Longitudinal—transverse splitting

The oscillator strengths and longitudinal transverse splitting of [37] must be divided by n. 

In the region of longitudinal-transverse splitting 0yb < u> < Op, where e(u>) < 0, surface biphonons should also exist. At the boundary with the vacuum, their dispersion law satisfies the relation... 

FlG. 6.11. Polariton dispersion in the NH4CI crystal. Longitudinal-transverse splitting of the biphonon is observed in the frequency region v 1460 cm-1 (from (61)). 

For electronic transitions in a dielectric the frequencies of Coulomb surface excitons are in the region of the longitudinal-transverse splitting, which is always small in comparison with the frequencies uy. Taking this fact into account, eqn (12.80) can be changed into... 

Extremely damaged of lumen, fibres partially convoluted Surface notches, longitudinal and transverse splits, fibrillation and marked deformation <400... 

Now let us estimate (see Fig 25) the so-called transverse optic-longitudinal optic splitting [8,50] characteristic for ice at v 230 cm-1. Namely, the loss curve e"(v) is shifted on the frequency scale with respect to the energy loss function ... 

In a homogeneous isotropic elastic medium it is possible to split acoustic waves in independent longitudinal and transverse waves, each travelling at a speed cL and cT, respectively. As 2 is greater than or equal to zero, cT is lower than or equal to cl/ J2. 

Bulk silicon is a semiconductor with an indirect band structure, as schematically shown in Fig. 7.12 c. The top of the VB is located at the center of the Brillouin zone, while the CB has six minima at the equivalent (100) directions. The only allowed optical transition is a vertical transition of a photon with a subsequent electron-phonon scattering process which is needed to conserve the crystal momentum, as indicated by arrows in Fig. 7.12 c. The relevant phonon modes include transverse optical phonons (TO 56 meV), longitudinal optical phonons (LO 53.5 meV) and transverse acoustic phonons (TA 18.7 meV). At very low temperature a splitting (2.5 meV) of the main free exciton line in TO and LO replicas can be observed [Kol5]. 

A larger frequency shift is possible if the laser is placed in longitudinal or transverse magnetic fields which cause a Zeeman splitting of the upper and lower laser level. With polarizers and quarter wavelength plates one can select the shifted a+ or a- component... 

In Eqs. (4)-(7) S is the electron spin quantum number, jh the proton nuclear magnetogyric ratio, g and p the electronic g factor and Bohr magneton, respectively. r//is the distance between the metal ion and the protons of the coordinated water molecules, (Oh and cos the proton and electron Larmor frequencies, respectively, and Xr is the reorientational correlation time. The longitudinal and transverse electron spin relaxation times, Tig and T2g, are frequency dependent according to Eqs. (6) and (7), and characterized by the correlation time of the modulation of the zero-field splitting (x ) and the mean-square zero-field-splitting energy (A. The limits and the approximations inherent to the equations above are discussed in detail in the previous two chapters. 

Another important parameter that influences the inner sphere relaxivity of the Gd(III)-based contrast agents is the electronic relaxation time. Both the longitudinal and transverse electron spin relaxation times contribute to the overall correlation times xa for the dipolar interaction and are usually interpreted in terms of a transient zero-field splitting (ZFS) interaction (22). The pertinent equations [Eqs. (6) and (7)] that describe the magnetic field dependence of 1/Tie and 1/T2e have been proposed by Bloembergen and Morgan and... 

The implication of Eq. (6.21) is that the criterion is dependent mainly on the ratio of the energies for longitudinal splitting and transverse cracking, and is relatively insensitive to crack length and the elastic modulus. It is also noted from experimental study that crack speed has a pronounced effect on the toughness ratio, Rl/Ri, and thus the crack deflection phenomenon. 

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