10.1007/s11448-008-1006-8

Abstract

23Collisions of particles in a gas lead to a shift of hyperfine transition frequencies with respect to isolated atoms [1][2][3][4]. Since the collision frequency shift is one of the major factors that affect the stability of the present frequency standards [5], its firm understanding is important for both fundamental physics and applications. This work was stimulated by the experiments to measure the collision frequency shift of hyperfine transitions in two-dimensional (2D), adsorbed on the surface of superfluid helium [3], and three-dimensional (3D) [4] spin-polarized atomic hydrogen at T ~ 0.1-0.3 K in a magnetic field of 4.6 T by means of ESR and ENDOR (electron-nuclear double resonance) techniques. While the experiments with ultracold alkali vapors [1, 2] demonstrate an excellent agreement with the spectroscopic data on scattering lengths [6], the measured shift of a certain transition in atomic hydrogen appeared to be two orders of magnitude lower than the expected value in both 2D and 3D cases [3,4]. Let us recall that the virtual absence of the collision frequency shift of ESR in two-dimensional hydrogen has been already observed in experiments by Shinkoda and Hardy [7] and, later on, by Vasiliev et al. [8,9]. As an explanation, Shlyapnikov and also Prokofiev and Svistunov [10] pointed out that triplet-singlet transitions in spin-polarized atomic hydrogen accompanied by the change in the scattering length are impossible, because the absorption of microwave quanta by the spin system is coherent. However, shortly after that, the experiments of Harber et al. with 87 Rb [1] and the accurate analyses of Zwierlein et al. [2] proved that the coherence of the interaction of spins with the microwave field is not directly related to the magnitude of the contact shift.The sharp contradiction between theory and experiment in the simplest system of atomic hydrogen, where the majority of the results may be obtained ab initio analytically with a high accuracy, seemingly questions the foundations of quantum mechanics. In this work, we show that the apparent contradiction may be resolved by taking into account the relation between the symmetry of the state of two atoms and their total electron spin S , such that triplet-singlet transitions are actually forbidden in some cases.To exclude the coherence-related effects, we assume the gas to be far from quantum degeneracy. The ground state of a separate hydrogen atom in a magnetic field B is known to split into four hyperfine sublevels [11] (1) where tan2 θ ≈ A /2 µ B B , the hyperfine constant for hydrogen is A / h ≈ 1420 MHz, and the arrows ⇓⇑ ( ↓↑ ) denote the projections of the electron (nuclear) spin on the direction of the magnetic field. In a high field, θ Ӷ 1, the hyperfine interaction is much smaller than the Zeeman interaction; therefore, the electron and nuclear spin almost independently interact with the magnetic field. This appears in the smallness of the impurity of inversed spin orientations in eigenstates a and c . At a low temperature, only the two lowest hy...