Correspondence between the fermion dynamic symmetry model and the interacting boson model in wave functions

The analytical wave functions for the ${\mathrm{SO}}_7$, ${\mathrm{SU}}_3$, and ${\mathrm{SU}}_2$×${\mathrm{SO}}_3$ limits of the fermion dynamic symmetry model are constructed. These wave functions along with the already known wave functions for the ${\mathrm{SU}}_2$×${\mathrm{SO}}_5$ and ${\mathrm{SO}}_6$ limits of fermion dynamic symmetry model are cast into such a form that their relation with the wave functions of the interacting boson model are vivid and transparent. According to the correspondence relation, the intrinsic wave functions for the interacting boson model ${\mathrm{SU}}_3$ limit are constructed from its fermion counterpart and analytic expressions are given for the ${\mathrm{SU}}_6$⊃${\mathrm{SU}}_3$ isoscalar factors. The correlation between the D pair abundance in the ground states and the interaction strength is discussed.