  We demonstrate the possibility of creating a self-bound stable
three-dimensional matter-wave spherical boson-fermion quantum ball in the
presence of an attractive boson-fermion interaction and a small repulsive
three-boson interaction. The three-boson interaction could be attractive or
repulsive whereas the fermions are taken to be in a fully-paired super-fluid
state in the Bardeen- Cooper-Schreifer ( quasi-noninteracting weak-coupling)
limit. We also include the Lee-Huang-Yang (LHY) correction to a repulsive
bosonic interaction term. The repulsive three-boson interaction and the LHY
correction can stop a global collapse while acting jointly or separately. The
present study is based on a mean-field model, where the bosons are subject to a
Gross-Pitaevskii (GP) Lagrangian functional and the fully-paired fermions are
described by a Galilean-invariant density functional Lagrangian. The
boson-fermion interaction is taken to be the mean-field Hartree interaction,
quite similar to the interaction term in the GP equation. The study is
illustrated by a variational and a numerical solution of the mean-field model
for the boson-fermion $^7$Li- $^6$Li system.
