Fine structure uncertainty

Another difficulty with the infrared method is that of determining the band center with sufficient accuracy in the presence of the fine structure or band envelopes due to the overall rotation. Even when high resolution equipment is used so that the separate rotation lines are resolved, it is by no means always a simple problem to identify these lines with certainty so that the band center can be unambiguously determined. The final difficulty is one common to almost all methods and that is the effect of the shape of the potential barrier. The infrared method has the advantage that it is applicable to many molecules for which some of the other methods are not suitable. However, in some of these cases especially, barrier shapes are likely to be more complicated than the simple cosine form usually assumed, and, when this complication occurs, there is a corresponding uncertainty in the height of the potential barrier as determined from the infrared torsional frequencies. In especially favorable cases, it may be possible to observe so-called hot bands i.e., v = 1 to v = 2, 2 to 3, etc. This would add information about the shape of the barrier. 

Besides a transition to a continuum level of an excited electronic state, dissociation can occur by another mechanism in electronic absorption spectroscopy. If the potential-energy curve of an excited electronic state A that has a minimum in UA(R) happens to be intersected by the U(R) curve of an unstable excited state B with no minimum in U, then a vibrational level of A whose energy lies near the point of intersection of UA and UB has a substantial probability to make a radiationless transition to state B, which then dissociates. This phenomenon is called predissociation. Predissociation shortens the lifetimes of those vibrational levels of A that are involved, and therefore by the uncertainty principle gives broad vibrational bands with rotational fine structure washed out. 

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]. 

The types of information that can be extracted are illustrated by a typical experiment involving, say, transitions between the 1s2s3S state and the fine structure levels of the ls2p3Po)i)2 manifold of states. The total transition frequency gives the QED shift, for which theory is not yet fully developed and experimental checks are very valuable. However, if one measures the 3He - 4He isotope shift for the same transition, then the QED uncertainty largely cancels, allowing the differential nuclear radius to be accurately determined. If one measures... 

Table 9 presents a summary of the known contributions to the fine structure intervals, and a comparison with several recent experiments. The theoretical uncertainty will remain at 15 kHz until the calculations described above have been completed. However, the present result is in remarkably good agreement with the measurement of Minardi et al. [67], which is within a factor of two of reaching the 1 kHz level for the larger i>oti interval. The measurements of Storry et al. [16] and Castilega et al. [18] at the 1 kHz level for the interval are not as sensitive to a, but they provide an important check on the theory. Once both theory and experiment are in place to the necessary accuracy, a new value for a can be derived. 

In future improvements the uncertainties of the fine structure transitions 23S i - 2P can be reduced to less than 0.5 MHz by using higher positron intensities and by eliminating known systematic errors. 

Concluding our consideration we would like to underline, that the study of the g factor of a bound electron [1] offers a new opportunity for us to precisely test bound state QED theory and to determine two important fundamental constants the fine structure constant a and the electron-to-proton mass ratio m/mp. The experiment can be performed at any Z with about the same accuracy [1] and one can expect new data at medium Z which will allow to verify the present ability to estimate unknown higher-order corrections (i. e. theoretical uncertainty) in both low-Z and high-Z calculations. 

Because of the high precision with which the frequencies of the interstellar lines can be measured (better than 1 part in 10s) there remains usually little doubt about the positive identification of the molecular species, despite the fact that only a few transitions out of the whole rotational spectrum of any one given molecule have been observed to date in the radio frequency range. Confirmation is obtained from observations of other rotational transitions, or from the detection of possible fine-structure components, or from observations of corresponding transitions of isotopically substituted species. However, some uncertainty still remains in the identification of formic acid, HCOOH, whose 1 io-ln transition is located in between two 18OH resonances. An independent search for the l0i — 0Oo transition for formic acid was negative (Snyder and Buhl, 1972). Similarly the identification of H2S and H20 still rests on only one observed interstellar radio transition and awaits further confirmation by the detection of other transitions. 

The details of the experiments that give rise to the results above are not important for our considerations. What is important is that each of the measurements (which contain experimental uncertainties that are not shown) arise from the different physical systems and, as is apparent, the values of the fine-structure constant emerging from these experiments are essentially in agreement. 

The stroboscopic pulse radiolysis system described above was modified at Argonne National Laboratory to use a single fine-structure pulse from a 20-MeV L-band linac [150]. This reduced the uncertainty in the age of the primary produets to the width of a fine-structure pulse and allowed kinetic measurements to be extended to 3.5 ns. In practice, the time resolution of absorbance measurements was 100 ps. 

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