  Kinetic rate factors of crystallization have a direct effect on formation and
growth of an ordered solid phase in supercooled liquids and glasses. Using
crystallizing Lennard-Jones liquid as an example, in the present work we
perform a \textit{direct} quantitative estimation of values of the key
crystallization kinetic rate factors -- the rate $g^{+}$ of particle
attachments to a crystalline nucleus and the rate $g^{-}$ of particle
detachments from a nucleus. We propose a numerical approach, according to which
a statistical treatment of the results of molecular dynamics simulations was
performed without using any model functions and/or fitting parameters. This
approach allows one to accurately estimate the critical nucleus size $n_{c}$.
We find that for the growing nuclei, whose sizes are larger than the critical
size $n_{c}$, the dependence of these kinetic rate factors on the nucleus size
$n$ follows a power law. In the case of the subnucleation regime, when the
nuclei are smaller than $n_{c}$, the $n$-dependence of the quantity $g^{+}$ is
strongly determined by the inherent microscopic properties of a system and this
dependence cannot be described in the framework of any universal law (for
example, a power law). It has been established that the dependence of the
growth rate of a crystalline nucleus on its size goes into the stationary
regime at the sizes $n>3n_{c}$ particles.
