Resonance, absorption width

In the earlier treatment we reached the conclusion that resonance absorption occurs at the Larmor precessional frequency, a conclusion implying that the absorption line has infinitesimal width. Actually NMR absorption bands have finite widths for several reasons, one of which is spin-lattice relaxation. According to the Heisenberg uncertainty principle, which can be stated... 

Experiments on the sky. Two experiments have been carried out at the sky, using two laser installations built for the American and French programmes for Uranium isotope separation, respectively AVLIS at the Lawrence Livermore Nat l Lab (California) in 1996 and SILVA at CEA/Pierrelatte (Southern France) in 1999. The average power was high pa 2 x 175 W, with a pulse repetition rate of 12.9 and 4.3 kHz, a pulse width of 40 ns and a spectral width of 1 and 3 GHz. Polarization was linear. The return flux was < 5 10 photons/m /s (Foy et al., 2000). Thus incoherent two-photon resonant absorption works, with a behavior consistent with models. But we do need lower powers at observatories ... 

Hence, nuclear resonance absorption of y-photons (the Mbssbauer effect) is not possible between free atoms (at rest) because of the energy loss by recoil. The deficiency in y-energy is two times the recoil energy, 2Er, which in the case of Fe is about 10 times larger than the natural line width F of the nuclear levels involved (Fig. 2.4). 

In a Mdssbauer transmission experiment, the absorber containing the stable Mdssbauer isotope is placed between the source and the detector (cf. Fig. 2.6). For the absorber, we assume the same mean energy q between nuclear excited and ground states as for the source, but with an additional intrinsic shift A due to chemical influence. The absorption Une, or resonant absorption cross-section cr( ), has the same Lorentzian shape as the emission line and if we assume also the same half width , cr( ) can be expressed as ([1] in Chap. 1)... 

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. 

It is a matter of historical interest that Mossbauer spectroscopy has its deepest root in the 129.4 keV transition line of lr, for which R.L. Mossbauer established recoilless nuclear resonance absorption for the first time while he was working on his thesis under Prof. Maier-Leibnitz at Heidelberg [267]. But this nuclear transition is, by far, not the easiest one among the four iridium Mossbauer transitions to use for solid-state applications the 129 keV excited state is rather short-lived (fi/2 = 90 ps) and consequently the line width is very broad. The 73 keV transition line of lr with the lowest transition energy and the narrowest natural line width (0.60 mm s ) fulfills best the practical requirements and therefore is, of all four iridium transitions, most often (in about 90% of all reports published on Ir Mossbauer spectroscopy) used in studying electronic stractures, bond properties, and magnetism. 

It is much more difficult to observe the Mossbauer effect with the 130 keV transition than with the 99 keV transition because of the relatively high transition energy and the low transition probability of 130 keV transition, and thus the small cross section for resonance absorption. Therefore, most of the Mossbauer work with Pt, published so far, has been performed using the 99 keV transition. Unfortunately, its line width is about five times larger than that of the 130 keV transition, and hyperfine interactions in most cases are poorly resolved. However, isomer shifts in the order of one-tenth of the line width and magnetic dipole interaction, which manifests itself only in line broadening, may be extracted reliably from Pt (99 keV) spectra. 

MeV a-particles and used the Au/Ir source after annealing without any further chemical or physical treatment. Commercially available sources are produced via Pt(p, n) Au. The most popular source matrix into which Au is diffused is platinum metal although it has the disadvantage of being a resonant matrix - natural platinum contains 33.6% of Pt. Using copper and iridium foils as host matrices for the Au parent nuclide, Buym et al. [327] observed natural line widths and reasonable resonance absorption of a few percent at 4.2 K. 

The first Mossbauer measurements involving mercury isotopes were reported by Carlson and Temperley [481], in 1969. They observed the resonance absorption of the 32.2 keV y-transition in (Fig. 7.87). The experiment was performed with zero velocity by comparing the detector counts at 70 K with those registered at 300 K. The short half-life of the excited state (0.2 ns) leads to a natural line width of 43 mm s Furthermore, the internal conversion coefficient is very large (cc = 39) and the oi pj precursor populates the 32 keV Mossbauer level very inefficiently ( 10%). 

This chapter deals mainly with (multi)hyphenated techniques comprising wet sample preparation steps (e.g. SFE, SPE) and/or separation techniques (GC, SFC, HPLC, SEC, TLC, CE). Other hyphenated techniques involve thermal-spectroscopic and gas or heat extraction methods (TG, TD, HS, Py, LD, etc.). Also, spectroscopic couplings (e.g. LIBS-LIF) are of interest. Hyphenation of UV spectroscopy and mass spectrometry forms the family of laser mass-spectrometric (LAMS) methods, such as REMPI-ToFMS and MALDI-ToFMS. In REMPI-ToFMS the connecting element between UV spectroscopy and mass spectrometry is laser-induced REMPI ionisation. An intermediate state of the molecule of interest is selectively excited by absorption of a laser photon (the wavelength of a tuneable laser is set in resonance with the transition). The excited molecules are subsequently ionised by absorption of an additional laser photon. Therefore the ionisation selectivity is introduced by the resonance absorption of the first photon, i.e. by UV spectroscopy. However, conventional UV spectra of polyatomic molecules exhibit relatively broad and continuous spectral features, allowing only a medium selectivity. Supersonic jet cooling of the sample molecules (to 5-50 K) reduces the line width of their... 

Thus, the region 2100-1830 cm 1 can be covered. This allows us to monitor CO(v,J) by resonance absorption and various M(CO)n [n = 3-6] as a result of near coincidences between the CO laser lines and the carbonyl stretching vibrations of these species. The temporal response of the detection system is ca. 100 ns and is limited by the risetime of the InSb detector. Detection limits are approximately 10 5 torr for CO and M(CO)n. The principal limitation of our instrumentation is associated with the use of a molecular, gas discharge laser as an infrared source. The CO laser is line tuneable laser lines have widths of ca. lO cm 1 and are spaced 3-4 cm 1 apart. Thus, spectra can only be recorded point-by-point, with an effective resolution of ca. 4 cm 1. As a result, band maxima (e.g. in the carbonyl stretching... 

The recoilless nuclear resonance absorption of y-radiation (Mossbauer effect) has been verified for more than 40 elements, but only some 15 of them are suitable for practical applications [33, 34]. The limiting factors are the lifetime and the energy of the nuclear excited state involved in the Mossbauer transition. The lifetime determines the spectral line width, which should not exceed the hyperfine interaction energies to be observed. The transition energy of the y-quanta determines the recoil energy and thus the resonance effect [34]. 57Fe is by far the most suited and thus the most widely studied Mossbauer-active nuclide, and 57Fe Mossbauer spectroscopy has become a standard technique for the characterisation of SCO compounds of iron. 

In the case of dipolar produced line width, a rigorous expression for the second moment (Equation 17) of the resonance absorption line allows one to obtain quantitative structural information (Section II,B and C). The... 

The line shapes of the resonance absorption curves were rather well described by a Gaussian shape, as is shown in Fig. 14. Two parameters are necessary in fitting a recorder derivative with a Gaussian shape function the maximum value of the derivative signal (dx"/3 f)m. and the width between points of maximum slope of the absorption, which are... 

In Fig. 16 is shown an experimental resonance absorption recorder curve of the above-mentioned protons. This signal is from a Davison silica gel (SG) with a BET surface area of 687 meterVgram, dehydrated in vacuum at 500°. The width between points of maximum slope of this resonance is 310 milligauss and the corresponding spin-spin relaxation time is 1.8 X 10 ... 

The chemical shift 5, defined by Equation (22), was measured at 40.0 and 15.6 Mc./sec. and was found to be —3 2 relative to water for both SA and SG. The derivatives of the resonance absorptions were recorded in the measurements. If the total anisotropy of the chemical shift of protons in the solid is somewhat less than the line width, the cross-over point of the derivative will correspond to the average value of S as for liquids, and will be directly comparable with the shifts for protons in the liquid state. Comparison of the shift value with those of H3O+ (aqueous) (1 1), S = -1-11, OH (aqueous) (121), S = -1-10 dilute solutions of alcoholic-type protons... 

Usually, in wide-line NMR experiments, the first derivative of the resonance absorption curve is obtained. Taking into account that the amplitude of this curve decreases with the square of the line width, the conclusion can be drawn from Table I that, besides the resonances from the Si sites, the contributions of the other sites should be hidden in the noise during measurement. 

The width AH0 of the resonance absorption curve measured at half peak power - the 3 dB resonance line width - should in general be as small as possible since this implies a narrow range of frequencies over which strong interaction with the ferrite can occur however, there are certain broad-band applications where this would not be the requirement. There are two main contributions to the linewidth ... 

Derivative Detection of EPR Transition. The EPR spectrum is usually displayed as the first derivative of the absorption y"(H), because the nonresonant low-frequency and low-amplitude RF modulation (co1/ 2% = typically 100 kHz) applied to the coils near the magnet is detected by a rectifier in addition to the drop in microwave power level due to the RF resonant absorption (typically co0/27c = 9.1 GHz if H0 = 0.34T) The signal is processed by a phase-sensitive circuit, which detects a back-and-forth sweep across resonance in small magnetic field increments (relative to the DC field and to the width of the measured spectrum), thus generating a response df /dH (see Fig. 11.60). 

The absorption technique employed by Parker [122] is a modified version of the resonance tube described by Knotzel and Knotzel [123], It consists of a Pyrex glass cylinder, 5 cm in diameter and about 75 cm in length. A cylindrical brass piston is used to generate standing waves in the tube. The sound pressure Pn is observed for frequencies near any of the n resonant frequencies / for the tube, and the resonance half-width <5, in Hz, is de-... 

Position of the emitting atom Resonance-absorption cross section Mass attenuation coefficients Line width Isotope abundance... 

Additionally and equally significant, the spectral features assigned to the antibonding state of Hf 5f electrons display seven features indicating a completely removal of the Hf 4fs/2 and Hf 4f7/2 degeneracies of three and four, respectively. This is consistent with the local field induced symmetries of Hf 4f orbitals that are mixed with O 2p, and possibly O 2s states as well. This is the same mechanism that activated the Ti 3p and O 2s virtual bound state resonance absorptions in Fig. 12. The spectral widths of the Hf 5d" features (4 states) and Hf 4f features (7 states)... 

The maximum d is reached in the region of the polaron resonance absorption with radiation frequency ft 4/0, // , where the width of the absorp-... 

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