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How can we differentiate an exciton Bohr radius and Debye length, or can we relate these two?
Correction of the exciton Bohr radius in monolayer transition metal dichalcogenidesNASA Astrophysics Data System (ADS)Li, Run-Ze; Dong, Xi-Ying; Li, Zhi-Qing; Wang, Zi-Wu2018-07-01We theoretically investigate the correction of exciton Bohr radius in monolayer transition metal dichalcogenides (TMDCs) on different polar substrates arising from the exciton-optical phonon coupling, in which both the intrinsic longitudinal optical phonon and surface optical phonon modes couple with the exciton are taken into account. We find that the exciton Bohr radius is enlarged markedly due to these coupling. Moreover, it can be changed on a large scale by modulating the polarizability of polar substrate and the internal distance between the monolayer TMDCs and polar substrate. Theoretical result provides a potential explanation for the variation of the exciton Bohr radius in experimental measurement.A New Contribution for WYP 2005: The Golden Ratio, Bohr Radius, Planck's Constant, Fine-Structure Constant and g-FactorsNASA Astrophysics Data System (ADS)Heyrovska, R.; Narayan, S.2005-10-01Recently, the ground state Bohr radius (aB) of hydrogen was shown to be divided into two Golden sections, aB,p = aB/ø2 and aB,e = aB/ø at the point of electrical neutrality, where ø = 1.618 is the Golden ratio (R. Heyrovska, Molecular Physics 103: 877-882, and the literature cited therein). The origin of the difference of two energy terms in the Rydberg equation was thus shown to be in the ground state energy itself, as shown below: EH = (1/2)e2/(κaB) = (1/2)(e2/κ) [(1/aB,p - (1/aB,e)] (1). This work brings some new results that 1) a unit charge in vacuum has a magnetic moment, 2) (e2/2κ) in eq. (1) is an electromagnetic condenser constant, 3) the de Broglie wavelengths of the proton and electron correspond to the Golden arcs of a circle with the Bohr radius, 4) the fine structure constant (α) is the ratio of the Planck's constants without and with the interaction of light with matter, 5) the g-factors of the electron and proton, ge/2 and gp/2 divide the Bohr radius at the magnetic center and 6) the ``mysterious'' value (137.036) of α -1 = (360/ø2) - (2/ø3), where (2/ø3) arises from the difference, (gp - ge).Excitonic effects and related properties in semiconductor nanostructures: roles of size and dimensionalityNASA Astrophysics Data System (ADS)Wu, Shudong; Cheng, Liwen; Wang, Qiang2017-08-01The size- and dimensionality-dependence of excitonic effects and related properties in semiconductor nanostructures are theoretically studied in detail within the effective-mass approximation. When nanostructure sizes become smaller than the bulk exciton Bohr radius, excitonic effects are significantly enhanced with reducing size or dimensionality. This is as a result of quantum confinement in more directions leading to larger exciton binding energies and normalized exciton oscillator strengths. These excitonic effects originate from electron-hole Coulombic interactions, which strongly enhance the oscillator strength between the electron and hole. It is also established that the universal scaling of exciton binding energy versus the inverse of the exciton Bohr radius follows a linear scaling law. Herein, we propose a stretched exponential law for the size scaling of optical gap, which is in good agreement with the calculated data. Due to differences in the confinement dimensionality, the radiative lifetime of low-dimensional excitons becomes shorter than that of bulk excitons. The size dependence of the exciton radiative lifetimes is in good agreement with available experimental data. This strongly enhanced electron-hole exchange interaction is expected in low-dimensional structures due to enriched excitonic effects. The main difference in nanostructures compared to the bulk can be interpreted in terms of the enhanced excitonic effects induced by exciton localization. The enhanced excitonic effects are expected to be of importance in developing stable and high-efficiency nanoscale excitonic optoelectronic devices.The Bohr paradoxNASA Astrophysics Data System (ADS)Crease, Robert P.2008-05-01In his book Niels Bohr's Times, the physicist Abraham Pais captures a paradox in his subject's legacy by quoting three conflicting assessments. Pais cites Max Born, of the first generation of quantum physics, and Werner Heisenberg, of the second, as saying that Bohr had a greater influence on physics and physicists than any other scientist. Yet Pais also reports a distinguished younger colleague asking with puzzlement and scepticism "What did Bohr really do?"."Bohr's Atomic Model."ERIC Educational Resources Information CenterWillden, Jeff2001-01-01"Bohr's Atomic Model" is a small interactive multimedia program that introduces the viewer to a simplified model of the atom. This interactive simulation lets students build an atom using an atomic construction set. The underlying design methodology for "Bohr's Atomic Model" is model-centered instruction, which means the central model of the…Revisiting the Bohr Atom 100 Years LaterNASA Astrophysics Data System (ADS)Wall, Ernst2013-03-01We use a novel electron model wherein the electron is modeled as a point charge behaving as a trapped photon revolving in a Compton wavelength orbit at light speed. The revolving point charge gives rise to spiraling Compton wavelets around the electron, which give rise to de Broglie waves. When applied to the Bohr model, the orbital radius of the electron scales to the first Bohr orbit's radius via the fine structure constant. The orbiting electron's orbital velocity, Vb, scales to that of the electron's charge's internal velocity (the velocity of light, c) via the fine structure constant. The Compton wavelets, if they reflect off the nucleus, have a round trip time just long enough to allow the electron to move one of its diameters in distance in the first Bohr orbit. The ratio of the electron's rotational frequency, fe, to its rotational frequency in the Bohr orbit fb, is fe/fb = 1/α2, which is also the number of electron rotations in single orbit. If we scale the electron's rotational energy (h*fe) to that of the orbit using this, the orbital energy value (h*fb) would be 27.2114 eV. However, the virial theorem reduces it to 13.6057, the ground state energy of the first Bohr orbit. Ref:A Theoretical Vortex Model of the Electron that provides the physical origin of electron spin, electron angular momentum and the Vortex Deuteron, as well as the Physical Origins of their Magnetic Moments and Angular Momentums, and a Longitudinal Electric Field Model of the Neutrino, A Negative Mass Tachyon Based Electron ModelOrigin of electron spin | origin of electron angular momentum |neutrino | negative mass tachyon "> The Electron’s Tiny Revolving Point Charge, and How it Generates its Magnetic Moment, its Angular Momentum, its Mass, and How it Gives Rise to de Broglie Waves in Electron-Electron Interactions Also: The First Direct Measurements of the PVT Surface and Melting Curve Minimum of Solid Helium-Three Ernst L. Wall Senior Scientist Institute for Basic Research Palm Harbor, FL To see the broad spectrum of the ongoing work at the Institute for Basic Research, visit their web site by clicking here . This web site was originally created in 1995. Last update is August 25, 2020 Also, see an analysis of global warming on the website by this author, www.gwphysics.com ========================================================================================= Abstract 1. In this model, the electron’s tiny charge revolves at the speed of light in a Compton wavelength orbit. Using this, we can derive the magnetic moment (the Bohr magneton), identically, in three simple algebraic equations. We also derive the mass-energy in 2 easy equations, and the spin-angular momentum, again, in 3 easy equations. 2. This model provides the basis for wave mechanics at the atomic level, but shows that wave mechanics is not necessary for describing the internals of the electron, and the results speak for themselves . The revolving charge generates an outward spiraling electrical field around the electron as opposed to a continuous static electric field. This spiraling field has a Compton wavelength, and that gives rise to a de Broglie wavelength interval for electron – electron interactions . 3. We expand these concepts to cover the proton and neutron. Then, there is a Yukawa-like deuteron model made up of two revolving charge protons that are mutually attracted to a pion. Using the diameter of the protons and the quadrupole moment of the deuteron, we determine its dimensions. It is interesting to note that using these discrete charges and their spacing, the electrostatic binding energy of this structure is 2.444 MeV, a small fraction larger than the known. (We note that there are likely those that will be upset about these results, but they can easily do the math for themselves in order to prove that this is true or not true.) 4. We also study the effects of the Compton wavelets on the first Bohr radius of the hydrogen atom, and find it is related to the radius of the electron by the fine structure constant. To do this, we have to define “electron coordinates” where the unit of time is the time that it takes for the revolving charge to do one revolution ( t e = 8.09329979E-21 seconds ), the unit of length is the Compton wavelength, and the unit of mass is the mass of the electron. Velocity, of course, is Comptons / rotation. ========================================================================================= Notes on author’s background are at the very end of this page. Fohttp://www.tachyonmodel.com.Influence of image charge effect on exciton fine structure in an organic-inorganic quantum well materialSciTech ConnectTakagi, Hidetsugu; Kunugita, Hideyuki; Ema, Kazuhiro2013-12-04We have investigated experimentally excitonic properties in organic-inorganic hybrid multi quantum well crystals, (C{sub 4}H{sub 9}NH{sub 3}){sub 2}PbBr{sub 4} and (C{sub 6}H{sub 5}−C{sub 2}H{sub 4}NH{sub 3}){sub 2}PbBr{sub 4}, by measuring photoluminescence, reflectance, photoluminescence excitation spectra. In these materials, the excitonic binding energies are enhanced not only by quantum confinement effect (QCE) but also by image charge effect (ICE), since the dielectric constant of the barrier layers is much smaller than that of the well layers. By comparing the 1s-exciton and 2s-exciton energies, we have investigated the influence of ICE with regard to the difference of the Bohr radius.Teaching Bohr Theory.ERIC Educational Resources Information CenterLatimer, Colin J.1983-01-01Discusses some lesser known examples of atomic phenomena to illustrate to students that the old quantum theory in its simplest (Bohr) form is not an antiquity but can still make an important contribution to understanding such phenomena. Topics include hydrogenic/non-hydrogenic spectra and atoms in strong electric and magnetic fields. (Author/JN)Einstein, Bohr, and BellNASA Astrophysics Data System (ADS)Bellac, Michel Le2014-11-01The final form of quantum physics, in the particular case of wave mechanics, was established in the years 1925-1927 by Heisenberg, Schrödinger, Born and others, but the synthesis was the work of Bohr who gave an epistemological interpretation of all the technicalities built up over those years; this interpretation will be examined briefly in Chapter 10. Although Einstein acknowledged the success of quantum mechanics in atomic, molecular and solid state physics, he disagreed deeply with Bohr's interpretation. For many years, he tried to find flaws in the formulation of quantum theory as it had been more or less accepted by a large majority of physicists, but his objections were brushed away by Bohr. However, in an article published in 1935 with Podolsky and Rosen, universally known under the acronym EPR, Einstein thought he had identified a difficulty in the by then standard interpretation. Bohr's obscure, and in part beyond the point, answer showed that Einstein had hit a sensitive target. Nevertheless, until 1964, the so-called Bohr-Einstein debate stayed uniquely on a philosophical level, and it was actually forgotten by most physicists, as the few of them aware of it thought it had no practical implication. In 1964, the Northern Irish physicist John Bell realized that the assumptions contained in the EPR article could be tested experimentally. These assumptions led to inequalities, the Bell inequalities, which were in contradiction with quantum mechanical predictions: as we shall see later on, it is extremely likely that the assumptions of the EPR article are not consistent with experiment, which, on the contrary, vindicates the predictions of quantum physics. In Section 3.2, the origin of Bell's inequalities will be explained with an intuitive example, then they will be compared with the predictions of quantum theory in Section 3.3, and finally their experimental status will be reviewed in Section 3.4. The debate between Bohr and Einstein goes much beyond aRutherford-Bohr atomNASA Astrophysics Data System (ADS)Heilbron, J. L.1981-03-01Bohr used to introduce his attempts to explain clearly the principles of the quantum theory of the atom with an historical sketch, beginning invariably with the nuclear model proposed by Rutherford. That was sound pedagogy but bad history. The Rutherford-Bohr atom stands in the middle of a line of work initiated by J.J. Thomson and concluded by the invention of quantum mechanics. Thompson's program derived its inspiration from the peculiar emphasis on models characteristic of British physics of the 19th century. Rutherford's atom was a late product of the goals and conceptions of Victorian science. Bohr's modifications, although ultimately fatal to Thomson's program, initially gave further impetus to it. In the early 1920s the most promising approach to an adequate theory of the atom appeared to be the literal and detailed elaboration of the classical mechanics of multiply periodic orbits. The approach succeeded, demonstrating in an unexpected way the force of an argument often advanced by Thomson: because a mechanical model is richer in implications than the considerations for which it was advanced, it can suggest new directions of research that may lead to important discoveries.Exciton confinement in strain-engineered metamorphic InAs/I nxG a1 -xAs quantum dotsNASA Astrophysics Data System (ADS)Khattak, S. A.; Hayne, M.; Huang, J.; Vanacken, J.; Moshchalkov, V. V.; Seravalli, L.; Trevisi, G.; Frigeri, P.2017-11-01We report a comprehensive study of exciton confinement in self-assembled InAs quantum dots (QDs) in strain-engineered metamorphic I nxG a1 -xAs confining layers on GaAs using low-temperature magnetophotoluminescence. As the lattice mismatch (strain) between QDs and confining layers (CLs) increases from 4.8% to 5.7% the reduced mass of the exciton increases, but saturates at higher mismatches. At low QD-CL mismatch there is clear evidence of spillover of the exciton wave function due to small localization energies. This is suppressed as the In content x in the CLs decreases (mismatch and localization energy increasing). The combined effects of low effective mass and wave-function spillover at high x result in a diamagnetic shift coefficient that is an order of magnitude larger than for samples where In content in the barrier is low (mismatch is high and localization energy is large). Finally, an anomalously small measured Bohr radius in samples with the highest x is attributed to a combination of thermalization due to low localization energy, and its enhancement with magnetic field, a mechanism which results in small dots in the ensemble dominating the measured Bohr radius.Exciton-dominated dielectric function of atomically thin MoS 2 filmsDOE PAGESYu, Yiling; Yu, Yifei; Cai, Yongqing; ...2015-11-24We systematically measure the dielectric function of atomically thin MoS 2 films with different layer numbers and demonstrate that excitonic effects play a dominant role in the dielectric function when the films are less than 5–7 layers thick. The dielectric function shows an anomalous dependence on the layer number. It decreases with the layer number increasing when the films are less than 5–7 layers thick but turns to increase with the layer number for thicker films. We show that this is because the excitonic effect is very strong in the thin MoS 2 films and its contribution to the dielectricmore » function may dominate over the contribution of the band structure. We also extract the value of layer-dependent exciton binding energy and Bohr radius in the films by fitting the experimental results with an intuitive model. The dominance of excitonic effects is in stark contrast with what reported at conventional materials whose dielectric functions are usually dictated by band structures. Lastly, the knowledge of the dielectric function may enable capabilities to engineer the light-matter interactions of atomically thin MoS 2 films for the development of novel photonic devices, such as metamaterials, waveguides, light absorbers, and light emitters.« lessA Simple Relativistic Bohr AtomERIC Educational Resources Information CenterTerzis, Andreas F.2008-01-01A simple concise relativistic modification of the standard Bohr model for hydrogen-like atoms with circular orbits is presented. As the derivation requires basic knowledge of classical and relativistic mechanics, it can be taught in standard courses in modern physics and introductory quantum mechanics. In addition, it can be shown in a class that…The BOHR Effect before PerutzERIC Educational Resources Information CenterBrunori, Maurizio2012-01-01Before the outbreak of World War II, Jeffries Wyman postulated that the "Bohr effect" in hemoglobin demanded the oxygen linked dissociation of the imidazole of two histidines of the polypeptide. This proposal emerged from a rigorous analysis of the acid-base titration curves of oxy- and deoxy-hemoglobin, at a time when the information on the…The Bohr effect before Perutz.PubMedBrunori, Maurizio2012-01-01Before the outbreak of World War II, Jeffries Wyman postulated that the Bohr effect in hemoglobin demanded the oxygen linked dissociation of the imidazole of two histidines of the polypeptide. This proposal emerged from a rigorous analysis of the acid-base titration curves of oxy- and deoxy-hemoglobin, at a time when the information on the chemistry and structure of the protein was essentially nil. The magnetochemical properties of hemoglobin led Linus Pauling to hypothesize that the (so called) Bohr histidines were coordinated to the heme iron in the fifth and sixth positions; and Wyman shared this opinion. However, this structural hypothesis was abandoned in 1951 when J. Wyman and D. W. Allen proposed the pK shift of the oxygen linked histidines to be the result of "...a change of configuration of the hemoglobin molecule as a whole accompanying oxygenation." This shift in paradigm, that was published well before the 3D structure of hemoglobin was solved by M.F. Perutz, paved the way to the concept of allostery. After 1960 the availability of the crystallographic structure opened new horizons to the interpretation of the allosteric properties of hemoglobin. Copyright © 2012 Wiley Periodicals, Inc.Timing and Impact of Bohr's TrilogyNASA Astrophysics Data System (ADS)Jeong, Yeuncheol; Wang, Lei; Yin, Ming; Datta, Timir2014-03-01In their article- Genesis of the Bohr Atom Heilbron and Kuhn asked - what suddenly turned his [Bohr's] attention, to atom models during June 1912- they were absolutely right; during the short period in question Bohr had made an unexpected change in his research activity, he has found a new interest ``atom'' and would soon produce a spectacularly successful theory about it in his now famous trilogy papers in the Phil Mag (1913). We researched the trilogy papers, Bohr`s memorandum, his own correspondence from that time in question and activities by Moseley (Manchester), Henry and Lawrence Bragg. Our work suggests that Bohr, also at Manchester that summer, was likely to have been inspired by Laue's sensational discovery in April 1912, of X-ray interference from atoms in crystals. The three trilogy papers include sixty five distinct (numbered) references from thirty one authors. The publication dates of the cited works range from 1896 to 1913. Bohr showed an extraordinary skill in navigating thru the most important and up-to date works. Eleven of the cited authors (Bohr included, but not John Nicholson) were recognized by ten Noble prizes, six in physics and four in chemistry.Even exciton series in Cu2ONASA Astrophysics Data System (ADS)Schweiner, Frank; Main, Jörg; Wunner, Günter; Uihlein, Christoph2017-05-01Recent investigations of excitonic absorption spectra in cuprous oxide (Cu2O ) have shown that it is indispensable to account for the complex valence-band structure in the theory of excitons. In Cu2O , parity is a good quantum number and thus the exciton spectrum falls into two parts: the dipole-active exciton states of negative parity and odd angular momentum, which can be observed in one-photon absorption (Γ4- symmetry), and the exciton states of positive parity and even angular momentum, which can be observed in two-photon absorption (Γ5+ symmetry). The unexpected observation of D excitons in two-photon absorption has given first evidence that the dispersion properties of the Γ5+ orbital valence band are giving rise to a coupling of the yellow and green exciton series. However, a first theoretical treatment by Uihlein et al. [Phys. Rev. B 23, 2731 (1981), 10.1103/PhysRevB.23.2731] was based on a simplified spherical model. The observation of F excitons in one-photon absorption is a further proof of a coupling between yellow and green exciton states. Detailed investigations on the fine structure splitting of the F exciton by F. Schweiner et al. [Phys. Rev. B 93, 195203 (2016), 10.1103/PhysRevB.93.195203] have proved the importance of a more realistic theoretical treatment including terms with cubic symmetry. In this paper we show that the even and odd parity exciton system can be consistently described within the same theoretical approach. However, the Hamiltonian of the even parity system needs, in comparison to the odd exciton case, modifications to account for the very small radius of the yellow and green 1 S exciton. In the presented treatment, we take special care of the central-cell corrections, which comprise a reduced screening of the Coulomb potential at distances comparable to the polaron radius, the exchange interaction being responsible for the exciton splitting into ortho and para states, and the inclusion of terms in the fourth power of p in theSpecial Bohr-Sommerfeld Lagrangian submanifoldsNASA Astrophysics Data System (ADS)Tyurin, N. A.2016-12-01We introduce a new notion in symplectic geometry, that of speciality for Lagrangian submanifolds satisfying the Bohr- Sommerfeld condition. We show that it enables one to construct finite-dimensional moduli spaces of special Bohr- Sommerfeld Lagrangian submanifolds with respect to any ample line bundle on an algebraic variety with a Hodge metric regarded as the symplectic form. This construction can be used to study mirror symmetry.One-dimensional carrier confinement in “Giant†CdS/CdSe excitonic nanoshellsDOE PAGESRazgoniaeva, Natalia; Moroz, Pavel; Yang, Mingrui; ...2017-05-23Here, the emerging generation of quantum dot optoelectronic devices offers an appealing prospect of a size-tunable band gap. The confinement-enabled control over electronic properties, however, requires nanoparticles to be sufficiently small, which leads to a large area of interparticle boundaries in a film. Such interfaces lead to a high density of surface traps which ultimately increase the electrical resistance of a solid. To address this issue, we have developed an inverse energy-gradient core/shell architecture supporting the quantum confinement in nanoparticles larger than the exciton Bohr radius. The assembly of such nanostructures exhibits a relatively low surface-to-volume ratio, which was manifestedmore » in this work through the enhanced conductance of solution-processed films. The reported core/shell geometry was realized by growing a narrow gap semiconductor layer (CdSe) on the surface of a wide-gap core material (CdS) promoting the localization of excitons in the shell domain, as was confirmed by ultrafast transient absorption and emission lifetime measurements. The band gap emission of fabricated nanoshells, ranging from 15 to 30 nm in diameter, has revealed a characteristic size-dependent behavior tunable via the shell thickness with associated quantum yields in the 4.4–16.0% range.« lessOne-dimensional carrier confinement in “Giant†CdS/CdSe excitonic nanoshellsSciTech ConnectRazgoniaeva, Natalia; Moroz, Pavel; Yang, MingruiHere, the emerging generation of quantum dot optoelectronic devices offers an appealing prospect of a size-tunable band gap. The confinement-enabled control over electronic properties, however, requires nanoparticles to be sufficiently small, which leads to a large area of interparticle boundaries in a film. Such interfaces lead to a high density of surface traps which ultimately increase the electrical resistance of a solid. To address this issue, we have developed an inverse energy-gradient core/shell architecture supporting the quantum confinement in nanoparticles larger than the exciton Bohr radius. The assembly of such nanostructures exhibits a relatively low surface-to-volume ratio, which was manifestedmore » in this work through the enhanced conductance of solution-processed films. The reported core/shell geometry was realized by growing a narrow gap semiconductor layer (CdSe) on the surface of a wide-gap core material (CdS) promoting the localization of excitons in the shell domain, as was confirmed by ultrafast transient absorption and emission lifetime measurements. The band gap emission of fabricated nanoshells, ranging from 15 to 30 nm in diameter, has revealed a characteristic size-dependent behavior tunable via the shell thickness with associated quantum yields in the 4.4–16.0% range.« less
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