  We revisit classical nucleation theory (CNT) for the homogeneous bubble
nucleation rate and improve the classical formula using a new prefactor in the
nucleation rate. Most of the previous theoretical studies have used the
constant prefactor determined by the bubble growth due to the evaporation
process from the bubble surface. However, the growth of bubbles is also
regulated by the thermal conduction, the viscosity, and the inertia of liquid
motion. These effects can decrease the prefactor significantly, especially when
the liquid pressure is much smaller than the equilibrium one. The deviation in
the nucleation rate between the improved formula and the CNT can be as large as
several orders of magnitude. Our improved, accurate prefactor and recent
advances in molecular dynamics simulations and laboratory experiments for argon
bubble nucleation enable us to precisely constrain the free energy barrier for
bubble nucleation. Assuming the correction to the CNT free energy is of the
functional form suggested by Tolman, the precise evaluations of the free energy
barriers suggest the Tolman length is $\simeq 0.3 \sigma$ independently of the
temperature for argon bubble nucleation, where $\sigma$ is the unit length of
the Lenard-Jones potential. With this Tolman correction and our new prefactor
one gets accurate bubble nucleation rate predictions in the parameter range
probed by current experiments and molecular dynamics simulations.
