The Physics of Circular Atoms and the Measurement of the Rydberg Constant

Abstract

Circular atoms are highly excited atoms, i.e. Rydberg atoms (with a large principal quantum number, n ≥ 10) with a maximum value of the angular momentum ι and of its projection m along a quantization axis (ι = | m | = n−1). These atoms are quasi-classical: the wave function of the valence electron has the shape of a thin torus lying around the classical circular orbit of the Bohr theory, whose radius is a_on² (where a_o is the Bohr radius). These atoms fit the Bohr model of Hydrogen and are well adapted for measuring the Rydberg constant R. This metrology is presently performed by optical laser spectroscopy of atomic hydrogen (1,2,3). The present accuracy (1.6 10⁻¹⁰) is limited by the laser wavelength measurement.