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Physical Review A

Recoil corrections to Rydberg energy levels in helium

C. K. Au, Gerald Feinberg, Joseph Sucher

Published Jan 1, 1991• 14 citations
Publisher

Abstract

We study the question of recoil corrections to Rydberg energy levels in helium, making use of a formalism in which the He-ion core is treated as an elementary particle of spin 1/2 and the Rydberg atom is regarded as a relativistic two-body bound state, described by a ``no-pair'' wave equation. We show that when recoil effects are correctly included, the agreement with experiment for the n=10 levels of He is improved.

DOI
10.1103/physreva.43.561

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We study the question of recoil corrections to Rydberg energy levels in helium, making use of a formalism in which the He-ion core is treated as an elementary particle of spin 1/2 and the Rydberg atom is regarded as a relativistic two-body bound state, described by a ``no-pair'' wave equation. We show that when recoil effects are correctly included, the agreement with experiment for the n=10 levels of He is improved.
We calculate the energy shifts, in Rydberg states of helium, due to retardation corrections to the two-photon exchange potential. The correction to the level spacings is at the accuracy of existing measurements in the n=10n=10n=10 states of neutral He. It may soon be possible for the first time to detect the effect of these corrections in atomic systems. Estimates of the energy shifts for high-ZZZ He-like ions yield effects of several percent of the total spacing.
The electrostatic fine structure for singly excited lithium is accurately calculated using an effective potential method that has proven to be very useful for helium. Relevant properties of the two-electron Li+{\mathrm{Li}}^{+}Li+ ionic core with finite nuclear mass are determined from variational wave functions. From these, non- relativistic level shifts are obtained analytically, and the leading relativistic correction is applied. A comparison with recent experimental results is made.
Rydberg atoms occupy a central role in quantum science; their loosely bound outer electron gives rise to properties that enable quantum information processing1 or the formation of exotic molecular bonds2. Beyond these roles, they have been proposed as a neutral platform for the observation of quantum effects in collisions and reactions of the ionic core with neutral particles3, 4, a long-standing goal of ion-based chemistry and physics. However, all of the experimental results so far could be explained using a classical description of the internuclear motion5. Here we demonstrate cold collisions inside a Rydberg helium atom, achieved by merging helium Rydberg and ground-state helium beams and imaging individual scattering events. We resolve the fully quantum-coherent motion and observe matter-wave diffraction and tunnelling-driven shape resonances down to collision energies of 90 mK. In the case of identical helium nuclei, we demonstrate a new regime of identical-particle Mott interference6, where quantum statistics begin to govern the total scattering cross section. For distinct isotopes, we show the breakdown of the Born-Oppenheimer approximation and benchmark parameter-free, state-of-the-art theory. We directly measure the helium isotope ionization-energy difference to be 15.0 +/- 0.1 K. Our experiments establish Rydberg atoms as a platform for the direct observation of quantum dynamics with a general class of ions, atoms and molecules.
New variational techniques are described which yield a factor of 1000 improvement in accuracy for the energies of the 1snd 1D^{1}\mathrm{D}1D and 3D^{3}\mathrm{D}3D states of helium up to n=8. Convergence to better than \ifmmode\pm\else\textpm\fi{}10 kHz is obtained, making possible high-precision comparisons with experiment for fine structure and singlet-triplet splittings. The comparisons are sensitive to QED, relativistic recoil, and second-order mass-polarization corrections.
In this chapter we study the energy levels of two-electron atoms, principally helium. A two-electron atom is a system of three interacting particles, a problem extremely difficult to analyze within classical mechanics. Since the mass of the nucleus is much larger than that of the electrons, the nuclear motion may be ignored and the problem reduces to two interacting particles moving in an external potential. This is still difficult to solve within classical mechanics. The old Bohr-Sommerfeld quantum mechanics also had little success with this problem. Thus it was a critical triumph for wave mechanics to provide correct calculations of the energy levels of two-electron atoms. Indeed it is remarkable that very little effort is required, as we shall see, to give a good estimate for the ground state energy. Further calculations for two-electron atoms provided six-figure agreement between theory and experiment, a striking proof of the validity of wave mechanics.
In high-LLL Rydberg states, where exchange interactions are of negligible size, spin-orbit interactions are expected to determine the energy differences between states of different spin orientations. This is well studied in the case of helium, where it results in a fourfold splitting of each high-LLL term, coming from the two electrons' spin-orbit interactions. A similar structure might be expected in heavier Rydberg states, whose core ion is a 2S1/2{}^{2}{S}_{1/2}2S1/2​ state. However, observations in barium Rydberg states and recent observations in Rydberg states of Si2+{\mathrm{Si}}^{2+}Si2+ reveal significant deviations from this expectation. Both can be explained as an indirect effect of spin-orbit interactions in virtual excitations of the core ion. A perturbative treatment predicts an indirect spin-orbit interaction for the Rydberg state proportional to the inverse sixth power of the Rydberg electron's radial coordinate. The significance of this term, relative to the direct magnetic interactions, varies by more than six orders of magnitude between the three systems studied, helium, Si2+,{\mathrm{Si}}^{2+},Si2+, and barium.