We investigate the effect of intercombination transitions in excitation hopping processes such as those found in Forster resonance energy transfer. Taking strontium Rydberg states as our model system, the breakdown of $LS$-coupling leads to weakly al
lowed transitions between Rydberg states of different spin quantum number. We show that the long-range interactions between two Rydberg atoms can be affected by these weakly allowed spin transitions, and the effect is greatest when there is a near-degeneracy between the initial state and a state with a different spin quantum number. We also consider a case of four atoms in a spin chain, and show that a spin impurity can resonantly hop along the chain. By engineering the many-body energy levels of the spin-chain, the breakdown of $LS$ coupling due to inter-electronic effects in individual atoms can be mapped onto a spatial separation of the total spin and the total orbital angular momentum along the spin chain.
Long-range dipole-dipole and quadrupole-quadrupole interactions between pairs of Rydberg atoms are calculated perturbatively for calcium, strontium and ytterbium within the Coulomb approximation. Quantum defects, obtained by fitting existing laser sp
ectroscopic data, are provided for all $S$, $P$, $D$ and $F$ series of strontium and for the $^3P_2$ series of calcium. The results show qualitative differences with the alkali metal atoms, including isotropically attractive interactions of the strontium $^1S_0$ states and a greater rarity of Forster resonances. Only two such resonances are identified, both in triplet series of strontium. The angular dependence of the long range interaction is briefly discussed.
