  The renormalization group and operator product expansion are applied to the
model of a passive scalar quantity advected by the Gaussian self-similar
velocity field with finite, and not small, correlation time. The inertial-range
energy spectrum of the velocity is chosen in the form $E(k)\propto
k^{1-2\eps}$, and the correlation time at the wavenumber $k$ scales as
$k^{-2+\eta}$. Inertial-range anomalous scaling for the structure functions and
other correlation functions emerges as a consequence of the existence in the
model of composite operators with negative scaling dimensions, identified with
anomalous exponents. For $\eta>\eps$, these exponents are the same as in the
rapid-change limit of the model; for $\eta<\eps$, they are the same as in the
limit of a time-independent (quenched) velocity field. For $\eps=\eta$ (local
turnover exponent), the anomalous exponents are nonuniversal through the
dependence on a dimensionless parameter, the ratio of the velocity correlation
time and the scalar turnover time. The universality reveals itself, however,
only in the second order of the $\eps$ expansion, and the exponents are derived
to order $O(\eps^{2})$, including anisotropic contributions. It is shown that,
for moderate $n$, the order of the structure function, and $d$, the space
dimensionality, finite correlation time enhances the intermittency in
comparison with the both limits: the rapid-change and quenched ones. The
situation changes when $n$ and/or $d$ become large enough: the correction to
the rapid-change limit due to the finite correlation time is positive (that is,
the anomalous scaling is suppressed), it is maximal for the quenched limit and
monotonically decreases as the correlation time tends to zero.
