162 

© 2024 The Author(s). Published by College of Education for Pure Science (Ibn Al-Haitham), 

University of Baghdad. This is an open-access article distributed under the terms of the Creative Commons 

Attribution 4.0 International License 

 

 

Theoretical Study of Energy Loss of Proton in Human Tissues 

 
*Musaab I. Mohammed  

General Directorate of Education of Salah Uddin, Salah Uddin, Iraq. 

*Corresponding Author 
 

Received: 28 June 2023                        Accepted: 1 August 2023                 Published: 20 October 2024 

  doi.org/10.30526/37.4.3636 

 
 Abstract 

        In this paper, a theoretical study was carried out to calculate the proton energy loss in 

human tissues (Adipose tissue, Blood, Bone (Compact), Bone (Cortical), Brain, Eye lens, Lung, 

Skin, and Testicles) within the energy range of 1 MeV to 1000 MeV. We calculated the total 

stopping power for each tissue element separately using the Bethe-Bloch equation, and then 

used Bragg's rule for compounds to determine the tissue's total stopping power. The total 

stopping power is directly proportional to the atomic number divided by the target material's 

atomic mass (Z/A) and target material density (ρ), and inversely proportional to the target 

material's mean excitation energy (I) and proton energy (E). The results indicate that the 

stopping power was highest in the adipose tissue, and the lowest value was in the bone (cortical) 

at the same proton energy. We performed all calculations using the MATLAB program. We 

found a good match between the obtained results and the value of the P-Star code. 

Keywords: Total stopping power, proton energy loss, human tissue, Bethe-Bloch equation, 

Bragg’s rule. 

 

1. Introduction 

The study of radiation energy loss in the material is one of the most important subjects in 

medical physics because of its multiple applications in radiation therapy. Furthermore, 

understanding the behavior of radiation in a material and its interactions plays a crucial role in 

determining the radiation dose during medical testing or radiation therapy, assessing the impact 

of this dose on cells adjacent to the target cells, and understanding the potential damage to 

adjacent tissues. Furthermore, estimating the appropriate radiation dose or determining the 

amount of a safe radiation dose during testing, therapy, or exposure to natural or artificial 

radiation is very important to protect a person from the possible risks of such radiation exposure 

[1-4]. 

Radiation therapy commonly treats cancer, with protons being the preferred choice due to 

their ability to regulate the radiation dose, concentrating the dose density in the affected area 

while exposing the surrounding area to minimal radiation [1,2]. Protons have properties that 

make them more efficient in radiation therapy than classical radiation since when protons enter 

the material, they lose a small amount of energy on the surface of the material, while the 

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IHJPAS. 2024, 37 (4)  

163 
 

maximum amount of energy loss occurs at the end of the path in the region called the Bragg 

Peak [3,4].This study aims to calculate the total stopping power of protons in some tissues of 

the body using the Bethe-Bloch equation for elements and Bragg's rule for compounds, and 

compare the results with P-Star results. 

Many researchers have studied proton energy loss within human tissue and the stopping power 

of protons. Ahmed et al. in 2020 conducted a study on the stopping power and range of protons 

in biological human soft and hard tissues, including blood, brain, skeleton-cortical bone, and 

skin, at energies ranging from 1 MeV to 350 MeV. They utilized the Bethe-Bloch formula and 

compared their findings with the SRIM program [5]. Ghossainin in 2021 conducted a study on 

the interaction of protons with water and human body parts, calculating the energy loss, 

stopping power, and proton range for water, skin, bone, and adipose tissue within the energy 

range of 10 keV to 1000 MeV using the Bethe-Bloch formula, P-Star, and MATLAB [6].   

[7] conducted a study on the mass stopping power, range, and important radiation quantities of 

protons in various biological human body parts, including water, muscle, skeletal, and cortical 

bone, within the energy range of 0.04 to 200 MeV, using the Bethe-Bloch formula and 

MATLAB program. Upon comparing the results with the data from P-STAR, they were found 

to be well-matched. 

 

2. Methods and Material 

2.1 Interaction of Nuclear Radiation with Material 

The study of the interaction of nuclear radiation with materials is one of the fundamental 

subjects in radiation dose measurement, nuclear detector building, and other medical and 

industrial applications. Depending on the type of reaction and the amount of energy lost in the 

material with which the radiation interacts, two types of nuclear radiation exist: ionizing 

radiation and non-ionizing radiation [8,9]. 

There is another classification of nuclear radiation that depends on the type of radiation: first, 

charged particle radiation, which includes heavy charged particles (such as protons, deuterons, 

and alpha particles) and light charged particles (such as electrons), and secondly, uncharged 

particle radiation, which includes neutrons and electromagnetic rays (X-rays and Gamma Rays) 

[10,11]. 

2.2 Interaction of Heavy-Charged Particles 

When heavy charged particles traverse a medium, they primarily interact with the 

medium's electrons due to the influence of Coulomb forces on both charged particles and 

electrons. Given the small size of the nucleus compared to the atom, the likelihood of heavily 

charged particles colliding with electrons is significantly higher than that of colliding with the 

nucleus. Therefore, the dominant mechanism for the loss of energy of charged particles is 

coulomb scattering by the electrons of atoms, which leads to excitation or ionization of the atom 

[12]. Heavy-charged particles can produce a large number of vertical and non-vertical collisions 

before they lose their entire energy, and since the range of Coulomb forces is infinite, these 

particles interact with a large number of electrons at the same time, so they will gradually lose 

their energy along their path until they stop moving and their path is almost in the form of a 

straight line [13]. 

2.3 Energy Loss of Proton in Material 

There are many mechanisms by which a proton interacts with an atom or nucleus in the 

target material. Protons may have Coulombic interactions with atomic electrons, Coulombic 



IHJPAS. 2024, 37 (4)  

164 
 

interactions with a nucleus, nuclear interactions, or the release of bremsstrahlung. A proton 

undergoes a set of these interactions through its path in material [14,15]. Table 1 shows possible 

proton interactions within the material. 

Protons lose their kinetic energy due to inelastic Coulomb interactions, which include numerous 

inelastic collisions with atomic electrons, and elastic Coulomb interactions, which include 

collisions with the nucleus. Additionally, inelastic collisions between a proton and a nucleus 

may occur, although these collisions are unlikely. Moreover, protons can engage in an inelastic 

nuclear reaction with the nucleus, where the nucleus absorbs the proton and potentially releases 

the neutron. Nuclear interaction removes these protons, leading to a rapid decrease in their 

number at the end of the path. As for the release of deceleration photons, it is theoretically 

possible to release deceleration photons, but the probability of their occurrence is almost nil at 

high energies [16]. 

Most protons move in an almost straight line because their rest mass is equal to 938 MeV, which 

is about 1832 times greater than the electron's rest mass of 0.511 MeV. Repulsion forces deflect 

a proton near the nucleus, causing it to lose a small amount of energy in this type of scattering 

and causing a slight change in its path [17-19]. 

 

Table 1. Proton interactions within material [16]. 

Type of Interaction Principal Ejectives 
Interaction 

Target 
Influence on Projectile 

Inelastic Coulomb 

scattering 

Primary proton, ionization 

electrons 

Atomic 

electrons 

Quasi-continuous 

energy loss 

Elastic Coulomb 

scattering 

Primary proton, recoil 

nucleus 

Atomic 

nucleus 
Change in trajectory 

Non-elastic 

nuclear reactions 

Secondary protons and 
heavier ions, 

neutrons, and gamma rays 

Atomic 
nucleus 

Removal of a primary 
proton from beam 

Bremsstrahlung 
Primary proton, 

Bremsstrahlung photon 

Atomic 

nucleus 

Energy loss, change in 

trajectory 

 

3. The Theoretical Calculations 

3.1 Stopping Power of Heavy Charged Particles 

The stopping power of heavy charged particles represents the amount of energy that these 

particles lose per path unit in the material, and it does not depend on the mass of the charged 

particle but depends on the square of the atomic number of the charged particle, the speed of 

the charged particle in the material, and the density of material through which the charged 

particle passes [20,21]. 

The calculation of the energy loss of heavy-charged particles is carried out in practice by 

calculating the number of ion pairs generated during the path of the charged particle. If the 

amount of energy that a charged particle loses when generating one ion pair is equal to w, then 

the number of ion pairs per length unit of the charged particle's path is given by - 
𝑑𝐸

𝑑𝑥
 = 𝑤𝑖 Where 

i is the number of ionic pairs [22]. 

The energy loss in the material has been calculated theoretically by many researchers, but the 

classical derivation was by Bethe, who developed a mathematical formula for calculating the 

energy loss in the material. Bloch has improved this formula, which represents the stopping 

power of a charged particle in a material. The full formula of this equation can be expressed as 

follows [6,20]: 



IHJPAS. 2024, 37 (4)  

165 
 

− 
𝑑𝐸

 𝑑𝑥
 =  (

𝑒2

4𝜋𝜖𝑜
)

2

(
4𝜋𝑁𝐴𝑧2𝑍𝜌

𝑚𝑒𝑐2𝛽2𝐴
) [𝑙𝑛 (

2𝑚𝑒𝑐2𝛽2

𝐼
) − 𝑙𝑛(1 − 𝛽2) − 𝛽2]                                           (1) 

Since the classical electron radius (𝑟𝑒) is given by the following formula: 

𝑟𝑒 = 
𝑒2

4𝜋𝜖𝑜𝑚𝑒𝑐2 =2.818 × 10−13 cm                                                                                            (2) 

When reformulating Equation (1) using the classical electron radius, we get the following 

formula: 

− 
𝑑𝐸

𝜌 𝑑𝑥
 =  (4𝜋𝑁𝐴𝑟𝑒

2 𝑚𝑒𝑐2) (
𝑧2

𝛽2) (
𝑍

𝐴
) [𝑙𝑛 (

2𝑚𝑒𝑐2𝛽2

𝐼
) − 𝑙𝑛(1 − 𝛽2) − 𝛽2]                              (3) 

A negative signal indicates that the particle's energy decreases as its range in the material 

increases. 

Where: 
𝑑𝐸

 𝑑𝑥
 stopping power, ρ density of material, 

𝑑𝐸

𝜌 𝑑𝑥
 mass stopping power, 𝑁𝐴 Avogadro 

number (6.022×1023 𝑚𝑜𝑙−1), 𝑚𝑒 electron mass, c speed of light in vacuum, 𝑚𝑒𝑐2 rest energy 

for the electrons (0.511 MeV), z atomic number of the incident particle, Z atomic number of 

material, A atomic mass of material, I mean excitation energy, 𝛽 is the rate between the speed 

of the particle and the speed of light in a vacuum. Since )4𝜋𝑁𝐴𝑟𝑒
2 𝑚𝑒𝑐2( = )0.307075 𝑚𝑜𝑙−1 

𝑐𝑚2) then: 

− 
𝑑𝐸

𝜌 𝑑𝑥
 =   0.307075 (

𝑧2

𝛽2) (
𝑍

𝐴
) [ln (

1.022 ×106 𝛽2

𝐼 
) − 𝑙𝑛(1 − 𝛽2) − 𝛽2]                                 (4) 

When calculating the total stopping power of heavy charged particles, the density correction 

resulting from the blocking of remote electrons by near electrons should be taken into account, 

which will reduce the energy loss of the charged particle at high energies, and the shell 

correction, which is important only at low energies, where the particle velocity is approximately 

equal to the orbital electron velocity [23,24]. 

It is important to note that the energy loss of the incident particle is inversely proportional to 

the square of the particle's velocity and directly proportional to the square of its charge and that 

the energy loss does not depend on the mass of the charged particle, but depends on the 

properties of the target material, which are density, atomic number, atomic mass, and mean 

excitation energy [25,26]. 

Table 2. Atomic number, atomic mass and mean excitation energy of the elements involved in the composition 

of the human tissue [27]. 

Element Z A (𝒎𝒐𝒍−𝟏) Z / A I ( e.V) 

Hydrogen 1 1.0079 0.99216 19.2 

Carbon 6 12.011 0.49955 78 

Nitrogen 7 14.007 0.49976 82 

Oxygen 8 15.999 0.50002 95 

Sodium 11 22.99 0.47848 149 

Magnesium 12 24.305 0.49373 156 

Silicon 14 28.086 0.49848 173 

Phosphorus 15 30.974 0.48428 173 

Sulfur 16 32.065 0.49899 180 

Chlorine 17 35.453 0.47951 174 

Potassium 19 39.098 0.48595 190 

Calcium 20 40.078 0.49903 191 

Iron 26 55.845 0.46557 286 

Zinc 30 65.39 0.45879 330 



IHJPAS. 2024, 37 (4)  

166 
 

 

3.2 The Total Stopping Power of Protons in Human Tissue 

When calculating the total stopping power of protons in the human tissue, human tissue is 

treated as a compound, composed of thin layers of pure elements included in the composition 

of that compound, and the energy of chemical bonds between the constituent elements is 

neglected, so the stopping power of the compound is equal to the sum of the total stopping 

power in each element, taking into account the percentage of participation of each element in 

that compound, and according to Bragg’s rule for compounds, that is, the total stopping power 

in the compound material is written by the following formula [28-30]: 

(
𝑆

𝜌
)

𝑐𝑜𝑚𝑝
= ∑ 𝑤𝑖 (

𝑆

𝜌
)

𝑖
𝑖                                                                                                                (5) 

(
𝑆

𝜌
)

𝑐𝑜𝑚𝑝
 is the stopping power of the compound and 𝑤𝑖 is the percentage weight of each element 

in the compound, which is calculated by the percentage weight ratios rule of the elements 

included in the chemical compounds, which is equal to the molar mass of the element in the 

number of atoms of the element on the molar mass of the compound and (
𝑆

𝜌
)

𝑖
 is the stopping 

power of each of the constituent elements of this compound. 

 

Table 3. The weight percentages of the elements contained in the structure of the human tissues [31]. 

E
le

m
e
n

t 

A
d

ip
o

se
 

ti
ss

u
e
 

B
lo

o
d

 

B
o

n
e
, 

C
o

m
p

a
c
t 

B
o

n
e
, 

C
o

r
ti

c
a

l 

B
r
a

in
 

E
y

e
 l

e
n

s 

L
u

n
g
 

S
k

in
 

T
e
st

ic
le

s 

Hydrogen 11.95 10.19 6.398 4.723 11.07 9.927 10.13 10.06 10.42 

Carbon 63.72 10.00 27.8 14.43 12.54 19.37 10.23 22.83 9.227 

Nitrogen 0.797 2.964 2.7 4.199 1.328 5.327 2.865 4.642 1.994 

Oxygen 23.23 75.94 41.00 44.61 73.77 65.38 75.71 61.9 77.39 

Sodium 0.05 0.185 0 0 0.184 0 0.184 0.007 0.226 

Magnesium 0.002 0.004 0.2 0.22 0.015 0 0.073 0.006 0.011 

Silicon 0 0.003 0 0 0 0 0 0 0 

Phosphorus 0.016 0.035 7 10.50 0.354 0 0.08 0.033 0.125 

Sulfur 0.073 0.185 0.2 0.315 0.177 0 0.225 0.159 0.146 

Chlorine 0.119 0.278 0 0 0.236 0 0.266 0.267 0.244 

Potassium 0.032 0.163 0 0 0.31 0 0.194 0.085 0.208 

Calcium 0.002 0.006 14.7 20.99 0.009 0 0.009 0.015 0.01 

Iron 0.002 0.046 0 0 0.005 0 0.037 0.001 0.002 

Zinc 0.002 0.001 0 0.01 0.001 0 0.001 0.001 0.002 

 

4. Results and Discussion  

The Bethe-Bloch equation was used to calculate the total stopping power of protons in 

human tissue (Adipose tissue, Blood, Bone (Compact), Bone (Cortical), Brain, Eye lens, Lung, 

Skin and Testicles) in the energy range from 1 MeV to 1000 MeV. The total stopping power of 

the constituent elements of these tissues was calculated (Hydrogen, Carbon, Nitrogen, Oxygen, 

Sodium, Magnesium, Silicon, Phosphorus, Sulfur, Chlorine, Potassium, Calcium, Iron, Zinc), 

and then Bragg’s rule for compounds was applied to calculate the total stopping power of the 

tissue, where the total stopping power of these elements was collected after multiplying it by 

the percentage of their participation in each tissue to find the total stopping power of each tissue 

separately. The total stopping power of the elements (Hydrogen, Carbon, Nitrogen, Oxygen, 



IHJPAS. 2024, 37 (4)  

167 
 

Silicon, and Iron) was compared with the values of the universal code P-Star and it was found 

that the largest error rate was about 6% for Carbon, 4.5% for Nitrogen, 4.4% for Oxygen and 

3.8% for Silicon and Iron, while the error rate of Hydrogen was less than 0.1%, as shown in 

Tables 4 and 5. As for the rest of the elements, they were not compared due to the unavailability 

of their data in the P-Star. 

The total stopping power of (Adipose Tissue, Bone (Compact), and Bone (Cortical)) was also 

compared with the values of the universal code P-Star, and the largest error rate was about 4.8% 

for Adipose Tissue, 6% for Bone (Compact) and 6.4% for Bone (Cortical), as shown in Table 

6. As for the rest of the tissues, they were not compared due to the unavailability of their data 

in the P-Star. Protons with energy that is less than 20 MeV lose a large amount of energy when 

they pass through the tissues compared to protons with greater energy (more than 20 MeV), 

because protons with large energy are fast and therefore will spend a short period inside the 

material and thus less likely to interact with the electrons and the nucleus, and thus the amount 

of energy lost decreases. It is noted that protons with large energy lose almost the same amount 

of energy, regardless of the target tissue, as shown in Table 7. From the obtained results, we 

notice that the protons behave the same in all the tissues studied and that the behavior of the 

protons is the same if the target material is an element or a compound, as shown in Figure 1– 

Figure 4. This process of proton energy loss in the material depends on the proton's properties 

(its energy and atomic number) and the target material's properties (its atomic number, mass, 

and mean excitation energy). This means that the proton's behavior in the material changes as 

its properties and the target material's properties change. However, the proton's behavior in the 

material stays the same whether it is an element or a compound as long as these properties stay 

the same. 

Although the results do not exactly match the values of the Universal P-Star Code, the largest 

error rate was about 6%, which is considered an acceptable percentage; therefore, the Bethe-

Bloch equation without corrections is considered an effective equation for calculating the total 

stopping power of the proton. We must add density correction and shell correction to the 

mentioned equation to obtain results that are completely identical to the P-Star values. 

 

Table 4. Total stopping power (MeV.cm2.g-1) for Hydrogen, Carbon, and Nitrogen compared with the value of 

the universal code P-Star [27]. 

Proton 

Energy 

Hydrogen Carbon Nitrogen 

P-Star This 

Work 

Error 

% 

P-Star This 

Work 

Error 

% 

P-Star This 

Work 

Error 

% 

1 677.1 677.12 0 226.3 239.88 6 226.1 236.38 4.5 

2 388.5 388.68 0 139.5 145.1 4 138.9 143.35 3.2 

4 219.7 219.77 0 83.3 85.27 2.4 82.91 84.4 1.8 

6 156.7 156.66 0 60.84 61.9 1.7 60.6 61.32 1.2 

8 123 123.02 0 48.47 49.17 1.4 48.31 48.73 0.9 

10 101.9 101.92 0 40.57 41.07 1.2 40.44 40.72 0.7 

20 56.79 56.77 0 23.18 23.38 0.8 23.13 23.2 0.3 

40 31.82 31.8 0.1 13.24 13.33 0.7 13.22 13.24 0.1 

60 22.85 22.84 0 9.6 9.66 0.6 9.59 9.59 0.1 

80 18.18 18.17 0 7.68 7.73 0.6 7.67 7.68 0.1 

100 15.3 15.3 0 6.49 6.53 0.6 6.49 6.49 0 

200 9.33 9.32 0 4 4.02 0.7 4 4 0 

400 6.24 6.24 0 2.69 2.72 1.1 2.7 2.7 0 

600 5.23 5.23 0 2.26 2.29 1.5 2.28 2.28 0 

800 4.76 4.76 0 2.05 2.09 2 2.08 2.08 0 

1000 4.5 4.5 0 1.94 1.98 2.4 1.97 1.97 0 

 



IHJPAS. 2024, 37 (4)  

168 
 

Table 5. Total stopping power (MeV.cm2.g-1) for Oxygen, Silicon and Iron compared with the value of the 

universal code P-Star [27]. 

Proton 

Energy 

Oxygen Silicon Iron 

P-Star This 

Work 

Error 

% 

P-Star This 

Work 

Error 

% 

P-Star This 

Work 

Error 

% 

1 216.3 225.89 4.4 175.4 182.08 3.8 131.3 136.29 3.8 

2 133.5 138.11 3.5 111.8 116.1 3.8 86.58 91.52 5.7 

4 80.11 81.78 2.1 68.6 70.7 3.1 54.82 57.55 5 

6 58.75 59.57 1.4 50.91 52.14 2.4 41.33 43.03 4.1 

8 46.93 47.42 1 41.01 41.82 2 33.62 34.79 3.5 

10 39.34 39.66 0.8 34.59 35.17 1.7 28.56 29.42 3 

20 22.58 22.67 0.4 20.2 20.37 0.9 16.97 17.29 1.9 

40 12.94 12.96 0.2 11.73 11.78 0.4 9.99 10.1 1.1 

60 9.4 9.4 0.1 8.56 8.59 0.3 7.35 7.41 0.8 

80 7.53 7.53 0.1 6.89 6.9 0.2 5.93 5.97 0.6 

100 6.37 6.37 0 5.84 5.85 0.2 5.04 5.07 0.6 

200 3.93 3.93 0 3.63 3.64 0.2 3.15 3.17 0.6 

400 2.66 2.66 0 2.46 2.47 0.4 2.15 2.17 0.9 

600 2.24 2.24 0 2.08 2.09 0.6 1.81 1.84 1.4 

800 2.05 2.05 0 1.9 1.91 0.8 1.66 1.69 1.7 

1000 1.95 1.95 0 1.8 1.82 1 1.57 1.61 2 

 

Table 6. Total stopping power (MeV.cm2.g-1) for Adipose tissue, Bone (Compact) and Bone (Cortical) compared 

with the value of the universal code P-Star [27]. 

Proton 

Energy 

Adipose tissue Bone, Compact Bone, Cortical 

P-Star This 

Work 

Error 

% 

P-Star This 

Work 

Error 

% 

P-Star This 

Work 

Error 

% 

1 275.5 288.66 4.8 233.9 247.88 6 219.6 233.63 6.4 

2 166.8 172.47 3.4 143.6 150.63 4.9 135.5 143.05 5.6 

4 98.35 100.48 2.2 85.76 88.81 3.6 81.42 84.79 4.1 

6 71.46 72.64 1.7 62.76 64.57 2.9 59.76 61.79 3.4 

8 56.77 57.55 1.4 50.08 51.33 2.5 47.77 49.2 3 

10 47.41 47.99 1.2 41.96 42.9 2.2 40.08 41.16 2.7 

20 26.96 27.19 0.8 24.06 24.46 1.7 23.07 23.53 2 

40 15.34 15.44 0.7 13.78 13.96 1.3 13.26 13.46 1.5 

60 11.1 11.17 0.6 10.01 10.12 1.1 9.64 9.77 1.4 

80 8.87 8.93 0.6 8.02 8.1 1.1 7.72 7.83 1.3 

100 7.5 7.54 0.6 6.78 6.85 1.1 6.54 6.62 1.3 

200 4.61 4.63 0.5 4.19 4.23 1 4.04 4.09 1.1 

400 3.11 3.12 0.5 2.83 2.86 0.9 2.74 2.77 1 

600 2.62 2.63 0.5 2.39 2.41 0.9 2.31 2.33 1 

800 2.39 2.4 0.5 2.17 2.2 1.3 2.11 2.13 1.2 

1000 2.26 2.27 0.8 2.05 2.09 1.7 1.99 2.02 1.6 

 

 

 

 



IHJPAS. 2024, 37 (4)  

169 
 

Table 7. Total stopping power (MeV.cm2.g-1) for Protons in the human tissues. 

P
r
o
to

n
 

E
n

e
r
g
y
 

A
d

ip
o
se

 

ti
ss

u
e
 

B
lo

o
d

 

B
o
n

e
, 

C
o
m

p
a
c
t 

B
o
n

e
, 

C
o
r
ti

c
a
l 

B
r
a
in

 

E
y
e
 l

e
n

s 

L
u

n
g
 

S
k

in
 

T
e
st

ic
le

s 

1 288.66 273.11 247.88 233.63 277.08 273.95 272.79 274.67 273.92 

2 172.47 164.25 150.63 143.05 166.46 164.62 164.08 165.01 164.72 

4 100.48 96.14 88.81 84.79 97.36 96.3 96.05 96.5 96.4 

6 72.64 69.66 64.57 61.79 70.52 69.75 69.6 69.9 69.85 

8 57.55 55.27 51.33 49.2 55.93 55.33 55.22 55.44 55.41 

10 47.99 46.13 42.9 41.16 46.67 46.17 46.08 46.26 46.25 

20 27.19 26.2 24.46 23.53 26.5 26.22 26.18 26.27 26.27 

40 15.44 14.91 13.96 13.46 15.08 14.92 14.9 14.94 14.95 

60 11.17 10.79 10.12 9.77 10.91 10.8 10.79 10.82 10.82 

80 8.93 8.63 8.1 7.83 8.73 8.63 8.63 8.65 8.65 

100 7.54 7.29 6.85 6.62 7.37 7.29 7.29 7.31 7.31 

200 4.63 4.49 4.23 4.09 4.54 4.49 4.49 4.5 4.5 

400 3.12 3.03 2.86 2.77 3.06 3.03 3.03 3.03 3.04 

600 2.63 2.55 2.41 2.33 2.58 2.55 2.55 2.56 2.56 

800 2.4 2.33 2.2 2.13 2.35 2.33 2.33 2.33 2.33 

1000 2.27 2.21 2.09 2.02 2.23 2.21 2.21 2.21 2.21 

 

 
Figure 1. The stopping power of Proton in human tissue at the energy range from 1 to 100 MeV. 

 

0
20
40
60
80

100
120
140
160
180
200
220
240
260
280
300

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

St
o

p
p

in
g 

p
o

w
e

r 
(M

e
V

.c
m

2 .
g-1

)

Energy of Proton (MeV)
Adipose tissue Blood Bone, Compact
Bone, Cortical Brain Eye lens



IHJPAS. 2024, 37 (4)  

170 
 

 

 

Figure 2. The stopping power of Proton in human tissue at the energy range from 200 to 1000 MeV. 

 

 
Figure 3. The stopping power of Proton in the constituent elements of human tissue at the energy range from 1 

to 100 MeV. 

 
Figure 4. The stopping power of Proton in the constituent elements of human tissue at the energy range from 

200 to 1000 MeV. 

1.5

2

2.5

3

3.5

4

4.5

5

200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

St
o

p
p

in
g 

p
o

w
er

 (
M

e
V

.c
m

2 .
g-1

)

Energy of Proton (MeV)

Adipose tissue Blood Bone, Compact

Bone, Cortical Brain Eye lens

0

100

200

300

400

500

600

700

0.00 20.00 40.00 60.00 80.00 100.00

St
o

p
p

in
g 

p
o

w
er

 (
M

e
V

.c
m

2
.g

-1
)

Energy of Proton (MeV)
Hydrogen Carbon Nitrogen Oxygen

Sodium Magnesium Silicon Phosphorus

0

1

2

3

4

5

6

7

8

9

10

200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

St
o

p
p

in
g 

p
o

w
er

 (
M

eV
.c

m
2 .

g-1
)

Energy of Proton (MeV)
Hydrogen Carbon Nitrogen Oxygen

Sodium Magnesium Silicon Phosphorus



IHJPAS. 2024, 37 (4)  

171 
 

5. Conclusion 

The stopping power depends on the energy of the incident proton and the target material's 

atomic number, atomic mass, and mean excitation energy. The stopping power decreases with 

increasing the incident proton energy, where the higher the proton's energy, the higher its speed, 

and therefore the amount of 𝛽 increases, which equals 
𝑣

𝑐
 , and since the stopping power is 

inversely proportional to 𝛽, this leads to a decrease in stopping power. 

The quantity (
𝑍

𝐴
) decreases with increasing the atomic number, and the stopping power decreases 

with decreasing the quantity (
𝑍

𝐴
). Therefore, the stopping power is inversely proportional to the 

atomic number Z of the target material. 

The stopping power is inversely proportional to the mean excitation energy I, the smaller the 

value of the mean excitation energy, the greater the amount of energy lost and the probability 

of ionization of the atom, and therefore the stopping power increases. 

The stopping power is directly proportional to the density of the target material, so the higher 

the density of the material, the greater the stopping power. 

The greatest value of the total stopping power is at low energies, and it begins to decrease as 

the energy of the incident proton increases. The stopping power of a slow proton (low energy 

proton) is much greater than the stopping power of a fast Proton (high energy proton) because 

the slow proton spends a longer period in the atom, and therefore the probability of its 

interaction with electrons increases, leading to excitation or ionization of the atom. 

The largest error rate was at low energies, and then the error rate began to decrease as the 

incident proton energy increased, and that is because of not adding shell correction to the 

equation used. 

 

Acknowledgment 

All thanks and appreciation to the College of Sciences, University of Tikrit for their valuable 

comments on this article, and thanks go to the journal’s management and members. 

 

  Conflict of Interest  

  The authors declare that they have no conflicts of interest. 

 

Funding 

None. 

 

Ethical Clearance  

   None. 

 

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