Interaction Cross-Section

1.

Interaction Cross-Section
Concept and Application in Nuclear Physics

2.

Definition
The interaction cross-section is the probability of interaction of ionizing particles with one atom,
an electron, the nucleus of an atom, or all the atoms (electrons, nuclei) located in a given volume
of matter..

3.

Historical Context
Rutherford Experiment (1909): α-particle scattering on gold nuclei
Rutherford Formula: description of elastic Coulomb scattering
Concept Introduction: cross-section as measure of process probability
Theory Development: quantum mechanics and nuclear physics

4.

Physical Meaning
Geometric Interpretation
If a particle were a solid sphere, σ would equal the cross-sectional area of that sphere
Probabilistic Interpretation
The larger σ, the higher the probability of interaction upon particle collision

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Main Formula
σ = N / (n × Φ)
N — number of particles interacting with the target
n — number of target nuclei per unit area
Φ — incident particle flux density

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Types of Cross-Sections
Total (σ_total): sum of all processes
Elastic Scattering: without particle energy change
Inelastic Scattering: with internal state change
Absorption/Capture: particle is absorbed by the nucleus

7.

Units of Measurement
Primary unit: barn (b)
1 barn = 10⁻²⁴ cm² = 10⁻²⁸ m²
Order of magnitude comparable to nuclear cross-sectional area
Name derived from the phrase "big as a barn"

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Energy Dependence
Neutron Capture: σ ∝ 1/v (inversely proportional to velocity)
Scattering: depends on type of interaction
Threshold Effects: emergence of new channels above certain energy
Resonances: significant σ increase at specific energies

9.

Practical Applications
Nuclear Energy
Chain reaction control in reactors
Radiation Protection
Shielding and safety calculations
Experimental Physics
Analysis of particle collision results

10.

Key Takeaways
Interaction cross-section is a fundamental characteristic of collision probability in particle physics