Comments: 7 pages with 1 figure
We calculate the explicit form of the real and imaginary parts of the effective potential for a uniform magnetic field which interacts with fermions with anomalous magnetic moments through the Pauli interaction. It is found that the non-vanishing imaginary part develops for a magnetic field stronger than a critical field, which is the ratio of the fermion mass to its anomalous magnetic moment. This implies the instability of the uniform magnetic field to produce fermion pairs with the production rate density $w(x) = \frac{m^{4}}{24\pi} (\frac{|\mu_a |}{m}-1)^3 (\frac{|\mu_a B|}{m}+3)$.
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