Resonance line shapes

JesJ73 Jesson, J. P., Meakin, P. Determination of mechanistic information for nuclear magnetic resonance line shape for intramolecular exchange. Accounts of Chem. Res. 6 (1973) 269-275. 

Fig. 8.23 Transmission spectra of a polystyrene microring resonator (a) without waveguide offsets and (b) sandwiched by two waveguide offsets. Asymmetric Fano resonant line shape is clearly observed. Reprinted from Ref. 49 with permission. 2008 American Institute of Physics...

Kittel and Abrahams 12S) have predicted an approximately Lorentzian magnetic resonance line shape for a system of spins which are randomly distributed over a small fraction of a large number of possible sites. This effect has been observed in electron spin resonance (124)- Kittel and Abrahams estimate that appreciable deviations from Gaussian shape will occur when the fraction of sites occupied, f, is less than 0.1, in the case of spins of / = H iu a simple cubic lattice with the magnetic field directed... 

M. Engelsberg, I.J. Lowe, J.L. Carolan, Nuclear magnetic resonance line shape of linear chain of spins, Phys. Rev. B 7 (1973) 924-929. 

Interpretation of NMR spectra is subject to the same types of errors encountered in other spectroscopic analyses. There are, however, several pitfalls unique to NMR that may not be avoided if all the factors that can affect resonance-line shape are not clearly understood. These factors are considered here to emphasize the need for care in interpretation. 

Symmetries of local electrical environments of quadrupolar nuclei (/ 1) profoundly influence relaxation times and resonance line shapes of such nuclei (9, 116). Consider a nucleus for which I = % (Br79, Bn). In the absence of quadrupolar perturbation, the nuclear spin levels are evenly spaced, as shown in I below, and the three possible nuclear resonance transitions have equal energies (Am = 1). If, however, eqQ 0... 

We note that A iE) and F ( ) are the energy-dependent shift and width of the state 10 ) in Q, which now has become a resonance, since A(5 , c) = (fg c,E ) give rise to a typical (scattering) resonance line shape. We also note that the shift A ( ) for each state vanishes if one neglects the energy variation of the A(i , c), which is the case when the resonance widths are independent of the energy, or equivalently, when an unstructured continuum in the V subspace is assumed. 

The steady-state methods involve theoretical analysis of magnetic resonance spectra observed under steady-state conditions. This typically involves assumptions regarding the adequacy of magnetic resonance line shape theory, some model for molecular motions and distances of closest approach on collision, and a comparison of calculated spectra for various assumed diffusion constants, and observed spectra. In general, the agreement between diffusion constants calculated using the transient and steady-state methods has been excellent. 

Fig. 1. Error bounds for the nuclear resonance line shape of crystalline CaF2, broadened by a Lorentzian slit function (i.e., the energy absorption by the coupled nuclear spins, due to an exponentially damped harmonic perturbation by a radiofrequency magnetic field).

I, must be deconvoluted from the laser line shapes the Raman resonance line shapes the detector slit function and the polarization properties of the laser and signal fields. 

Fig. 9.6 Resonance line shapes in model He 1I, complex. The Q space composed of the He H, complex in which the H2 fragment is confined to the / — 2 rotational state is coupled by potential anisotropy to the P space composed of the He-H2 (j — 0) manifold. Shown are four (l> = 0, 1,2, 3) vibrational resonances, with v = 0 marked as O, i = 1 marked as A, v = 2 marked as +, and v — 3 marked as X, in the vicinity of the center of the v — 2 resonance. Left-hand scale pertains to o = 2 and right-hand scale to all other resonances. We see that although the resonances do not overlap appreciably (note difference between the v = 2 scale on left-hand side and right-hand scale pertaining to the tails of the other resonances), each of the o — 0, 1, 3 resonance exhibits a hole at the exact position of v = 2 maximum.

During the course of laser resonance experiments it was noticed that the central wavelengths shift depending on the helium density. Thus, the resonance line shapes at various target gas conditions were measured precisely with a reduced laser bandwidth and an improved wavelength calibration [18]. Figure 5 shows resonance profiles taken for the 597.26 nm line at different pressures ranging from 530 mb to 8.0 bar at temperatures of 5.8-6.3 K. The results are summarized in Table 2. 

From the simpler resonance line-shape and H/D-exchange analysis to the more complex studies of inherent dynamics, occurring on various time scale of motion, NMR remains a good choice to investigate protein flexibility and plasticity. If linebroadening due to exchange and inhomogeneity is minimized (or completely eliminated), then half-width, Aom, of a line becomes proportional to R, the transverse relaxation rate constant. 

The composition of bovine casein micelles was analyzed by MAS solid-state NMR, by looking at isotropic and anisotropic chemical shift parameters, resonance line shapes, the combination of single-pulse and to P CP spectra. 

Raman gain coefficient, whose maximum occurs at exact resonance, line shape, the maximum gain coefficient is given by... 

W. H. Jones, Jr., T. P. Graham, and R G. Barnes, "Nuclear magnetic resonance line shapes resulting from the combined effects of nuclear quadrupole and anisotropic shift interactions," Phys. Rev. 132, 1898-1909, (1963). 

Deuteron Magnetic Resonance Line Shape and Relaxation Analysis... 

Anet FAL, Bourn AJR (1967) Nuclear magnetic resonance line-shape and double-resonance studies of ring inversion in cydohexane-d,j. J. Am. Chem. Soc. 89 760... 

Fig. 17. Proton pulsed and cw ENDOR taken at gj for the mononuclear Fe protein nitrile hydratase. The proton resonances are centered at vf H) (filled circles). Representative splittings by A( H) are indicated by the bars. (A) Davies proton ENDOR spectrum. The resonances are not shown owing to interference from N. (B) 35 GHz cw ENDOR spectrum. The resonance line shapes are affected because of the sweep conditions. (From Doan et al. )...

For irradiations A-Il, A-II2, B-I and C on PP fibers, no significant dependence of RO resonance line shape parameters (g value, resonance line width, resonance line shape) except resonance line intensity is observed. Under these circumstances, the temperature dependence of s.s. is anomalous and cannot be simple correlated to Curie, Curle-Welss or even exclton spin susceptibility. In the case of A-11 irradiation a weak Increase of s.s. associated to ROa centers is observed eu ound Tq (Figure 2). As the Integral dose Is Increased, the nun er of RO centers Increases and the anomaly In s.s. around Tq is enhanced, as may be observed in Figure 3. After a B-1 irradiation, the anomaly observed in the temperature dependence of s.s. is dramatic, as may be observed in Figure 4. As C-1 irradiation is limited to few MRads, the anomaly in the s.s. dependence on temperature is spectacular, but the anomaly in s.s. around Tq is not further enhanced. 

The lower spectrum is the resonance line-shape obtained by integration of the evolution time histogram (upper spectrum) at each magnetic field. The ordinate is the ratio of the counts of the upstream (F) and downstream (B) positron counters on resonance divided by that off resonance, and is proportional iol-AJl+A ... 

If the radiofrequency field Hi is very small, i.e. yHi = toi Y o> fben it is easy to achieve the experimental condition for protons in which t(jfTiT2 1. so that the last term may be neglected in the denominator. The resonance line shape then takes a Lorentzian form, which can be written as... 

MHz at room temperature. Due to the small concentration (apprx.0.1%) of the magnetic ( Ge) isotope, the magnetic dipole-dipole interaction is negligible in the samples studied, and the observed specific features of the resonance line shapes (a narrow central peak and a wide plateau) are determined mainly by the quadrupole interaction of magnetic nuclei with the random electric-field gradient (EFG) induced by the isotopic disorder. 

Jameson, C.J. de Dios. A.C. Xe nuclear magnetic resonance line shapes in nanochannels. J. Chem. Phys. 2002. 116. 3805-3821. 

A different approach to probe the ion-neutral potential involves the analysis of collision-broadened ion cyclotron resonance line shapes. For ions undergoing elastic collisions, the power absorption curve is Lorentzian in shape with a half-width at half-maximum equal to the collision frequency (J, which is then simply related to the reduced collision frequency, the diffusion cross section, and the ion mobility. For a series of nonreactive alkyl cations in methane, excellent agreement is found between experimental values for these quantities and theoretical values predicted from the Langevin model.H Unexpectedly, this finding may be interpreted to suggest that other mechanisms for collision broadening, namely inelastic collisions and, specifically, collisions involving complex formation, appear to be unimportant. ... 

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