Intensity/energy response function

The intensity/energy response function (lERF) of a spectrometer is the product of the area from which photoelectrons are collected, of the transmission function (T), and of the detector efficiency D). With a microfocused X-ray beam, such as in SSX 100/206 spectrometer, the area of collection is defined by the X-ray spot size and is smaller than the acceptance area of the analyzer. The relative intensity of the peaks is sensitive to the position of the sample on the vertical axis. When a broad X-ray source is used, the lERF includes also the variation of the area of collection as the latter may depend on the energy of the photoelectrons detected (cf. the section on Basic Equations). 

Seah et al. [20,32] have addressed the calibration of the intensity/energy response function for valid analytical measurements with electron spectrometers used in XPS and AES. Both techniques have matured to a sufficient level that calibration systems are now available which allow spectral intensities to be related from instrument to instrument. The KE axis is usually calibrated with reference to a signal belonging to an internal calibrant, e.g. the Cl - level of adventitious carbon due to pump oil or the Au4/7/2 level of gold vacuum-deposited on the sample. 

Fig. 2. Time resolved fluorescence spectra of all-trans PRSB in methanol (black) and octanol (grey) for a) t<50 fs and b) t>50 fs. The intensity of the octanol spectra is adjusted the methanol spectra. The spectra are not corrected for self-absorption (for >19.500 cm 1), or for the detector response function. A residual signal appearing at energies <14.000 cm"1 is due to incomplete background subtraction (see above).

However, usually EELS can be easily measured over an extended energy range Ifom 1 eV upwards and very accurately. Together with suitable extrapolation down to 0 eV (usually with the aid of optical data), the function Im[— ] can be deduced over the whole energy range where it has significant intensity. The causality relation governing linear response functions can be used to relate Re[— ] with Im[— ] ... 

To date, not much use has been made of the MCSCF based EOM theories as developed in the author s group. Instead, the framework of time-dependent response theory, which can treat essentially any kind of reference wave function l0,A ) including the MCSCF variety, has superceded the EOM-based developments for such cases. It is important to keep in mind, however, that both the EOM and response function theories involve formulating and solving sets of equations whose solution (i.e. the unknown energy) is an intensive energy. 

The microcanonical ensemble describes an "isolated" system. The dynamical approach says all states for a given energy are equally likely and the energy is fixed in an isolated system. From conservation of probability, = 1/Q( ) if = E and is zero otherwise. In the variational approach, one maximizes S[P.y] subject to the constraints that = 1 and that E = E. The result is the same from both approaches. There is a microcanonical temperature, which is a response function and is an intensive quantity. The inverse temperature P = f Iv,n measures how the entropy changes as the energy is varied. 

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