Minimum Splitting Research Articles

Ab initio study of long-range electron transfer between biphenyl anion radical and naphthalene

After the separation of the donor, the acceptor, and the σ-type bridge from the π-σ-π system, the geometries of biphenyl, biphenyl anion radical, naphthalene, and naphthalene anion radical are optimized, and then the reorganization energy for the intermolecular electron transfer (ET) at the levels of HF/4-31G and HF/DZP is calculated. The ET matrix elements of the self-exchange reactions of theπ-σ-π systems have been calculated by means of both the direct calculation based on the variational principle, and the transition energy between the molecular orbitals at the linear coordinateR = 0.5. For the cross reactions, the ET matrix element and the geometry of the transition state are determined by searching the minimum energy splitting Δmin along the reaction coordinate. In the evaluation of the solvent reorganization energy of the ET in solution, the Marcus’ two- sphere model has been invoked. A few of ET rate constants for the intramolecular ET reactions for the π-σ-π systems, which contain the biphenylyl as the donor and both biphenylyl and naphthyl as the acceptor, have been obtained.

Vortex viscosity in superconductors with short coherence length.

In superconductors where the coherence length is comparable to the Fermi wavelength, electronic levels within a vortex core are quantized and separated by energies of the order of the superconducting gap. These compounds can easily be in the ultraclean limit, where the conventional Bardeen-Stephen theory cannot be applied. In addition, a significant range of temperatures exists where transitions between vortex states are suppressed. This effect modifies the energy dissipation due to vortex motion, at sufficiently low temperatures. The minimum energy splitting defines a vortex velocity, below which the vortex viscosity is strongly reduced. In this regime, the $I\ensuremath{-}V$ characteristics are non-Ohmic.

Momentum-space solution of exciton excited states and heavy-hole-light-hole mixing in quantum wells.

A full valence-band mixing model for excitons in quantum wells is presented. The exciton equation is solved in momentum space using the modified Gaussian quadrature method, taking into account the angular dependence of the excitons. The theory accounts for the mixing of the ground state of the light-hole exciton and the excited states of the heavy-hole exciton at low temperatures reported previously by Vi\~na et al. [Phys. Rev. Lett. 58, 832 (1987)]. Our calculations reproduce correctly the resonant field, the minimum energy split at the resonant field, and the fine structure of the competing 2s and 2p states resolved in the experimental data. For the s-states-dominated spectra, the full model can be simplified to include only s-states coupling. We show that the numerical results based on the simplified model match very well the polarization-dependent room-temperature exciton absorption spectra of Miller et al. [IEEE J. Quantum Electron. QE-22, 1816 (1986)].

Anticrossing Due to Resonant Coupling of Hole Levels in Asymmetric Coupled-Quantum-Wells

We present distinct evidence of anticrossing behavior for excitonic transitions due to resonant coupling of heavy-hole ground levels in a biased GaAs/Al0.35Ga0.65As/GaAs (50/40/100 Å) asymmetric coupled-double-quantum-wells p-i-n structure by using photoluminescence spectra. The minimum level splitting is about 2.5 meV.

Excitonic effects in coupled quantum wells.

Electron-sublevel-anticrossing effects have been studied in coupled quantum wells where the exciton binding energy is comparable to the minimum sublevel splitting. The anticrossing was induced by applying an electric field to align the first and second sublevels of adjacent wells. In this situation the electron-hole Coulomb interaction has a strong effect on the splittings measured by optical techniques, because the optical spectra typically measure exciton energies rather than single-particle energies. The most striking effect is that the minimum splitting of the excitons associated with each of the split electron levels does not occur at the same field as for the minimum splitting of the bare-electron levels. One unexpected but readily observable consequence is that when the same electron-sublevel splitting is measured using two different pairs of intrawell and interwell exciton transitions, the field for minimum exciton splitting can differ by up to \ensuremath{\sim}10% from one pair of transitions to the other. We have constructed a variational model of the coupled excitons that explains these effects in terms of Coulomb mixing of the delocalized electron states. We have measured the exciton splittings directly by photocurrent spectroscopy in three GaAs/${\mathrm{Al}}_{0.3}$${\mathrm{Ga}}_{0.7}$As multiple-quantum-well structures. The samples were similar in design except that the ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As barrier thickness varied from 15 to 35 \AA{}. By fitting our variational model to the experimental anticrossing data, we have been able to deduce the actual bare-electron level splittings rather than the exciton splittings. Within the experimental accuracy, we find that the minimum splitting decreased exponentially with increasing barrier thickness, as would be expected for simple quantum-mechanical tunneling.

Photoluminescence in GaAsAlGaAs coupled double quantum wells in electric and magnetic fields

Photoluminescence (PL) spectroscopy has been used to study energy levels in GaAsAlGaAs coupled quantum well structures. Low temperature investigations were made as a function of (i) applied electric field and (ii) applied magnetic field for asymmetric (ACDQW) and symmetric (SCDQW) coupled double quantum well systems, respectively. The transformation from spatially direct and spatially indirect electron transitions to heavy and light hole states in the wide well of the ACDQW was accomplished by the application of an electric field. Anticrossing behavior associated with both the heavy and light hole excitons were observed. The observed minimum energy splitting of ∼1.6 meV was in good agreement with the electron tunneling energy obtained from single particle calculation; the results provided more refined values for the barrier width. The magnetic field investigations of a SCDQW, under flat band conditions, showed several allowed magneto-excitonic intersubband transitions. The binding energy and effective mass of the |E0, H0, 1s〉 exciton state in the SCDQW were deduced from the magnetic field data.

Microwave spectrum of the gauche and trans isomers of methylsilanethiol: Determination of molecular structure, dipole moment, and internal rotation potential functions of methyl and mercapto groups

Microwave spectra of methylsilanethiol and three of its deuterated species were measured and assigned for the gauche and trans isomers. The double minimum splitting due to internal rotation of the mercapto group in the gauche isomer was directly observed in c-type transitions for all the species measured. Rotational constants and the pure torsional energy difference, Δ ν, between the (+) and (−) states in the gauche isomer of the parent species were determined to be A(+) = 15 567.654 ± 0.040, B(+) = 3663.038 ± 0.004, C(+) = 3179.727 ± 0.005, Δ A = −4.328 ± 0.021, Δ B = −0.220 ± 0.012, Δ C = −0.008 ± 0.011, and Δ ν = 2826.371 ± 0.045 MHz, where A(+) represents the A rotational constant of the (+) state and Δ A = A(−) – A(+) and so on. For the trans isomer of the parent species, the following rotational constants were determined: A = 14 745.953 ± 0.051, B = 3841.291 ± 0.010, C = 3220.350 ± 0.010. Additional splittings due to internal rotation of the methyl group were also observed for both of the isomers. Analysis of these splittings derived barrier heights of the methyl internal rotations to be 1581 ± 26 and 1729 ± 23 cal/mol for the trans and gauche isomers of the parent species, respectively. Dipole moments were obtained from Stark effect measurement to be 1.056 ± 0.006 and 1.604 ± 0.006 D for the trans and gauche isomers of the parent species, respectively. Potential function of the mercapto internal rotation and plausible structures for both the isomers were discussed.

Optimal constructions of reversible digraphs

The paper deals with optimal methods for finding a minimum homeomorph and a minimum split of a digraph which are line digraphs. The algorithms may be used as approximate methods for finding a PERT network with the minimum number of dummy activities.

Magnetic properties of a basalt glass and glass-ceramics

Mössbauer, ESR and magnetization measurements have been carried out on a basalt glass heat-treated at different temperatures (600, 650, 700, 800 and 900°C for 8 h). The as-annealed glass and the above five samples showed two-doublet Mössbauer spectra, while the last two samples also showed a six line magnetic hyperfine pattern at 300 K. At 4 K, the last four samples showed magnetic hyperfine patterns, while the as-annealed glass showed that there was already short range magnetic ordering present. High field Mössbauer data at 4 K showed that the surface spins are canted. The minimum quadrupole splitting and the maximum isomer shift around 700°C are related to the improved symmetry of the magnetite lattice. ESR spectra showed paramagnetic resonances at g = 4.3 and g = 2.0 for the first two samples, while the last four samples showed superparamagnetic resonance centred around g = 2.0 at 300 K. At lower temperatures, the 650 and 700°C samples showed ferrimagnetic resonance. Magnetization curves against H/T superpose well both at 300 and 77 K, showing the typical superparamagnetic behaviour of the small magnetite particles. The saturation magnetization (at 270 K) showed a sharp change around 700°C, showing the formation of magnetite. The magnetic structure of the small magnetite particles are discussed in terms of the above results.

Oxidised polyethylene as a paraelectric

A new experimental study of a known low temperature dielectric relaxation in oxidised polyethylene confirms that it is a manifestation of paraelectricity with certain similarities to the doped alkali halide systems. The tunnel splitting parameter (half the minimum energy splitting) is found to be 3.9 μeV ± 10%, while the strain coefficient of the double-well asymmetry is ≈ 5 meV. The multiphonon regime takes over from the one-phonon range at characteristic temperature T o = 7.2 ± 0.5 K. A rather well oxidised sample shows a relaxation rate which varies as T 0.4 when T < 1 K, while the spread becomes markedly broader than a Debye curve. Oxidation with O 2 18 leads to a 4.2 K peak at a frequency 13–15% lower than oxidation with O 2 16. When the oxidised polyethylene is vacuum annealed the relaxation intensity diminishes. The half life at 126 C is about 2 hr and the activation energy of the annealing process is 40 ± 5 kcal/mole. A contaminated specimen showed accelerated oxidation kinetics and also accelerated anneal effect. These results lead to a suggested attribution of the relaxation to the rotation of the dihedral angle of isolated hydroperoxide groups. It is suggested that other hydrocarbon type materials may exhibit paraelectricity.

Ferromagnetic resonance in CdCr2Se4 with Fe addition

AbstractThe temperature and angle dependences of the resonance field and resonance linewidth have been measured for ferromagnetic CdCr2Se4 crystals with Fe addition. An attempt is made to interpret the observations on the basis of the Fe2+ energy level model proposed by Hoekstra et al. and generalized for the case of finite minimum level splitting. The contributions of relaxation mechanisms to the linewidth and resonance field are discussed and the parameters of the model are roughly estimated.

Mössbauer Study of the Structure and Decomposition of Wustite

A series of Mössbauer, x-ray, and magnetic measurements has been made on wustite (Fe1−xO). The main new results are: (a) The dependence of the Mössbauer quadrupole splitting on heat treatment is very similar to that of the atomic constant, confirming Hoffman's conclusions on the variation of x. (b) The Zeeman Mössbauer lines of untreated wustite below the Curie temperature are completely smeared out; for a sample treated so as to give minimum quadrupole splitting (minimum x) these lines appear. (c) In a heat-treated sample a Zeeman splitting in the Mössbauer spectrum is observed well above the bulk wustite Curie temperature. This is interpreted as the imposition by the magnetic decomposition products of a magnetic ordering on the otherwise paramagnetic residual wustite with which they are in intimate contact.