Half energy width

The best surface roughness ever made has been achieved for the ROSAT (Rontgen satellite) mirrors with about two A RMS (root mean square) microroughness. This value has been measured by X-ray scatter measurement at the PANTER test facility of the MPE (Max Planck Institut fiir Extrater-restrische Physik). The contour accuracy of the mirror shells with parabolic shape in the primaries and hyperbolic shape in the secondaries reached an X-ray performance of three arcsec HEW (half energy width) for the complete mirror system of Wolter type I with four concentric nested mirrors [4.39]. 

X-ray performance of three arc seconds HEW (half energy width) for the complete mirror system of Wolter t3rpe I with four concentric nested mirrors [4.39]. 

The measured half-life of the state is 89.4 ps, which corresponds to a energy width, T, or AE, due to the Heisenberg uncertainty principle of ... 

The conditions for such a nuclear resonance absorption are very stringent. Using the Heisenberg relationship (4.66) we can estimate the half-value width of the 129 keV peak to be 5 X 10 eV. We can also use relation (4.34) to calculate the iridium atom recoil energy to be 46 X 10 eV. Thus the 7-my leaves the source with an energy of (129 x 10 ... 

The peak related to the (3-relaxation is rather broad and symmetric. Using the half-height width of the loss peak, it can be four to six decades wide. With increasing temperature, the width of the 3-peak decreases. Quite often the width of the 3-relaxation is modeled by both a distribution of the activation energy and the preexponential factor (in the sense of Eq. 12.27) which might be related to a distribution of molecular environments of the relaxing dipole. In most cases it is difficult to extract information on the basic mechanisms of molecular motion. In other cases the broadness of the 3-peak can be also due to the overlapping of different relaxation processes as demonstrated for polycarbonate (see Fig. 12.11). 

Values of the Energy of the Solvatochromic Band E-pCSB), kcal/mol of SB, and Values of Et(SB) Imbedded in PMA, PHEMA, PBMA, and PS in Several Solvents (Half-Band Widths, Ai cm"l)... 

With all of these parameters, it was possible to calculate the energy levels of the 4f and 4f 5d electron configurations of the Tm " ions in SrCl2. In addition, probabilities of the electric dipole transitions between all possible states were also calculated. Finally, the simulated and measured 4f-5d spectra of SrCl2 Tm are shown together shown in Fig. 5.9 where the pure 4f-5d transition lines are represented by the vertical bars, and the broad bands are reproduced by using the Gaussian-shaped curves with a full width at half maximum width = 400 cm... 

Lattice Energy, Lattice Vibrational Frequencies, and Intensity Ratios for a-Nj [Frequencies are in units of cnr with half-intensity widths in parentheses. Calculated values are listed for two potential models (I) Lennard-Jones potential plus quadrupole-quadrupole term (Ron and Schnepp, 1967 Walmsley and Pople, 1964). Nearest neighbor interactions only (11) Diatomic Potential (Kuan, Warshel, and Schnepp, 1970) with 6-12 terms Raman assignments as in Cahill and Leroi (1969) and Brith, Ron, and Schnepp (1969).]... 

The decay rate assumed in Equation 7.41 corresponds to a half life of t = (In 2)/W. We thus have the relation between the energy width T and t ... 

The charge-transfer transition energy and the half band width vary considerably with solvent. 

Thus, hE for the 661.7 keV level of Ba whose half-life is 2.552 min, will be about 3 x 10 eV - exceedingly small. The level involved in the decay of Co at 1332.5 keV (see Figure 1.8) has a lifetime of 7 x 10 s this implies an energy width of about 9 x 10 " eV. This is still very small compared to the precision with which gamma energies can be measured and to the FWHM of spectrum peaks, typically 1.9 keV at 1332.5 keV. In general, the widths of the nuclear energy levels involved... 

The energy distribution of the emitted radiation and that of the resonant absorption cross section have identical lineshapes. Both are Lorentzian lines centered at the nuclear transition energy E, with fullwidth at half height given by the uncertainty principle energy width of the nuclear excited state. This width, the natural linewidth, is defined by... 

Figure 6 The energy-resolved metastable peaks for the loss of H from three isomeric C2H40 + ions. Note that the peak widths do not have a common scale. The half-height widths for the three signals are 35, 11 and 41 V from left to right.

Relativistic electrons radiate not only at the gyrofrequency, but also at the harmonics. The relativistic mass increase with energy causes the harmonic spacing to decrease with increasing energy until the synchrotron spectrum is essentially smeared into a continuum. The radiation from a relativistic electron is highly nonisotropic. The emitted radiation is concentrated within a narrow cone about the instantaneous direction of the velocity vector with an approximate half-cone-width given by... 

The energy spectrum of the resonance states will be quasi-discrete it consists of a series of broadened levels with Lorentzian lineshapes whose full-width at half-maximum T is related to the lifetime by F = Fn. The resonances are said to be isolated if the widths of their levels are small compared with the distances (spacings) between them, that is... 

The ability to identify different mass species depends on the energy resolution of the detector which is typically 15 keV fiill width at half maximum (FWFIM). For example, silver has a mass M2 = 108 and tin has a mass A , = 119. The difference between . = 0.862 and = 0.874 is 0.012. For 2 MeV helium ions the... 

The exponential decay of the A population corresponds to a Lorentzian line shape for the absorption (or emission) cross section, a, as a fiinction of energy E. The lineshape is centred around its maximum at E. The fiill-width at half-maximum (F) is proportional to... 

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