Experimental line width

When calculating the rate constants, two potentials were used the anisotropic 6-12 Lennard-Jones from [209] and the anisotropic Morse [216] for comparison. The results appeared to be very similar, thus indicating low sensitivity of the line widths to the potential surface details. The agreement with experimental data shown in Fig. 5.6(h) is fairly good. Moreover, the SCS approximation gives a qualitatively better approach to the problem than the purely non-adiabatic IOS approximation. As is seen from Fig. 5.6 the significant decrease of the experimental line widths with j is reproduced as soon as adiabatic corrections are made [215]. 

For homonuclear molecules s = / — j takes only even values whereas j is even for para modification and odd for ortho modification of the molecules. With a proper choice of fitting parameters any fitting law reproduces experimental line width rather well. Hence the good fit to their -dependence may not be considered as a criterion of quality of a fitting law. To discriminate between models it is necessary to gain agreement with experimental data on te or xE, which are much more... 

Fig. 5.19. Experimental line width and calculated line widths predicted by the fitting laws in binary collision approximation [251] (o) experimental (+) PEG (A) ECS-EP ( ) MEG ( ) ECS-P.

Fig. 2.7 Dependence of the experimental line width Cexp on the effective absorber thickness t for Lorentzian lines and inhomogenously broadened lines with quasi-Gaussian shape (from [9])...

The experimental line width is 2F because an emission line of the same width scans the absorption line see Fig. 2.6. 

In addition, Coulomb excitation can be used to populate the Mossbauer levels of I77,i78,i80j j [165-167]. The experimental line width using these sources is only slightly larger than the natural line width (e.g., the thickness corrected line width of Hf in a tantalum foil is in good agreement with the natural line width Texp = 1.90 0.07 mm s T at = 1-99 0.04 mm s [168]). 

Nuclear resonance absorption for the 136 keV transition has been established by Steiner et al. [174]. The authors used a metal source and an absorber of metallic tantalum to determine the mean lifetime of the 136 keV level from the experimental line width ( 52.5 mm s for zero effective absorber thickness) and found a value of 55 ps. This has been the only report so far on the use of the 136 keV excited state of Ta for Mossbauer experiments. 

Table 7.5 ° Ta isomer shift, experimental line width and resonance effect, observed for sources of diffused into various transition metal hosts against tantalrun metal as absorber, and for...

Table 7.7 Quadrupole coupling constants e qQ (mm 7 = Kti — VyyiVzz, and experimental line width tungsten compounds...

Table 7.8 Summary of results obtained for the four Os Mossbauer transitions studied. The absorber thickness d refers to the amount of the resonant isotope per unit area. The estimates of the effective absorber thickness t are based on Debye-Waller factors / for an assumed Debye temperature of 0 = 400 K. For comparison with the full experimental line widths at half maximum, Texp, we give the minimum observable width = 2 S/t as calculated from lifetime data.

Table 7.9 Summary of the results obtained from the Mossbauer spectra of the 36.2 and 69.6 keV y-rays of Os in absorbers of various osmium compounds containing d mg of is the full experimental line width at half maximum, 5 the isomer shift with respect to the source of Ir metal. 

Typical absorbers contain 50-700 mg cm of natural platinum. The observed experimental line widths in Pt (99 keV) spectra range from values close to the natural width (2F at (99 keV) = 16.28 mm s ) to 25 mm s. With respect to the line width, the 130 keV transition with a natural width of (130 keV) = 3.40 mm s seems to be more favorable for the study of hyperfine interaction in platinum compounds in practice, experimental line widths of 3.4 0.4 [328] and 3.5 0.7 mm s [329] have been measured. The considerably higher energy resulting in a much smaller recoiUess fraction and the lower probability for the population... 

Debye-Walter factors of the source and the absorber, respectively 5r, experimental correction factor, which is constant as function of the mercury concentration), experimental line width F/2 and isomer shift 5 as a function of the Hg content of the PtHg alloy (taken from [482])... 

There is a second relaxation process, called spin-spin (or transverse) relaxation, at a rate controlled by the spin-spin relaxation time T2. It governs the evolution of the xy magnetisation toward its equilibrium value, which is zero. In the fluid state with fast motion and extreme narrowing 7) and T2 are equal in the solid state with slow motion and full line broadening T2 becomes much shorter than 7). The so-called 180° pulse which inverts the spin population present immediately prior to the pulse is important for the accurate determination of T and the true T2 value. The spin-spin relaxation time calculated from the experimental line widths is called T2 the ideal NMR line shape is Lorentzian and its FWHH is controlled by T2. Unlike chemical shifts and spin-spin coupling constants, relaxation times are not directly related to molecular structure, but depend on molecular mobility. 

Figure 4. Electric quadrupole spectrum of Te in pure Te at 4.8°K. Source, in Cu at 82°K. Total absorber thickness, 30.0 mg./sq. cm. of tellurium enriched in Te—i.e., Te/Te = 40.4%. Individual lines (A this doublet have a full width at half maximum of 0./3 cm./sec. Our experimental line widths for absorbers vary from 0.67-101 cm./sec.

B. Experimental Line Widths for Ln + and An + Transitions. The first detailed quantitative study of the temperature dependence of the line width in a lanthanide system was done on Pr + in LaF3 by Yen, Scott, and Shawlow (43). Since that time line widths as low as 15 kHz have been observed for the D2 to 4 transition of Pr + in LaF2 at 2 K (44). To observe such narrow homogeneous line widths within the strain broadened inhomogeneous line width found in solid systems, experimental techniques involving tunable dye lasers are usually employed. These techniques have been reviewed by Selzer (45) while specific results for the lanthanide systems have been reviewed by Yen (46). ... 

The 237 nm " Indium line (Max Planck Institute at Garching and Erlangen University in Germany) [60,61] of 0.8 Hz natural width is expected to have an accuracy of 10 , see Figure 11.21. The clock transition measured with an experimental line width of 170 Hz (1.3 x 10 ), has an accuracy of 230 Hz. 

H coupling was determined by substitution. H3 coupling constant was not resolved but was consistent with the experimental line width. C.V., Ey2 = -1.91 V in DMF. 

Figure 5.16 Photoabsorption cross-section of neutral/singly and doubly charged clusters, each having 40 valence electrons. The solid line is from Ref. [54], whose results have been averaged over the experimental line width of 0.25 eV. The resonances are more blue-shifted and narrower for the higher charge states...

The experimental line width data were analyzed in very much the same way as for the zinc-nucleotide diphosphate complexes. The concentrations of the different liganded species ZnL, ZnL and Zn(HL), where HL symbolizes a protonated ligand, were calculated and employed to derive values of the molar relaxivities v. The results are summarized in Table 8.2. 

In Table 8.4 we have collected values of Cl quadrupole coupling constants and correlation times for a number of protein-chloride complexes. In a few cases, has been obtained experimentally from a comparison of T and T2 or from the frequency dependence of relaxation. In order to make possible a comparison between different proteins we have also calculated from experimental line width data using correlation times estimated by means of the Debye-Stokes-Einstein relation for spherical molecules. We then proceeded similarly as described in Ref. [4Z1],... 

Figure 6 (A) Expanded areas comparing some cross-peaks in SA-and SAPS-HSQC spectra of the racemic compound (3)// -PA (Pirkle Alcohol) mixture acquired with a reduced spectral width of 2.5 ppm. (B) Experimental line widths and relative sensitivities obtained in conventional HSQC, pure shift HSQC (PS-HSQC) and pure shift sensitivity-improved HSQC (PS-HSQCsi) experiments. Qne-dimensional traces correspond to the H12/C12 cross-peak. Adapted from Ref. [72].

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