We investigate the effect of series perturbation on the second order
dipole-dipole interactions between strontium atoms in 5sns(1S0β) and
5snp(1P1β) Rydberg states as a means of engineering long-range
interactions between atoms in a way that gives an exceptional level of control
over the strength and the sign of the interaction by changing n. We utilize
experimentally available data to estimate the importance of perturber states at
low n, and find that van der Waals interaction between two strontium atoms in
the 5snp(1P1β) states shows strong peaks outside the usual hydrogenic
n11 scaling. We identify this to be the result of the perturbation of
5snd(1D2β) intermediate states by the 4d2(1D2β) and 4dnβ²s(1D2β)
states in the n<20 range. This demonstrates that divalent atoms in general
present a unique advantage for creating substantially stronger or weaker
interaction strengths than those can be achieved using alkali metal atoms due
to their highly perturbed spectra that can persist up to high-n