The Interaction of Differently Excited Like Atoms at Large Distances

The theory of long-range first-order interaction energies is discussed for two like odd-electron atoms in different doublet states, for the case that spin-orbit coupling is smaller than the other splittings. The treatment involves some revision and some extension of previous work. At interatomic distances sufficiently large that overlap of the wave functions of the two atoms is negligible, only the first-order dispersion (dipole-dipole and higher multipole) forces remain, but it is shown that even at rather large distances there often is sufficient overlap that valence forces predominate over first-order dispersion forces.For the case of two H atoms one in a ²S and the other in a ²P state it is shown that the first-order dispersion energy corresponds explicitly to a particular e²r₁₂ integral which represents precisely the mutual electrostatic energy, falling off approximately as 1R³, of two dipolar charge distributions one on each atom. (All the other, valence-force e²r₁₂ integrals fall off exponentially with R.) Tables are given for the first-order dispersion splitting patterns (out to terms in 1R³) for the interaction of a ²P with a ²S or with a ²D atom.Finally, the first-order splittings for pairs of like even-electron atoms is discussed. The results are simpler than for odd-electron atoms, and are applicable also to any pair of such atoms either in singlet states or in any states in which spin-orbit coupling is strong. For atoms both in, for example, triplet, states with weak spin-orbit coupling, different formulas will be needed.