almost an exponential decay of the stopping power of alpha particle; these due to passing through matter, charged particles ionize and thus loss energy gradually but continuously along its path until their energy is (almost) zero, after traveling a certain distance this refer [10].

Figure 13: The Electron Stopping power of Alpha Particles in Carbon with differences of energy.

Figure 14: The Electron Stopping power of Alpha Particles in Calcium with differences of energy.

Figure 15: The Electronic Stopping power of Alpha Particles in Phosphor with differences of energy.

Figure 16: The Electronic Stopping power of Alpha Particles in Magnesium with differences of energy.

Figure 1: HPLC chromatogram of the nine reference compounds in 50% aqueous methanol, measured at 370nm. Retention times for rutin, sutherlandin A, sutherlandin B, kaempferol-3-O-rutinoside, sutherlandin C, sutherlandin D, quercitrin, quercetin and kaempferol were 11.9, 12.7, 13.8, 15.3, 16.2, 17.0, 18.0, 26.2 and 28.1 minutes, respectively.

Conclusions

• The alpha particles would go further in the human bone when energy is higher.

• The alpha particles would go further in the human bone when energy is higher.

• At lower energies of alpha, nuclear stopping power most contributed in the energy losing of alpha particles in that medium.

• The nuclear stopping power decreased exponentially with increasing the energy of alpha particles.

• When alpha particles energy less than (0.7) MeV, the electronic stopping power increased with increasing energy of alpha particles.

• When alpha particles energy nearly greater than (0.7) MeV, The electronic stopping power deceased with increasing energy of alpha particles.

• The Hydrogen atoms are most responsible to energy losing in the human bones.

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