Cross sections
Purely leptonic reactions: calculated total cross sections
Neutrinos interact only by the weak force: hence the reaction cross
sections are much smaller than those of other particle species.
For electron neutrinos the elastic scattering with electrons can
be mediated by charged and neutral weak bosons (W and Z), whereas
the scattering of muon and tau neutrinos from electrons is mediated only
by the neutral boson. Hence the differences of the total cross sections.
The inelastic scattering processes are caused only by the charged currents.
The cross section formulae for tau neutrinos are the same as for muon neutrinos.
| Elastic scattering | Inelastic scattering |
|---|---|
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Neutrino reactions with nucleons and nuclei
The cross sections for neutrino-nucleon scatterings are not so precisely known as for leptonic reactions. This is due to the poor theoretical knowledge of the nucleon form factors.Neutrino-nucleon inelastic cross sections:
For energies < 1 GeV:
At low energies the neutrino-nucleon cross sections acquire the
following form, where Q = 1.3 MeV is the nucleon mass difference and
theta(E-Q) is just the threshold function:
| Neutrino-nucleon | Antineutrino-nucleon |
|---|---|
 |
 |
| The vector and axial-vector coefficients
have values g_V = 1 and g_A = 1.23. Hence the multiplier in the equations has the value  |
For very high energies (50 GeV < E < 250 GeV) the neutrino-nucleon inclusive cross sections are approximately:
| Neutrino-nucleon | Antineutrino-nucleon |
|---|---|
 |
 |
For energies around 1...10 GeV the cross sections are not so accurately
known:
Below is a plot of different experimental results for the muon and
antimuon -neutrino total cross sections. (Taken from K.
Hagiwara et al., Phys. Rev. D 66 (Review of
Particle Physics 2002))
| Neutrino-nucleon elastic c.s. |
|---|
 |
These are valid for all neutrino species.
For more detailed cross section information (differential cross sections, etc.) see Appendix chapter 4.3.2.
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