  The interaction of two excited hydrogen atoms in metastable states
constitutes a theoretically interesting problem because of the quasi-degenerate
2P_{1/2} levels which are removed from the 2S states only by the Lamb shift.
The total Hamiltonian of the system is composed of the van der Waals
Hamiltonian, the Lamb shift and the hyperfine effects. The van der Waals shift
becomes commensurate with the 2S-2P_{3/2} fine-structure splitting only for
close approach (R < 100 a_0, where a_0 is the Bohr radius) and one may thus
restrict the discussion to the levels with n=2 and J=1/2 to good approximation.
Because each S or P state splits into an F=1 triplet and an F=0 hyperfine
singlet (eight states for each atom), the Hamiltonian matrix {\em a priori} is
of dimension 64. A careful analysis of symmetries the problem allows one to
reduce the dimensionality of the most involved irreducible submatrix to 12. We
determine the Hamiltonian matrices and the leading-order van der Waals shifts
for states which are degenerate under the action of the unperturbed Hamiltonian
(Lamb shift plus hyperfine structure). The leading first- and second-order van
der Waals shifts lead to interaction energies proportional to 1/R^3 and 1/R^6
and are evaluated within the hyperfine manifolds. When both atoms are
metastable 2S states, we find an interaction energy of order E_h chi (a_0/R)^6,
where E_h and L are the Hartree and Lamb shift energies, respectively, and chi
= E_h/L ~ 6.22 \times 10^6 is their ratio.
