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Mass Stopping Power and Range of Alpha Particles in Biological Human Body (Water and Eye Lens Tissue)

Arwa

Alshibel

¹Khalda

T. Osman

Department of Physics, College of Sciences, Qassim University, Buraidah, Saudi Arabia

03012024

11011186, December 202314, January 2024 17, January 2024

2014

This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/

We used the MATLAB Program to calculate the mass stopping power and range of alpha particles in biological human body tissues (such as water and the eye lens tissues) at energies between 0.2 and 200 MeV. The Bethe Block formula was used to calculate the mass stopping power, and the simple integration (continuous slowing down approximation) method was used to calculate the alpha particle ranges. Empirical formulae were developed to determine mass-stopping power and ranges of water and eye lens tissues. The results of graphing the mass-stopping power versus energy and range versus energy are presented, and compared the ASTAR (Alpha Stopping Power and Range) results with the present results for the mass-stopping powers and ranges of water. The results indicated remarkable agreement, particularly for energies that extend from 2 to 200 MeV, with a percentage deviation error of 4.81% - 6.39%. A graphical representation of the mass stopping power of water and eye lens tissue with their compositions is also provided. In addition, various radiation parameters essential in cancer treatment, such as absorbed dose, equivalent dose, effective dose, alpha particle depth, and linear energy transfer, are computed in this study.

Human Body Tissues Alpha Particles MATLAB Mass Stopping Power Range

1. Introduction

For the last century, scientists have been studying how charged particles interact with matter in order to understand their stopping power and energy dissipation. This research has a wide range of important applications, including ion implantation, fundamental particle physics, nuclear physics, radiation damage, and radiography [1] [2] [3] [4] . As heavy charged particles move through matter, they primarily lose energy through ionization and atomic excitation. This process has been extensively researched and is crucial to various scientific and technological advancements.

When heavy charged particles travel through matter, they tend to lose energy primarily through ionization and atomic excitation [4] [5] [6] .

The stopping power is defined as the mean energy loss per unit path length ?dE/dx. It depends on the charge and velocity of the projectile and, of course, the target material [7] [8] [9] . Early investigations of the energy loss of charged particles traversing matter arrive at a general stopping power formula. If an ion beam penetrates through matter, it loses energy due to collisions with electrons (electronic stopping) and target nuclei (nuclear stopping) [1] . The total stopping power is then just the sum of the stopping powers due to electronic and nuclear interactions [5] [6] . At low energies the total energy loss is usually described in terms of electronic stopping power [4] [5] [6] . The nuclear component of the stopping power can also be ignored [1] .

In this work, we will examine the interactions between alpha particles and matter. The mass stopping power of alpha particles will be studied at a range of energies, from 0.2 to 200 MeV. We will also investigate how these interactions affect water and eye lens tissues. Additionally, we will calculate the alpha particle ranges in water and lens tissues at energies between 0.2 and 200 MeV.

2. Stopping Power

The electronic mass stopping power for alpha particles on water and eye lens tissues is calculated by the Bethe-Bloch formula. The full expression for the Bethe-Bloch formula can be written as:

− d E d x = 5.08 × 10 − 31 z 2 n β 2 [ F ( β ) − ln I ] (1)

where: β is v/c where v is the velocity and c is light speed, I is the mean excitation energy and F(β) is given by [10] :

F ( β ) = ln ln 1.02 × 10 6 β 2 1 − β 2 − β 2 (2)

The electron density n is calculated by:

n = N a v 〈 z A 〉 = 6.02 × 10 23 ρ 〈 z A 〉 (3)

2.1. Mass Stopping Power of Eye Lens

The mass stopping power of eye lens tissues is calculated after substituting the appropriate constant of electron density n and mean excitation energy I given in Table 1 in Equation (1) by the following equation:

Table 1 Basic data for calculating mass stopping powers

n = ρ z N a A (electrons/m³)	Density (ρ) (g/cm³)	I (eV)		Material
3.52987 × 10²⁹	1.070E+00	74.3	0.54709	Eye Lens (ICRU-44)
3.34713 × 10²⁹	1.000E+00	75.0	0.55508	Water

− d E d x ρ = 0.717269584 β 2 × 1.070 [ F ( β ) − 4.308110952 ] (4)

2.2. Mass Stopping Power of Water

The mass stopping power of water is calculated after substituting the appropriate constant of electron density n and mean excitation energy I given in Table 1 in Equation (1) by the following equation:

− d E d x ρ = 0.680136816 β 2 × 1.00 [ F ( β ) − 4.317488114 ] (5)

3. Calculation of Alpha Particles Range

As it passes through the material, the alpha particle’s range ionizes, reducing its energy slowly until it is almost zero. Because of the infinite range of Coulomb, the particle interacts with multiple electrons simultaneously and loses energy gradually but steadily as it moves. Following a predetermined distance, it then runs out of energy. The alpha particle range is the name given to this distance. The alpha particle’s range is therefore defined as the average distance covered before it loses all of its initial kinetic energy [11] .

The range of charged particle is computed by numerical integration of the stopping power [12] . The range of the alpha particles for the tissues under considerations is calculated using the following relation:

R = ∫ E 0 E f d E M S ( E ) (6)

where, E 0 is the initial energy of incident charged particle in material, E f is the final energy of incident charged particle in material and M S ( E ) is the mass stopping power.

The higher alpha particles energy, the stronger their penetration through a given substance because the more Colombian interactions between the particles of alpha and absorption electrons will be required to dissipate energy before coming to rest [12] . All calculations were done using MATLAB program.

4. Alpha Depths, Absorbed Dose, Equivalent Dose, and Effective Dose

The Depth

The depth of a charged particles in the tissue or substance is given by the following relation:

T = R ρ (7)

where R is the range and is ρ the density of the tissue or substance.

Absorbed Dose

Two different materials, if subjected to the same gamma-ray exposure, will in general absorb different amounts of energy. Because many important phenomena, including changes in physical properties or induced chemical reactions, would be expected to scale as the energy absorbed per unit mass of the material, a unit that measures this quantity is of fundamental interest. The mean energy absorbed from any type of radiation per unit mass of the absorber is defined as the absorbed dose. The historical unit of absorbed dose has been the rad, defined as 100 ergs/gram. As with other historical radiation units, the rad has been replaced by its SI equivalent, the gray (Gy) defined as 1 joule/kilogram. The two units are therefore simply related by: 1 Gy = 100 rad the absorbed dose is a reasonable measure of the chemical or physical effects created by a given radiation exposure in an absorbing material. The absorbed dose is calculated by the following relation:

A d = E 1 grm 1.6 × 10 − 13 J 1 MeV 10 7 erg 1 J 1 rad 100 erg gram (8)

Equivalent Dose

The equivalent dose is calculated by the following relation:

H T = ∑ R W R × D (9)

where W R = Weighting factor = 20 for Alpha particle and D is Absorbed dose.

Effective Dose

The tissues differ in their sensitivity to the late effects of radiation, which represent the biological responses to the tissue, which are delayed for a long period of time, often several years. The effective dose is used to estimate the incidence of delayed effects in the future. If a part of the body such as the lungs receives a radiation dose, it represents a risk factor of lung cancer. If the same dose is given to another organ, it causes a different risk factor and is called the dose measured by the effective dose, is designated E.

E = ∑ T W T H T (10)

where W T is the weighting factor of tissue.

And for water and eye lens W T = 0.12 .

5. Percentage Deviation Error

The percentage deviation error for the present results of mass stopping power and that of ASTAR results of water are calculating by the following relation:

DeviationError = ( PresentResult − ASTARResult ASTARResult ) × 100 % (11)

the Percentage deviation error was calculated in a Table 13 for the tissues that were compared to the Aster.

6. Results and Discussion

The Bethe Block theory and the MATLAB application were used in the current work to determine the mass stopping power using Equation (4) and Equation (5). The range of alpha particles in water and eye lens tissues is calculated using Equation (6). Table 2 shows the elemental composition of water and eye lens. The results of mass stopping powers and range of alpha particles in water, and eye lens respectively are given in Table 3 and Table 4. In Table 5 a comparison between the present results and that of ASTAR results of mass stopping powers of water are given while a comparison between the present results and that of ASTAR result of alpha particles range for water are given in Table 6. Table 7 is Values of mass stopping power of Water and its compositions and Table 8 for the Values of mass stopping power of Eye lens and its some of compositions.

To study the relation between the mass stopping power and the alpha particles energy the graphical method is used as shown in Figure 1 and Figure 2 for the tissues under consideration. The empirical formula for calculating mass stopping powers knowing alpha particles energy are obtained for all tissues under study as given in Table 9. Figure 3 depicts a comparison of the mass stopping power of an alpha particle in water for the current results and those of ASTAR. In Figure 4 and Figure 5 the relationship between the range and alpha particles for the tissues under study are shown while the empirical formula for calculating alpha particles range of all studied tissues is given in Table 10. In Table 11 and Table 12 the calculated depth of alpha particles, LET, absorbed dose, equivalent dose and effective dose of alpha particle for both water and eye lens are given. The percentage deviation errors of mass stopping power for water are given in Table 13.

Table 2 Elemental composition of water and eye lens

Composition	Material
1:0.096000 H 6:0.195000 C 7:0.057000 N 8:0.646000 O 11:0.001000 Na 15:0.001000 P 16:0.003000 S 17:0.001000 Cl	Eye Lens (ICRU-44)
1:0.111898 H 8:0.888102 O	Water

Table 3 Values of mass stopping power (MeV∙cm2/g) of water and eye lens

d E d x ρ ( MeV ⋅ cm 2 g ) Eye lens	d E d x ρ ( MeV ⋅ cm 2 g ) Water	Energy (MeV)
2408.65305062471	2384.22475403096	0.2
3375.76682499890	3395.26985256277	0.4
3097.31868738319	3122.68961199742	0.6
2773.60364305991	2799.21374595122	0.8
2498.50202763589	2523.07437079105	1
1683.53933217218	1702.16894269649	2
1291.72133621023	1306.61486200367	3
1058.91422947724	1071.40076011691	4
903.055516828838	913.861598045919	5
790.624160042245	800.185413092180	6
705.273148707949	713.871579595160	7
638.030206437612	645.859346277533	8
583.537500926490	590.736276465791	9
538.386718633458	545.058465969393	10
312.624876337861	316.595133121707	20
225.355761871248	228.250022083824	30
178.032310775232	180.334690817695	40
148.021536980534	149.945174521898	50
127.162424591830	128.821123405981	60
111.759310349188	113.221409208821	70
99.8844855919807	101.194424044129	80
90.4296777128844	91.6180727928889	90
82.7105618050238	83.7994542394653	100
76.2807946937883	77.2866088775882	110
70.8363332270320	71.7716546686581	120
66.1626241157140	67.0373213031586	130
62.1037638892161	62.9257258579161	140
58.5436331508260	59.3192711893148	150
55.3938980512388	56.1284969629590	160
52.5861224863810	53.2840926935507	170
50.0664326671761	50.7314950861815	180
47.7918173890647	48.4271415891798	190
45.7275059064572	46.3358150948924	200

Table 4 Values of range (in g/cm2) of water and eye lens

Range (g/cm²) Eye lens	Range (g/cm²) Water	Energy (MeV)
1.71824E−05	1.71308E−05	0.2
5.59033E−05	5.5658E−05	0.4
0.000111467	0.000110888	0.6
0.000181882	0.000180834	0.8
0.000265908	0.000264257	1
0.000865136	0.000858572	2
0.00172501	0.001710535	3
0.002814734	0.00278951	4
0.00411508	0.004076382	5
0.00561235	0.005557546	6
0.007296056	0.007222584	7
0.009157786	0.009063144	8
0.011190566	0.011072309	9
0.013388481	0.013244206	10
0.043559648	0.043030551	20
0.086854372	0.085729848	30
0.141722047	0.139806674	40
0.207194516	0.204303086	50
0.282582158	0.278537097	60
0.367356877	0.361986677	70
0.461095058	0.454233224	80
0.56344569	0.554929976	90
0.674110839	0.663782684	100
0.792832893	0.780536979	110
0.919385798	0.904969697	120
1.053568786	1.036882674	130
1.195201767	1.176098184	140
1.344121825	1.322455475	150
1.500180515	1.475808098	160
1.663241735	1.636021795	170
1.833180013	1.80297281	180
2.009879121	1.976546519	190
2.193230933	2.156636302	200

Table 5 Comparison of mass stopping power (MeV∙cm2/g) of this work and that of ASTAR results for water

d E d x ρ ( MeV ⋅ cm 2 g )
A star	This work (water)
1.582E+03	2384.22475403096
2.062E+03	3395.26985256277
2.240E+03	3122.68961199742
2.256E+03	2799.21374595122
2.190E+03	2523.07437079105
1.624E+03	1702.16894269649
1.255E+03	1306.61486200367
1.034E+03	1071.40076011691
8.848E+02	913.861598045919
7.771E+02	800.185413092180
6.949E+02	713.871579595160
6.301E+02	645.859346277533
5.776E+02	590.736276465791
5.340E+02	545.058465969393
3.144E+02	316.595133121707
2.284E+02	228.250022083824
1.815E+02	180.334690817695
1.516E+02	149.945174521898
1.308E+02	128.821123405981
1.155E+02	113.221409208821
1.036E+02	101.194424044129
9.416E+01	91.6180727928889
8.645E+01	83.7994542394653
-	77.2866088775882
7.215E+01	71.7716546686581
-	67.0373213031586
-	62.9257258579161
6.229E+01	59.3192711893148
-	56.1284969629590
5.505E+01	53.2840926935507
-	50.7314950861815
-	48.4271415891798
4.950E+01	46.3358150948924

Table 6 Comparison of range (in g/cm2) of water of this work and ASTAR results

Range (cm²/g)
ASTAR	This work (water)
2.151E−04	1.71308E−05
3.230E−04	5.5658E−05
4.150E−04	0.000110888
5.034E−04	0.000180834
5.931E−04	0.000264257
1.123E−03	0.000858572
1.829E−03	0.001710535
2.711E−03	0.00278951
3.759E−03	0.004076382
4.967E−03	0.005557546
6.330E−03	0.007222584
7.842E−03	0.009063144
9.500E−03	0.011072309
1.130E−02	0.013244206
3.668E−02	0.043030551
7.452E−02	0.085729848
1.240E−01	0.139806674
1.845E−01	0.204303086
2.557E−01	0.278537097
3.372E−01	0.361986677
4.287E−01	0.454233224
5.300E−01	0.554929976
6.409E−01	0.663782684
	0.780536979
9.588E−01	0.904969697
	1.036882674
	1.176098184
1.333E+00	1.322455475
	1.475808098
1.760E+00	1.636021795
	1.80297281
	1.976546519
2.240E+00	2.156636302

Table 7 Values of mass stopping power (in MeV∙cm2/g) of water and its compositions

Energy (MeV)	Mass stopping power (MeV∙cm²/g)
Energy (MeV)	Water	H	O
0.2	2384.22475403096	6.019E+03	1.272E+03
0.4	3395.26985256277	7.915E+03	1.639E+03
0.6	3122.68961199742	8.222E+03	1.792E+03
0.8	2799.21374595122	7.808E+03	1.820E+03
1	2523.07437079105	7.157E+03	1.777E+03
2	1702.16894269649	4.588E+03	1.329E+03
3	1306.61486200367	3.351E+03	1.038E+03
4	1071.40076011691	2.675E+03	8.602E+02
5	913.861598045919	2.242E+03	7.395E+02
6	800.185413092180	1.939E+03	6.519E+02
7	713.871579595160	1.713E+03	5.845E+02
8	645.859346277533	1.538E+03	5.313E+02
9	590.736276465791	1.398E+03	4.880E+02
10	545.058465969393	1.283E+03	4.520E+02
20	316.595133121707	7.238E+02	2.688E+02
30	228.250022083824	5.156E+02	1.963E+02
40	180.334690817695	4.047E+02	1.564E+02
50	149.945174521898	3.353E+02	1.309E+02
60	128.821123405981	2.875E+02	1.131E+02
70	113.221409208821	2.524E+02	9.997E+01
80	101.194424044129	2.256E+02	8.979E+01
90	91.6180727928889	2.043E+02	8.166E+01
100	83.7994542394653	1.870E+02	7.502E+01
110	77.2866088775882	-	-
120	71.7716546686581	1.552E+02	6.270E+01
130	67.0373213031586	-	-
140	62.9257258579161	-	-
150	59.3192711893148	1.334E+02	5.418E+01
160	56.1284969629590	-	-
170	53.2840926935507	1.174E+02	4.792E+01
180	50.7314950861815	-	-
190	48.4271415891798	-	-
200	46.3358150948924	1.053E+02	4.311E+01

Table 8 Values of mass stopping power (in MeV∙cm2/g) of Eye lens and its some of compositions

Energy (MeV)	Mass stopping power (MeV∙cm²/g)
Energy (MeV)	Eye lens	H	C	O	N
0.2	2408.65305062471	6.019E+03	1.595E+03	1.272E+03	1.486E+03
0.4	3375.76682499890	7.915E+03	1.862E+03	1.639E+03	1.940E+03
0.6	3097.31868738319	8.222E+03	1.906E+03	1.792E+03	2.086E+03
0.8	2773.60364305991	7.808E+03	1.866E+03	1.820E+03	2.069E+03
1	2498.50202763589	7.157E+03	1.795E+03	1.777E+03	1.978E+03
2	1683.53933217218	4.588E+03	1.372E+03	1.329E+03	1.406E+03
3	1291.72133621023	3.351E+03	1.085E+03	1.038E+03	1.088E+03
4	1058.91422947724	2.675E+03	8.982E+02	8.602E+02	8.985E+02
5	903.055516828838	2.242E+03	7.720E+02	7.395E+02	7.711E+02
6	790.624160042245	1.939E+03	6.804E+02	6.519E+02	6.785E+02
7	705.273148707949	1.713E+03	6.102E+02	5.845E+02	6.080E+02
8	638.030206437612	1.538E+03	5.544E+02	5.313E+02	5.523E+02
9	583.537500926490	1.398E+03	5.090E+02	4.880E+02	5.069E+02
10	538.386718633458	1.283E+03	4.712E+02	4.520E+02	4.691E+02
20	312.624876337861	7.238E+02	2.788E+02	2.688E+02	2.777E+02
30	225.355761871248	5.156E+02	2.028E+02	1.963E+02	2.021E+02
40	178.032310775232	4.047E+02	1.612E+02	1.564E+02	1.608E+02
50	148.021536980534	3.353E+02	1.348E+02	1.309E+02	1.344E+02
60	127.162424591830	2.875E+02	1.163E+02	1.131E+02	1.161E+02
70	111.759310349188	2.524E+02	1.027E+02	9.997E+01	1.025E+02
80	99.8844855919807	2.256E+02	9.214E+01	8.979E+01	9.197E+01
90	90.4296777128844	2.043E+02	8.375E+01	8.166E+01	8.360E+01
100	82.7105618050238	1.870E+02	7.690E+01	7.502E+01	7.677E+01
110	76.2807946937883	-	-	-	-
120	70.8363332270320	1.552E+02	6.420E+01	6.270E+01	6.410E+01
130	66.1626241157140	-	-	-	-
140	62.1037638892161	-	-	-	-
150	58.5436331508260	1.334E+02	5.543E+01	5.418E+01	5.536E+01
160	55.3938980512388	-	-	-	-
170	52.5861224863810	1.174E+02	4.899E+01	4.792E+01	4.894E+01
180	50.0664326671761	-	-	-	-
190	47.7918173890647	-	-	-	-
200	45.7275059064572	1.053E+02	4.406E+01	4.311E+01	4.401E+01

Table 9 The empirical formulae for calculating mass stopping powers

y = y 0 + A 1 ∗ ( 1 − exp ( − x / t 1 ) ) + A 2 ∗ ( 1 − exp ( − x / t 2 ) )	Equation
A₁ = −525.17835 ± 281.24707 t₁ = 30.29513 ± 27.2601 A₂ = −2749.90762 ± 270.11886 t₂ = 2.72637 ± 0.627 y₀ = 3330.68748 ± 146.50026 R² = 0.96955	Water
A₁ = −531.86671 ± 269.70529 t₁ = 29.57687 ± 25.25264 A₂ = −2739.78871 ± 258.80006 t₂ = 2.66924 ± 0.59292 y₀ = 3327.15093 ± 142.5736 R² = 0.97145	Eye lens

Table 10 The empirical formulae for calculating range

y = a × x^b	Equation
a = 2.64257E−4 ± 1.99087E−18 b = 1.7 ± 1.47723E−15 R² = 1	Water
a = 2.65908E−4 ± 1.49334E−18 b = 1.702 ± 1.10114E−15 R² = 1	Eye lens

Table 11 Alpha depth in the tissue, LET, absorbed dose, equivalent dose and effective dose of Alpha particle in water

Effective dose (rem)	Equivalent dose (rem)	Absorbed dose (rad)	LET (MeV/cm)	Alpha depth in the Water(cm)	Energy (MeV)
7.68E−09	0.000000064	3.2E−09	2384.22475403096	1.71308E−05	0.2
1.54E−08	0.000000128	6.4E−09	3395.26985256277	5.5658E−05	0.4
2.3E−08	0.000000192	9.6E−09	3122.68961199742	0.000110888	0.6
3.07E−08	0.000000256	1.28E−08	2799.21374595122	0.000180834	0.8
3.84E−08	0.00000032	1.6E−08	2523.07437079105	0.000264257	1
7.68E−08	0.00000064	3.2E−08	1702.16894269649	0.000858572	2
1.15E−07	0.00000096	4.8E−08	1306.61486200367	0.001710535	3
1.54E−07	0.00000128	6.4E−08	1071.40076011691	0.00278951	4
1.92E−07	0.0000016	8E−08	913.861598045919	0.004076382	5
2.3E−07	0.00000192	9.6E−08	800.185413092180	0.005557546	6
2.69E−07	0.00000224	1.12E−07	713.871579595160	0.007222584	7
3.07E−07	0.00000256	1.28E−07	645.859346277533	0.009063144	8
3.46E−07	0.00000288	1.44E−07	590.736276465791	0.011072309	9
3.84E−07	0.0000032	1.6E−07	545.058465969393	0.013244206	10
7.68E−07	0.0000064	3.2E−07	316.595133121707	0.043030551	20
1.15E−06	0.0000096	4.8E−07	228.250022083824	0.085729848	30
1.54E−06	0.0000128	6.4E−07	180.334690817695	0.139806674	40
1.92E−06	0.000016	8E−07	149.945174521898	0.204303086	50
2.3E−06	0.0000192	9.6E−07	128.821123405981	0.278537097	60
2.69E−06	0.0000224	1.12E−06	113.221409208821	0.361986677	70
3.07E−06	0.0000256	1.28E−06	101.194424044129	0.454233224	80
3.46E−06	0.0000288	1.44E−06	91.6180727928889	0.554929976	90
3.84E−06	0.000032	1.6E−06	83.7994542394653	0.663782684	100
4.22E−06	0.0000352	1.76E−06	77.2866088775882	0.780536979	110
4.61E−06	0.0000384	1.92E−06	71.7716546686581	0.904969697	120
4.99E−06	0.0000416	2.08E−06	67.0373213031586	1.036882674	130
5.38E−06	0.0000448	2.24E−06	62.9257258579161	1.176098184	140
5.76E−06	0.000048	2.4E−06	59.3192711893148	1.322455475	150
6.14E−06	0.0000512	2.56E−06	56.1284969629590	1.475808098	160
6.53E−06	0.0000544	2.72E−06	53.2840926935507	1.636021795	170
6.91E−06	0.0000576	2.88E−06	50.7314950861815	1.80297281	180
7.3E−06	0.0000608	3.04E−06	48.4271415891798	1.976546519	190
7.68E−06	0.000064	3.2E−06	46.3358150948924	2.156636302	200

Table 12 Alpha depth in the tissue, LET, absorbed dose, equivalent dose and effective dose of Alpha particle in eye lens

Effective dose (rem)	Equivalent dose (rem)	Absorbed dose (rad)	LET (MeV/cm)	Alpha depth in the Eye lens(cm)	Energy (MeV)
7.68E−09	0.000000064	3.2E−09	2577.25876416844	1.61E−05	0.2
1.54E−08	0.000000128	6.4E−09	3612.07050274882	5.22E−05	0.4
2.3E−08	0.000000192	9.6E−09	3314.13099550001	1.04E−04	0.6
3.07E−08	0.000000256	1.28E−08	2967.75589807411	1.70E−04	0.8
3.84E−08	0.00000032	1.6E−08	2673.39716957040	2.49E−04	1
7.68E−08	0.00000064	3.2E−08	1801.38708542424	8.09E−04	2
1.15E−07	0.00000096	4.8E−08	1382.14182974495	1.61E−03	3
1.54E−07	0.00000128	6.4E−08	1133.03822554065	2.63E−03	4
1.92E−07	0.0000016	8E−08	966.269403006857	3.85E−03	5
2.3E−07	0.00000192	9.6E−08	845.967851245202	5.25E−03	6
2.69E−07	0.00000224	1.12E−07	754.642269117505	6.82E−03	7
3.07E−07	0.00000256	1.28E−07	682.692320888245	8.56E−03	8
3.46E−07	0.00000288	1.44E−07	624.385125991344	1.05E−02	9
3.84E−07	0.0000032	1.6E−07	576.073788937800	1.25E−02	10
7.68E−07	0.0000064	3.2E−07	334.508617681511	4.07E−02	20
1.15E−06	0.0000096	4.8E−07	241.130665202236	8.12E−02	30
1.54E−06	0.0000128	6.4E−07	190.494572529498	1.32E−01	40
1.92E−06	0.000016	8E−07	158.383044569171	1.94E−01	50
2.3E−06	0.0000192	9.6E−07	136.063794313258	2.64E−01	60
2.69E−06	0.0000224	1.12E−06	119.582462073631	3.43E−01	70
3.07E−06	0.0000256	1.28E−06	106.876399583419	4.31E−01	80
3.46E−06	0.0000288	1.44E−06	96.7597551527863	5.27E−01	90
3.84E−06	0.000032	1.6E−06	88.5003011313755	6.30E−01	100
4.22E−06	0.0000352	1.76E−06	81.6204503223535	7.41E−01	110
4.61E−06	0.0000384	1.92E−06	75.7948765529242	8.59E−01	120
4.99E−06	0.0000416	2.08E−06	70.7940078038140	9.85E−01	130
5.38E−06	0.0000448	2.24E−06	66.4510273614613	1.12E+00	140
5.76E−06	0.000048	2.4E−06	62.6416874713838	1.26E+00	150
6.14E−06	0.0000512	2.56E−06	59.2714709148255	1.40E+00	160
6.53E−06	0.0000544	2.72E−06	56.2671510604277	1.55E+00	170
6.91E−06	0.0000576	2.88E−06	53.5710829538784	1.71E+00	180
7.3E−06	0.0000608	3.04E−06	51.1372446062992	1.88E+00	190
7.68E−06	0.000064	3.2E−06	48.9284313199092	2.05E+00	200

Table 13 Percentage of deviation error of stopping power for water

Deviation (water)	Energy (MeV)
5.07E+01	0.2
6.47E+01	0.4
3.94E+01	0.6
2.41E+01	0.8
1.52E+01	1
4.81E+00	2
4.11E+00	3
3.62E+00	4
3.28E+00	5
2.97E+00	6
2.73E+00	7
2.50E+00	8
2.27E+00	9
2.07E+00	10
6.98E−01	20
−6.57E−02	30
−6.42E−01	40
−1.09E+00	50
−1.51E+00	60
−1.97E+00	70
−2.32E+00	80
−2.70E+00	90
−3.07E+00	100
-	110
−5.24E−01	120
-	130
-	140
−4.77E+00	150
-	160
−3.21E+00	170
-	180
-	190
−6.39E+00	200

7. Conclusions

Our research aims to evaluate how much energy alpha particles deposit in water and eye lens tissues. We used energy levels between 0.2 and 200 MeV and calculated the mass stopping power for each beam with the Bethe-Bloch formula. Based on our findings, we can draw the following conclusions:

1) The mass stopping power is proportional to Z (the charge of the incident particles), Z/A (the ratio of atomic and mass’ number of the tissue) and I (the ionization energy of the tissues).

2) The mass stopping power increases rapidly at low energies reaches a maximum and decreases gradually with increasing energy.

3) The mass stopping power allows us to calculate the range of the heavy particles in the absorber material.

4) The current fitting curves for mass stopping power and alpha particle range in water are excellent and accord with ASTAR data in the alpha energy rage of 2 to 200 MeV, with a deviation error of 4.81% - 6.39%.

5) Semi-empirical formulas for mass stopping power and range of alpha particles in water and eye lens tissues were developed for alpha particle energies ranging from 0.2 to 200 MeV.

6) The mass stopping power of alpha particles in water and eye lens tissues is equal to their average composition values.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Alshibel, A. and Osman, K.T. (2024) Mass Stopping Power and Range of Alpha Particles in Biological Human Body (Water and Eye Lens Tissue). Open Access Library Journal, 11: e1081. https://doi.org/10.4236/oalib.1111081

References1

Berger, M.J. (1993) ESTAR, PSTAR, ASTAR. A PC Package for Calculating Stopping Powers and Ranges of Electrons, Protons and Helium Ions. Version 2 (No. IAEA-NDS-144), International Atomic Energy Agency, Vienna. https://2u.pw/wiKocY4

National Research Council (1990) Health Effects of Exposure to Low Levels of Ionizing Radiation: BEIR V. https://2u.pw/jKZskul

El-Ghossain

M.O.

,et al. (2017)Calculations of Stopping Power, and Range of Ions Radiation (Alpha Particles) Interaction with Different Materials and Human Body Parts International Journal of Physics 5, 92-98.

Porter, L.E. (2003) Further Observations of Projectile-z Dependence in Target Parameters of Modified Bethe-Bloch Theory. International Journal of Quantum Chemistry, 95, 504-511. https://2u.pw/mRH1duC https://doi.org/10.1002/qua.10589

Almutairi, A.S. and Osman, K.T. (2021) Mass Stopping Power and Range of Protons in Biological Human Body Tissues (Ovary, Lung and Breast). International Journal of Medical Physics, Clinical Engineering and Radiation Oncology, 11, 48-59. https://2u.pw/pZbO9Xe https://doi.org/10.4236/ijmpcero.2022.111005

Osman, K.T. (2020) Stopping Powers of Protons in Biological Human Body Substances (Water, Tissue, Muscles and Bones). International Journal of Novel Research in Physics Chemistry & Mathematics, 7, 8-12. https://2u.pw/NGDFF5H

Almutairi, A.S. and Osman, K.T. (2022) Calculation of Mass Stopping Power and Range of Protons as Well as Important Radiation Quantities in Some Biological Human Bodyparts (Water, Muscle, Skeletal and Bone, Cortical). International Journal of Medical Physics, Clinical Engineering and Radiation Oncology, 11, 99-112. https://2u.pw/ouff9QE https://doi.org/10.4236/ijmpcero.2022.112009

Alshibel, A. and Osman, K.T. (2023) Mass Stopping Power and Range of Alpha Particles in Biological Human Body Tissues (Blood, Brain, Adipose and Bone). Open Access Library Journal, 10, 1-17. https://2u.pw/1JX1Jb9 https://doi.org/10.4236/oalib.1110775

Osman, K.T. (2020) Stopping Powers of Alpha particles in Biological Human Body Substances (Water, Tissue, Muscules and Bones). International Journal of Novel Research and Development, 5, 362-398. https://2u.pw/5QSO9aJ

Osman, K.T. (2020) Mass Stopping Powers of Alpha Particles in Eye Lens and Its COMPOSITIONS (H, C, N, O, Na, P, S, Cl). International Journal of Novel Research in Physics Chemistry & Mathematics, 7, 5-8. https://2u.pw/oOWBVXx

Krane, K.S. (1991) Introductory Nuclear Physics. John Wiley & Sons, New York. https://2u.pw/lBJQfAk

L’Annunziata, M.F. (2016) Radioactivity: Introduction and History, from the Quantum to Quarks. Elsevier, New York. https://2u.pw/yQWvDkS