\[\sigma_{\mathrm{tot}}=\sigma_1+\sigma_2+\sigma_3+\cdots\]
Variables
sigmat[σtot]total cross section
sigma1[σ₁]partial cross section for channel 1
sigma2[σ₂]partial cross section for channel 2
sigma3[σ₃]partial cross section for channel 3
Description
What is this formula?
The total cross section formula calculates the total interaction probability by summing the partial cross sections of all possible interaction or decay channels.
When to use it
Use this formula when analyzing scattering processes, particle interactions, nuclear reactions, or decay channels with multiple possible outcomes.
Example
An interaction has three measured partial cross sections:
sigma1 = 2.5
sigma2 = 1.8
sigma3 = 0.7
Formula:
sigmat = sigma1 + sigma2 + sigma3
Substitution:
sigmat = 2.5 + 1.8 + 0.7
Result:
sigmat = 5.0
The total cross section is 5.0 in units consistent with the partial cross sections.
Applications
Particle collisions, nuclear reactions, scattering experiments, detector analysis, branching channel studies, and accelerator physics.