The mean excitation energy for stopping power I, the Bragg rule, and chemical and phase effects. Application of a statistical treatment to the determination of I for chemically bound particles

Electronic Excitation Dynamics in Liquid Water under Proton Irradiation

“…At a scientific level, the Bragg curve profile is determined by the electronic stopping power (also known as unrestricted linear energy transfer), which measures the rate of energy transfer from the charged particle to electrons in matter per unit distance of the energetic particle’s movement678910. The stopping power is a continuous function of the particle velocity (or kinetic energy), and the velocities nearest to the maximum of the stopping power are responsible for the formation of the sharp Bragg peak.…”

Ion-Type Dependence of DNA Electronic Excitation in Water under Proton, α-Particle, and Carbon Ion Irradiation: A First-Principles Simulation Study

“…Linear response theory is widely used for determining the stopping power, and it is of interest to examine this approximate description in the light of our first-principles dynamics result. The observed shift in the Bragg peak velocity among different projectile ions is beyond the description based on linear response (LR) theory, which can be expressed as S ( v ) = 4 π Z 2 v 2 L ( v ) where S ( v ) is the electronic stopping power, v is the projectile ion velocity, and L ( v ) is the velocity-dependent term known as the stopping logarithm. , There exist a number of different expressions for the stopping logarithm, , which incorporates information on the target material only. Generally, in LR theory, the charge of the projectile ion is treated as a velocity-independent quantity and ions are assumed to be fully ionized. , This assumption leads to well-known issues such as incorrectly predicting the same Bragg peak position for all ions. ,, Instead, the ion charge can be treated as a function of the ion velocity, Z ( v ), being equal to the mean charge for each ion in liquid water for this study.…”

“…where S(v) is the electronic stopping power, v is the projectile ion velocity, and L(v) is the velocity-dependent term known as the stopping logarithm. 73,74 There exist a number of different expressions for the stopping logarithm, 75,76 which incorporates information on the target material only. Generally, in LR theory, the charge of the projectile ion is treated as a velocityindependent quantity and ions are assumed to be fully ionized.…”

Beam–plasma interaction experiments using electromagnetically driven shock waves

“…Here we evaluate the dissociation effect on the stopping power of hydrogen gas for low-energy protons. To evaluate the mean excitation energy of hydrogen atom and molecule, we used a local plasma approximation [21]. This approximation treats atomic electrons as a free electron gas confined in an attractive potential induced by nuclear charge, which gives distributions of atomic potential and electron density in a reasonable accuracy.…”