Transition frequency central

The second order contribution to the transition frequency of a single nucleus (central ion or ligand) with spin I is given by... 

In practice this condition may be fulfilled not only in excitation, e.g. by means of a pulsed laser or a continuous dye laser with insufficient frequency selectivity, but also by means of fines from a continuous gas laser working in simultaneous axial mode u>i (multimode) generation regime see Fig. 3.10(a). Let Au>i = u>i+1 — uii = itc/L denote the mode separation in a laser, L being the resonator length. Then, as pointed out in [110, 127, 231], broad line approximation works if Awj is smaller than the width of the Bennet holes r en [268, 320] in the absorption contour see Fig. 3.10(6). The positions of the Bennet holes are determined by the condition ujq — w/ + kv = 0, where luq is the central transition frequency, k is the wave vector and v is the velocity of the absorbing particle. The broad fine approximation is valid if the following conditions are fulfilled (see Fig. 3.10) ... 

SLiJlio), which is excited by the combined action of two laser pulses, with central uencies co0 and co to a continuum of states associated with two or more srent product channels at energy E. The frequency co0 is assumed to be in ir resonance with the transition to an intermediate bound state [ i), and is near resonance with the transition frequency between ,) and the continuum. P oj0 can ies the system from E0) to [ )), and co carries the system from ) to Lcpntinuum. To avoid confusion, note that the energy levels are labeled somewhat Terentiy from that in the previous section, q addition, as shown in Figure 11.3, the continuum is coupled to a third bound 2) by a laser of central frequency co2. Basically, the three-level two-laser ne described in Section 11.1 is being extended here to a four-level three-4 control scheme. 

Eq. (34c) for MAS], and st Ibe second-order quadrupolar contribution to the central and satellite transition frequencies, respectively... 

Table 4. Characteristic central-transition frequencies for the second-order hne shapes of halfinteger quadrupolar nuclei in static or magic-angle spinning samples using frequency units of a = 3j /4fo ...

Non-zero covariance values in V, between experimental results from Q, come from experiments that are related. For instance, some contributions are common to some experiments performed with similar set-ups. An example is the set of hydrogen spectroscopy experiments performed at the Laboratoire Kastler Brossel in Paris [3, A2-A6 in Table XI, p. 49] the transitions frequencies measured there between the 2S level and other levels are correlated, as they used the same reference laser, the same line shape analysis method, similar estimates of the Stark effect contribution to the final transition frequencies, etc. Thus, any deviation of one of the measured frequencies from its central measured value implies a correlated deviation of any of its related measured frequencies. Corresponding non-zero, non-diagonal elements in the covariance matrix V quantify such correlations. 

As with the CODATA 2002 adjustment of the fundamental constants, covariances between all the adjusted variables Z can be calculated. Unlike in the calculation of central values for the new energy levels, the matrix S [1, Eq. (2)] of covariances between the new S s is involved in the formula that gives the covariance matrix of the new adjusted variables Z . It is indeed expected that the precision on the adjusted S s depends on their uncertainty as predicted from theoretical considerations (through the order of magnitude of successive perturbation terms). Precise uncertainties on predicted energies and transition frequencies can then be calculated through standard propagation of uncertainties (see, e.g., Eq. (F7) in [3]), as expressed in Eqs. (17) and (18) in [1]. 

The NMR transition frequencies for quadrupolar nuclei are generally discussed in terms of first- and second-order perturbation theory where the quadrupolar interaction is treated as a perturbation of the Zeeman inter-action. Although the central transition (CT) is not perturbed by the first-order quadrupolar interaction, the remaining ZI— 1 single-quantum transitions (i.e., the satellite transitions (STs)) are perturbed by both the first-and second-order quadrupolar interactions (vide infra). 

The central frequency of the spontaneous or stimulated emission (or absorption) spectrum of an atom is shifted relative to the transition frequency because of the translational degree of freedom of the atomic motion, owing to two effects the Doppler... 

Fig. 2.7 Excitation resonance broadening of a two-level system with increasing laser radiation intensity (w is the field frequency, ujo is the central transition frequency, F = jTi is the homogeneous spectral-line half-width, and G is the saturation parameter).

Despite the limitations, matrix isolation has been used to generate a large number of transition metal fragments containing carbonyl groups. The frequencies of their C—O bands have been measured and these data form a spectral library which has played a central role in the interpretation of time-resolved IR experiments. 

Significant progress in signal enhancement methods for the central transition has been achieved by the implementation of double frequency sweeps (DFS) [62]. The basic idea of DFS, applicable for both static and MAS experiments, is to invert simultaneously the STs so that the populations of the outer spin levels are transferred to the CT energy levels before they are selectively excited (Fig. 4). 

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