We have studied the magnetic properties of Cs atoms trapped in cubic a
nd hexagonal solid He-4 matrices. Observations in the cubic phase supp
ort the assumption of a highly symmetrical trapping site (spherical bu
bble), while zero-field magnetic resonance spectra and magnetic dipole
-forbidden transitions observed in the hexagonal phase are interpreted
in terms of a quadrupolar distortion of the atomic bubbles. From the
perturbed hyperfine interaction in the hexagonal phase we infer a bubb
le deformation of 6%-7%.