  The dynamics of dilute electrons can be modeled by the fundamental
one-species Vlasov-Poisson-Boltzmann system which describes mutual interactions
of the electrons through collisions in the self-consistent electrostatic field.
For cutoff intermolecular interactions, although there are some progress on the
construction of global smooth solutions to its Cauchy problem near Maxwellians
recently, the problem for the case of very soft potentials remains unsolved. By
introducing a new time-velocity weighted energy method and based on some new
optimal temporal decay estimates on the solution itself and some of its
derivatives with respect to both the spatial and the velocity variables, it is
shown in this manuscript that the Cauchy problem of the one-species
Vlasov-Poisson-Boltzmann system for all cutoff soft potentials does exist a
unique global smooth solution for general initial perturbation which is
unnecessary to satisfy the neutral condition imposed in [13] for the case of
cutoff moderately soft potentials but is assumed to be small in certain
weighted Sobolev spaces. Our approach applies also to the case of cutoff hard
potentials and thus provides a satisfactory global well-posedness theory to the
one-species Vlasov-Poisson-Boltzmann system near Maxwellians for the whole
range of cutoff intermolecular interactions in the perturbative framework.
