**Barn** The SI unit of measurement for the cross section, \(1~\mathrm{b}=10^{-28}\) m\(^2\)

**Collision length** The distance over which the number of incident particles interacting with scattering centers, uniformly distributed in a volume, are reduced by a factor of \(e\simeq 2.7\)

**Compton scattering** Elastic scattering of light off particles

**Cross section** Effective area or scattering probability off a target center, measured in barn

**Elastic collision (relativistic)** A collision that leads to the same particles as the initial state

**Energy-momentum vector** A four-vector containing the energy and momentum components of a particle

$$\begin{aligned} \underline{q}=\left( E/c,\mathbf {p}\right) \end{aligned}$$

**Invariant mass** For a set of particles, the same as

*Mass of a set of particles* **Kinetic Energy (classical)** Scalar quantity (

*T*) defined by:

$$\begin{aligned} T = \frac{1}{2}m\mathbf {v}^2=\frac{\mathbf {p}^2}{2m}, \end{aligned}$$

where

*m* is the mass,

\(\mathbf {v}\) is velocity and

\(\mathbf {p}\) is momentum

**Length contraction** Relativistic effect seeing lengths change between two reference frames moving with relative speed

*v* parallel to the measurement direction. The equation:

$$\begin{aligned} \varDelta l=\frac{1}{\gamma }\varDelta \ell \end{aligned}$$

relates the length

\(\varDelta \ell \) measured at rest with the length

\(\varDelta \ell \) measured in the moving frame

**Mass of a set of particles (also Invariant mass)** The Lorentz-invariant quantity

*M* obtained from the modulus of the energy-momentum vector of the particles system:

$$\begin{aligned} \underline{P}^2=M^2 = \left( \sum _{i=1}^{n} E_i\right) ^2-\left( \sum _{i=1}^{n}\mathbf {p}_i\right) ^2, \end{aligned}$$

where

*i* is the particle index and

\(E_i\),

\(\mathbf {p}_i\) are the particles energy and momentum, respectively

**Mean free path** See *Collision length*

**Momentum (classical)** Three-dimensional vector obtained from the product of mass

*m* and velocity

\(\mathbf {v}\):

$$\begin{aligned} \mathbf {p}=m\mathbf {v} \end{aligned}$$

**Relativistic** \(\beta \) The ratio

$$\begin{aligned} \beta ={{\textsf {\textit{v}}}}/c, \end{aligned}$$

between the an object speed,

\({{\textsf {\textit{v}}}}\), and the speed of light,

*c*, and is bound to values between 0 and 1

**Relativistic** \(\gamma \) The quantity defined as

$$\begin{aligned} \gamma =1/\sqrt{1-\mathbf {\beta }^2}, \end{aligned}$$

taking values between 1 and infinity (ultra-relativistic)

**Relativistic kinetic energy** For a particle moving with relativistic

\(\gamma \), the kinetic energy is given by the expression

$$\begin{aligned} T= \left( \gamma -1\right) m_0c^2, \end{aligned}$$

where

\(m_0\) is the rest mass and

*c* is the speed of light

**Relativistic momentum** For a particle moving with relativistic

\(\gamma \), the momentum is given by the product:

$$\begin{aligned} \mathbf {p} = \gamma m_0\mathbf {v}, \end{aligned}$$

where

\(m_0\) is the rest mass and

\(\mathbf {v}\) is the velocity

**Relativistic total energy** For a particle moving with relativistic

\(\gamma \), the total energy is given by the expression

$$\begin{aligned} E = T+m_0c^2 = \gamma m_0 c^2 = \sqrt{\left( \mathbf {p}c\right) ^2+\left( m_0c^2\right) ^2} \end{aligned}$$

where

\(m_0\) is the rest mass,

*c* is the speed of light,

\(\mathbf {p}\) the relativistic momentum

**Rest energy** The energy of a particle at rest, also written as

$$\begin{aligned} E=m_0c^2 \end{aligned}$$

**Rest mass** The ratio between the energy of a particle at rest and the constant factor

\(c^2\) **Time dilation** Relativistic effect seeing time intervals change between two reference frames moving with relative speed

*v*. The equation:

$$\begin{aligned} \varDelta t=\gamma \varDelta \tau \end{aligned}$$

relates the time interval

\(\varDelta \tau \) measured at rest with the time interval

\(\varDelta t\) seen by a frame moving with relativistic speed

\(\gamma \)