  We study the theoretical foundations for the pressure shifts in
high-precision atomic beam spectrosopy of hydrogen, with a particular emphasis
on transitions involving higher excited P states. In particular, the long-range
interaction of an excited hydrogen atom in a 4P state with a ground-state and
metastable hydrogen atom is studied, with a full resolution of the hyperfine
structure. It is found that the full inclusion of the 4P_1/2 and 4P_3/2
manifolds becomes necessary in order to obtain reliable theoretical
predictions, because the 1S ground state hyperfine frequency is commensurate
with the 4P fine-structure splitting. An even more complex problem is
encountered in the case of the 4P-2S interaction, where the inclusion of
quasi-degenerate 4S-2P_1/2 state becomes necessary in view of the dipole
couplings induced by the van der Waals Hamiltonian. Matrices of dimension up to
40 have to be treated despite all efforts to reduce the problem to irreducible
submanifolds within the quasi-degenerate basis. We focus on the
phenomenologically important second-order van der Waals shifts, proportional to
1/R^6 where R is the interatomic distance, and obtain results with full
resolution of the hyperfine structure. The magnitude of van der Waals
coefficients for hydrogen atom-atom collisions involving excited P states is
drastically enhanced due to energetic quasi-degeneracy; we find no such
enhancement for atom-molecule collisions involving atomic nP states, even if
the complex molecular spectrum involving ro-vibrational levels requires a
deeper analysis.
