Triplet amplitude

Here / -I- g and / — g are the singlet and triplet amplitudes respectively. The exchange asymmetry is given by (Kessler, 1985)... 

Figure 42. Triplet amplitudes fl( D2) of msnd D Rydberg states of Ca, Sr, and Ba, derived from hyperfine structure data. ...

The resonant variation of the triplet amplitudes ft( D2) may be visual-ized as a rotation of the projection of the true state vector msnd D2) onto the PD2), D2) plane (cf. Figure 43). In barium, for example, the projection of the state vector is found to be close to the axis at n = 15. Approaching... 

Figure 45. Experimental (O) and calculated ( ) triplet amplitudes Cl(6snd D2), (+) indicates agreement within experimental accuracy, (a) Theoretical values were calculated using the values listed in Table 2 (/ = (b) Spin-...

Figure 51. Singlet amplitudes - 1 02) of 6snd D2 Rydberg states (A) of Ba. For comparison the triplet amplitudes CIOD2) of 6snd D2 Rydberg states, reported in Ref. 18 (+) and Ref. 35 ( ), are also shown. (Taken from Ref. 35.)...

Figure 56. Triplet amplitudes of 6snp Rydberg states of Ba. Experimental amplitudes (ftexp) ave been derived from hyperfine structure data theoretical ones have been calculated using the results of the MQDT analysis by Armstrong et (Taken from Ref. 44.)...

Figure 57. Theoretical triplet amplitudes IthCPi) of 6snp Pi Rydberg states of Ba, obtained from a five-channel quantum defect analysis. For comparison, experimental amplitudes included. A cross indicates agreement within error limits. The...

Figure 60. Triplet amplitude of 6snp P, Rydberg states of Yb. The amplitudes were derived from hyperfine structure splittings (open squares), a five-channel quantum defect analysis using term values and hyperfine structure data (open circles), and measurements of diamagnetic shifts (crosses). (Taken from Ref. 46.)...

The envelope of the Stark structure of the rotator in a constant orienting field, calculated quantum-mechanically in [17], roughly reproduces the shape of the triplet (Fig. 0.5(c)). The appearance of the Q-branch in the linear rotator spectrum indicates that the axis is partially fixed, i.e. some molecules perform librations of small amplitude around the field. Only molecules with high enough rotational energy overcome the barrier created by the field. They rotate with the frequencies observed in the... 

As mentioned already, the INEPT spectra are typified by the antiphase character of the individual multiplets. The INEPT C-NMR spectrum of 1,2-dibromobutane is shown, along with the normal off-resonance C-NMR spectrum, in Fig. 2.12. Doublets show one peak with positive phase and the other with negative phase. Triplets show the outer two peaks with positive and negative amplitudes and the central peak with a weak positive amplitude. Quartets have the first two peaks with positive amplitudes and the remaining two peaks with negative amplitudes. 

In the fast regime we still observe an isotropic triplet, but the widths of the individual lines (and, therefore the amplitudes) varies with m1 according to... 

Figure 13. Principle of direct methods using triplet relations. As shown in the lower right-hand image the trial structure eonsists of atoms which are located at the eomers of the unit eell. Aeeording to the Z2 formula (Sayre equation) a strict phase relation exists within a eertain set of three reflections (a triplet) with large normalized structure factor amplitudes Eu. Sueh a triplet or origin invariant sum is defined as hiEli + + h k h = 0 or hiEli +...

The reflections involved in these triplets have i u and iii.u large but l i small. This differs from the other figures of merit in that it establishes a consistency between the amplitudes and phases of the strong reflections with a small set of weak reflections. Correct phase sets usually give a value of To close to unity. 

Fig. 15. Comparison of a water suppressed muscle spectrum and a spectrum from yellow bone marrow containing almost pure fat (triglycerides). Measurement parameters STEAM sequence, TE=10 ms, TM=15 ms, TR = 2 s, 40 acq., VOI (11 X 11 X 20) mm. (a) Spectrum from TA muscle recorded after careful positioning of the VOI, avoiding inclusion of macroscopic fatty septa allows separation of extramyocellular (EMCL, broken lines) and intramyocellular lipid signals (IMCL, dotted lines) based on susceptibility differences. For this reason characteristic signals from fatty acids occur double. Signals of creatine (methyl, Crs, and methylene, Cr2) show triplet and doublet structure, respectively, due to dipolar coupling effects. Further signals of TMA (including carnitine and choline compartments), Taurine (Tau), esters, unsaturated fatty acids (-HC=CH-), and residual water are indicated, (b) Spectrum from yellow fatty bone marrow of the tibia with identical measuring parameters, but different amplitude scale.

Fig. 35. Part of the spectrum recorded at 3.0 T from TA (shown in Fig. 33b) demonstrating the line splitting caused by dipolar coupling. Triplet structure of Cr3 is resolved, Tau/TMA lead to 4 signal components. The frequency difference between the two Ct2 signals centred at 3.95 ppm is smaller compared to 1.5 T, but these signals are of higher amplitude than in Cr3.

It can be shown [95] that in such a case the T4 contribution cancels the exclusion principle violating (EPV) quadratic terms [59]. This realization led us to the formulation of the so-called ACPQ method (CCSD with an approximate account for quadruples) [95], as well as to CCDQ and CCSDQ [86], the latter also accounting for singles. Up to a numerical factor of 9 for one term involving triplet-coupled pp-hh t2 amplitudes [95], this approach is identical with an earlier introduced CCSD-D(4,5) approach [59] and an independently developed ACCD method of Dykstra et al. [96,97]. This method arises from CCSD by simply discarding the computationally most demanding (i.e., nonfactorizable) terms (see Refs. [59,95-97] for details). 

Fig. 2.50. Generation of /-resolved two-dimensional 13C NMR spectra (a) flux diagram (b) /-modulation of Cl l doublets, CH2 triplets and CH3 quartets during evolution, vector diagrams in the x y plane and cosine curves described by the signal maxima (c) series of 13C NMR spectra of CHn groups with t1 dependent /-modulation of the signal amplitudes (d) series of /-resolved two-dimensional 13C NMR spectra formethine, methylene and methyl carbon atoms, stacked plots and contour plots (e).

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