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Assuming that neutrinos have non-vanishing magnetic moments, we discuss thepossibility of pair production through annihilation of charged fermions inhigh-energy collisions. Adopting the Pauli interaction for photon-neutrinocoupling, we calculate the neutrino pair production cross section in the photonchannel and compare the result with the standard model in $ Z^{0} $ channel. wedemonstrated that the enhancement of the production rate for Majorana neutrinopairs over the standard model rate can be possible at the center-of-mass energyof $10 - 100$ TeV for the Large Hadron Collider or the ultra-high-energy cosmicRay when the transition magnetic moment is not smaller than $10^{-9} - 10^{-10}\mu_B$.

Pair Production of Majorana Neutrinos by Annihilation of Charged Particles in High Energy Collision