  Substitutional defects in a cubic symmetry (such as a lithium defect in a KCl
host crystal) can be modeled appropriately by an eight-state-system. Usually
this tunneling degree of freedom is approximated by a two-level-system. We
investigate the observable differences between the two models in three
contexts. First we show that the two models predict different relations between
the temperature dependence of specific heat and static susceptibility. Second
we demonstrate that in the presence of external forces (pressure and electric
field) the eight-state-system shows features that cannot be understood within
the framework of the two-level-approximation. In this context we propose an
experiment for measuring the parameter for tunneling along the face diagonal.
Finally we discuss the differences between the models appearing for strongly
coupled pairs. Geometric selection rules and particular forms of asymmetry lead
to clear differences between the two models.
