On the electron energy spectrum in heavily doped non-parabolic semiconductors

An attempt is made to present a simple theoretical analysis of the energy-wave vector dispersion relation of the conduction electrons in heavily doped non-parabolic semiconductors forming band tails. We observe that the complex energy spectrum in doped small-gap materials whose unperturbed conduction band is described by the three band model of Kane is due to the interaction of the impurity atoms in the tail with the spin-orbit splitting constant of the valence band (Δ), For band-gap (E_g)<Δ the imaginary part predominates which tails in to the conduction band. For the opposite inequality the real part comes in to play which tails in to the split-off band. In the absence of the band tailing effect, the imaginary part of the complex energy spectrum vanishes and the same is also true for doped two-band Kane-type and parabolic energy bands respectively. The present formulation helps us in investigating the Boltzmann transport equation dependent transport properties of degenerate semiconductors and are expected to agree better with experiments. The well-known results of unperturbed three and two band models of Kane together with wide-gap parabolic energy bands have been obtained as special cases of our generalized analysis under certain limiting conditions.     

Probe-type time-of-flight momentum and energy mapping system

A new time-of-flight (TOF) momentum and energy mapping system is proposed. The system consists of two sub-regions with different axial uniform decelerating field. Two position-sensitive detectors (PSDs) on opposite side of the tube are used for the detection of electrons with different axial motion length due to their initial energy ? and emission angle θ. A non-monotonic dependence of energy-resolving performance on electron initial energy can be achieved by choosing appropriate electric field deceleration for these two sub-regions, which forms an “energy resolution probe” possessing a higher level of energy resolution than that of lower energy part. And the local resolution in the probe region could be specifically enhanced while the other parts of all the detection range do not change so much. It is verified by the illustrating example with relative energy resolution Δ?/? smaller than 0.5% for electron energy in probe range from 36 eV to 45 eV.     

Instanton molecular vacuum in N = 1 supersymmetric quantum mechanics

The vacuum of N = 1 quantum mechanics is shown to be the dilute gas of instanton-anti-instanton molecules with zero topological charge. The quantum fluctuations near these molecules are nontrivial due to the quasizero mode. The special technique of integration along this mode in the functional space beyond the gaussian approximation is worked out. We also discuss nonsupersymmetric quantum mechanics with fermions and calculate the nonperturbative part of the corresponding vacuum energy.     

The p-40Ca and n-40Ca mean fields from the iterative moment approach

The real part V(r; E) of the p-⁴⁰Ca and n-⁴⁰Ca mean fields is extrapolated from positive towards negative energies by means of the iterative moment approach, which incorporates the dispersion relation between the real and imaginary parts of the mean field. The potential V(r; E) is the sum of a Hartree-Fock type component V^HF, (r; E) and a dispersive correction δV(r; E); the latter is due to the coupling of the nucleon to excitations of the ⁴⁰Ca core. The potentials V(r; E) and V_HF(r; E) are assumed to have Woods-Saxon shapes. The calculations are first carried out in the framework of the original version of the iterative moment approach, in which both the depth and the radius of the Hartree-Fock type contribution depend upon energy, while its diffuseness is constant and equal to that of V(r; E). The corresponding extrapolation towards negative energies is somewhat sensitive to the detailed parametrization of the energy dependence of the imaginary part of the mean field, which is the main input of the calculation. Moreover, the radius of the calculated Hartree-Fock type potential then increases with energy, in contrast to previous findings in ²⁰⁸Pb and ⁸⁹Y. A new version of the iterative moment approach is thus developed in which the radial shape of the Hartree-Fock type potential is independent of energy; the justification of this constraint is discussed. The diffuseness of the potential V(r; E) is assumed to be constant and equal to that of V_HF(r; E). The potential calculated from this new version is in good agreement with the real part of phenomenological optical-model potentials and also yields good agreement with the single-particle energies in the two valence shells. Two types of energy dependence are considered for the depth U_HF(E) of the Hartree-Fock type component, namely a linear and an exponential form. The linear approximation is more satisfactory for large negative energies (E < −30 MeV) while the exponential form is better for large positive energies (E > 50 MeV). This is explained by relating the energy dependence of U_HF(E) to the nonlocality of the microscopic Hartree-Fock type component. Near the Fermi energy the effective mass presents a pronounced peak at the potential surface. This is due to the coupling to surface excitations of the core and reflects the energy dependence of the potential radius. The absolute spectroscopic factors of low-lying single-particle excitations in ³⁹Ca, ⁴¹Ca, ³⁹K and ⁴¹Sc are found to be close to 0.8. The calculated p-⁴⁰Ca and n-⁴⁰Ca potentials are strikingly similar, although the two calculations have been performed entirely independently. The two potentials can be related to one another by introducing a Coulomb energy shift. Attention is drawn to the fact that the extrapolated energy dependence of the real part of the mean field at large positive energy sensitively depends upon the assumed behaviour of the imaginary part at large negative energy. Yet another version of the iterative moment approach is introduced, in which the radial shape of the HF-type component is independent of energy while both the radius and the diffuseness of the full potential V(r; E) depend upon E. This model indicates that the accuracy of the available empirical data is probably not sufficient to draw reliable conclusions on the energy dependence of the diffuseness of V(r; E).     

Global predictions of T2 symmetric deep level wavefunctions in semiconductors

Numerical results of T₂ symmetric SP₃ bonded deep level wavefunctions due to short range defect potentials in Si, Ge, GaAs and InP are presented. The general features of defect wavefunctions are insensitive to either the band structure of the host of defect energy level. The total occupation probability of wavefunction located on 0 . 1 . 2 shells around the defect center is about 60–85%. This part of wavefunction may be expressed in several simple symmetric combinations of SP³ hybrid orbitals. The rest part of the wavefunction extends diversely over a wide range of space.     

Point-contact spectroscopy of electron relaxation mechanisms in semiconductors

The I–V characteristic of a tiny semiconducting channel connecting bulk electrodes is shown to have singularities arising due to phonon emission by hot electrons at energies eV = n?ω₀, where ω₀ is the optical phonon frequency and n = 1, 2, 3,…. The nonlinear part of the I–V curve provides direct information concerning the energy dependence of the elastic-scattering time of charge carriers.     

Spectra of neutrons from μ capture in thallium,lead and bismuth

The energy distributions of neutrons fromμ capture in Tl, Pb, and Bi were measured applying a time-of-flight technique, using de-excitationγ-rays from final nuclei as a time reference. The spectra exhibit an evaporation part, which is described by nuclear temperatures varying fromθ=1.06 MeV for Bi toθ=1.22 MeV for Pb, and an exponentially decreasing high-energy distribution with a relative intensity of ～10%, which is interpreted, on the basis of a simple model, as being due to direct and pre-compound processes.     

Effect of the hexagonal warping on the dynamical conductivity of surface states in a topological insulator

We report on the effect of hexagonal warping on the dynamical conductivity of the surface states of a topological insulator in the presence of nonmagnetic impurities. It is found that the photon energy dependent conductivities are determined by a polarization-function-liked term,  Π₂ (q,ω), which contains a velocity term corresponding to the difference of group velocities between the two states due to an electron-impurity scattering. This is different from the conductivity of 2-dimentional electron systems where the conductivity depends on the inverse imaginary part of the dielectric function Im [1/κ(q,ω)]. We present both the real part and imaginary part of the polarization function with different warping strength. It is found that the warping strength can both enhance single particle excitations (SPEs) and suppress the screening effect of electrons. As a result the inverse scattering time is enhanced by up to about two orders of magnitudes. The real part of the longitudinal conductivity of the intra-band process is analog to the case with a conductivity of σ ~ μδ(ω). The broadening of the spectrum in the low energy is not only determined by chemical potential, but also dependent on the warping strength. At higher frequency, the real part of conductivity shows a jump at the threshold photon energy of μ, where the inter-band contribution takes over.     

The stabilization mechanism of titanium cluster

A systematic and comparative theoretical study on the stabilization mechanism of titanium cluster has been performed by selecting the clusters Ti_n (n=3, 4, 5, 7, 13, 15 and 19) as representatives in the framework of density-functional theory. For small clusters Ti_n (n=3, 4 and 5), the binding energy gain due to spin polarization is substantially larger than that due to structural distortion. For medium clusters Ti₁₃ and Ti₁₅, both have about the same contribution. For Ti_n (n=4, 5, 13 and 15), when the undistorted high symmetric structure with spin-polarization is changed into the lowest energy structure, the energy level spelling due to distortion fails to reverse the level order of occupied and unoccupied molecular orbital (MO) of two type spin states, the spin configuration remains unchanged. In spin restricted and undistorted high symmetric structure, d orbitals participate in the hybridization in MOs, usually by way of a less distorted manner, and weak bonds are formed. In contrast, d orbitals take part in the formation of MOs in the ground state structure, usually in a distorted manner, and strong covalent metallic bonds are formed.     

Bandgap evolution of GaN1−x As x in the whole composition range

The bandgap evolution of GaN_1?x As _x in the whole composition range is investigated and a model describing its bandgap energy is developed. It is found that the bandgap evolution is due to two factors. One is the interaction between the impurity band and the Γ conduction band or the Γ valence band of the host materials. The other one is the intraband coupling within the conduction band and separately within the valence band. The former is dominant in the As-rich GaNAs and the N-rich GaNAs. The latter plays an important part in the N-rich range and the moderate composition range.     

Ionization of hydrogen and deuterium atoms in thermal energy collisions with state-selected Ne(3s 3 P 2,3 P 0) metastable atoms

High resolution energy spectra of electrons and ions resulting from thermal energy collisions of hydrogen and deuterium atoms with state-selected metastable Ne(Ne(3s ³ P ₂,³ P ₀) atoms are reported. The electron spectra for Ne(³ P ₂)+H(D) are very broad: The high energy part due to formation of NeH⁺ (NeD⁺) bound states (associative ionization), amounts to about 30% of the ionizing events, whereas the dominant part of the spectrum including a prominent low-energy peak is due to Penning ionization out of a strongly-attractive entrance potential curve. Comparison of the spectra with quantum mechanical fit calculations yields fairly accurate information on this potential, in particular its well depthD _e [Ne(³ P ₂)?H,D]= 2.0(1) eV. The spectra for Ne(³ P ₀)+H, D are comparatively narrow with much lower cross sections than the one for the Ne(³ P ₂) state. The corresponding entrance channel is a weakly bound van der Waals molecule with a well depth below 0.1 eV. A perturbation calculation of the Ne(3s)+H(1s) potential energy curves at large distances explains the observed difference between the Ne(³ P ₂)+H(D) and Ne(³ P ₀)+H(D) systems. Symmetry arguments are given that the major contribution to the Ne(³ P ₂)+H(D) spectra is due to the² Σ potential.     

Historical overview and introduction

The complex balance of processes occurring at the cascade of exotic H-atoms is usually described by the so-called standard cascade model, but this model neglects variations of the kinetic energy T of the exotic atom during the cascade which are crucial for the analysis of several important experiments. New experimental results on T _μp at H₂ pressures between 0.063 and 4 hPa demonstrate the importance of acceleration due to Coulomb de-excitation processes at highly excited μp levels n > 9. The data at the lowest density are sensitive to the initial values of the kinetic energy and n-levels at the moment of atomic capture. From the measured low-energy tail of the T _μp-distribution it can be concluded that a considerable part of the μp(2s) atoms is metastable at pressures of a few hPa. This revised version was published online in August 2006 with corrections to the Cover Date.     

Hydrodynamic parameters and correlation functions of superfluid 3He

In this paper we present the first of two closely related studies devoted to the connection between the phenomenological hydrodynamics and microscopic theories of superfluid ³He. In this first part, we express in a systematical way all the phenomenological parameters appearing in the hydrodynamic equations in terms of microscopically well defined correlation functions. The method used for this purpose goes back to the work of Kadanoff and Martin on normal fluids and has recently been formulated in the framework of Mori's projector formalism by Forster. Apart from the assumptions about the structure of the superfluid phases of ³He and certain regularity assumptions about the collision-dominated part of the correlation functions, which have to be satisfied if the hydrodynamic limit exists at all, but which remain unproven, this part of our work is nearly exact. The only approximation made is the perturbative treatment of the very small magnetic dipole energy. The k → O limit of various correlation functions is considered. Novel consequences of the directional long range order for the transverse momentum density correlation function of the A phase, which are unique to that phase, are obtained. The instantaneous reactive parameters of the system are expressed as equal time commutators and evaluated rigorously. Some reactive parameters, e.g. the one leading to “orbit waves” are shown to have a collisional part, which has not yet been evaluated in a microscopic theory. NMR is considered as the k → O limit of spin wave resonances with an energy gap due to the magnetic dipole-dipole interaction at k = 0. The NMR linewidth is thereby fixed by the same transport parameter, which determines the spin wave damping in the theory where the gap is neglected. The relevant transport parameter is expressed along with all others by the rigorous Kubo formulae of the theory in which the magnetic dipole energy is neglected. The close analogy of the NMR linewidth parameter to transport parameters like the shear viscosity, which are measured in quite different experiments, is thereby elucidated. Further, approximate evaluations of the Kubo relations of these parameters, within a common microscopic approach will be given in a second related study.     

An investigation of the effect of the nearest surroundings on the formation of V Lα emission bands for solid solutions of rare earth orthovanadates—orthophosphates

The V Lα, P Kβ and O Kα X-ray emission spectra for solid solutions YVO₄—YPO₄ and EuVO₄—EuPO₄ have been studied. It is shown that with an increase in concentration of orthophosphate in a substitutional solid solution a hump appears in the low energy part of the V Lα spectrum, corresponding in energy to the P Kβ spectrum. The cluster calculation of the electronic structure of solid solutions YVO₄—YPO₄, carried out by the Extended Hückel method, explains this effect as due to the hybridization of V 3d and P 3p states when [PO₄ ] complexes are introduced into the orthovanadate tetrahedral lattice.     

Perturbative contributions to the electroweak interface tension

The main perturbative contribution to the free energy of an electroweak interface is due to the effective potential and the tree level kinetic term. The derivative corrections are investigated with one-loop perturbation theory. The action is treated in derivative, in heat kernel, and in a multi local expansion. The massive contributions turn out to be well described by the Z-factor. The massless mode, plagued by infrared problems, is numerically less important. Its perturbatively reliable part can by calculated in derivative expansion as well. A self consistent way to include the Z-factor in the formula for the interface tension is presented.     

Ensemble of ultra-high intensity attosecond pulses from laser-plasma interaction

The efficient generation of intense X-rays and γ-radiation is studied. The scheme is based on the relativistic mirror concept, i.e., a flying thin plasma slab interacts with a counterpropagating laser pulse, reflecting part of it in the form of an intense ultra-short electromagnetic pulse having an up-shifted frequency. In the proposed scheme a series of relativistic mirrors is generated in the interaction of the intense laser with a thin foil target as the pulse tears off and accelerates thin electron layers. A counterpropagating pulse is reflected by these flying layers in the form of an ensemble of ultra-short pulses resulting in a significant energy gain of the reflected radiation due to the momentum transfer from flying layers.     

Spatial-dispersion induced birefringence in cubic crystals: CuBr and CuI

A natural birefringence in single crystals of copper halides is observed and measured in the exciton part of the spectrum. This intrinsic birefringence is due to the spatial dispersion of the dielectric constant ?(ω, q). Its spectral dependence and strong enhancement near the energy gap can be explained only, if we take account of the strong excitonic contribution in these compounds. This effect is related to the valence band anisotropy (warning) and thus allows a direct determination of the Luttinger band parameters | γ₂ - γ₃ | for these compounds.     

Interferometrical signature of mixed phase in A+A collisions

We have calculated the pion rapidity distribution, the transversal momentum spectrum and the pion correlator in outward, sideward and longitudinal directions for S+S collisions at high energy. We used a two-temperature model that allows us to explain the abundance of pions at smallp _T and highp _T . The first source, which is at high temperature, is in a quark-gluon-hadron mixed phase radiating pions due to a deflagration shock wave on the background of longitudinal expansion. The second source consists of the unburnt part of the matter in hadronic phase. The interferometrical analysis at differentp _T gives a signature for two expanding sources separated in time and allows the measurement of the lifetime and other parameters of each of them.     

The method of unitary transformations in the theory of nuclear matter

The theory of nuclear matter is investigated by means of the method of unitary transformations in the special case of point transformations. The general formula for the energy per particle as a function of the density is given in Hartree-Fock approximation being neglected the induced three and more body forces for reasonable correlation functions. This function always shows saturation due to a term proportional tok _F ⁵ in the direct part of the approximation. The physical connexion of this term with the scattering amplitudes of the potential is shown. We point out the equivalence to orderk _F ³ of the energy per particle function of the unitary method with Jastrow and separation methods in their simplest form. The saturation properties are calculated for certain classes of correlations using the realistic potential of Gammel, Christian and Thaler.