Fine-Structure Splittings with Experiment

COMPARISON OF FINE-STRUCTURE SPLITTINGS WITH EXPERIMENT 

Spectroscopic parameters of a molecule are derived from experimentally determined spectra by fitting term values to a properly chosen model Hamiltonian.161 Usually, the model Hamiltonian is an effective one-state Hamiltonian that incorporates the interactions with other electronic states parametrically. In rare cases, experimentalists have used a multistate ansatz like the supermultiplet approach162 to fit the rovibronic spectra of strongly interacting near-degenerate electronic states. The safest way of comparing theoretical data to experiment is to compute the spectrum and to fit the calculated term energies to the same model Hamiltonian as the experimentalists use. 

The vibrational dependence of an effective molecular parameter A is usually expressed as 

Alternatively, expectation values computed at the equilibrium geometry of a given electronic state can be directly compared with experimental parameters extrapolated from rovibrational branches. 

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Comparison of Fine-Structure Splittings with Experiment 171... 

The various transition energies of the gold atom and its ions are shown and compared with experiment [53] in table 2. The nonrelativistic results have errors of several eV. The RCC values, on the other hand, are highly accurate, with an average error of 0.06 eV. The inclusion of the Breit effect does not change the result by much, except for a some improvement of the fine-structure splittings. 

In an initial experiment [97], spectroscopy was performed with the output beam of the unmodified laser counter-propagating to the ion beam. The beam velocity was measured using nuclear resonance and time-of-fiight techniques. The weak, hyperfine-induced 21S o — 23Po resonance was then observed [98], see fig. 9. This enabled the J = 0 — 1 fine structure splitting to be obtained by using suitable laser lines to take account of most of the frequency difference, and then measuring the small interval in beam velocity between the resonances. 

Interest in highly ionized systems stems in part from the recent availability of high precision measurements of transition frequencies in these systems, and in part from potential applications in plasma diagnostics. The theory of relativistic and QED effects in two-electron systems requires further development before full agreement with experiment jan be achieved. For example, the fine structure splittings of F are now known about a factor of 10 more accurately than what has been achieved theoretically. 

In the case of the positronium spectrum the accuracy is on the MHz-level for most of the studied transitions (Is hyperfine splitting, Is — 2s interval, fine structure) [13] and the theory is slightly better than the experiment. The decay of positronium occurs as a result of the annihilation of the electron and the positron and its rate strongly depends on the properties of positronium as an atomic system and it also provides us with precise tests of bound state QED. Since the nuclear mass (of positronium) is the positron mass and me+ = me-, such tests with the positronium spectrum and decay rates allow one to check a specific sector of bound state QED which is not available with any other atomic systems. A few years ago the theoretical uncertainties were high with respect to the experimental ones, but after attempts of several groups [17,18,19,20] the theory became more accurate than the experiment. It seems that the challenge has been undertaken on the experimental side [13]. 

At present, five experimental measurements for the 23P splittings are available all but the first [6] are from groups still active and working at helium FS measurements [4,7,8,9,10,11]. Although these experiments use different approaches to measure the fine structure, ranging from microwave spectroscopy in the 23P levels [6,9,10] to frequency difference of the 23,S —> 23P optical transitions [4,7,8,11], helium spectroscopy at 1083 nm is always present (see Fig. 1). A detailed description of all related experiments is out of the scope of this paper, and we will confine the discussion to our measurement [4], and briefly, to other measurements to compare with it. 

Our target is to develop a theory for the Lamb shift and the fine structure in these two atomic systems. Eventually we need to determine the 2s — 2pi/2 splitting in the helium ion (for comparison with the experiment [6]), difference of the Lamb shifts ER(2s) — ER(3s) in 4He+ (for the project [7]) and the 2p3/2 — 2s interval in hydrogen-like nitrogen. The difference mentioned is necessary [12,1] if one needs to compare the results of the Lamb shift (n = 2) measurement [6] and the 2s — 3s experiment. 

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