  Finite fermion systems are known to exhibit shell structure in the
weakly-interacting regime, as well known from atoms, nuclei, metallic clusters
or even quantum dots in two dimensions. All these systems have in common that
the particle interactions between electrons or nucleons are spatially
isotropic. Dipolar quantum systems as they have been realized with ultra-cold
gases, however, are governed by an intrinsic anisotropy of the two-body
interaction that depends on the orientation of the dipoles relative to each
other. Here we investigate how this interaction anisotropy modifies the shell
structure in a weakly interacting two-dimensional anisotropic harmonic trap.
Going beyond Hartree-Fock by applying the so-called "importance-truncated"
configuration interaction (CI) method as well as quadratic CI with single- and
double-substitutions, we show how the magnetostriction in the system may be
counteracted upon by a deformation of the isotropic confinement, restoring the
symmetry.
