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