(unit1:terms)=
# Unit 1 : Equations & Terms

## Equations
To aid with exam revision below is a list of all equations that you should learn for this unit in the course.

**Atomic Mass Unit**
```{math}
\begin{equation}
u = 1.66056\times 10^{-27}~\textnormal{kg} = 931.5 \textnormal{MeV/c}^2.
\end{equation}
```

**Nuclear Mass Deficit**
```{math}
\begin{equation}
\Delta M(A,Z) = M(A,Z) - (ZM_{p} + NM_{n} + Zm_{e}).
\end{equation}
```

**Binding Energy Equation**
```{math}
\begin{equation}
-\Delta M(A,Z) = B
\end{equation}
```

**Nuclear Mass Density**
```{math}
\begin{equation}
\rho_{m} = \frac{M}{V} = \frac{3m_{n}}{4\pi r^{3}_{0}}
\end{equation}
```

**Nuclear Charge Density**
```{math}
\begin{equation}
\rho_{c} = \frac{Q}{V} = \frac{3Ze}{4\pi r^{3}_{0} A}\\
\end{equation}
```

**Cross-sectional Area**
```{math}
\begin{equation}
\sigma = \pi (2R)^{2}
\end{equation}
```

**Mean Free Path**
```{math}
\begin{equation}
\lambda = \frac{1}{n\sigma}.
\end{equation}
```

**Beam Intensity Reduction in Target**
```{math}
\begin{equation}
N = N_0 e^{-x/\lambda}
\end{equation}
```

**N Collisions in Target**
```{math}
\begin{equation}
C=N_0-N=N_0(1-e^{-x/\lambda}).
\end{equation}
```

**Rutherford Scattering**
```{math}
\begin{equation}
\frac{d\sigma}{d\Omega_{R}} = \frac{z^{2}Z^{2}\alpha^{2}\hbar^{2}c^{2}}{4E^{2}} \frac{1}{sin^{4}(\theta/2)} \\
\end{equation}
```
- $z$ is the charge of the projectile.
- $Z$ is the charge of the scatterer.
- $E$ is kinetic energy of the particle
- $\theta$ is the scattering angle
- $\alpha$ is the **fine structure constant**

**Mott Scattering Form**
```{math}
\begin{equation}
\frac{d\sigma}{d\Omega_{M}} = \frac{d\sigma}{d\Omega_{R}} \times [1-\beta^{2} sin^{2} (\theta/2)]
\end{equation}
```
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## Terms
For the following terms you should have a basic understanding of what they are for the course.
- Nuclear Reactions, Radioactive Isotope, Half-Life
- Quarks, Leptons, Deuterons
- Alpha, Beta, Gamma, Fission, Fusion, ITER
- Marie Curie, Radium, Radon Damage
- Radium, Radon Gas, NORMs, Gray, Sievert, Q-Value
- Ununoctium, Line of Stability, Binding Energy, Nuclear Mass
- Atomic Mass, Nucleons, Unified Mass Constant, Mass Deficit
- Scattering Experiments, Interaction Cross-section
- Cross-section Area, Mean Free Path, Thin Target Approximation
- Total Cross Section, Partial Cross Section, Differential Cross Section
- Scattering Angles, Isotropic Scattering, Rutherford, Incompressible Nuclei
- Rutherford Scattering, Mott Scattering, Hofstadter Experiment
- Nuclear Recoil, Electron Scattering Experiments, Top-Hat Nuclear Distribution -->