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.
Using the reactance matrix approach, we systematically develop new multichannel quantum defect theory models for the singlet and triplet S, P, D and F states of strontium based on improved energy level measurements. The new models reveal additional i
nsights into the character of doubly excited perturber states, and the improved energy level measurements for certain series allow fine structure to be resolved for those series perturbers. Comparison between the predictions of the new models and those of previous empirical and emph{ab initio} studies reveals good agreement with most series, however some discrepancies are highlighted. Using the multichannel quantum defect theory wave functions derived from our models we calculate other observables such as Lande $g_J$-factors and radiative lifetimes. The analysis reveals the impact of perturbers on the Rydberg state properties of divalent atoms, highlighting the importance of including two-electron effects in the calculations of these properties. The work enables future investigations of properties such as Stark maps and long-range interactions of Rydberg states of strontium.
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.
