Resonance characterization

In order to determine the resonance energy and total width alone, it is sufficient to look for the poles of the determinant of S(E) 

The density of states so defined can be shown to be connected to the time delay that an electron experiences when scattering off the parent ion. The connection between time delay and energy derivative of the phase shift in the single channel case was first discussed by Eisenbud and Wigner [71,72], and later generalized and extended, with the concept of dwell time, to the multichannel case by Smith [73]. Smith introduced a time-delay matrix Q, defined as 

In the case of a single-channel, this relation reduces to the well-known expression for the Eisenbud-Wigner-Smith time delay 

Conversely, a coherent superposition of continuum states with a population closely reproducing an isolated peak in the density of states, which corresponds to a resonance, can be built in such a way to give rise to a localized state. From this localized state, there will be an outward probability density flux, i.e., it will have a finite lifetime. In the limit of a resonance position far from any ionization threshold and a narrow energy width, the decay rate will be exponential with the rate constant T/ft. The decay is to all the available open channels, in proportion to their partial widths. 

For energy intervals comprising Nres resonances and which are not too large, detS(E) can be approximated with a product of Nies Breit-Wigner phase factors times a smooth background phase factor  

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Konovalova, T. A., L. D. Kispert et al. (2004). Multifrequency high-field electron paramagnetic resonance characterization of the peroxyl radical. Location in horse heart myoglobin oxidized by H202. J. Phys. Chem. BIOS 11820-11826. 

Y.D. Jin, Y. Shao, and S.J. Dong, Direct electrochemistry and surface plasmon resonance characterization of alternate layer-by-layer self-assembled DNA-myoglobin thin films on chemically modified gold surfaces. Langmuir 19, 4771—4777 (2003). 

Servili M, Baldioli M, Selvaggini R, Macchioni A and Montedoro GF. 1999. Phenolic compounds of olive fruit one and two-dimensional nuclear magnetic resonance characterization of niizhenide and its distribution in the constitutive parts of fruit. J Agric Food Chem 47(1) 12—18. 

Newman, R. H., Davies, L. M., Harris, P. J. (1996). Solid-state C nuclear magnetic resonance characterization of cellulose in the cell walls of Arabidopsis thaliana leaves. Plant Physiol, III, 475 85. 

Hubbard B, Kuang W, Moser A, Facey GA, DeteUier C (2003) Structural study of maya blue textural, thermal and solid-state multinuclear magnetic resonance characterization of the palygroskite-indigo and sepioUte-indigo adducts. Clays Clay Miner 51 318-326. 

In the classical limit h - 0, the spectrum of the Landau-von Neumann superoperator tends to the spectrum of the classical Liouvillian operator. If the classical system is mixing, the classical Liouvillian spectrum is always continuous so that we may envisage an analytic continuation to define a discrete spectrum of classical resonances. It has been shown that such classical resonances are given by the zeros of the classical zeta function (2.44) and are called the Pollicott-Ruelle resonances sn(E) [63], These classical Liouvillian resonances characterize exponential decay and relaxation processes in the statistical description of classical systems. The leading Pollicott-Ruelle resonance defines the so-called escape rate of the system,... 

Happe, J. A., Morgan, R. J., Walkup, C. M. H, 19F and, lB Nuclear Magnetic Resonance Characterization of BF3 Amine Catalysts Used in the Cure of C Fiber-Epoxy Prepregs, Polymer (In press)... 

Carr AC, Winterboum CC, Blunt JW, Phillips AJ, Abell AD (1997) Nuclear Magnetic Resonance Characterization of 6v.-Ch loro-5 -cholestane-3p,5-diol Formed from the Reaction of Hypochlorous Acid with Cholesterol. Lipids 32 363... 

The ESR spectra of HAs and FAs of any nature and origin, including native soils, organic amendments, and amended soils, show a sharp and narrow resonance characterized by a g value at about 2.0040 and by a line width ranging from 0.60 to 0.80 mT, which is attributed to indigenous organic free radicals of semiquinonic... 

Filip, Z., Newman, R.H., and Alberts, J.J. (1991) Carbon-13 nuclear magnetic resonance characterization of humic substances associated with salt marsh environments. Sci. Total Environ. 101, 191-199. 

Avdeef A, Box KJ, Comer EA et al. (1998) pH metric logP 10. Determination of liposomal membrane-water partition coefficients of ionizable drugs. Pharm Res 15 209-215 Baird CL, Courtenay ES, Myszka DG (2002) Surface plasmon resonance characterization of drug/liposome interactions. Anal Biochem 310 93-99... 

Murphy AJ, Kemp F, Love J (2008) Surface plasmon resonance characterization of calsper-min-cahnodulin binding kinetics. Anal Biochem 376 61-72... 

Kaganer, E., Pogreb, R., Davidov, D., and Willner, I. Surface plasmon resonance characterization of photoswitchable antigen-antibody interactions. Langmuir 1999,15, 3920-3923. 

Mutlib AE, Chen H, Nemeth G, et al. Liquid chromatography/mass spectrometry and high-field nuclear magnetic resonance characterization of novel mixed diconjugates of the non-nucleoside human immunodeficiency virus-1 reverse transcriptase inhibitor, efavirenz. Drug Metab Dispos. 1999 27(9) 1045-1056. 

Randall, J.C. A review of high-resolution liquid carbon-13 nuclear magnetic resonance characterizations of ethylene-based polymers. J. Mac. Sci. Rev. Macromol. Chem. Phys. 1989, C29, 201-317. 

Characterization of Nanophase Materials, ed. Z.-L. Wang, Wiley-VCH Verlag GmbH, Weinheim, Germany, 2000 R135 L.-Q. Wang, G. J. Exarhos and J. Liu, Nuclear Magnetic Resonance. Characterization of Self-Assembled Nanostructural Materials , p.243... 

Cross TA. Solid-state nuclear magnetic resonance characterization of gramicidin channel structure. Methods Enzymol 1997 289 672-696. 

Wang, L.-Q., Exarhos, G.J., and Liu, J., Nuclear magnetic resonance — characterization of self-assembled nanostructured materials, Arfv. Mater, 11, 1331, 1999. 

In the case of the magnetic resonance characterization, both 13c NMR and proton NMR were employed to obtain the percentages of aromatic carbon and hydrogen. The results are shown in Table IV. Although the measured levels of aromatic hydrogen are within experimental uncertainty of each other, the difference in aromatic carbon is probably significant. Nevertheless, this difference is small and indicates that the aromatic carbon contents are quite similar. In addition, attempts to discern qualitative differences in the 13c NMR were in vain. These results imply that very little, if any, dealkylation or aromatiza-tion has occurred during the crude distillation procedure. 

Dong P, Pan Y (2002) F-Cl-Br partitioning between apatites and halide-rich melts Experimental studies and applications. Geol Ass Can Mineral Ass Can Abstr 27 29 Dowker SEP, Elliott JC (1983) Infrared study of the formation, loss and location of cyanate and cyanamide in thermally treated apatites. J Solid State Chem 49 334-340 Dugas J, Rey C (1977) Electron spin resonance characterization of superoxide ions in some oxygenated apatites. J Phys Chem 81 1417-1419... 

Guth, J. R., and Petuskey, W. P., Silicon-29 magic angle sample spinning nuclear resonance characterization of SiC polytypes, J. Phys. Chem., 91, 5361 (1987). 

Kaplan O, Jaroszewski JW, Clarke R, et al. The multidrug resistance phenotype 3 IP nuclear magnetic resonance characterization and 2-deoxyglucose toxicity. Cancer Res 1991 51 1638-1644. 

Binman, S., S. Vega, S. Belfar, and A. Shani, Functionalization at the Double-Bond Region of Jojoba OH. 9. Solid-State Nuclear Magnetic Resonance Characterization of Substituted Jojoba Wax Chemically Bonded to a Polystyrene Matrix, J. Am. Oil Chem. Soc. 75 521-525 (1998). 

Fig. 6.13. Auger electron yield carbon K-edge NEXAFS spectra of rubbed poly-imide (top), ion beam irradiated polyimide (middle), and ion beam irradiated amorphous carbon (bottom) for the indicated geometries. The intensity ratios of the plotted TT resonances characterize the in-plane asymmetry (left column) and the molecular tilt direction (right column).

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