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Calculations of mass stopping power and range of protons in organic compounds (CH3OH, CH2O, and CO2) at energy range of 0.01–1,000 MeV

  • Abrar Taha EMAIL logo and Rashid O. Kadhim
Published/Copyright: September 20, 2024
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Abstract

The determination of stopping power and the range of protons present in CH3OH, CH2O, and CO2 was accomplished within the energy range of 0.01–1,000 MeV by employing the Bethe equation and Ziegler equation. The latter two equations utilize quantum mechanics to derive an approximation of the stopping force formula, which applies to highly charged particles. The software MATLAB was utilized in the calculation of the results. A suitable equation for computing the halting power of protons in the range of 0.01–1,000 MeV has been identified. A correlation coefficient of 0.999 was determined, suggesting a high degree of concordance between the derived results and those of the SRIM 2013 and P-STAR programs. Proton stopping power analyses of this nature will aid the scientific community in selecting the optimal formulation of stopping power.

1 Introduction

The study of charged particle penetration in matter has been considered a significant aspect of atomic modern physics. Niels Bohr was the pioneer in investigating this phenomenon and formulated a theoretical model based on classical mechanics. Subsequently, other scientists have expanded on Bohr’s ideas by incorporating quantum mechanics, aiming to comprehend how energy is transferred from the projectile to the target atom [1]. As a charged particle traverses a substance, it emits energy via its interactions with the atoms of the material. The stopping power, denoted as −dE/dx, refers to the rate of energy loss per unit distance in a material. The stopping power of a particle is influenced by both its charge and the properties of the substance it traverses [2,3]. In recent years, there has been a significant amount of theoretical and experimental study focused on the range of charged particles and their stopping power (SP), especially in the field of radiation physics. Numerous successful theoretical and experimental studies have been conducted on this topic. The user’s input is incomplete and does not contain any text [4].

Specifically, there is a growing trend in radiotherapy to replace external photon beams with protons or other heavier ions. The Bragg curve enables the precise delivery of energy in the form of focused radiation beams to sick tissue, ensuring that the desired dosage is maintained while maximizing the dose given to the tumor. The dominant contribution to the overall stopping power for protons comes from the electronic stopping power, which is determined by the interactions involving inelastic collisions with the electrons of the target. Conversely, the nuclear stopping power, arising from elastic collisions with the nucleons of the target, has the smallest contribution to the overall stopping power and is only significant at very low energies. Only when proton energies are below 20 KeV can the nuclear stopping power account for more than 1% of the overall stopping power [5]. Therefore, accurate information about the stopping power and proton range is required to determine the precise dosimetry of radiation from protons. To investigate the range and stopping power of protons in biological tissues, one must ascertain or gather information from experiment [6,7].

The major mechanism by which heavy charged particles dissipate energy while traversing matter is via the process of ionization and excitation of atoms. The stopping power is defined as the negative derivative of energy with respect to route length, or −dE/dx. The outcome is contingent on the charge, velocity, and composition of the projectile, as expected [7,8].

The utilization of protons or heavier ions is on the rise in radiotherapy as an alternative to external photon beams. This trend is driven by the fact that these ions maintain the intended dose and guarantee a greater delivery of energy to the tumor and, by virtue of the Bragg curve, is capable of transferring energy through diseased tissue as a point discharge [9]. A multitude of techniques have been documented for quantifying the stopping power of charged particles. These techniques include direct energy loss measurements through films, backscattering from thick substrates with deposited absorbing layers, gamma resonance shift measurements, self-supporting methods, and indirect verification of stopping power through alpha energy losses in the air [4,10,11].

Several academics have done a great deal of study on this topic. Tufan et al. [12] measured the total stopping power and route length of electrons in certain biological components that ranged in energy from 100 eV to 1 GeV. Comparing the findings of the Penelope [13], Hadi calculated the mass stopping power (in MeV cm2/g) and the range (cm) of proton in one of the types and found that the calculation results show that the Ziegler equation gives better results than using the Bethe equation [14]. Singh and Singh electronic stopping power of various organic compounds for proton (0.05–10 MeV): a comparative study [15]. Almutairi and Osman calculated mass stopping power and range of protons in biological human body tissues (ovary, lung and breast), where the Bethe formula was used to compute the mass stopping power. Moreover, the protons range at the tissues was calculated using the simple integration (continuous slowing down approximation) approach. The empirical equations for calculating the mass stopping power and the ranges were developed, and the results of the mass stopping power versus energy and the range versus energy were given graphically [16].

In the present work, the electronic mass stopping power and range of proton in some organic compounds (CH3OH, CH2O, and CO2) are calculated using the Bethe and Ziegler formulas as reported in the references. As it is known in any therapeutic unit with protons, it needs to calculate the absorbed dose, the equivalent dose to the tissue, and the effective dose according to the energy of the protons. Therefore, in this work, protons in CH3OH, CH2O, and CO2 were also computed at the proton energy range of 0.01–1,000 MeV.

2 Stopping power formulations

Bethe performed the initial quantum mechanical investigation into halting power. The theory maintains its validity when the velocity of the projectile surpasses the Bohr velocity. In the case of inelastic collisions between massive particles and atomic electrons, the energy loss is calculated using the Born approximation. It is postulated that the hefty projectile particle lacks structure [17].

The stopping-power equation resulting from “Bethe’s quantum-mechanical formulation” is as follows: where β represents the geometric mean cyclic frequency of the orbital electrons in the medium, e and m denote the electronic charge and mass, respectively, n indicates the quantity of atoms per unit volume in the medium, Z denotes the atomic number, and dE/dx denotes the energy dissipated per unit path length by a particle with ionic charge ze and velocity V. The mean excitation potential of the medium is represented by the additional parameter I, whereas β is equal to v/c, where c is the speed of light [18].

The following equation represents the Bethe formula-derived expressions for the energy loss per unit travel length for [19]:

(1) d E d x = 4 π k 0 2 e 4 Z 2 2 n ρ m c 2 β 2 ln 2 m c 2 β 2 I ( 1 β 2 ) β 2 ,

where d E ρ d x is the mass stopping power, k 0 = 8.99 × 109 N m2 C –2, Z 2 is the atomic number of the heavy particle, e is the electron charge, n is the number of electrons per unit volume in the medium, m represents the rest mass of electron, c represents the speed of light in vacuum, β = v /c represents the speed of the particle relative to c, and I is the mean ionization potential of the medium.

Since I indicates the magnitude of the ionization energy,

(2) n = N av ρ Z A .

The mass stopping power of a substance is calculated by dividing the stopping power by the density ρ. The standard values for mass stopping power, which measures the energy loss per unit distance travelled through a material, are MeV cm2/g. The mass stopping power is a valuable measure since it indicates the rate at which a charged particle loses energy when passing through a material, per gram per square centimeter [1].

The Ziegler equation is a semi-empirical equation, which can be utilized for determining the electronic stopping power of protons within the energy range of 1–10 keV. The stopping power is measured in units of eV per 1015 atoms per square centimeter [20]:

(3) d E ρ d x e = A 1 E 1 / 2 .

When the energy is 10–999 keV,

(4) d E ρ d x n e 1 = d E ρ d x e low 1 + d E ρ d x e high 1 ,

(5) d E ρ d x e low = A 2 E ( 0.45 ) ,

(6) d E ρ d x e high = A 3 E In ( 1 + A 4 E + ( A 5 E ) .

One can ascertain the range of charged particles R in a medium by integrating the stopping power between 0 and E:

(7) R ( E ) = E 0 1 S ( E ) d E .

According to Equation (8), the range is an average value because scattering is a probabilistic process and individual particles will have a range of values. The range will be larger for lighter particles and smaller for heavier particles. These characteristics are important to consider when using radiation in medical treatment [1].

By utilizing the stopping-power formula, one can determine the rate at which a heavily charged particle decelerates. By employing the chain rule of differentiation, one can ascertain the rate of energy loss (−dE/dt). Rewriting the formula as −dE/dt = −(dE/dx)/(dt/dx) = V(−dE/dx), where V represents the particle’s velocity. Under the assumption of a constant deceleration rate, the time required for the particle to completely halt in a given medium can be approximated using this formula. This estimation is possible using the kinetic energy (T) of the particle as a basis [20]. The stopping time is given by:

(8) t ( E ) = E 0 1 vS ( E ) d E .

3 Results and discussion

The Bethe formula and Ziegler equation were used to compute the stopping power, range, and stopping time for compounds. The results are shown in Tables 13, the stopping power calculations S total of the protons in C2 H2, C2 H4, and C6 H6. The energy range of protons spans from 0.01 to 1,000 MeV. In this study, the Bethe equation and the Ziegler equation were used to analyze the behavior of the protons in C2 H2, C2 H4, and C6 H6, and the result showed consistency with the program P-STAR results.

Table 1

Stopping power calculations S total for protons in CH3OH

E (MeV) P-STAR Bethe SRIM Ziegler Fitting
0.010000 614.337554 −8949.758482 552.644551 619.224642 613.644205
0.020000 796.450028 −1668.159713 739.709942 811.525231 788.811386
0.030000 907.374096 −17.546325 854.933198 930.056535 921.395270
0.040000 979.125039 569.301499 927.031638 1003.592376 997.756330
0.060000 1049.062103 926.840087 992.629562 1067.152970 1050.306836
0.080000 1056.401261 986.385442 995.950935 1066.056552 1038.909241
0.100000 1030.667131 969.851931 967.230802 1032.890879 1002.848773
0.200000 798.318772 765.705039 741.199940 788.965416 786.443451
0.300000 623.785634 620.017773 584.565476 619.972155 632.920317
0.400000 517.458005 523.338151 487.008463 515.073518 529.703051
0.600000 395.901124 403.741336 373.783524 394.033274 402.528175
0.800000 325.137491 332.030442 309.393906 324.637157 327.561767
2.000000 167.836995 170.211170 171.392421 158.525452 165.233671
3.000000 123.519189 124.610253 125.574755 115.861675 121.481524
4.000000 98.871063 99.436184 100.191686 92.289480 97.571445
6.000000 71.858963 71.984314 72.575857 66.563889 71.482787
7.000000 63.543692 63.583903 64.115701 58.689273 63.444088
8.000000 57.079528 57.077232 57.567009 52.590297 57.182030
10.000000 47.673295 47.617023 48.038048 43.725775 48.000350
20.000000 27.109721 27.018785 27.261068 24.465706 27.525627
30.000000 19.475077 19.400230 19.574226 17.379492 19.730370
40.000000 15.428217 15.364681 15.496209 13.644097 15.556978
60.000000 11.163577 11.117506 11.207085 9.735322 11.156082
80.000000 8.924620 8.888155 8.955971 7.697293 8.860321
100.000000 7.536440 7.506803 7.561882 6.441079 7.451694
200.000000 4.635120 4.619582 4.648057 3.837606 4.576467
400.000000 3.120733 3.114626 3.127560 2.493563 3.133951
600.000000 2.624241 2.623360 2.629518 2.052982 2.655559
800.000000 2.391010 2.393821 2.395757 1.843434 2.405958
1000.000000 2.263132 2.269098 2.267410 1.726202 2.238901
Table 2

Stopping power calculations S total for protons in CH2O

E (MeV) P-STAR Bethe SRIM Ziegler Fitting
0.010000 494.310661 −9683.985505 446.296928 499.627043 494.334134
0.020000 641.315520 −2179.630953 599.764920 657.813526 632.884730
0.030000 732.897649 −414.826196 696.848020 757.324603 743.755651
0.040000 794.896307 241.381134 760.294461 821.251446 811.240859
0.060000 862.277756 680.072487 824.875786 882.009379 865.324761
0.080000 878.233837 786.325852 837.668745 889.237503 865.228799
0.100000 865.341644 800.504891 821.596778 868.551138 842.602288
0.200000 690.376144 666.581649 647.421963 681.380131 679.266994
0.300000 547.833854 548.295165 517.256850 543.233131 554.830893
0.400000 459.209665 466.541808 434.262827 455.451432 468.752303
0.600000 354.736555 363.049876 336.282643 352.228999 360.322271
0.800000 292.797799 300.004077 279.793022 292.024788 295.206079
2.000000 153.021282 155.465757 155.775942 143.022765 151.063578
3.000000 113.093354 114.200885 114.792421 104.889098 111.454155
4.000000 90.758389 91.316911 91.892098 83.705922 89.676935
6.000000 66.162582 66.272278 66.810675 60.492646 65.821309
7.000000 58.564703 58.588295 59.092997 53.366786 58.453637
8.000000 52.653508 52.629557 53.105973 47.841085 52.709591
10.000000 44.032416 43.954497 44.375400 39.799337 44.280858
20.000000 25.116933 25.012828 25.264530 22.284007 25.460894
30.000000 18.069468 17.985140 18.168391 15.825369 18.284972
40.000000 14.327643 14.256646 14.395839 12.418078 14.438326
60.000000 10.378930 10.327377 10.422863 8.851120 10.375166
80.000000 8.303198 8.262388 8.335098 6.990985 8.250953
100.000000 7.015180 6.981879 7.040942 5.844438 6.945145
200.000000 4.320031 4.302580 4.333393 3.468701 4.270656
400.000000 2.911434 2.904381 2.918589 2.242387 2.921977
600.000000 2.449286 2.447912 2.454915 1.839931 2.475156
800.000000 2.232153 2.234794 2.237250 1.648034 2.244625
1000.000000 2.113146 2.119162 2.117762 1.540269 2.093156
Table 3

Stopping power calculations S total for protons in CO2

E(MeV) P-STAR Bethe SRIM Ziegler Fitting
0.010000 343.771031 −10809.304093 298.812444 346.946811 344.559302
0.020000 450.162503 −2907.049342 408.918129 461.589542 441.355255
0.030000 520.397896 −964.027934 484.891121 537.270144 527.168155
0.040000 571.443098 −204.715467 539.554733 589.719571 584.512847
0.060000 635.371031 350.540778 605.786773 649.222265 640.914342
0.080000 661.761222 522.074672 632.131117 669.704493 654.652935
0.100000 664.650771 578.489574 633.149379 667.196624 648.380276
0.200000 560.644150 539.079927 526.484179 554.476247 549.669242
0.300000 457.004913 456.855107 429.733602 452.397475 460.674464
0.400000 389.240519 394.531681 365.161225 383.966534 395.445450
0.600000 305.339237 311.814850 286.709940 301.152607 309.740300
0.800000 253.947765 259.855828 240.567390 251.827641 256.506798
2.000000 135.137529 137.195421 136.773044 127.675592 134.124076
3.000000 100.502645 101.358206 101.693825 94.518305 99.439965
4.000000 80.980619 81.327382 81.814542 75.884211 80.200910
6.000000 59.320406 59.269594 59.821053 55.267350 59.011688
7.000000 52.593071 52.471689 53.008873 48.892646 52.448400
8.000000 47.350299 47.189621 47.704916 43.933044 47.326610
10.000000 39.675693 39.482491 39.946918 36.687563 39.804577
20.000000 22.743753 22.575138 22.860516 20.773514 22.986250
30.000000 16.399169 16.269693 16.479097 14.846922 16.560941
40.000000 13.021876 12.915579 13.074694 11.703167 13.109538
60.000000 9.450311 9.373069 9.483961 8.395945 9.453229
80.000000 7.568938 7.507625 7.592884 6.663106 7.534401
100.000000 6.400023 6.349377 6.418970 5.591608 6.351008
200.000000 3.949921 3.921679 3.959555 3.361284 3.913155
400.000000 2.667642 2.652384 2.672675 2.204828 2.674158
600.000000 2.247275 2.237921 2.251281 1.826208 2.265437
800.000000 2.050273 2.044657 2.053898 1.647228 2.059332
1000.000000 1.942817 1.940044 1.946104 1.548102 1.928846

Figures 13 show the relationship between the stopping force and mass of protons in the molecules CH3OH, CH2O, and CO2, respectively, within the energy range from 0.01 to 1,000 MeV. The calculations were carried out using MATLAB and compared with the international P-Star program to ensure that the results are accurate. To highlight the differences between the curves, the calculations for all curves were multiplied by the coefficients. This was done because the curves were fairly similar, and the numbers indicate a slight increase in the global stopping force within the energy range of 0.01–0.05 MeV. The observed phenomenon can be attributed to the propagation of the nuclear stall, which leads to an increase in the global stall force within the energy range 0.05–0.1 MeV. The maximum mass stopping power is achieved at an energy of 0.085 MeV and then gradually decreases with increasing energy until it reaches its minimum value at 1,000 MeV. The decrease in stopping force value with increasing power is attributed to electronic stopping. Excitation and ionization of atoms occurs at energy levels of 0.05–0.5 MeV due to electronic discontinuity. The Ziegler equation showed excellent agreement with our results, but the Bethe equation failed at low energies.

Figure 1 
               Stopping power calculations S
                  total for protons in CH3OH.
Figure 1

Stopping power calculations S total for protons in CH3OH.

Figure 2 
               Stopping power calculations S
                  total for protons in CH2O.
Figure 2

Stopping power calculations S total for protons in CH2O.

Figure 3 
               Stopping power calculations S
                  total for protons in CO2.
Figure 3

Stopping power calculations S total for protons in CO2.

According to Table 4, the energy range E = 0.06 MeV, V p = 0.3392 × 107 (m/s) had the maximum stopping power, whereas the energy range E = 1,000 MeV, V p = 26.250 × 107 (m/s) had the lowest stopping power. At low energies, a falling particle’s mass stopping power grows as its energy does. This is because when a positively charged particle moves through a material, it interacts with the positive nuclei and negative electrons that make up the substance’s atoms via Columb interactions. Low-energy particles, or those with low velocity, therefore have enough time to interact with nuclei and electrons via inelastic collisions; this may lead to a substantial energy transfer from the moving charged particle to the bound electron through excitation or ionization.

Table 4

Stopping power calculations S total for compounds with velocity of protons

Compound E = 0.06 MeV, V p = 0.3392 × 107 (m/s) × 107 E = 1,000 MeV, V p = 26.250 × 107 (m/s) × 107
d E ρ d x max (MeV cm2/g) d E ρ d x min (MeV cm2/g)
CH3OH 1050.307 2.238
CH2O 865.324 2.093
CO2 654.652 1.928

The range values for protons capable of losing energy throughout their trajectory in CH3OH, CH2O, and CO2 compounds were computed using Equation (7) and recorded in Figures 46. Regarding the statistics or numerical data. It is observed that the tracks are mostly straight because the particles do not vary much during each contact, and interactions happen in all directions at the same time, except at the very end. The range of heavy ions is essentially equivalent to the depth of penetration due to the fact that these highly charged particles move along linear trajectories. The user’s text is presented in the previous study [21]. The range of energy values (102 MeV) increases as the energy values grow.

Figure 4 
               Rang calculations of proton in CH3OH.
Figure 4

Rang calculations of proton in CH3OH.

Figure 5 
               Rang calculations of proton in CH2O.
Figure 5

Rang calculations of proton in CH2O.

Figure 6 
               Rang calculations of proton in CO2.
Figure 6

Rang calculations of proton in CO2.

The stopping time is shown in Figures 79, where the stopping time values for compounds are calculated using Equation (8). The results show that the stopping time is constant in the energy value of 0.02–12 MeV and then increases with increasing proton energy, that is, it increases with the increasing proton energy.

Figure 7 
               Stopping time calculations of proton in CH3OH.
Figure 7

Stopping time calculations of proton in CH3OH.

Figure 8 
               Stopping time calculations of proton in CH2O.
Figure 8

Stopping time calculations of proton in CH2O.

Figure 9 
               Stopping time calculations of proton in CO2.
Figure 9

Stopping time calculations of proton in CO2.

Considering the abundance of formaldehyde in biological fluids, tissues, and the surroundings, the findings of this research may be extrapolated. There is a potential for home building materials to release biological formaldehyde into the environment over time. Formaldehyde is used for sterilization in laboratories dedicated to education, research, and healthcare. Biology has a strong reaction to formaldehyde. The research on carbon dioxide collection and use also examine the correlation between rising carbon dioxide levels and climate change. The conversion of CO2 into liquid fuels or its use as a fuel source for automobiles is of utmost importance. Both natural and synthetic carbon dioxide materials may be manufactured at a low cost and without the need for insulation or air emissions. An example of a such situation is the worldwide demand for 70 million metric tons of methanol in 2015. R1 methanol produces hydrogen and carbon dioxide [2225].

4 The fitting equation

The data were taken from the SRIM2013 and P-STAR program, using the Bethe and Ziegler equations and applied using the MATLAB program. An equation was extracted representing the stopping power in the energy range of 0.01–1,000 MeV and its constants with a fitting equation in Table 5 for the compounds CH3OH, CH2O, and CO2. This formula is considered suitable for computing the electron-stopping energy of these compounds in the range of 0.01–1,000 MeV.

Table 5

Correlation and fitting equation for halting power in CH3OH, CH2O, and CO2 compounds

S fit ( E ) = 1 0 a + bx + c x 2 + d x 3 + e x 4 + f x 5 + g x 6 + h x 7 , where x = lo g 10 ( E )
Compound a b c d e f g h
CH3OH 2.44409 −0.74053 −0.05251 0.07881 −0.05870 0.00341 0.00836 −0.00169
CH2O 2.40086 −0.72204 −0.06773 0.08173 −0.05541 0.00221 0.00819 −0.00161
CO2 2.34284 −0.69367 −0.09433 0.08926 −0.05068 −0.00003 0.00805 −0.00150

5 Conclusions

Experimental results were obtained using the MATLAB program to determine the relationship between the mass stopping forces of protons in CH3OH, CH2O, and CO2, which fall within the energy range 0.01–1,000 MeV, and the variation. Results with those obtained from the P-Star and SRM2013 programs. The results indicate that there is a marginal increase in the mass-stopping potential between 0.01 and 0.05 MeV. This is a result of the fact that stopping the use of nuclear weapons is the most important thing. After that, the block stopping force increases between 0.05 and 0.1 MeV, reaches its maximum value at 0.085 MeV, and then resumes. As the energy level increases, the value gradually decreases until it reaches a minimum of 1,000 MeV.

The decrease in stopping power value with increasing power can be attributed to electronic stopping. Atomic ionization and electronic excitation occur at energies ranging between 0.05 and 0.5 MeV. The matching equation was found, which is considered a suitable equation for calculating the stopping power of organic compounds within the energy range of 0.01–1,000 MeV. In the context of determining the value of the range for protons that may be lost during their path in compounds CH3OH, CH2O, and CO2, it was observed that the paths are mostly linear due to the minimal deviation of molecules during a single encounter and the simultaneous occurrence of interactions in all directions, except in cases where the path reaches His end. The range of heavy-charged particles is approximately equal to their penetration depth due to their linear line of motion. Likewise, for the stopping time, the stopping time values for the compounds were calculated, and it was found that the stopping time remains constant at an energy level ranging from 0.021 to 12 MeV. Still, it later increases with the proton energy. He increases. This article also provided important information for those interested in proton therapy. Subsequent research is encouraged to modify the media and atomic compounds within a similar energy range. In addition, it expands the energy range of the power system.

Suggestions for future work are to change the atomic media such as using light particles as projectiles of the same energy range. The energy range can also be changed to the larger energy range.

  1. Funding information: Authors state no funding involved.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and consented to its submission to the journal, reviewed all the results and approved the final version of the manuscript. AT performed the computations developed for the theoretical formalism, the analytic calculations, and the numerical simulations to the writing of the manuscript. ROK conceived of the presented idea, supervised the project, and contributed to the interpretation of the results.

  3. Conflict of interest: Authors state no conflict of interest.

  4. Data availability statement: The most datasets generated and/or analysed in this study are comprised in this submitted manuscript. The other datasets are available on reasonable request from the corresponding author with the attached information.

References

[1] Turner JE. Atoms, radiation, and radiation protection, third, completely revised and enlarged edition; 2007. 978-3-527-40606-7.Search in Google Scholar

[2] Csete. Experimental investigations of the energy loss of slow protons and antiprotons in matter. M.Sc. thesis. Instute of Physics And Astronomy. University of Aarhus; 2002.Search in Google Scholar

[3] Turner JE. Interaction of ionizing radiation with matter. Health Phys. 2004;86(3):228–52.10.1097/00004032-200403000-00002Search in Google Scholar PubMed

[4] Ahmed I, Nowrin H, Dhar H. Stopping power and range calculations of protons in human tissues. Baghdad Sci J. Article No. 1223, 2020;17.10.21123/bsj.2020.17.4.1223Search in Google Scholar

[5] Usta M, Tufan MÇ, Aydın G, Bozkurt A. Stopping power and dose calculations with analytical and monte carlo methods for protons and prompt gamma range verification. Nucl Instrum Methods Phys Res, Sect A. 2018;897:106–13.Search in Google Scholar

[6] Usta M, Tufan MÇ. Stopping power and range calculations in human tissues by using the hartree-fock-roothaan wave functions. Radiat Phys Chem. 2017;140:43–50.10.1016/j.radphyschem.2017.03.005Search in Google Scholar

[7] Tai H, Bichsel H, Wilson JW, Shinn JL, Cucinotta FA, Badavi FF. Comparison of stopping power and range databases for radiation transport study. NASA Technical Paper 3644; 1997.Search in Google Scholar

[8] Csete A. Experimental investigations of the energy loss of slow protons and antiprotons in matter. Doctoral Dissertation. University of Aarhus; 2002.Search in Google Scholar

[9] Tufan MC, Gümüs H. Stopping power calculations of compounds by using thomas-fermi-dirac-weizsäcker density functional. Acta Phys Pol A. 2008;114:703–11. 10.12693/APhysPolA.114.703.Search in Google Scholar

[10] Usta M, Tufan MÇ, Aydın G, Bozkurt A. Stopping power and dose calculations with analytical and monte carlo methods for protons and prompt gamma range verification. Nucl Instrum Methods Phys Res Sect A. 2018;897:106–13. 10.1016/j.nima.2018.04.045.Search in Google Scholar

[11] Almutairi AS, Osman KT. Mass stopping power and range of protons in biological human body tissues (ovary, lung and breast). Int J Med Phys Clin Eng Radiat Oncol. 2021;11:48–59, https://www.scirp.org/journal/paperinformation.aspx? paperid = 11522110.4236/ijmpcero.111005, 2022.Search in Google Scholar

[12] Tufan MÇ, Gumus H, Namdar T. Stopping power and CSDA range calculations for incident electrons and positrons in breast and brain tissues. Springer-Radiat Environ Biophys. 2013;246:196–203. 10.1007/s00411-013-0457-x.Search in Google Scholar PubMed

[13] Krane K. Introductory nuclear physics. Oregon: Oregon state University; 1987.Search in Google Scholar

[14] Hadi SM. Stopping power and range for proton interaction with lymph tissues. Int J Environ Eng Educ. 2021;3(3):110–4.10.55151/ijeedu.v3i3.57Search in Google Scholar

[15] Singh M, Singh L. Electronic stopping power of various organic compounds for proton (0.05–10 mev): a comparative study. Mater Phys Mech. 2011;12:43–57.Search in Google Scholar

[16] Almutairi AS, Osman KT. Calculated mass stopping power and range of protons in biological human body tissues (ovary, lung and breast). Int J Med Phys Clin Eng Radiat Oncol. 2022;11:48–59.10.4236/ijmpcero.2022.111005Search in Google Scholar

[17] Jassim WN. Study of proton stopping power in Be, C, Al and Cu with energy (1-12) MeV. Int J Sci Res. 2015;4:874–7.Search in Google Scholar

[18] Bethe H. Theory of the passage of fast corpuscular rays through matter. Ann Phys (Leipz,). 1930;5:325–400.10.1002/andp.19303970303Search in Google Scholar

[19] Turner JE. Atoms, radiation and radiation protection. Weinheim: Wiley-VCH Verlag GmbH & Co.; 2007.10.1002/9783527616978Search in Google Scholar

[20] Sigmund P. Charge – dependent electronic stopping of swift nonrelativistic heavy ions. Phys Rev. 1997;56(5):3781.10.1103/PhysRevA.56.3781Search in Google Scholar

[21] Ziegler JF, Biersack JP. The stopping and range of ions in matter. In: Treatise on heavy-ion science, Volume 6: Astrophysics, chemistry, and condensed matter. Boston, MA: Springer US; 1985. p. 93–129.10.1007/978-1-4615-8103-1_3Search in Google Scholar

[22] Knoll, GF. Radiation detection and measurement. 3th edn. John Wiley & Sons; 1979Search in Google Scholar

[23] WHO. Concise International Chemical Assessment Document 40: Formaldehyde. Geneva: World Health Organization; 2002.Search in Google Scholar

[24] Donovan J, Skotnicki-Grant S. Allergic contact dermatitis from formaldehyde textile resins in surgical uniforms and nonwoven textile masks. Dermatitis. 2007;18:40–4.10.2310/6620.2007.05003Search in Google Scholar PubMed

[25] Richard AR, Fan M. Low-pressure hydrogenation of CO2 to CH3OH using Ni-In-Al/SiO2 catalyst synthesized via a phyllosilicate precursor. ACS Catal. 2017;7(9):5679–92.10.1021/acscatal.7b00848Search in Google Scholar

Received: 2024-01-24
Revised: 2024-03-28
Accepted: 2024-04-07
Published Online: 2024-09-20

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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