  Pycnonuclear reactions in the compact stars at zero temperatures are studied
on quantum mechanical basis in the paper. Formalism of multiple internal
reflections is generalized for analysis, that was developed for nuclear decays
and captures by nuclei with high precision and tests. For the chosen reaction
$^{12}$C + $^{12}$C = $^{24}$Mg, we find the following. A quantum study of the
pycnonuclear reaction requires a complete analysis of quantum fluxes in the
internal nuclear region. This reduces rate and number of pycnonuclear reactions
by 1.8 times. This leads to the appearance of new states (called as quasibound
states) where the compound nuclear system is formed with maximal probability.
As shown, minimal energy of such a state is a little higher than energy of
zero-point vibrations in lattice sites in pycnonuclear reaction, however
probability of formation of compound system at the quasibound state is
essentially larger than the corresponding probability at state of zero-point
vibrations. Hence, there is a sense to tell about reaction rates in such
quasibound states as more probable, rather than states of zero-point
vibrations. This can lead to the essential changes in estimation of the rates
of nuclear reactions in stars.
