  The unstable mass transfer situation in binary systems will asymptotically
cause the adiabatic expansion of the donor star and finally lead to the common
envelope phase. This process could happen in helium binary systems once the
helium donor star fills its Roche-lobe. We have calculated the adiabatic mass
loss model of naked helium stars with a mass range of 0.35\,$M_{\odot}$ to
10\,$M_{\odot}$, and every mass sequence evolved from the He-ZAMS to the
cooling track of white dwarf or carbon ignition. In consideration of the
influence of stellar wind, massive helium stars are not considered in this
paper. Comparing stellar radius with the evolution of the Roche-lobe under the
assumption of conservative mass transfer, we give the critical mass ratio
$q_{\textrm{crit}}=M_{\textrm{He}}/M_{\textrm{accretor}}$ as the binary
stability criteria of low and intermediate-mass helium binary stars. On He-MS,
the result shows $1.0<q_{\textrm{crit}}<2.6$, which is more unstable than the
classical result of polytropic model $q_{\textrm{crit}}=3$. After early He-HG,
the $q_{\textrm{crit}}$ quickly increases even larger than 10 (more stable
compared with widely used result $q_{\textrm{crit}}=4$), which is dominated by
the expansion of radiative envelope. Our result could be useful for these quick
mass transfer binary systems such as AM CVns, UCXBs, and helium novae, and it
could guide the binary population synthesis for the formation of special
objects such as SNe Ia and GW sources.
