# Stopping Power

### Basic Information

Definition: Stopping power refers to the energy loss by charged particles per unit path length of a material.

Symbol: $$S(E)$$

Equation: \begin{equation}S(E) = \frac{-dE}{dx}\end{equation}

Range (R) is related to stopping power as:
\begin{equation} R = \frac{E}{\frac{-dE}{dx}} = \frac{E}{S(E)} \end{equation}

Mass Stopping Power $$(\frac{S}{\rho})$$: Stopping power is commonly presented as mass stopping power which is the ratio of stopping power to the material density.

### Key Points

Stopping power is a property of the material that the charged particles are passing through.

Stopping power is proportional to the square of the particles charge and inversely proportional to the square of the particle’s velocity.

\begin{equation} \frac{dE}{dx} \propto \frac{z^2}{v^2} \end{equation}

Stopping power tends to vary slowly with energy for relativistic particle energies because of its proportionality to velocity. At lower energies, where velocity varies directly with energy, stopping power varies significantly with energy, giving rise to a Bragg peak.

### Restricted Mass Collision Stopping Power (L/ρ)

\begin{equation} \frac{\bar{L}}{\rho} = \frac{\int_{\Delta}^{E_0} \Phi(E) \cdot \frac{L}{\rho}(E)dE}{ \int_{\Delta}^{E_0} \Phi(E) dE } \end{equation}

• Δ corresponds to the energy required for an electron to cross the cavity.
• Δ is typically taken to be 10-20keV.
• Electrons with energy <Δ are assumed to deposit their energy where created.
• Electrons with energy >Δ dissipate their energy through the Continuous Slowing Down Approximation (CSDA).

Key Point: Restricted Mass Collision Stopping Power introduces a cutoff energy Δ.

Mass Stopping Power Approximations

ParticleMass Stopping Power (MeV-cm2/g)
Electron2
Proton50 (for 10MeV proton)
Alpha Particle1,000 (for 5MeV alpha particle)