Non-resonant

The term resonance has also been applied in valency. The general idea of resonance in this sense is that if the valency electrons in a molecule are capable of several alternative arrangements which differ by only a small amount in energy and have no geometrical differences, then the actual arrangement will be a hybrid of these various alternatives. See mesomerism. The stabilization of such a system over the non-resonating forms is the resonance energy. 

The population in the upper state as a flinction of time is shown in figure A1.6.2. There are several important things to note. At early times, resonant and non-resonant excitation produce the same population in the upper state because, for short times, the population in the upper state is independent of the Rabi frequency ... 

One should also notice that resonant excitation completely cycles the population between the lower and upper state with a period of 2ji/0. Non-resonant excitation also cycles population between the states but never completely depopulates the lower state. Finally, one should notice that non-resonant excitation cycles population between the two states at a faster rate than resonant excitation. 

Figure Al.6.2. The population in the upper state as a fiinction of time for resonant excitation (frill curve) and for non-resonant excitation (dashed curve).

In words, equation (Al.6.89) is saying that the second-order wavefunction is obtained by propagating the initial wavefunction on the ground-state surface until time t", at which time it is excited up to the excited state, upon which it evolves until it is returned to the ground state at time t, where it propagates until time t. NRT stands for non-resonant tenn it is obtained by and cOj -f-> -cOg, and its physical interpretation is... 

Equation (A 1.6.94) is called the KHD expression for the polarizability, a. Inspection of the denominators indicates that the first temi is the resonant temi and the second temi is tire non-resonant temi. Note the product of Franck-Condon factors in the numerator one corresponding to the amplitude for excitation and the other to the amplitude for emission. The KHD fonnula is sometimes called the siim-over-states fonnula, since fonnally it requires a sum over all intennediate states j, each intennediate state participating according to how far it is from resonance and the size of the matrix elements that coimect it to the states i. and The KHD fonnula is fiilly equivalent to the time domain fonnula, equation (Al.6.92). and can be derived from the latter in a straightforward way. However, the time domain fonnula can be much more convenient, particularly as one detunes from resonance, since one can exploit the fact that the effective dynamic becomes shorter and shorter as the detuning is increased. 

With this convention, we can now classify energy transfer processes either as resonant, if IA defined in equation (A3.13.81 is small, or non-resonant, if it is large. Quite generally the rate of resonant processes can approach or even exceed the Leimard-Jones collision frequency (the latter is possible if other long-range potentials are actually applicable, such as by pennanent dipole-dipole interaction). 

Non-resonant processes include vibration-translation (V-T) processes with transfer probabilities decreasing... 

Schaertel S A and Albrecht A C 1994 Interferometric coherent Raman spectroscopy resonant and non-resonant contributions J. Raman Spectrosc. 25 545-55... 

Friedrich B and Herschbach D 1996 Alignment enhanced spectra of molecules in intense non-resonant laser fields Chem. Phys. Lett. 262 41... 

For the system (16) it is known [5] under non-resonance assumptions that in the limit m/M 0 the motion of the classical particle is governed... 

Quasi-resonant converters are a separate class of switching power supplies that tune the ac power waveforms to reduce or eliminate the switching loss within the supply. This is done by placing resonant tank circuits within the ac current paths to create pseudo-sinusoidal voltage or current waveforms. Because the tank circuits have one resonant frequency, the method of control needs to be modified to a variable frequency control where the resonant period is fixed and the control varies the period of the non-resonant period. The quasi-resonant converters usually operate in the 300 kHz to 2 MHz frequency range. 

Surface analysis by non-resonant (NR-) laser-SNMS [3.102-3.106] has been used to improve ionization efficiency while retaining the advantages of probing the neutral component. In NR-laser-SNMS, an intense laser beam is used to ionize, non-selec-tively, all atoms and molecules within the volume intersected by the laser beam (Eig. 3.40b). With sufficient laser power density it is possible to saturate the ionization process. Eor NR-laser-SNMS adequate power densities are typically achieved in a small volume only at the focus of the laser beam. This limits sensitivity and leads to problems with quantification, because of the differences between the effective ionization volumes of different elements. The non-resonant post-ionization technique provides rapid, multi-element, and molecular survey measurements with significantly improved ionization efficiency over SIMS, although it still suffers from isoba-ric interferences. 

As illustrated in Fig. 3.41, several laser schemes can be used to ionize elements and molecules. Scheme (a) in this figure stands for non-resonant ionization. Because the ionization cross-section is very low, a very high laser intensity is required to saturate the ionization process. Scheme (b) shows a simple single-resonance scheme. This is the simplest but not necessarily the most desirable scheme for resonant post-ionization. Cross-... 

A versatile Laser-SNMS instrument consists of a versatile microfocus ion gun, a sputtering ion gun, a liquid metal ion gun, a pulsed flood electron gun, a resonant laser system consisting of a pulsed Nd YAG laser pumping two dye lasers, a non-resonant laser system consisting of a high-power excimer or Nd YAG laser, a computer-controlled high-resolution sample manipulator on which samples can be cooled or heated, a video and electron imaging system, a vacuum lock for sample introduction, and a TOF mass spectrometer. 

Fig. 3.42. Non-resonant laser-SNMS spec- riety oftransition metals and hydrocarbons trum ofa Si wafer contaminated with a va- [3.105].

Element mapping with non-resonant laser- SNM S can be used to investigate the structure of electronic devices and to locate defects and microcontaminants [3.114]. Typical SNMS maps for a GaAs test pattern are shown in Fig. 3.43. In the subscript of each map the maximum number of counts obtained in one pixel is given. The images were acquired by use of a 25-keV Ga" liquid metal ion source with a spot size of approximately 150-200 nm. For the given images only 1.5 % of a monolayer was consumed -"static SNMS". 

Fig. 3.43. Non-resonant laser-SNMS mapping of a contact test structure on GaAs. Field of view 40 x 40 pm [3.114],...

Eor a non-resonant nuclear reaction with emission of an ion, a depth scale can be obtained from the measured energy of the emitted ions. If ions emitted from a depth x are lower in energy by AE than ions emitted from the surface, a relationship between AE and x can be found, similarly to RBS and ERDA analysis ... 

Using the calculated phonon modes of a SWCNT, the Raman intensities of the modes are calculated within the non-resonant bond polarisation theory, in which empirical bond polarisation parameters are used [18]. The bond parameters that we used in this chapter are an - aj = 0.04 A, aji + 2a = 4.7 A and an - a = 4.0 A, where a and a are the polarisability parameters and their derivatives with respect to bond length, respectively [12]. The Raman intensities for the various Raman-active modes in CNTs are calculated at a phonon temperature of 300K which appears in the formula for the Bose distribution function for phonons. The eigenfunctions for the various vibrational modes are calculated numerically at the T point k=Q). 

Ignoring any interactions with non-resonant nuclei we have 4G... 

For fixed non-resonant sign, when the dipole moment of a molecule rotates by... 

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