Single-particle excitations

This dependence on ordering occurs because, unlike the set of operators and in the 3-positivity conditions, the operators do not include the set of single-particle excitation and deexcitation operators, that is,... 

A. B. Harris and R. B. Lange, Single particle excitations in narrow energy bands, Phys. Rev. 157 295-314 (1967). 

The detection and measurement through photoemission spectroscopy of the single particle excitation associated with surface valence electron states is made difficult by the accompanying spectrum of the bulk material. When there is a gap in the bulk density of states at e, as in insulators and semiconductors, there is the possibility of observing surface states which lie in the gap. UPS has been used to observe such states in Si (60). It is practicable also to search for these states in metals at energies where the densities of bulk valence states are low or relatively structureless. Some suitable candidates for investigation should be the transition metals Ti, Zr, Hf, Cr, Mo, and W, which have low q(e) in the vicinity... 

At this point it is worth rephrasing some of the issues of the above discussions. The UPS spectra are a measure of the single-particle excitation spectrum of the molecule, in so far as removal of an electron is concerned, while UAS data are a measure of the particle-hole excitation spectrum. In other terms, UPS measures the molecular-ion states while UAS measures excited states of the neutral molecule. For a molecule in isolation, in a one-electron picture the valence electron molecular cation states are comprised of the set of one-electron molecular orbitals (mo s) containing one half-filled (usually non-degenerate) molecular orbital and the totality of other fully occupied orbitals, distorted from their situation in the neutral molecule due to the removal of an electron from the molecule in a photoelectron... 

Pickett, W. E., and C. S. Wang (1984). Local-density approximation for dynamical correlation corrections to single-particle excitations in insulators. Phys. Rev. B30, 4719-33. 

In the examples presented here, the extension to the Lindhard RPA [23] suggested by Mermin [24] is used for the bulk dielectric function. This allows one to use non-zero values of the electron gas damping, keeping the number of electrons in the system constant. We want to emphasize that this description incorporates both single-particle excitations (creation of electron-hole pairs) and collective excitations (bulk and surface plasmons). 

In liquid the low k collective excitations stiU involve phonons [137, 138]. However, in this strongly correlated dense fluid the phonon branch does not cross directly to single-particle excitations. The dispersion curve reaches... 

The 4>n > may contain contributions from the scattering continuum of the same channel. We concluded that "it is reasonable to expect that in reality these optimum conditions cannot be satisfied exactly and thus physical spectra must contain some single-particle excitation character even in regions where the spectrum is characterized mainly by a single, strongly absorbing peak" [143, p. L262]. 

Acf and AExz,/z z2,x2-/ = 3B- -2Acf. We extract the Racah B parameter from the two single-particle excitations, and use the derived value to calculate the energy of the two-particle excitation, as a check on the consistency of the mapping as can be seen in Table 10, the agreement is excellent. The free ion value for B is most closely matched by a weight of 50%, but this is purely due to the difference between excitation energies a better match with their absolute placement is obtained by uncorrelated UHF calculations. We may further conclude that density functional theory is unable to captme the small but subtle correlation corrections involved in d—>d excitations, at least not in NiO. 

Furthermore, in treating the electrical conductivity we have thus far considered only single-particle excitations and, in particular at T< T, only thermal excitations of the charge carriers across the Peierls band gap 2A. As we shall see later, the charge-density wave itself can also be transported. This charge-density-wave transport is strongly frequency and electric-field dependent (see Sect. 9.6.6). 

In concluding this section it should be mentioned that Bohr and Mottelson, in Appendix 5 of their comprehensive treatise on the collective model [4] give a somewhat similar treatment of resonance processes. They treat the coupling of the single particle excited state with the other excited configurations as occurring in a thin layer near the nuclear surface. 

Besides the information on the deformation of the fission isomers based on rotational excitations described above, some information can also be obtained on the level density of vibrational and single-particle excitations in fission isomers. 

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