Particle-hole continuum

The Franz-Keldysh effects (Weiser and Horvath 1997) have been successfully used to distinguish the particle-hole continuum from exciton states in polydiacetylene crystals (Sebastian and Weiser 1981). 

Figure 10.2 illustrates the electroabsorption spectrum of phenyl-substituted traras-polyacetylene thin film (Liess et al. 1997). The feature at 2.0 eV is the red-shifted l Bu exciton. The feature at 2.5 eV is attributed to a dipole-forbidden state, namely the m Ag state. Unlike polydiacetylene crystals, disordered trans-polyacetylene thin film does not exhibit Pranz-Keldysh oscillations (described in Chapter 8) and therefore a definite assignment of a conduction band edge cannot made. However, because disordered polydiacetylene also does not exhibit Pranz-Keldysh oscillations, but a smeared-out feature similar to the one exhibited at 2.5 eV in Fig. 10.2 it is sometimes assumed that this feature does mark the band edge. Another interpretation is that this feature represents the n = 2 Mott-Hubbard exciton, described in Chapter 6, with the particle-hole continuum lying close in energy (possibly at 2.7 eV, which is three times the THG feature at... 

Table 11.4 shows that the 2 A+ state has a large transition dipole moment with the l Bfu state, and unlike the case for polyenes, it is not predominantly a pair of bound magnons, but a particle-hole excitation. (It is usually labelled the m Ag state.) This particle-hole excitation is either an n = 2 Mott-Wannier exciton, or the edge of the unbound particle-hole continuum. 

Fig. E.l. The dispersion curves of the four lowest bound states (solid and dashed) for a regularized Coulomb potential with a K = 0) = 1. Even (odd n) parity states (solid curves) and odd (even n) parity states (dashed curves). The particle-hole continuum is bounded by the dotted curves. The energies are in units of Ej.

A remarkable point in our treatment of dynamical exchange effects, is the fact that G q, u) (Eq. 19) is logarithmically divergent at the boundaries of the particle-hole continuum. The physical significance of these singularities... 

Certainly the most important models for the development of modem scaling theory of critical phenomena have been the discrete Ising model of ferromagnetism and its antipode - the continuum van der Waals model of fluid. The widespread belief is that real fluids and the lattice-gas 3D-model belong to the same universality class but the absence of any particle-hole-type symmetry in fluids requires the revised scaling EOS. The mixed variables were introduced to modify the original Widom EOS and account the possible singularity of the rectilinear diameter. 

The phenomenological FEOS-model and its consequence - the HPD with the formal particle-hole-type symmetry of a quasibinodal has some specific distinctions from the relevant conventional approaches. First of all, it is based on the continuum, exactly solvable WMG-model of a phase transition without any adjustable parameters. Besides, the study of the novel substances and mixtures can be carried out within the framework of the common FEOS which is applicable to any low-molecular and high-molecular compounds. This property can be quite useful in many applications such as the supercritical extraction or the low-temperature phase transition in the complex mixtures. 

The calculated photoabsorption spectrum of this cluster shows a collective excitation with a peak at 2.12 eV. The tail of the resonance extends up to 3 eV, and concentrates a sizable amount of strength, due to particle-hole transitions that interact with the collective excitation and lead to its broadening. One of the most important particle-hole transitions is that from the HOMO level to the continuum the energy of this ionization threshold is indicated by the arrow at 2.6 eV. Similar TDLDA calculations have been performed for pure Na [104] and pure K [127] clusters. Comparing the positions of the collective resonances, it can be concluded that the position of the resonance in K2oNa2o is closer to that in pure K clusters thus, the surface, made of K atoms, controls the frequency of the collective resonance. 

As a consequence of the local nature of V (x) the TDLDA possesses several desirable qualities not available in the usual RPAE. From a purely practical point of view, the differential equations approach permits all the excited orbitals (bound and continuum) to be automatically included through the Green function regardless of the size of the atom. In the language of perturbation theory, one easily sums all the dipolar particle-hole channels which couple the atomic shells. More Importantly however, the effective field, (x o)), depends explicitly on space and frequency which allows a pictorial representation of atomic dynamics. In particular, one can define an effective local dielectric function,... 

Given the diversity of relevant applications, it is not surprising that the characterization of voids in disordered systems has an appreciable history, which can be traced back to primitive hole theories of the liquid state (Frenkel, 1955 Ono and Kondo, 1960). While the early theories offer an admittedly rudimentary lattice description of voids, recent computational advances permit an exact (and highly efficient) characterization of the continuum void geometry present in particle packings in two (Rintoul and Torquato, 1995) and three dimensions (Sastry et al., 1997a). 

The confinement of electrons or holes in potential wells leads to the creation of discrete energy levels in the wells, compared with the continuum of states in hulk material quantisation also leads to a major change in the density of states. The energy levels can be calculated by solving the Schrodinger equation for the well-known particle in a box problem. Using the effective mass envelope function approximation (Bastard, 1981 and 1982 Altarelli, 1985 Bastard and Brum, 1986), the electron wavefunction % is then... 

Auger spectroscopy prepares a system in a core-hole state by ionizing radiation and measures the kinetic energy of secondary electrons produced when the highly excited core-hole state makes a radiationless transition to a continuum state with two valence-holes and a free electron. The initial photoelectron and the secondary (Auger) electron make this a two-electron detachment process leading to the two-particle two-hole propagator... 

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