  We analyze the ground-state properties of an artificial atom made out of
repulsive bosons attracted to a center for the case that all the interactions
are short-ranged. Such bosonic atoms could be created by optically trapping
ultracold particles of alkali vapors; we present the theory describing how
their properties depend on experimentally adjustable strength of ``nuclear''
attraction and interparticle repulsion. The binding ability of the short-range
potential increases with space dimensionality - only a limited number of
particles can be bound in one dimension, while in two and three dimensions the
number of bound bosons can be chosen at will. Particularly in three dimensions
we find an unusual effect of enhanced resonant binding: for not very strong
interparticle repulsion the equilibrium number of bosons bound to a nuclear
potential having a sufficiently shallow single-particle state increases without
bound as the nuclear potential becomes less attractive. As a consequence of the
competing nuclear attraction enhanced by the Bose statistics and interparticle
repulsions, the dependence of the ground-state energy of the atom on the number
of particles has a minimum whose position is experimentally tunable. This
implies a staircase dependence of the equilibrium number of bound bosons on
external parameters which may be used to create a single-atom pipette - an
arrangement which allows the transport of atoms into and out of a reservoir,
one at a time.
