  We made use of supersymmetric (SUSY) quantum mechanics to find a condition
under which the Stark effect problem for a polar and polarizable closed-shell
diatomic molecule subject to collinear electrostatic and nonresonant radiative
fields becomes exactly solvable. The condition, $\Delta \omega =
\frac{\omega^2}{4 (m+1)^2}$, connects values of the dimensionless parameters
$\omega$ and $\Delta \omega$ that characterize the strengths of the permanent
and induced dipole interactions of the molecule with the respective fields. The
exact solutions are obtained for the $|\tilde{J}=m,m;\omega,\Delta \omega>$
family of "stretched" states. The field-free and strong-field limits of the
combined-fields problem were found to exhibit supersymmetry and
shape-invariance, which is indeed the reason why they are analytically
solvable. By making use of the analytic form of the
$|\tilde{J}=m,m;\omega,\Delta \omega>$ wavefunctions, we obtained simple
formulae for the expectation values of the space-fixed electric dipole moment,
the alignment cosine, the angular momentum squared, and derived a "sum rule"
which combines the above expectation values into a formula for the eigenenergy.
The analytic expressions for the characteristics of the strongly oriented and
aligned states provide a direct access to the values of the interaction
parameters required for creating such states in the laboratory.
