Stopping Power and Range Calculations of Electrons Interaction with CH3OH, CH2O and CO2

Ion implantation, particle physics, nuclear physics, radiation damage, and radiology are just a few of the fields that have benefited from the knowledge of charged particles' propensity to slow down and release energy. This understanding has been the subject of a substantial amount of attention over the course of the last century [1].

To precisely estimate how intermediate energy neutrons deposit energy in tissue, it is essential to comprehend the stopping capabilities and projected ranges of secondary charged particles of low energy [2].

In several fields of study and application, an understanding of the properties of ion behavior in diverse materials—such as air, tissue, and polymers—is essential. These include nuclear physics, radiation chemistry, radiation dosimetry, radiation biology (including cell mortality, cytogenesis alterations, mutagenesis, and DNA recombination), and radiotherapy. The stopping power of charged particles can be determined using a variety of methods, including self-supporting techniques, studying backscattering from the substrate with deposited absorbing layers, measuring energy loss through films directly, analysing gamma resonance shift, and indirectly verifying stopping power based on alpha energy losses in air [3].

The total mass specific energy (SPE) of an electron refers to the average energy loss per unit distance due to radiation, ionization, and excitation [4]. In the analysis of the SPE, it is crucial to quantify two distinct processes of energy loss: first, from electron collisions with the target's extra electrons (collisional SPE), and second, from interactions with the target's nuclear field (radiative SPE). The second component is crucial for light particles as its worth escalates with elevated energy levels [5].

The understanding of radiation's interaction with matter This will facilitate the determination of dose limits and enhance protection, as radiation therapy is based on diverse radiation types and their interactions with matter, energy dissipation, and the exposure levels permissible for the human body during medical procedures, accidents, or natural radioactivity.

A plethora of studies have been undertaken by many researchers on this topic. Tufan et al. [5] quantified the route length and stopping power of electrons with energies between 100 eV and 1 GeV in certain biological substances. El-Ghossain [6] calculated of electron interaction range and stopping power with various materials and human body parts. Evaluating the findings of Gümüs [7] on electron stopping power and range in materials like water and bone against the Penelope and ESTAR codes [8, 9]. Kadhim and Yassin [10] quantified the total electron-stopping power in human tissues (bone, brain, and eyes) at energy levels between 0.01 and 1000 MeV using the relative Beth–Bloch equation. Alina Kononov et al. [11] studied the repeatability of real-time time-dependent density functional theory calculations of electronic stopping power in warm dense matter in 2024.

This research constitutes a theoretical examination of the stopping capability of these organic compounds, applicable in medical and radiotherapeutic contexts.

Understanding the interactions of radiation with various materials Considering that radiation therapy relies on the interactions between different radiation types and matter, energy dissipation, and the radiation exposure levels individuals may experience during medical procedures, accidents, or natural radioactivity, this will facilitate the establishment of dose limitations and enhance protective strategies [5].

The aim of this research endeavor is to assess the halting power of the electron projectile and illustrate the magnitude of its impact on vehicles, and determine a mathematical equation that describes this behavior and mentions within the energy range the stopping power and stopping range. Which represent the average unit of energy dissipation to which charged particles are exposed along their path and the distance the radiation travels, respectively [12].

The Bethe formula for molecules was utilized to calculate the stopping power and stopping range. Tables 1-3 as well as Figures 1-3 provide the calculated values. The electron energy range considered was from (0.01 to 1000) MeV. The Bethe equation was employed for three different organic compounds CH₃OH, CH₂O and CO₂.

The computation of stopping power applies to electrons traveling through matter in the same way as it applies to particles that are significantly charged. The "Collisional Stopping Power" is a representation of the interaction between incoming electrons and atomic electrons that leads to excitation and ionization. This interaction is calculated using Bethe's theory. Additionally, electromagnetic radiation often referred to as "Bremsstrahlung" is created when electrons are accelerated inside the coulomb field of nuclei. The stopping power that corresponds to the phrase "Radiative Stopping Power" is referred to by the word [21].

Table 1. Calculations of stopping power S_total for electron in CH₃OH

Table 2. Calculations of stopping power S_total for electron in CH₂O

Table 3. Calculations of stopping power S_total for electron in CO₂

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Figure 1. Calculations of stopping power S_total for electron in CH₃OH

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Figure 2. Calculations of stopping power S_total for electron in CH₂O

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Figure 3. Calculations of stopping power S_total for electron in CO₂

The graphical representations of the halting power calculations conducted on CH₃OH, CH₂O, and CO₂ are depicted in Figures 1-3, respectively. The MATLAB software was employed to perform these computations, and the results obtained were agreed to those obtained from the E-Star software. It is evident that the results of the present investigation and ESTAR [22] are in substantial agreement.

To emphasize the differences between the curves, coefficients were used to enhance them, since they were originally similar. A significant increase in stopping power was seen for electron energies ranging from 10 MeV to 1 MeV. The stopping power exhibits a gradual decline with increasing energy, finally reaching a value of 1 MeV, which is within the specific range of (10^-2 to 1) MeV. A retarding force is generated when electrons from the target material impede electrons from the projectile. A decrease in stopping power arises from reduced attenuation in this area, attributable to an increase in the energy of the emitted electron. The energy in this area is inversely related to the stopping power. The braking mechanism generates the stopping force by transferring electrons from the medium to the projectile.

The atomic number of the target material may elucidate, especially about radiative stopping power. Moreover, stopping power is influenced by the value, particularly for targets with high atomic numbers.

Table 4 indicates that the maximum stopping power occurred at an energy level of 2 MeV and an electron velocity of 29.37 m/s, while the minimum stopping power was seen at an energy level of 1000 MeV and an electron velocity of 29.99 m/s. As the energy of a particle increases at low energy levels, the mass stopping power of the particle escalates correspondingly. When a positively charged particle traverses a material, it interacts via Coulomb forces with the negatively charged electrons and positively charged nuclei constituting the atoms of that substance. This is the rationale for the occurrence of this event. Consequently, low-energy particles (low velocity) possess sufficient time to engage with electrons and nuclei via inelastic collisions. This interaction may lead to a significant transfer of energy from the moving charged particle to the bound electron via ionization or excitation. This signifies that a high-energy particle has a reduced duration for interacting with atomic electrons and nuclei, leading to less energy loss, even when it has strong stopping power at lower energy levels. The CH₃OH molecule had the maximum stopping power, measured at 1.913869.

Table 4. Stopping power calculations S_total for compounds with velocity of electrons

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Figure 4. Calculations of stopping rang for rang of electron in CH₃OH

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Figure 5. Calculations of stopping rang for rang of electron in CH₂O

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Figure 6. Rang calculations of electron in CO₂

In order to determine the range value of electrons that may be lost along their journey in compounds CH₃OH, CH₂O, and CO₂, Eq. (4) was used. This was done for the aim of estimating the overall range value. The data that was gathered as a result of this are shown in Figures 4-6. After analyzing the data, it was discovered that the paths tended to be straight at energy levels ranging from 0.01% to 1.01% MeV. This was brought to light by the findings of the investigation. This might be explained by the fact that during a single touch, the molecules do not move much apart from one another, and interactions take place simultaneously in all directions. As a consequence of this, the range begins to expand as the energy level rises from 12 MeV to more than 1000 MeV.