Nature of a nonzero frequency shift of a hyperfine transition in two-dimensional atomic hydrogen

We propose the explanation of a small yet finite frequency shift of a hyperfine transition in two-dimensional atomic hydrogen bound to the surface of superfluid helium at T < 0.1 K. The nonzero shift is caused, first, by the interaction between adsorbed atoms, which effectively reduces their binding energy to the helium surface by a value proportional to their density and, consequently, reduces the deviation of the hyperfine constant from the free-atom value. Second, the transition between the hyperfine states b and c is shifted owing to a difference in the interaction of the b and c atoms with the residual atoms in the state a that appear due to one and two-body nuclear relaxation. This shift is also linear in the density of the two-dimensional gas. The net effect of the two contributions qualitatively agrees with the experimentally observed value of the shift.