Cross-section for resonant absorption

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. 

If the above three conditions are satisfied, the Mdssbauer effect is observed, and the cross section for resonant absorption resonant absorption per unit flux of impinging y photons with energy E) is given by... 

In contrast to nonresonant two-photon excitation, the cross-section for resonant two-photon excitations is relative large if the atoms are excited via a strong resonance transition. To achieve resonant two-photon excitation, however, two tunable lasers are necessary with sufficiently narrow spectral bandwidths. The laser beams intersect the absorbing volume in CO- or counter-propagating direction. If the first laser is tuned to the Doppler profile of the lower transition, atoms are excited with a well-defined velocity component in beam direction, whereas the second laser probes the population density of the excited atoms within this velocity group (Figure 4). The basic arrangement for isotope-selective analysis makes use of two absorption volumes, which are intersected by... 

By means of this combination of the cross section for an ellipsoid with the Drude dielectric function we arrive at resonance absorption where there is no comparable structure in the bulk metal absorption. The absorption cross section is a maximum at co = ojs and falls to approximately one-half its maximum value at the frequencies = us y/2 (provided that v2 ). That is, the surface mode frequency is us or, in quantum-mechanical language, the surface plasmon energy is hcos. We have assumed that the dielectric function of the surrounding medium is constant or weakly dependent on frequency. 

Resonances are features inherent in the Hamiltonian and show up as more or less sharp structures in all quantities that contain the wave functions, for example, the absorption cross section uabs( ). The absorption spectrum obviously depends on the initial-state wave function xo, and therefore the various resonances are weighted with different Franck-Condon factors, which complicates the analysis of the spectrum. A numerically more convenient quantity is... 

The resonant absorption cross section for radiation at Lyman-a can be as high as 3A /27r [39]. Consider a volume of 1 mm diameter being illuminated with InW resonant radiation at Lyman-a. The excitation rate for an atom is then 5s-1. Suppose that we would like to cool antihydrogen atoms in a magnetic... 

The magnitude of the observed absorption depends on the absorption cross-section for y-rays to excite a transition between the nuclear ground and excited states at resonance. This cross-section per nucleus (Tq is given by the following equation ... 

Figure 11 shows the d band cross sections for the group 6 hexacarbonyls M(CO)6, where M = Cr, Mo, or the effect of the resonance absorption on the cross sections is clearly evident at energies around that needed for inner np shell ionization, which is indicated on the energy scale. Two resonances are seen for W 5d ionization as the spin-orbit splitting of the 5p core hole is of the order of lOeV and is sufficiently large to be resolved. 

Two basic and unique advantages are implicit in the resonance ionization process ionization efficiency and wavelength selectivity Absorption cross-sections for excitation to the first energy... 

These include nanoshells [359] composed of a dielectric core coated by a thin layer of metal nanodisks and nanorings [360], These unique nanoparticles exhibit plasmon resonance frequencies in the near-infrared at dimensions significantly smaller than 100 nm. By variation of the aspect ratio of these particles, it is possible to tune the plasmon resonance frequency as well as the cross sections for scattering and absorption, respectively. 

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