  The pairing properties of the neutrinoless double beta decay $(0\nu2\beta)$
candidate $^{100}$Mo have been studied, along with its daughter $^{100}$Ru, to
provide input for nuclear matrix element calculations relevant to the decay.
The $(p,t)$ two-neutron transfer reaction was measured on nuclei of
$^{102,100}$Ru and $^{100,98}$Mo. The experiment was designed to have
particular sensitivity to $0^{+}$ states up to excitation energies of $\sim 3$
MeV with high energy resolution. Measurements were made at two angles and L=0
transitions identified by the ratio of yields between the two angles. For the
reactions leading to and from $^{100}$Ru, greater than 95% of the L=0 $(p,t)$
strength was in the ground state, but in $^{100}$Mo about 20% was in excited
$0^{+}$ states. The measured $(p,t)$ data, together with existing $(t,p)$ data,
suggest that $^{100}$Mo is a shape-transitional nucleus while $^{100}$Ru is
closer to the spherical side of that transition. Theoretical calculations of
the $0\nu2\beta$ nuclear matrix element may be complicated by this difference
in shape.
