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The long-range interaction of excited neutral atoms has a number ofinteresting and surprising properties, such as the prevalence of long-range,oscillatory tails, and the emergence of numerically large can der Waals C_6coefficients. Furthermore, the energetically quasi-degenerate nP states requirespecial attention and lead to mathematical subtleties. Here, we analyze theinteraction of excited hydrogen atoms in nS states (3 <= n <= 12) withground-state hydrogen atoms, and find that the C_6 coefficients roughly growwith the fourth power of the principal quantum number, and can reach values inexcess of 240,000 (in atomic units) for states with n = 12. The nonretarded vander Waals result is relevant to the distance range R << a_0/alpha, where a_0 isthe Bohr radius and alpha is the fine-structure constant. The Casimir-Polderrange encompasses the interatomic distance range a_0/alpha << R << hbar c/L,where L is the Lamb shift energy. In this range, the contribution ofquasi-degenerate excited nP states remains nonretarded and competes with the1/R^2 and 1/R^4 tails of the pole terms which are generated by lower-lying mPstates with 2 <= m <= n-1, due to virtual resonant emission. The dominant poleterms are also analyzed in the Lamb shift range R >> hbar c/L. The familiar1/R^7 asymptotics from the usual Casimir-Polder theory is found to becompletely irrelevant for the analysis of excited-state interactions. Thecalculations are carried out to high precision using computer algebra in orderto handle a large number of terms in intermediate steps of the calculation, forhighly excited states.

Long-range interactions of hydrogen atoms in excited states. III. nS-1S interactions for n >= 3