  By means of a mean-field method, we have studied the zero temperature
structure and excitation spectrum of a three-dimensional soft-core bosonic
system for a value of the interaction strength that favors a crystal structure
made of atomic nano-clusters arranged with FCC ordering. In addition to the
longitudinal and transverse phonon branches expected for a normal crystal, the
excitation spectrum shows a soft mode related to the breaking of gauge
symmetry, which signals a partial superfluid character of the solid. Additional
evidence of supersolidity is provided by the calculation of the superfluid
fraction, which shows a first-order drop, from 1 to 0.4, at the
liquid-supersolid transition and a monotonic decrease as the interaction
strength parameter is increased. The conditions for the coexistence of the
supersolid with the homogeneous superfluid are discussed, and the surface
tension of a representative solid-liquid interface is calculated.
