Calculation of Stopping Power and Range of Nitrogen Ions with the Skin Tissue in the Energies of ( 11000 ) MeV

The use of heavy ions in the treatment of cancer tumors allows for accurate radiation of the tumor with minimal collateral damage that may affect the healthy tissue surrounding the infected tissue. For this purpose, the stopping power and the range to which these particles achieved of Nitrogen (N) in the skin tissue were calculated by programs SRIM (The Stopping and Range of Ions in Matter),(SRIM Dictionary) [1],(CaSP)(Convolution approximation for Swift Particles  )[2]which are famous programs to calculate stopping power of material and Bethe formula , in the energy range (1 1000) MeV .Then the semi empirical formulas to calculate the stopping power and range of Nitrogen ions in the skin tissue were founded from fitting for average the values which calculated by using these programs using (MATLAB2016) program,the maximum value of energy for Nitrogen ions can lose along its path in skin tissue is founded and the range correspond to this value, the maximum range for Nitrogen ions can be reached in the skin tissue is founded too .The importance of the research is to know the data of thes particles and their use in treatment without causing a bad effect on the patient.


Introduction
Of the important quantities that must be known when studying the particles therapy field or interaction of heavy particles with matter is the stopping power and range.The stopping power is the ability of the medium to stop the particles which penetrate it,the mass stopping power of a material is obtained by dividing the stopping power by the density (ρ).Unit for mass stopping power is Mev.cm g 3,4 , the range of the particle is the average distance travelled before the particle loses all its original kinetic energy [5],which computed by numerical integration of the stopping power.These quantities are studied to determine the energy needed for the particle to penetrate a specific dimension in the tissue,the energy range (1-1000)MeV has been chosen because in low energies heavy ions cannot penetrate the materials as the light particles.
The interaction of charged particles with materials enters a number of medical fields and nuclear interactions; generally, the interaction of heavy charged particles such as Nitrogen (N) is different from that of other particles such as protons and alpha particles, which makes it more positive in the treatment of cancer diseases because of the ionic density in the latter orbit, making the damage in the RNA molecule in one cell more effective and this increases the biological efficiency of the dose factor (1.5-3) compared with the use of protons [6].
The aim of this work is to study appropriate database can be chosen by selecting the appropriate energy of Nitrogen ions to irradiate the infected skin tissue and prevent the passage of these particles into adjacent non-infected tissues, which may cause adverse medical effects on the patient, tables (1) & (2) show some properties of both Nitrogen ion and skin tissue respectively [18,19].Thus, the range and stopping power of the skin tissue for Nitrogen ions will be studied using several programs which are CaSP, SRIM and SRIM Dictionary and Bethe formula, also we calculate the range of this particle.Previous research in this area has been carried out on this ion and carbon such as shown in references [7,8].In the present work we compared some famous and available theoretical (Casp 5.2) [13] and semi-empirical (SRIM 2008)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 [14 & 15], procedures of stopping power calculation has been checked using statistical analysis of deficits between computed and experimental data of (skin tissue) for (Nitrogen) ions in energy range of (1-1000) MeV.The range formulas were obtained by directly integrating the reciprocal of stopping power for (Nitrogen) ions and the values of the range for the (skin tissue) are calculated and compared with (SRIM).

Theory Stopping power
The Bethe -Bloch formula is used to calculate the stopping power of heavy charged particles derived using relative quantitative e mechanics given by the relationship [9,10] Where (dE/dx): stopping power Z: charge of the incident particle n: number of electrons per unit volume.m0: rest mass of electron.Ѵ: velocity of incident particle.e: electron charge.K0: 1/4 ЛЄ 0 I: mean excitation or the ionization energy of the medium.This equation shows dependence of (dE/dx) on the velocity of interact particle but (ln ) almost does not give any little change in (v) .Many researchers have reported different tables and relationships for stopping power.For mixture or compound the stopping power can be calculated from the following relation [11]: Where  :Wight fraction of I the element, (dE/dx):stopping power

Range of Nitrogen ions
Because the stopping power depends on the energy of particle, thenit is possible to calculate the path of the particle which corresponds to the lower particle energy from the initial value to some smaller value .Based on the definition of the stopping power, that path is equal to the integral [12] Where dx: path length variable of integration.(dE/dx): stopping power.T0: the initial kinetic energy of the charge particles.T1: some limit of energy below the calculation cannot be performed.

Results and discussion
In the present work the calculations of the mass stopping power and range of Nitrogen ions in the elements of skin tissue (C=20.4%,Cl=0.3%,H=10%,K=0.1%,N=4.2%,Na=0.2%,O=64.5% ,P= 0.1%andS=0.2%)[14]  1-Using MATLAB 2016 we obtained the following semi-empirical formula for mass stopping power for Nitrogen ions by calculation of the weighted average for mass stopping power.1.794 , c = 0.002386 R-square: 1 3-We note that the maximum value of mass stopping powers found in Hydrogen element, because Hydrogen was gas molecules in the traversing path of the heavy ions and hence the more probability of interaction and more energy loosed, this conclusion is identical to what is stated in the reference [15].
4-From table(3)we found that the maximum value of energy the Nitrogen ions can lose along its path in skin tissue are ( 9989.691218MeV.cm 2 /g ) which correspond to the energy ( 6.5 MeV) .Figure (4), illustrates this.
5-We note that the range corresponds to energy which can lose along its path of Nitrogen ions in skin tissue is (0.002518656cm) in energy (6.5 MeV). Figure (5), illustrates this.

Conclusions
The menders can be provided with a database of Nitrogen ions to enable them to deal with these ions to treat tumors in the skin tissue,we conclude that the atoms most responsible for loss of energy in the skin tissue are Hydrogen atoms,the maximum value of energy the Nitrogen ions can lose along its path in skin tissue are ( 9989.691218MeV.cm 2 /g ) which correspond to the energy ( 6.5MeV) ,the Range correspond to energy which can lose along its path of Nitrogen ion in skin tissue is (0.002518656cm) in energy ( 6.5 MeV).Nitrogen ions can penetrate skin tissue a distance (1.115039336 cm) in the energy (1000MeV),which allows the processor to take into account this energy and the corresponding range of the reach of this particle when used in treatment.

2 -
The following semi-empirical equation were obtained from same program for range of Nitrogen ions in skin tissue: equation constants which are as follows: a = 4.617e-06 ,b =

6 -
From figures (4) note that the theoretical values are consistent with the present work values of the mass stopping power values for Nitrogen ions in skin tissue indicating the validity of the present results.

7 -
From figures(5) note that the theoretical values correspond to the present work values of the range for Nitrogen ions in skin tissue, this indicates the validity of the present results.8-Figure(6) shows the of the Bruuge peak the range to which the Nitrogen ions loses most of its energy in skin tissue.

Figure ( 3 )Figure ( 4 )
Figure (3): Mass stopping power for N with skin tissue using SRIM ,SRIM Dictionary, CaSP programs, Bethe formulae and average for these values

): Mass stopping power for nitrogen in elements presented in skin using SRIM program Figure (2): Mass stopping power for nitrogen in elements presented in skin using CaSP program https
://doi.org/10.30526/31.2.1945 Physics | 76