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Free electron model
About: Free electron model is a research topic. Over the lifetime, 4678 publications have been published within this topic receiving 103535 citations.
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TL;DR: In this paper, it was shown that electrons, apart from the spin effect, gave a diamagnetic contribution to the susceptibility of an electron in a magnetic field, which was further considered by Bloch, who gave, as a higher approximation at low temperatures, MP = 3/2 Nμ2H/e{1-π2/12(k T/e)2}
Abstract: One of the earliest applications of the Fermic-Dirac statistics was that of pauli to the treatment of the paramagnetism, due to the electron spin, of an electron gas The result he obtained, for low temperatures, may be put in the form Mp = 3/2 Nμ2H/e, where Mp is the total magnetic moment due to the spin effect, N the number of electrons, μ the Bohr magneton, and e the maximum electron energy in the completely degenerate state It was later shown by Landau that electrons, apart from the spin effect, gave a diamagnetic contribution to the susceptibility The diamagnetic effect (which is zero on a classical basis) arises from the discreteness of the energy states of an electron in a magnetic field For low temperatures the result obtained is MD = -½ Nμ2H/e, where MD is the diamagnetic contribution to the moment The spin effect was further considered by Bloch, who gave, as a higher approximation at low temperatures, MP = 3/2 Nμ2H/e{1-π2/12( k T/e)2}
38 citations
TL;DR: In this article, the authors investigated the frequency dispersion of complex photoconductivity of TiO2 nanoparticles by laser-flash frequency-modulated time-resolved microwave conductivity (FM-TRMC) in the 9-34 GHz region.
Abstract: In a quest to explore the prominent electronic properties of titanium dioxide (TiO2), precise knowledge on the electron mobility and trapping process is an immensely important part of organic photovoltaic applications. We have investigated the frequency dispersion of complex photoconductivity of TiO2 nanoparticles by laser-flash frequency-modulated time-resolved microwave conductivity (FM-TRMC) in the 9–34 GHz region. The absolute ratio of imaginary to real transient conductivities was analyzed by the combination of Drude–Smith and Drude–Zener models, which allows for determining the trap depth (ET) and population of trapped electrons (ftrap). We have identified that the shallowly trapped electrons (ET = 70–110 meV, ftrap > 0.8) have a large impact on the negative imaginary conductivity, while the free electron confined in TiO2 nanoparticle significantly contributes to the positive real part in spite of its small population (<0.2). The kinetic mismatch of real and imaginary conductivities suggests the inv...
37 citations
TL;DR: In this paper, a series of experiments with a superconducting 500 MHz single cell cavity of "spherical" shape fabricated from niobium sheet material is reported. But, the results are limited by thermal instabilities (quenching) originating from point like loss regions predominantly found at the bottom part of the cavity.
37 citations
37 citations
TL;DR: In this paper, a selfconsistent, nonlinear description of the free electron laser using single-particle dynamics and Maxwell's wave equation was developed, where electron bunching drives the amplitude and phase of the optical wave.
37 citations