• Volume 7, Issue 2

August 1976,   pages  63-140

• Electron-electron interaction and instabilities in one-dimensional metals

The possible instabilities of a 1-dimensional itinerant electron gas are discussed, assuming electron-electron interaction to play the dominant role. As is well known, in the RPA, a 1-dimensional metal is prone to spin density wave (SDW), charge density wave (CDW) and Cooper pair (CP) instabilities. The spin channel decomposition of the irreducible scattering amplitude I is made and the spin channel projections are evaluated in terms of the matrix elements of bare electron-electron interactionV(x) for momenta of interest. It is found that if the bare electron interactionV(x) is repulsive and decreases monotonically with separation, only the SDW instability will occur. If the small separation (x≳(2kF)−1) part of the interaction is greatly reduced or is made attractive,V(x) is non-monotonic,Vq(q≅2kF) is negative, and a CDW instability is preferred. A CP instability is possible if the electron interaction is attractive,i.e., if [Vq(0&lt;q&lt;kF)+Vq(q⋍2kF)]&lt;0.

The above RPA results serve only as rough indicators, since in general there are important two-electron configurations with two-electron momentum close to zero and with electron hole momentum close to 2kF, an example being the near Fermi energy configurationk1kF,k2⋍−kF,k3⋍−kFk4kF. Therefore as pointed out first by Bychkov, Gorkov and Dzhyaloshinskii (BGD), cross channel coupling is especially significant. It is shown that the cross channel coupling is constructive is some cases,eg., exchange of CD fluctuations leads to an effective electron-electron spin singlet attraction and vice-versa. A formalism for studying such effects is set up, and the particular example mentioned above is discussed. An RPA-like approximation is made for the form of the reducible singlet electron hole scattering amplitudeγsd and the resulting induced Cooper pair attraction is calculated to be$$\begin{gathered} [I_s ^e ]_{ind.} \rho _{{}^\varepsilon F} = [ln(\lambda \beta \omega _c )]^{ - 1} ln\{ [1 + 2\pi ^{ - 1} ln(\lambda \beta \omega _c )^2 ]/ \hfill \\ 1 + [8\pi ^{ - 1} \gamma _s ^d (q = 2k_F )^{ - 1} )^2 ]\} \hfill \\ \end{gathered}$$ where λ=1.14,β=(kBT)−1 andω0 is an electronic energy cut-off ∼εF. The induced electron hole attraction due to the exchange of virtual Cooper pairs has a similar expression, but with a factor of (1/4) and withγse(q=0) replacingγsd(q=2kF). The induced Cooper pair attraction is seen to be quite large over a broad range of temperatures close to but aboveTCDW [i.e., aboveT such thatγsd(q=2kF)−1=0]. There is no requirement thatγsd(q=2kF) andγse(q=0) become singular at the same temperature, as found by BGD. The BGD prediction is seen to arise from the neglect of real particle hole and particle-particle excitations while calculatingγsdandγse. The effect of impurities, of electron-phonon coupling, of interchain coupling and of interaction between thermal order parameter fluctuations is discussed. The results are then applied to a discussion of the properties of TTF-TCNQ, where it is suggested that a CDW instability occurs becauseVq(q=2kF)&lt;0,i.e., because the small separation electron repulsion is strongly reduced by the highly polarizable TTF. Because of substantial interchain coupling, the bulk CDW instability occurs close to the RPA instability temperature. The giant conductivity observed by Colemanet al is attributed to superconductive fluctuations in a 1-dimensional system with large mean field superconductive transition temperatureTCPMF of order 300°K. Such a largeTCPMF is shown to result from the induced Cooper pair attraction due to CD fluctuation exchange.

• Low frequency electroluminescence in ferroelectric BaTiO3 single crystals

Electroluminescence has been studied in ferroelectric BaTiO3 single crystals. The variation of EL with potential temperature and d.c. biasing suggests the existence of complex surface charge layer on the surface of these crystals. The mode of growth of EL pulses reveals the nature of these layers.

• Impurity pair modes in a diatomic linear chain: nearest neighbour pair

The behaviour of the impurity modes due to a pair of substitutional impurities characterized by both mass as well as force-constant changes and occupying nearest neighbour positions in a diatomic linear chain, is studied. The results are compared with those for the case of impurity pairs occupying next nearest neighbour sites discussed earlier as well as the existing three dimensional calculations of Elliott and Pfeuty. The nearest neighbour impurity pair gap and local modes can be interpreted in terms of two single impurities substituted in the two different sublattices unlike the next nearest neighbour pair modes. The inband resonant modes are totally new features characteristic of the pair. Finally, the predictions of the theory are compared with the available experimental data for Si-impurity-pair-complexes and qualitative agreement is shown.

• Paracharge phenomenology: systematics of the new hadrons

A systematic semiquantitative account of all aspects of the strong and electromagnetic interactions of all the newly discovered hadronic states (theψ’s, theχ’s, etc.) is presented within the framework of the paracharge scheme. Extensions of ideas familiar from the SU3 classification scheme to SU4 are shown to provide an understanding of the new states seen in the decays ofψ (3.1) andψ′ (3.7), including their masses and gross decay characteristics. The decays ofψ (3.1) andψ′ (3.7) themselves are studied in some detail. Since these are of electromagnetic origin in the scheme, their electromagnetic mixing with the resonance at 4.15 GeV (theP-state of the scheme) is important. Once this is taken into account, the resulting picture is in excellent agreement with available data.

• Scission configuration in quaternary fission

Trajectory calculations have been carried out to obtain information about scission configuration in quaternary fission on the basis of observed angular-correlation and energy correlations between two alpha particles in the spontaneous quaternary fission of252Cf. A number of plausible hypotheses for the scission configuration were tested against the experimental observations on the two alpha particles. The role of mutual repulsion between two alpha particles at scission in deciding the final energy angular correlations has been examined. It was found that only one hypothesis regarding scission configuration is consistent with the experimental data.

• An interpretation of the rise of associated multiplicities with momentum transfer

We present an interpretation of the recently observed phenomenon of rise of associated multiplicity with momentum transfer as an overlap effect of two independent physical processes, the first one dominating the small momentum transfer region and the second one correspondingly the large angle region.

• # Pramana – Journal of Physics

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Posted on July 25, 2019