Reduced-energy spectrum

Fig. 1.3. Reduced-energy spectrum showing in-band variation of X(0k) = cos 0k between band edges at Xk = 1 for gs < 1 and Ok real. V — (Af—) localized states appear above (below) band for Ok complex and zs > 1.

Equations (3.38) and (3.48) are the analytical expressions for the band and adstate contributions to the total reduced-energy spectrum of the adatom DOS, pa(x), respectively. Their graphs are displayed in Fig. 3.4 for 2/3 = 1 and the parameter values indicated. As can be seen, the presence of the large adstate spike at X = Xa markedly reduces the area under the in-band portion of the DOS, in accordance with the sum rule (cf. (3.34))... 

The X-ray spectrum observed in PIXE depends on the occurrence of several processes in the specimen. An ion is slowed by small inelastic scatterings with the electrons of the material, and it s energy is continuously reduced as a frmction of depth (see also the articles on RBS and ERS, where this part of the process is identical). The probability of ionizii an atomic shell of an element at a given depth of the material is proportional to the product of the cross section for subshell ionization by the ion at the reduced energy, the fluorescence yield, and the concentration of the element at the depth. The probability for X-ray emission from the ionized subshell is given by the fluorescence yield. The escape of X rays from the specimen and their detection by the spectrometer are controlled by the photoelectric absorption processes in the material and the energy-dependent efficiency of the spectrometer. 

In quantum wires formed in a two-dimensional electron gas (2DEG) by lateral confinement the Rashba spin-orbit interaction is not reduced to a pure ID Hamiltonian H[s = asopxaz. As was shown in Ref. [4] the presence of an inplane confinement potential qualitatively modifies the energy spectrum of the ID electrons so that a dispersion asymmetry appears. As a result the chiral symmetry is broken in quantum wires with Rashba coupling. Although the effect was shown [4] not to be numerically large, the breakdown of symmetry leads to qualitatively novel predictions. 

The Compton continuum, present in gamma energy spectra recorded either by a Nal(Tl) scintillator or by a Ge detector, is a nuisance that impedes the analysis of complex spectra. It is therefore desirable to eliminate or at least reduce that part of the spectrum relative to the gamma energy peak. One way to achieve this is to use two detectors and operate them in anticoincidence. Such an arrangement, known as the Compton-suppression spectrometer, is shown in Fig. 12.9. A large NaI(Tl) scintillator surrounds a Ge detector, and the two detectors are operated in anticoincidence. The energy spectrum of the central... 

Figure 13.10 Measured ( ) and unfolded (O) beta spectra from fission fragments. Unfolding removes the effect of backscattering in the detector thus, it reduces the spectrum at the low-energy end (from Ref. 26).

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