Systematics of Feshbach resonances in the molecular halogens

Using an electron transmission spectrometer the energetically lowest-lying Feshbach resonances in the molecular halogens ${\mathrm{F}}_2$, ${\mathrm{Cl}}_2$, ${\mathrm{Br}}_2$, and ${\mathrm{I}}_2$ are located. These resonances are associated with Rydberg states and have symmetry $\left(X{}_{}{}^2{}_{}{}^{}\Pi _g^{}{}_{}{}^{}\right){\left(ns\sigma \right)}^2\left[{}_{}{}^2{}_{}{}^{}\Pi _{\frac{1}{2},\frac{3}{2}}^{}{}_{}{}^{}\right]$, where $n=3,4,5, \mathrm{and} 6$ for ${\mathrm{F}}_2$, ${\mathrm{Cl}}_2$, ${\mathrm{Br}}_2$, and ${\mathrm{I}}_2$, respectively. The binding energy of the lowest pair of $\mathrm{ns}\sigma$ electrons to the ground-state positive ion core decreases monotonically as the size of the molecules increases from 4.45 ± 0.05 eV in fluorine to 3.57 ± 0.05 eV in iodine. A simple qualitative theoretical argument, based on an atomic model, satisfactorily describes the decrease in the binding energy.