  It is shown that it is possible to obtain the analytical expression for the
effective mixing angle in matter using the formalism which was developed by
Kimura, Takamura and Yokomakura for the neutrino oscillation probability in
matter with constant density. If we assume that the imaginary part of the
integral of the difference of the energy eigenvalues of the two levels at each
level-crossing is given by the ratio $\gamma$ of the difference of the energy
eigenvalues of the two levels to the derivative of the effective mixing angle
at the level-crossing, then the nonadiabatic contribution to the oscillation
probability can be expressed analytically by this formalism. We give one
example in which the energy eigenvalues cannot be expressed as roots of a
quadratic equation and we show that our assumption is correct in the
approximation of the small mixing angle.
