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We study neutrino oscillations and the level-crossing probability$P_{LZ}=\exp(-\gamma_n\F_n\pi/2)$ in power-law like potential profiles$A(r)\propto r^n$. After showing that the resonance point coincides only for alinear profile with the point of maximal violation of adiabaticity, we pointout that the ``adiabaticity'' parameter $\gamma_n$ can be calculated at anarbitrary point if the correction function $\F_n$ is rescaled appropriately. Wepresent a new representation for the level-crossing probability,$P_{LZ}=\exp(-\kappa_n\G_n)$, which allows a simple numerical evaluation of$P_{LZ}$ in both the resonant and non-resonant cases and where $\G_n$ containsthe full dependence of $P_{LZ}$ on the mixing angle $\theta$. As an applicationwe consider the case $n=-3$ important for oscillations of supernova neutrinos.Comment: 4 pages, revtex, 3 eps figure

Nonadiabatic level crossing in resonant and nonresonant neutrino oscillations