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The scattering of neutrinos assuming a "secret" interaction at low energy isconsidered. To leading order in energy, the two-body potential is a$\delta$-potential, and it is used as a motivation to study generic short-rangeelastic interactions between neutrinos. The scattering cross section andSommerfeld enhancement depend on two phenomenological parameters deriving fromthe exact form of the potential, akin to "renormalized" coupling constants.Repulsive potentials lead to a decrease in the total cross section, resultingin an enhancement of the neutrino density. For attractive potentials of theright form, substantial Sommerfeld enhancement can appear.

Cosmic Four-Fermion Neutrino Secret Interactions, Enhancement and Total Cross Section