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Physical Review A

Theoretical study of helium Rydberg states

T. N. Chang, Robert T. Poe

Published Dec 1, 1974• 39 citations
Publisher

Abstract

A detailed theoretical investigation of the helium atomic Rydberg states is carried out. Results for level transition energies and doublet level splittings are found to agree extremely well with the recent high-precision microwave-optical experiments. The physical effects contributing to the electrostatic fine structures are systematically studied.

DOI
10.1103/physreva.10.1981

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A detailed theoretical investigation of the helium atomic Rydberg states is carried out. Results for level transition energies and doublet level splittings are found to agree extremely well with the recent high-precision microwave-optical experiments. The physical effects contributing to the electrostatic fine structures are systematically studied.
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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.
A new technique of microwave spectroscopy is proposed for application to excited states of short lifetime. If atoms are excited by electron bombardment, closely-spaced energy levels may be unequally populated. The radiation emitted in decay to lower states may have an angular distribution and polarization character correlated with the direction of bombardment. When such atoms are acted on by radio-frequency fields, transitions may occur between excited states which cause an observable change in the pattern of decay radiation. An analysis is made of the possibility of applying such a method to a determination of the finestructure patterns (1snp)3PJ(J=0,1,2)(1snp)^{3}P_{J}(J=0, 1, 2)(1snp)3PJ​(J=0,1,2) of the helium atom. After a review of previous optical spectroscopic work and theory of this fine structure, an old unsolved mystery concerning the polarization of collision light is discussed. The theory of the Zeeman effect is worked out in a form applicable to the microwave experiments. Expected transition frequencies and rf matrix elements, intensity changes and shape of resonance curves, Stark effect and singlet-triplet mixing are also considered. An estimate is made of the signal to be expected in the experiment described in the following paper.
The helium dimer in its metastable triplet state is a promising candidate to be the first laser-cooled homonuclear molecule. An ultracold gas of He2∗_2^*2∗​ would enable a new generation of precision measurements to test quantum electrodynamics for three- and four-electron molecules through Rydberg spectroscopy. Nearly diagonal Franck-Condon factors are obtained because the electron employed for optical cycling occupies a Rydberg orbital that does not take part in the chemical bond. Three possible laser cooling transitions are identified and the spin-rovibronic energy-level structure of the relevant states as well as electronic transition moments, linestrengths, and lifetimes are determined. The production of He2∗_2^*2∗​ molecules in a supersonic beam is discussed, and a laser slowing scheme to load a magneto-optical trap under such conditions is simulated using a rate equation approach. Various repumping schemes involving one or two upper electronic states are compared to maximize the radiative force. Loss mechanisms such as spin-forbidden transitions, predissociation, and ionization processes are studied and found to not introduce significant challenges for laser cooling and trapping He2∗_2^*2∗​. The sensitivity of the vibrational levels of He2+_2^+2+​ with respect to the static polarizability of atomic helium is determined and its implications for a new quantum pressure standard are discussed.
We present a detailed theoretical investigation of the sodium-helium interaction and report results of quantum close-coupled calculations for the pressure-broadened widths and shifts of the sodium D lines and the 819.48 nm line over the temperature range 70-500 K, and for the total and fine-structure cross sections in the 3p 2 P level. We also present the first theoretical investigation of the hyperfine pressure shifts using a semiclassical scattering formalism and report results for the hyperfine transition in the 3s 2 S 1/2 ground state over the temperature range 70-1000 K. Finally, we calculate the refractive index of helium for sodium matter waves with velocities up to 2000 m s -1 . Several of the calculations were performed using two versions of the adiabatic molecular potentials of Peach (Peach G 1996 unpublished) and the results compared with those obtained using the l -dependent pseudo-potentials of Pascale (Pascale J 1985 XIII Summer School on Quantum Optics ed J Fiutak and J Mizerski pp 39-91) and Peach (Peach G 1996 unpublished). Detailed comparisons with other theoretical calculations and experimental results are also made.