STOPPING POWER CALCULATION OF
PROTONS AND ⍺–PARTICLES FOR C2H4
AND C6H6 IN ENERGY RANGE 0.01-1000
MEV
Ebtehaj H. Ali*
Department of Physics, College of Education for Girls, University of Kufa, Najaf,
Iraq.
ebtehajalsultani2020@gmail.com
Rashid O. Kadhim
Department of Physics, College of Education for Girls, University of Kufa, Najaf,
Iraq.
Reception: 29/11/2022 Acceptance: 28/01/2023 Publication: 23/02/2023
Suggested citation:
H. A., Ebtehaj and O. K., Rashid. (2023). Stopping Power Calculation of
Protons and α–Particles for C2H4 and C6H6 in Energy Range 0.01-1000
MeV. 3C Tecnología. Glosas de innovación aplicada a la pyme, 12(1), 191-200.
https://doi.org/10.17993/3ctecno.2023.v12n1e43.191-200
https://doi.org/10.17993/3ctecno.2023.v12n1e43.191-200
3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254-4143
Ed.43 | Iss.12 | N.1 January - March 2023
191
ABSTRACT
In this research, a theoretical study was conducted to calculate the total stopping
power of some relativistic heavy ions (protons and alpha particles) during their
passage through some media (ethylene and benzene) in the energy range (0.01-1000
MeV). The equations were programmed using MATLAB2021, the curve fitting tool was
used, and the calculated results were compared with the experimental data of the P-
Star and A-Star programs for the same missiles in those organic compounds.
KEYWORDS
Mass stopping power, Bethe formula, Relativistic heavy ions, MATLAB2021, P-Star, A-
Star.
PAPER INDEX
ABSTRACT
KEYWORDS
INTRODUCTION
THEORY
RESULTS AND DISCUSSION
CONCLUSIONS
REFERENCES
https://doi.org/10.17993/3ctecno.2023.v12n1e43.191-200
3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254-4143
Ed.43 | Iss.12 | N.1 January - March 2023
192
ABSTRACT
In this research, a theoretical study was conducted to calculate the total stopping
power of some relativistic heavy ions (protons and alpha particles) during their
passage through some media (ethylene and benzene) in the energy range (0.01-1000
MeV). The equations were programmed using MATLAB2021, the curve fitting tool was
used, and the calculated results were compared with the experimental data of the P-
Star and A-Star programs for the same missiles in those organic compounds.
KEYWORDS
Mass stopping power, Bethe formula, Relativistic heavy ions, MATLAB2021, P-Star, A-
Star.
PAPER INDEX
ABSTRACT
KEYWORDS
INTRODUCTION
THEORY
RESULTS AND DISCUSSION
CONCLUSIONS
REFERENCES
https://doi.org/10.17993/3ctecno.2023.v12n1e43.191-200
INTRODUCTION
Nuclear and electronic stopping power are two categories of stopping power that
measure the energy loss rate per unit distance in a material [1]. The mechanism of
energy loss depends on the charge and velocity of the charged particle and the nature
of the material medium [2]. When passing in the material medium, As is well known,
charged particles lose some of their kinetic energy when colliding with the target
matter. The continuous operation on the particle path in the medium causes charged
particles to lose kinetic energy until they reach zero, at which point they lose all kinetic
energy and reach the using Bethe equations. [3] It is denoted by the symbol -dEdx
and is measured in MeV.cm-1. The mass stopping power, -dEdx, is calculated by
dividing the stopping power by the density of the material and is measured in MeV
cm2 g-1 [4]. Electromagnetic force causes an electron to lose energy in collisions with
atomic electrons, resulting in excitation and ionization [5]. In an inelastic collision,
atomic orbital electrons collide. This is so-called because it causes middle-atom
excitations and ionizations (Collisional Stopping Power). In the case of the inelastic
nuclear collisional, "Bremsstrahlung" radiation is produced, with a stopping power
equal to (radiative stopping power) [6]. The overall stopping power of target materials
is calculated when the product of inelastic collisions and excitation is proportional to
the stopping power.Combining the collisional and radiative stopping powers produces
the total stopping power:
(1)
THEORY
The stopping power of a medium is defined as the average unit of energy loss
suffered by charge particles per unit path length in the medium under consideration,
which can be written as (-dE/dx) depending on the projectile charge and the target
matter. [5]. Mass collision-stopping power is widely used to reduce reliance on
medium density (ρ). These studies were both theoretical and experimental, employing
a variety of methods. [6]. For compounds, the Bragg additive rule has been found to
be quite effective. According to the rule, The mass-stopping power of a multi-element
substance is equal to the weighted sum of the mass-stopping power of its constituent
atoms. [7].
(2)
Where ωi: the ratio of the weight of the elements in the compound.
(3)
(
−
dE
d x
)tot
=
(
−
dE
d x
)col
+
(
−
dE
d x
)rad
(−dE
ρd x
)com
=∑
i
ωi
(−dE
ρd x
)i
ω
i=
n
i
A
i
A
comp
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ni : number of atoms. Ai: atomic mass of elements in medium, Acomp: atomic mass of
medium, ρ: the density of the medium, ((-dE)/ρdx)_com: Mass stopping power of
compound, ((-dE)/ρdx)i: Mass-stopping power for the elements in the compound.
Because the radiative stopping power is efficient, increasing the energy at the
incident -particle energies (100-103) MeV reduces the mass stopping power. [8].
(4)
where,
(5)
, the atomic number of elements, the atomic
number of ions (projectile), atomic mass of elements, ratio of the velocity of a
projectile to the speed of light, Mass of electron, speed of light, and ionization
potential of the medium in eV [9].
The stopping power is calculated by multiplying the stopping power multiplied by
the linear attenuation coefficient for a given type of charged particle at a given energy.
(, the probability of an electronic collision per unit distance traveled), as well as the
average energy loss per collision (Qavg). [10].
(6)
The maximum possible energy transfer (max), or the energy transfer by head-on
collision (2γ^2v2), and the minimum possible energy transfer (
min), or the
medium's mean excitation energy (I). [11].
Because it accounts for all possible atomic ionizations, as well as atomic
excitations, an atom's mean The energy of excitation is always greater than the
energy of ionization, whereas the atomic ionization energy is the energy required to
remove the least bound atomic electron (i.e., valence electron in the outer shell)
[12-13].
RESULTS AND DISCUSSION
The mass stopping power was calculated using the Bethe formula for two
materials, ethylene C2H4 and benzene C6H6, with a proton and α-particle energy
range from 10-2 MeV to 103 MeV. Using “MATLAB2021” program.
The table (1) show the stopping power values for protons and α-particle in ethylene
and benzene. Figures (1,2,3,4) showed a strong agreement between the current work
with P-Star and A-Star at all energies in target materials, as shown in table.3.
−dE
d x
=K
Z
2
Z2
1
Aβ
2L
Bethe
L
Bethe =ln
[2m
e
c2β2
1−β2
]
−β2−ln <I>
K= 0.307075MeV .cm2/g
Z2
Z1
A
β
me
c
I
−dE
ρd
x=
μQ
avg
ρ=
μ
ρ
Q
m a x
Qmin
QW(Q)d
Q
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ni : number of atoms. Ai: atomic mass of elements in medium, Acomp: atomic mass of
medium, ρ: the density of the medium, ((-dE)/ρdx)_com: Mass stopping power of
compound, ((-dE)/ρdx)i: Mass-stopping power for the elements in the compound.
Because the radiative stopping power is efficient, increasing the energy at the
incident -particle energies (100-103) MeV reduces the mass stopping power. [8].
(4)
where,
(5)
, the atomic number of elements, the atomic
number of ions (projectile), atomic mass of elements, ratio of the velocity of a
projectile to the speed of light, Mass of electron, speed of light, and ionization
potential of the medium in eV [9].
The stopping power is calculated by multiplying the stopping power multiplied by
the linear attenuation coefficient for a given type of charged particle at a given energy.
(, the probability of an electronic collision per unit distance traveled), as well as the
average energy loss per collision (Qavg). [10].
(6)
The maximum possible energy transfer (max), or the energy transfer by head-on
collision (2γ^2v2), and the minimum possible energy transfer (min), or the
medium's mean excitation energy (I). [11].
Because it accounts for all possible atomic ionizations, as well as atomic
excitations, an atom's mean The energy of excitation is always greater than the
energy of ionization, whereas the atomic ionization energy is the energy required to
remove the least bound atomic electron (i.e., valence electron in the outer shell)
[12-13].
RESULTS AND DISCUSSION
The mass stopping power was calculated using the Bethe formula for two
materials, ethylene C2H4 and benzene C6H6, with a proton and α-particle energy
range from 10-2 MeV to 103 MeV. Using “MATLAB2021” program.
The table (1) show the stopping power values for protons and α-particle in ethylene
and benzene. Figures (1,2,3,4) showed a strong agreement between the current work
with P-Star and A-Star at all energies in target materials, as shown in table.3.
−dE
d x =KZ2Z2
1
Aβ2LBethe
LBethe =ln[2mec2β2
1−β2]−β2−ln <I>
K= 0.307075MeV .cm2/g
Z2
Z1
A
β
me
c
I
−dE
ρdx=μQavg
ρ=μ
ρ
Qm a x
Qmin
QW(Q)dQ
https://doi.org/10.17993/3ctecno.2023.v12n1e43.191-200
Table 1. Mass stopping power for proton and α-particle in ethylene C2H4 and benzene C6H6.
Energy
(MeV)
Proton
Mass Stopping
Power
(MeV cm2/g)
Mass Stopping Power
(MeV cm2/g)
C2H4C6H6C2H4C6H6
0.01 0.000021 1384599.00 -7852.4 -8611.1 0.000005 694820.70 -304822.6 -306563.1
0.02 0.000043 1958103.04 -1076.8 -1619.4 0.000011 982622.87 -107151.2 -110612.7
0.03 0.000064 2398157.50 393.282 -32.006 0.000016 1203459.90 -53783.89 -57102.12
0.04 0.000085 2769131.64 886.274 533.449 0.000021 1389633.00 -30945.63 -33972.06
0.05 0.000106 3095958.56 1075.954 772.682 0.000027 1553653.81 -18928.33 -21683.17
0.06 0.000128 3391425.60 1146.474 879.440 0.000032 1701939.05 -11805.29 -14328.20
0.07 0.000149 3663129.05 1163.762 924.506 0.000038 1838300.58 -7242.972 -9570.128
0.08 0.000170 3916018.40 1155.540 938.330 0.000043 1965222.03 -4157.814 -6318.883
0.09 0.000192 4153531.58 1134.760 935.521 0.000048 2084428.54 -1986.755 -4005.564
0.1 0.000213 4378171.74 1107.924 923.647 0.000054 2197176.18 -412.133 -2307.846
0.2 0.000426 6191175.36 839.016 730.547 0.000107 3107213.86 4320.087 3113.057
0.3 0.000639 7582004.78 670.562 591.876 0.000161 3805467.69 4645.263 3739.487
0.4 0.000852 8754245.98 562.137 499.727 0.000215 4394087.21 4423.349 3690.215
0.5 0.001064 9786763.18 486.476 434.440 0.000268 4912640.04 4121.660 3501.760
0.6 0.001277 10720006.14 430.447 385.646 0.000322 5381419.30 3831.700 3292.375
0.7 0.001489 11578005.86 387.120 347.676 0.000375 5812480.28 3572.041 3093.279
0.8 0.001702 12376421.14 352.508 317.204 0.000429 6213677.83 3343.647 2912.233
0.9 0.001914 13126129.51 324.151 292.148 0.000483 6590468.06 3143.163 2749.883
1 0.002127 13835051.47 300.446 271.143 0.000536 6946823.60 2966.558 2604.714
2 0.004247 19550123.42 178.982 162.674 0.001072 9822317.05 1936.584 1729.670
3 0.006360 23924853.58 130.633 119.107 0.001607 12027414.67 1468.118 1320.013
4 0.008467 27604077.67 104.049 95.052 0.002142 13885271.85 1195.475 1078.973
5 0.010566 30837790.82 87.044 79.625 0.002677 15521087.77 1015.060 918.483
6 0.012659 33754316.50 75.153 68.817 0.003211 16999085.82 885.915 803.130
7 0.014746 36429950.03 66.331 60.788 0.003744 18357425.61 788.426 715.791
8 0.016826 38914444.53 59.505 54.569 0.004278 19620975.41 711.953 647.124
9 0.018899 41242388.30 54.055 49.598 0.004810 20807012.35 650.195 591.568
10 0.020966 43438986.55 49.593 45.526 0.005343 21928118.41 599.173 545.599
20 0.041280 60952149.63 28.066 25.835 0.010643 30949015.06 346.153 316.661
30 0.060967 74074752.06 20.126 18.551 0.015900 37829067.08 249.383 228.630
40 0.080055 84881964.82 15.926 14.693 0.021116 43594415.15 197.198 181.032
50 0.098566 94185858.35 13.308 12.285 0.026291 48643452.36 164.229 150.910
60 0.116525 102407122.21 11.512 10.632 0.031425 53180963.13 141.379 130.009
70 0.133952 109798179.81 10.200 9.424 0.036518 57328875.04 124.546 114.596
80 0.150868 116525142.64 9.197 8.500 0.041571 61166812.12 111.594 102.729
(m/sec)
v
β2
-particle
α
(m/sec)
v
β2
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Table 2. Rates of elements in ethylene C2H4, and benzene C6H6.
Table 3. Correlation coefficient between positive calculations Bethe relative equation and
values P-star for the proton and values A-star for -particle.
90 0.167293 122704532.11 8.406 7.771 0.046584 64750208.80 101.300 93.291
100 0.183247 128422011.09 7.764 7.179 0.051559 68119520.35 92.909 85.593
200 0.320379 169806066.13 4.772 4.418 0.099230 94502418.39 52.924 48.856
300 0.425665 195729016.46 3.734 3.460 0.143396 113602884.92 38.452 35.532
400 0.508253 213875689.79 3.214 2.979 0.184391 128822328.17 30.889 28.562
500 0.574229 227333673.23 2.905 2.694 0.222512 141513629.59 26.219 24.255
600 0.627766 237694985.92 2.705 2.509 0.258022 152387617.68 23.043 21.325
700 0.671805 245891097.08 2.567 2.382 0.291154 161875929.18 20.742 19.201
800 0.708467 252511435.02 2.467 2.290 0.322114 170265367.43 18.998 17.591
900 0.739312 257949799.09 2.394 2.222 0.351090 177758605.24 17.631 16.329
1000 0.765509 262480130.00 2.338 2.170 0.378247 184505413.74 16.532 15.314
Target C H
C2H40.8563 0.1437
C6H60.9226 0.0774
α
Target Proton
C2H40.9745 0.9711
C6H60.9877 0.9823
-particle
α
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Table 2. Rates of elements in ethylene C2H4, and benzene C6H6.
Table 3. Correlation coefficient between positive calculations Bethe relative equation and
values P-star for the proton and values A-star for -particle.
90
0.167293
122704532.11
8.406
7.771
0.046584
64750208.80
101.300
93.291
100
0.183247
128422011.09
7.764
7.179
0.051559
68119520.35
92.909
85.593
200
0.320379
169806066.13
4.772
4.418
0.099230
94502418.39
52.924
48.856
300
0.425665
195729016.46
3.734
3.460
0.143396
113602884.92
38.452
35.532
400
0.508253
213875689.79
3.214
2.979
0.184391
128822328.17
30.889
28.562
500
0.574229
227333673.23
2.905
2.694
0.222512
141513629.59
26.219
24.255
600
0.627766
237694985.92
2.705
2.509
0.258022
152387617.68
23.043
21.325
700
0.671805
245891097.08
2.567
2.382
0.291154
161875929.18
20.742
19.201
800
0.708467
252511435.02
2.467
2.290
0.322114
170265367.43
18.998
17.591
900
0.739312
257949799.09
2.394
2.222
0.351090
177758605.24
17.631
16.329
1000
0.765509
262480130.00
2.338
2.170
0.378247
184505413.74
16.532
15.314
Target
C
H
C2H4
0.8563
0.1437
C6H6
0.9226
0.0774
α
Target
Proton
C2H4
0.9745
0.9711
C6H6
0.9877
0.9823
-particle
α
https://doi.org/10.17993/3ctecno.2023.v12n1e43.191-200
Figure 1. Show the P-Star mass stopping power in C2H4 as a function of proton energies
Figure 2. Show the P-Star mass stopping power in C6H6 as a function of proton energies.
10-2 10-1 100101102103
Energy (MeV)
100
101
102
103
Stopping Power (MeV.cm 2/g)
proton in C2H4
Pstar
Bethe
Fitting
10-2 10-1 100101102103
Energy (MeV)
100
101
102
103
Stopping Power (MeV.cm 2/g)
proton in C6H6
Pstar
Bethe
Fitting
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Figure 3. Show the A-Star mass stopping power in C2H4 as a function of -particle energies.
Figure 4. Show the work with A-Star mass stopping power in C6H6 as a function of -particle
energies.
10-2 10-1 100101102103
Energy (MeV)
101
102
103
104
Stopping Power (MeV.cm 2/g)
He+2 in C2H4
Astar
Bethe
Fitting
10-2 10-1 100101102103
Energy (MeV)
101
102
103
104
Stopping Power (MeV.cm 2/g)
He+2 in C6H6
Astar
Bethe
Fitting
α
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Figure 3. Show the A-Star mass stopping power in C2H4 as a function of -particle energies.
Figure 4. Show the work with A-Star mass stopping power in C6H6 as a function of -particle
energies.
10-2 10-1 100101102103
Energy (MeV)
101
102
103
104
Stopping Power (MeV.cm 2/g)
He+2 in C2H4
Astar
Bethe
Fitting
10-2 10-1 100101102103
Energy (MeV)
101
102
103
104
Stopping Power (MeV.cm 2/g)
He+2 in C6H6
Astar
Bethe
Fitting
α
https://doi.org/10.17993/3ctecno.2023.v12n1e43.191-200
CONCLUSIONS
1.
The Bethe formula is adequate for regulating the mass-stopping power of the
organic compounds investigated.
2.
Calculations show that the mass-stopping power increases with increasing energy
at incident proton energies (10-1-101) MeV due to the collision-stopping power.
3.
Because the radiative stopping power is efficient, the mass stopping power
decreases as the energy at the energies of incident particles (10-1-103
) MeV
increases.
4.
Calculations show the mass-stopping power increases with increasing energy at
incident-particle energies (10-2-100
) MeV because the collision-stopping power is
the result.
5.
Because the radiative stopping power is efficient, increasing the energy at the
incident-particle energies (100-103) MeV reduces the mass stopping power.
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