Transition frequency reduced

For Bo oriented parallel to one of the principal axes of coaxial g, A and Q tensors, the first order transition frequencies in (3.3) reduce to... 

The modulus squared ICf1 (T)l2 gives the probability of finding the molecule in the final state T> at time T, given that it was in j at time t = 0. If the light s frequency co is tuned close to the transition frequency C0 j of a particular transition, the term whose denominator contains (co - C0 4) will dominate the term with (co + C0 q) in its denominator. Within this "near-resonance" condition, the above probability reduces to ... 

The strategy we have been following is to pump the v" = 0 - V = 0 vibrational band in the UV and observe the resulting fluorescence. This method reduces complexity caused by eliminating the need to consider vibrational relaxation and results in most of the fluorescence signal appearing in the 0-0 vibrational band. Moreover, the energy levels, transition frequencies and transition probabilities for this band have been studied extensively and can be found in the literature. 

In conclusion, we have computed the three-loop slope of the Dirac form factor. Thanks to this calculation the theoretical uncertainty in the predictions for the IS1 Lamb shift is reduced. Comparison of the theoretical and experimental results for the IS1 level shift permits an accurate determination of the proton charge radius. Further improvements in theoretical predictions for the IS1 level shift would be possible if subleading a2(Za)6 log2 a corrections are calculated. Only then can the theoretical uncertainty be brought down to several kHz and can the potential of the recent measurement of the 15 — 2S transition frequency [6] be fully exploited. 

All previous 2S Lamb shift measurements for medium-Z hydrogen-like ions have been carried out using fast ion beams, and uncertainties associated with Doppler shifts form a significant source of error in all these experiments. Various methods have been employed or suggested for reducing the sensitivity of fast beam experiments to Doppler corrections [22]—[24]. A measurement of the 2S1/2-2P3/2 transition frequency in N6+ using a fast ion beam is currently under way at Florida State University [25]. Our approach, however, is to reduce such... 

Positronium still presents rather formidable theoretical challenges [39], since it is a relativistic two-body system which cannot be approximated by the motion of a particle of reduced mass in a fixed Coulomb potential. In addition, QED calculations must include annihilation terms. First laser measurements of the 1S-2S two-photon transition frequency in positronium [40] give a result about five standard deviation lower than the theoretical predictions, after taking a recalibration of the tellurium reference line into account [41]. On the other hand, as yet uncalculated higher order terms could well account for this discrepancy. 

The spectrum k(p,T) thus calculated should be corrected, since, as pointed out by KRO, the asymptotic value p( ) from their calculations should be increased by 1050 cm (i.e. by a factor of 1.066) in order to obtain the correct experimental Na D transition frequency. Previously (L2) our correction procedure has been to multiply the frequency scale of the calculated spectrum by this factor of 1.066. It has been pointed out to us (D.D. Konowalow, private communication) that a more appropriate correction procedure is to increase the separation of the KRO potential curves involved by 1050 cm", i.e. to add 1050 cm to the frequency scale of the spectrum as calculated in the previous paragraph. We have adopted this latter procedure and a resulting spectrum of the reduced absorption coefficient k(i, T)/[Na] is given by the fully drawn curves in Figure 3 for T= 2000 K. The spectrum contains four partly overlapping contributions due to the four optically allowed Na2 transitions in the visible and near-infrared part of the spectrum, namely X Sg,... 

Figure 3. The drawn curves represent the reduced absorption coefficient k/[Nap as a function of wavelength, calculated for 2000 K from Table III of Ref. 14, using Eq. 1, and adding 1050 cm to all transition frequencies. The spectrum has been folded with a Gaussian curve 7 nm wide (FWHM) to smooth the satellites. The four contributions from the four optically allowed Na ...

The transit frequencies are estimated and tabulated in Table I for a channel length of 2.6 nm. The transit frequencies range from 1.4 X 107 to 9.1 X 107 for applied potentials from 10 to 150 mV, respectively. The results are comparable to those obtained by Andersen and Procopio (23) for large transmembrane potentials. However, it is important to note that the actual distance covered at the observed velocity is not known with certainty. Shorter distances of steady velocity motion will produce a higher transit frequency. At the same time, however, a delay time near the channel mouth while the ion loses some waters of hydration may significantly reduce the net transit frequency. The experiments detect only motions in a region where the ion moves with a constant, directed velocity. 

In this section, it is summarized the new and faster way (mathematical formulation and numerical treatment), which is widely explained in Moura Droguett (2009), for solving CTNHSMP. The approach involves transition frequency densities and general quadrature methods in order to tackle the problem and as an attempt to reduce the inherent computational cost that is present in the solution of CTNHSMP through the -method. 

In Table 16.1, we present a list of molecules reported in Ref. [74] whose ground state is split into two fine-structure levels such that Equation 16.44 is approximately fulfilled. The molecules Clj and SiBr are of particular interest. For both molecules, the frequency co, as defined by Equation 16.44, is on the order of 1 cm and thus comparable to the rotational constant B. This means that co can be further reduced by a proper choice of isotopes, the rotational quantum number J, and the hyperfine components. New measurements are needed to determine the exact values of the transition frequencies and to identify the best transitions. The required accuracy of the frequency-shift measurements is easily found according to Equation 16.45, the expected frequency shift is... 

Here, p. is the reduced mass of the two nuclei and Roo is the Rydberg energy. These dependencies offer two opportunities (1) the determination of the ratios melirip, mefmd, me/mtm, ntp/md, mp/mt mt is the mass of the tritium nucleus) by measurement of transition frequencies of the one-electron hydrogen molecular ions hJ, D, HD+, HT+ combined with high-precision ab initio theory, and (2) the search for a time-dependence of the ratio of electron to nuclear mass [3]. The latter option is not restricted to diatomics and therefore offers the option of choice of molecular systems with suitably low systematic shifts. 

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