  We study the zero-temperature phase diagram of bosons interacting via
screened Coulomb (Yukawa) potential by means of the diffusion Monte Carlo
method. The Yukawa potential is used as a model interaction in the neutron
matter, dusty plasmas and charged colloids. As shown by D. S. Petrov et al.
[Phys. Rev. Lett. 99, 130407 (2007)], interactions between weakly bound
molecules of heavy and light fermionic atoms are described by an effective
Yukawa potential with a strength related to the heavy-light mass ratio M/m
which might lead to crystallization in a two-dimensional geometry if the mass
ratio of heavy-light fermions exceeds a certain critical value. In the present
work we do a thorough study of the quantum three-dimensional Yukawa system. For
strong interactions (equivalently, large mass ratios) the system experiences
several phase transitions as the density is increased, passing from gas to
solid and to gas phase again. Weakly interacting Yukawa particles do not
crystallize at any density. We find the minimal interaction strength at which
the crystallization happens. In terms of the two-component fermionic system,
this strength corresponds to a heavy-light mass ratio of M/m ~ 180, so that it
is impossible to realize the gas-crystal transition in a conventional bulk
system. For the Yukawa model of fermionic mixtures we also analyze the
possibility of building molecular systems with very large effective mass ratios
by confining the heavy component to a sufficiently deep optical lattice. We
show how the effective mass of the heavy component can be made arbitrarily
large by increasing the lattice depth, thus leading to a tunable effective mass
ratio that can be used to realize a molecular superlattice.
