  The pancake collapse of pregalactic clouds under UV background radiation is
explored with a one-dimensional sheet model. Here, attention is concentrated on
elucidating the basic physics on the thermal evolution of pregalactic clouds
exposed to diffuse UV radiation. So, we treat accurately the radiation transfer
for the ionizing photons, with solving chemical reactions regarding hydrogen
molecules as well as atoms. The self-shielding against UV radiation by H$_2$
Lyman-Werner bands, which regulates the photo-dissociation of hydrogen
molecules, is also taken into account. As a result, it is found that when the
UV background radiation is at a level of $10^{-22} (\nu/\nu_L)^{-1} {\rm erg~
s^{-1} cm^{-2} Hz^{-1} str^{-1}}$, the cloud evolution bifurcates with a
critical mass as $M_{\rm SB} = 2.2\times 10^{11} M_\odot [(1+z_c)/5]^{-4.2}$,
where $z_c$ is the final collapse epoch. A cloud more massive than $M_{\rm SB}$
cools below $5\times 10^3$K due to H$_2$ line emission at the pancake collapse
and would undergo the initial starburst. The pancake possibly evolves into a
virialized system in a dissipationless fashion. Consequently, this leads to the
dissipationless galaxy formation at $3\lsim z_c \lsim 10$. A cloud less massive
than $M_{\rm SB}$ cannot cool by H$_2$ emission shortly after the pancake
collapse, but could cool in the course of shrinking to the rotation barrier.
This is likely to lead to the dissipational galaxy formation at relatively low
redshifts as $0\lsim z_c \lsim 4$. The present results provide a solid physical
mechanism which controls the star formation efficiency in the pregalactic
clouds. In the context of a standard CDM cosmology, $M_{\rm SB}$ lies between
1$\sigma$ and 2$\sigma$ density fluctuations.
