Trajectory-Dependent Proton Stopping Power in Lithium Fluoride

The stopping power of particles, or how much energy they lose as they pass through a material, has been a subject of research for many years. Most studies have centered on how this energy loss is related to the particle’s speed. When a proton moves quickly, it interacts mainly with the material’s electrons, a process known as electronic stopping. At slower speeds, however, the particle begins to interact more with atomic nuclei, and the dynamics shift. A long-standing question in this field is whether there is a specific velocity threshold where electronic stopping becomes negligible. This question becomes especially intriguing in insulating materials like lithium fluoride (LiF), which have wide energy gaps. Protons moving at low speeds might not have enough energy to excite electrons across this gap, leading to very little energy loss. But studying these effects in solid materials, as opposed to simpler gaseous systems, presents unique challenges because the structured nature of solids adds layers of complexity. On top of this, the path that a proton takes through the material—its trajectory—plays a critical role. A proton passing close to an atomic nucleus will interact much more strongly with the electrons than one that travels through a more open area of the material. This means the stopping power does not just depend on how fast the proton is moving; it also depends on exactly where it travels within the material. This trajectory-dependent behavior makes it even harder to create a universal model for predicting how energy is lost in different materials.

To tackle these unanswered questions, new research paper published in Physical Chemistry Chemical Physics and conducted by Ya-Ting Sun, Cong-Zhang Gao and led by Professor Feng Wang from the School of Physics at Beijing Institute of Technology focuses on the relationship between a proton’s trajectory and its stopping power, specifically looking at how these dynamics change in lithium fluoride nanosheets. LiF is an ideal material for this study because its wide band gap makes it interesting for investigating low-energy interactions. Using advanced computational tools, the team combined time-dependent density functional theory (TDDFT) with molecular dynamics simulations to examine proton interactions in unprecedented detail. The researchers simulated how protons travel through LiF nanosheets at a range of velocities, from very slow to moderately fast. They examined three distinct types of trajectories: one where protons passed directly near the atomic nuclei, another at intermediate distances, and a third further away from the nuclei, moving through the open spaces of the lattice structure. These differences in trajectory were essential to explore because earlier studies had hinted that a proton’s stopping power—how much energy it loses—depends not just on its speed but also on the specific path it takes through the material.

One of the standout discoveries was a velocity-dependent threshold in energy loss, but only for protons traveling further from the nuclei. When these protons moved slowly, they did not excite enough electrons to lose significant energy. This behavior matched expectations given LiF’s wide band gap, which makes it harder for low-energy protons to transfer energy to electrons. On the other hand, protons passing very close to the nuclei showed no such threshold effect. Even at low speeds, these protons managed to excite deeper valence electrons, bypassing the band gap limitations. This finding challenges the traditional assumption that velocity alone determines stopping power, highlighting just how critical the trajectory is in these interactions. Another fascinating observation was how the protons lost energy as they moved through the material. The researchers noticed that energy loss was most rapid at the very start when the protons enter the nanosheet and they attributed this to intense interactions between the protons and electrons which caused significant disturbances in the material’s electronic structure. As the protons continued through the nanosheet, the energy loss became steadier and more balanced, as the system reached a kind of equilibrium between electron excitations and damping effects. Moreover, the authors showed interesting details about how protons captured electrons during their journey with protons traveling closer to nuclei, fewer electrons were captured, as many of the tightly bound electrons near the nuclei were inaccessible. In contrast, protons passing further from the nuclei captured more electrons, mainly from the fluorine atoms in the lattice. According to the authors, this subtle but important variation emphasized the complex relationship between a proton’s path, electron dynamics, and energy transfer in materials like LiF. The team’s time-resolved simulations also painted a detailed picture of how the material’s electronic states changed as the protons moved through. Early in the interaction, the protons primarily excited shallow electrons, which caused ripples in the material’s electron density. As the protons progressed, deeper electrons became involved, especially in trajectories that brought the protons closer to the nuclei. By the time the protons exited the nanosheet, the material’s conduction band had been noticeably altered, showing how the interactions left a cumulative effect on the electronic structure. The crystalline nature of the nanosheets added yet another layer of complexity. The researchers observed periodic fluctuations in energy loss, tied to the arrangement of atoms in the lattice. These oscillations showed that the nanoscale structure of LiF plays a significant role in how energy is transferred, proving that materials like these cannot simply be treated as uniform or homogeneous.

In conclusion, Professor Feng Wang and his team have uncovered something deeply informative about how protons interact with insulating materials like LiF at the nanoscale and studied the relationship between a proton’s trajectory and how energy is transferred, showing us that the path a proton takes is just as important as its speed. For decades, scientists have focused almost entirely on velocity when studying stopping power—the rate at which particles lose energy as they travel through a material. This study, however, demonstrates that the story is far more complex, and these new findings challenge long-held assumptions while filling important gaps in our understanding.

One of the most practical takeaways from this research is its potential to reshape how we think about radiation shielding. Materials like LiF are already used in environments that are bombarded by charged particles, such as spacecraft and radiation therapy systems. By understanding how a proton’s trajectory affects its energy loss, engineers can design shielding materials that are far more effective. For example, tweaking the thickness or crystalline structure of LiF layers could make them better at absorbing or deflecting high-energy protons which will ultimately improve both safety and system performance. Additionally, proton therapy for cancer which is one of the most precise forms of radiation treatment, the results provided a clearer picture of how protons lose energy as they interact with tissues or materials inside the body and by this open the door to more refined control over how deeply protons penetrate. With this level of precision, doctors could deliver powerful doses directly to tumors while reducing the impact on surrounding healthy tissue. The research’s focus on trajectory dependence could inspire new methods for optimizing these therapies, making them even safer and more effective. Furthermore, the work is also incredibly relevant for nanotechnology. As devices like sensors and transistors shrink to nanoscale dimensions, they become more sensitive to the effects of charged particles. The detailed modeling in this study could help scientists design materials that are more resilient to radiation and high-energy impacts such as in space exploration or high-radiation industrial settings.