The standard model prediction for a magnetic dipole moment of a neutrino is
proportional to the neutrino mass and extremely small. It also generates a
flavor-changing process, but the GIM mechanism reduces the corresponding
amplitude. These properties of a neutrino magnetic moment change drastically in
a degenerate electron plasma. We have shown that an electron-hole excitation
gives a contribution proportional to the electrons' Fermi momentum. Since this
effect is absent in μ and τ sector, the GIM cancellation does not
work. The magnetic moment induces a neutrino oscillation if a strong enough
magnetic field exists in the plasma. The required magnitude of the field
strength that affects the \nue\ burst from a supernova is estimated to be the
order of 108 Gauss.Comment: 10 pages, Latex, Misleading terminology and typographical errors are
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