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Particle and Nuclear Physics

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Prerequisites

ArithmeticLogic
GeometryAlgebra
TrigonometryFunctions
VectorsLimits
Physics IMatricesDerivatives
Physics IIRelativityEigenvaluesIntegrals
Electricity and MagnetismQuantum Physics I
Particle and Nuclear Physics

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Prerequisites and outcomes

This note assumes special relativity, introductory quantum mechanics, and conservation-law reasoning. By the end, you should be able to test reactions for kinematic and charge constraints, compute decay quantities from mass differences or half-lives, and distinguish a measured cross section from a probability for one particular event.

1. Scales and constituents

Particle physics studies elementary constituents and their interactions. Nuclear physics studies protons, neutrons, nuclei, and the reactions that change them. Relativistic quantum mechanics is needed because particle creation and annihilation are possible.

The Standard Model contains matter fermions and force bosons. Quarks combine into hadrons such as protons and neutrons; leptons include the electron and neutrinos. The strong, electromagnetic, and weak interactions are described within the Standard Model. Gravity is not included in it.

2. Relativistic kinematics

Energy and momentum satisfy

$$ E^2=p^2c^2+m^2c^4. $$

For a particle at rest, $E_0=mc^2$. In a collision, the invariant mass of a system is determined by the total four-momentum, making it more useful than ordinary kinetic energy for relativistic reactions.

Conservation of energy, momentum, angular momentum, electric charge, and other applicable quantum numbers constrains every reaction. A reaction is possible only if all required conservation laws are satisfied.

3. Nuclei and binding energy

A nucleus with $Z$ protons and $N$ neutrons has mass number $A=Z+N$. Its binding energy is the mass defect converted to energy:

$$ B=\left[Zm_p+Nm_n-m_{\text{nucleus}}\right]c^2. $$

The semi-empirical mass formula estimates nuclear binding through volume, surface, Coulomb, asymmetry, and pairing terms. Binding energy per nucleon is large near iron, so fusion of light nuclei and fission of heavy nuclei can release energy.

4. Radioactive decay

Radioactive decay is probabilistic. If $N$ nuclei remain,

$$ N(t)=N_0e^{-\lambda t}, \qquad A(t)=\lambda N(t), \qquad t_{1/2}=\frac{\ln2}{\lambda}. $$

Alpha decay emits a helium nucleus. In beta-minus decay a neutron changes into a proton while an electron and electron antineutrino are emitted; beta-plus decay changes a proton into a neutron while emitting a positron and electron neutrino. Gamma decay emits electromagnetic radiation from an excited nucleus. Energy, charge, and lepton-number bookkeeping identify the allowed daughter products.

5. Scattering and detectors

Scattering experiments infer small-scale structure from changes in momentum and angle. Cross section measures the effective likelihood of an interaction:

$$ \text{rate}=\text{luminosity}\times\sigma. $$

Detectors may track charged particles, measure deposited energy, identify time of flight, or detect missing momentum carried by weakly interacting particles. Accelerators increase collision energy; colliders can convert beam energy into new particles.

6. Problem-solving workflow

  1. Draw the initial and final particles and assign charges and quantum numbers.

  2. Apply conservation laws before using dynamics.

  3. Use invariant energy for relativistic collisions and mass differences for decays.

  4. Check threshold energies, units, and whether the result is physically allowed.

Summary

Particle and nuclear physics uses conservation laws, relativistic kinematics, and measured decay or scattering patterns to connect fundamental interactions with the structure of matter.