BC model

It was argued that the Raman spectra of the B local mode provide further evidence for the BC configuration of the B—H complex (Stutzmann and Herrero, 1988b Herrero and Stutzmann, 1988a). The B vibration of the complex is not affected by the substitution of D for the lighter H this implies that the B—H bond is weak, consistent with the BC model. 

This two-phonon transition was subsequently observed as predicted in infrared-absorption (Stavola et al., 1989a). Furthermore, its polarization is the same as the fundamental one-phonon (111) transition from which it gains its oscillator strength, providing further support for the BC model. Finally, a considerably weaker two-phonon infrared absorption was observed for nB, also consistent with predictions based on this model. 

Despite the precise knowledge of the muon hyperfine interaction and a wealth of other complementary information on Mu, no compelling theory emerged until 1986 when Cox and Symons proposed a molecular-orbital bond-center (BC) model to explain the muon hyperfine interaction (Symons, 1984 Cox and Symons, 1986). Since then it has been tested both theoretically (Van de Walle, 1991) and experimentally. 

The muon and 29Si hyperfine parameters provide compelling evidence in support of the BC model. In the simple molecular-orbital model proposed by Cox and Symons (1986) the muon is located at the center of a Si—Si bond near a node in the unpaired electron spin density, which is... 

The work on diamond is important both from an experimental and a theoretical viewpoint. Since the carbon atoms that make up diamond are simpler to deal with theoretically, some calculations on hydrogen and muonium in diamond are considered to be more reliable than similar calculations on higher-Z materials. Thus diamond can be used as a testbed for new ideas on simple defects such as muonium or hydrogen and the associated theoretical methods. For example, the first theoretical confirmation of the BC model of Mu and the metastablility of Mu was made for diamond (Claxton et al., 1986 Estle et al., 1986 Estle et al., 1987). 

The most convincing evidence for the BC model of Mu in III-V materials comes from the nuclear hyperfine structure in GaAs. The hyperfine parameters for the nearest-neighbor Ga and As on the Mu symmetry axis and the corresponding s and p densities are given in Table I. One finds a total spin density on the As(Ga) of 0.45 (0.38) with the ratio of p to 5 density of 23 (4) respectively. The fact that 83% of the spin density is on the two nearest-neighbor nuclei on the Mu symmetry axis agrees with the expectations of the BC model. From the ratios of p to s one can estimate that the As and Ga are displaced 0.65 (17) A and 0.14(6) A, respectively, away from the bond center. The uncertainties of these estimates were calculated from spin polarization effects, which are not known accurately, and they do not reflect any systematic uncertainties in the approximation. These displacements imply an increase in the Ga—As bond of about 32 (7)%, which is similar to calculated lattice distortions for Mu in diamond (Claxton et al., 1986 Estle et al., 1986 Estle et al., 1987) and Si (Estreicher, 1987). 

The entire situation changed when Bednorz and Muller (1986) discovered 30 K superconductivity in a cuprate of the La-Ba-Cu-O system. This broke the apparent 23 K barrier for the T. Since 1986, a variety of cuprates have been synthesized and characterized with the maximum reaching 150K. The cuprates are unusual in many ways and do not seem to follow the BCS model. We shall discuss the cuprates at length later in Chapter 7. Alkali and alkaline-earth derivatives of Cgo (buckminsterful-lerene) exhibit superconductivity with a maximum of 35 K. We shall examine these... 

Spectra like the ones shown in Fig. 3.10 may be readily decomposed into their line profiles. As an example, we show that the low-temperature measurement may be accurately represented by three identical profiles. Using the so-called BC model profile with three adjustable parameters and centering one at zero frequency (the Qo(l) line), another one at 354 cm-1 (the H2 So(0) line) and the third one at 587 cm-1 (the So(l) line), one may fit the measurement using least mean squares techniques, Fig. 3.11. The superposition (heavy line type) of the three profiles (thin... 

The BC model. Birnbaum and Cohen start from a two-parameter time correlation function [36, 38]... 

The inverse system of equations which permits the computation of the parameters of the BC model from the moments, M for n = 0...2, is readily derived from these expressions [52, 290]. 

Fig. 5.8. Root mean square relative errors of model line shapes fitted to a quantum profile, the quadrupole-induced (XL = 23) component [69], The abscissa gives the ratio of peak intensity and wing intensity of the fitted portion of the exact profile. The superiority of the BC model (lower set of data points) over the desymmetrized Lorentzian (upper set) is evident.

The BC and K0 models, on the other hand, show much smaller root mean square errors, typically in the 1 % range, over an amazingly substantial range x of intensities fitted, Fig. 5.8, lower set of data points. Maximal deviations from the exact profiles amount to no more than twice the root mean square errors shown, that is well within the experimental uncertainties of the best measurements. The BC model is especially well suited to approximate quadrupole-induced profiles. The K0 model, on the other... 

Nilsson diagram for protons with tc = 0.067 and m 0.53 BCS model Fermi level for Y with Ap 0.69 MeV is indicated by dots. 

A number of experiments, shown in Fig.l, were used to determine the value of the energy gap parameter and its temperature dependence according to the modified model of Blonder, Tinkham, and Klapwijk [22]. This model takes into consideration the finite lifetime of quasiparticles as a result of inelastic scattering processes. In this way we got a value A0 - 3 meV which is close to from the value 3.4 meV found in NbsSn [23]. The BCS model describes quite well the dependence A(T) (Fig.2) obtained from the experimental results. 

Abstract By relating the Cooper/BCS model inter-electron interaction dimension-... 

Rosseinsky et al. also suggested a simple reason for the large increase in transition temperature when Rb is substituted for K. The most elementary, widely understood theory of superconductivity, the weak-coupling Bardeen-Cooper-Schrieffer (BCS) model,[Bat57] predicts a simple connection between transition temperature Tc, phonon energy w, electron-phonon coupling strength V, and the density of electron states at the Fermi surface N EfI... 

We speculated previously that superconductivity in KjCso and Rb3Ceo resulted from electron pairing mediated by high-frequency intramolecular phonons of the Qo molecule, with the change in between KaCeo and RbaCso explained by a change of the density of states at the Fermi level by about 10%. In this weak-coupling BCS model, the variation of is given by... 

Fig. 20. The reflected energy fraction is shown as a function of the total scatter angle for both the single-scatter and the double half-scatter BC models. Mass ratios /x = 1.43. (From Helmer and Graves, 1998.)...

The first conclusion to be drawn from this work is that calculations based on the BCS model cannot presently explain the Tc s of order 90 K given the phonon frequencies and band structures calculated. This points out that perhaps a mechanism other than an electron-phonon mechanism is involved, which depends on parameters with larger energy scales. A possibility is an electronic mechanism, many of which have been proposed. We will discuss one of these in the next section. 

---