Lorentz-Lorenz Correction Research Articles

Electrical resistivity, MNM transition and band-gap narrowing of cubic GaN:Si

The electrical resistivity of the Si-donor cubic GaN is investigated theoretically at low temperature. The critical impurity concentration, Nc, for the metal–nonmetal transition is estimated in three different ways: from using the generalized Drude approach (GDA) for the resistivity; from the vanishing of the chemical potential calculated using the dielectric function model with a Lorentz-Lorenz correction; from finding the crossing point between the energy in the insulating and metallic states. The bandgap narrowing (BGN) has been determined theoretically and experimentally above the MNM transition. The experimental data have been obtained with photoluminescence measurements. Theoretical and experimental results are in rough agreement in the range of impurity concentration of interest.

Electrical resistivity and band-gap shift of Si-doped GaN and metal-nonmetal transition in cubic GaN, InN and AlN systems

The critical impurity concentration N c of the metal–nonmetal (MNM) transition for the cubic GaN, InN and AlN systems, is calculated using the following two different criteria: vanishing of the donor binding energy and the crossing point between the energies in the metallic and insulating phases. A dielectric function model with a Lorentz–Lorenz correction is used for the insulating phase. The InN presents an order of magnitude increase in N c as compared to the other two systems. The electrical resistivity of the Si-donor system GaN is investigated theoretically and experimentally from room temperature down to 10 K. It presents a metallic character above a certain high impurity concentration identified as N c. The samples were grown by plasma assisted molecular beam epitaxy (MBE) on GaAs (0 0 1) substrate. The model calculation is carried out from a recently proposed generalized Drude approach (GDA) presenting a very good estimation for the metallic region. The band-gap shift (BGS) of Si-doped GaN has also been investigated above the MNM transition where this shift is observed. Theoretical and experimental results have a rough agreement in a range of impurity concentration of interest.

Coherent pion emission via a mesonic C̆erenkov mechanism in relativistic proton-nucleus collisions

We obtain the pionic refractive index of nuclear media via a multiple scattering approach using the experimental data for the forward πN scattering amplitudes. On this basis we find that coherent π emission as classical mesonic C̆erenkov radiation is possible in a pion energy band just below the Δ (1236) resonance region where the coherence condition is fulfilled at kinetic projectile energies higher than 750 MeV/ nucleon. Numerical predictions for the spectral intensities as well as for the nuclear cross sections of C̆erenkov pions produced in p+ 120Sn and p+ 208Pb are presented. Effects of absorption and density as well as of the Lorentz-Lorenz correction on the pionic refractive index and also on the C̆erenkov pionic yields are discussed.

The Ericson-Ericson Lorentz-Lorenz correction

The Lorentz-Lorenz correction is briefly reviewed for the electromagnetic system and then the arguments of the Ericsons for the pion-nucleus many-body system are given. A transparent discussion by Torleif Ericson is repeated. The importance of the Ericson-Ericson Lorentz-Lorenz correction is discussed. In particular, it is shown that with the classical value of this correction, multiple scattering of the pions is highly suppressed. Experimental data confirms such a suppression, indicating that in pionic units the value of the EELL parameter cannot be far from the classical (g′ 0 ) N Δ = 1 3 . No stiffness is seen in the longitudinal response of 208Pb to polarized protons, indicating that ( g′ 0) NN must be substantially greater than 1 3 , seeming to require (g′ 0) NN ⪆0.9 . This poses a problem, however, because reanalysis of the Bonn potential in nucleon-nucleon scattering, together with a G-matrix calculation for nuclear matter, does not allow ( g′ 0) NN to be larger than ∼0.525. This value would, however, give pionic contributions which would strongly disagree with EMC and especially, Drell-Yan experiments which measure the change in quark sea in going from deuterium to medium weight nuclei. Some of the discrepancy is removed by noting that the p-meson exchange contribution to ( g′ 0) NN is increased in medium by the factor ( m n m n ∗) 2 , where m n nucleon effective mass. Since, however, the proton scattering favors the nuclear surface where m n ∗ is not much smaller than m n, this enhancement is not large for this experiment. It is pointed out that when the decrease with momentum of screening by isobar-hole excitations and the increase in p-exchange tensor contribution with angle is taken into account, ( g′ 0) NN becomes a function of momentum. Its value is estimated to be ⪆0.9 for the momentum transfer k = 1.75 fm −1 where the experiments were performed. Possible reasons why ( g′ 0) N Δ is so much smaller than ( g′ 0) NN are discussed.

Linearly velocity-dependent potentials and the Lorentz-Lorenz correction

The Lorentz-Lorenz correction for linearly velocity-dependent potentials saturates at the second-order term. This sheds some new light onto the role of tensor potentials in the relativistic Dirac approach to proton nucleus scattering.

The Dirac distorted wave impulse approximation revisited

Recently, we have proposed a new interpretation of the successful Dirac approach to protonnucleus elastic scattering, based on relativistic kinematics and the Lorentz-Lorenz correction. Here, we show that the Dirac distorted wave impulse approximation for low-lying collective states can be understood along the same lines. This confirms our view that relativistic effects are not the only possible explanation of the polarization data at intermediate energies.

On the relation between relativistic and non-relativistic mean-field theories

It is shown that the relativistic mean-field theories (Dirac-Hartree approximation) based on one-boson exchange potentials can also be interpreted in more traditional terms, in the case of nuclear ground states. This requires the use of velocity-dependent two-body forces (of Skyrme type, in the limit of large meson masses), and application of the Lorentz-Lorenz correction.

Chiral bag models and the Lorentz-Lorenz correction

The classical Lorentz-Lorenz correction to the pion-nucleus optical potential is shown to arise naturally as a consequence of chiral bag model boundary conditions.

First-order dielectric susceptibilities of tetrahedrally coordinated semiconductors

This work describes the computation of the first-order dielectric susceptibilities of tetrahedrally coordinated semiconductors, within a molecular model. It allows the discussion of several approximations which have been frequently used in the study of second-order dielectric susceptibilities and the estimation of local-field effects. First of all, it is shown that the accuracy of a bonding-antibonding model decreases with increasing ionicity. Secondly, using a method of moments and a model curve for the ${\ensuremath{\epsilon}}_{2}(E)$ spectrum, reasonable values of the low-energy threshold of ${\ensuremath{\epsilon}}_{2}(E)$ as well as of the average dielectric gap defined by Phillips are obtained. Then local-field effects are estimated. A Lorentz-Lorenz correction seems to be valid, if one includes the drastic reduction due to self-polarization effects. Finally, the separation of the contributions of bond charge and charge transfer to ${\ensuremath{\epsilon}}_{1}(0)$ is discussed.

The infrared optical constants of sulfuric acid at 250 K*

Results are presented for measurements of the IR spectral reflectance at near-normal incidence of aqueous solutions of sulfuric acid with acid concentrations of 75% and 95.6% by weight. Kramers-Kronig analyses of the reflectance data are employed to obtain values of the optical constants n(nu) and k(nu) in the spectral range from 400 to 6000 cm to the -1 power. The optical constants of these solutions at 250 K and 300 K are compared. It is found that in spectral regions remote from strong absorption bands, the values of the n(nu) indices obtained at 250 K agree with the values given by Lorentz-Lorenz correction of the same indices at 300 K. All absorption bands observed at 300 K are found to be present at 250 K with slight shifts in frequency and with significant differences in the k(nu) indices at the band maxima. Based on these results, it is concluded that the clouds of Venus probably consist of droplets of aqueous solutions of sulfuric acid with acid concentrations of about 75% by weight.

Equation of state for neutron matter in the presence of a pion condensate

The energy density for neutron matter including a pion condensed phase is studied, with particular emphasis on the role of Δ-isobars. Relativistic corrections to vertex functions involving isobars are considered and turn out to be important in the high density region. We arrive at a simple schematic model in which the inclusion of isobars leads to an effective enhancement of the axial vector coupling constant, which competes with an effective reduction due to the Lorentz-Lorenz correction. In the equation of state, inclusion of a pion condensed phase can lead to an appreciable reduction of total pressure.

The Lorentz-Lorenz correction

The Ericson-Ericson Lorentz-Lorenz correction in the propagation of pions in matter is derived in a relativistic theory for general pion frequency and wave vector, in terms of the nucleon-nucleon pair correlation function. The relation to the electromagnetic Lorentz-Lorenz correction is described. It is shown that ρ-meson exchange between nucleons can be expected to give contributions to the Lorentz-Lorenz correction comparable to those from π-mesons. The precise magnitude of the ρ-contributions depends sensitively on the detailed behaviour of the two-body correlation function, since the range of the interaction through ρ-exchange is comparable to that of the repulsive correlations.

On van der Waals dipole-dipole coefficients in alkali halides

The van der Waals dipole-dipole coefficients have been calculated for KC1, KBr, KI and AgCl from recent optical data using a method introduced by Mayer. A unique separation of the absorption into anion and cation contributions cannot be made, but by making a reasonable division into such components, ionic polarizabilities and van der Waals dipole-dipole coefficients can be calculated. These depend strongly on the local field correction made in calculating the electric dipole matrix element from the absorption coefficient. Using both no correction and the Lorentz-Lorenz correction, van der Waals coefficients considerably different from those of Mayer are found. For AgCl the concept of interionic dipole-dipole forces is vague, so that the van der Waals coefficients and ionic polarizabilities obtained from optical data are not meaningful.

Does Ultraviolet Absorption Intensity Increase in Solution?

Absolute absorption intensities and oscillator strengths were determined for isoprene and cis- and trans-piperylenes in the region 1750–2400A, in vapor and in n-heptane solution, using a vacuum fluorite spectrograph. More accurate oscillator strengths are obtained if our measurements at short wave-lengths are combined with the Beckman data of Shell Development Company at longer wave-lengths. For the three compounds the best values of the experimental Lorentz-Lorenz correction, or ratio of integrated intensities under the molar absorption curves for solution and vapor, were close to unity, a result obtained previously by Pickett and co-workers for cyclopentadiene and cyclohexadiene absorption in this same region. A value of 0.98±0.04 for this correction represents the mean of all five of these determinations. Although the values obtained from our data alone without using the Shell curves showed a much larger spread, every determination was substantially below the correction factor of 1.30 predicted by Chako's classical oscillator theory for this wave-length region and these solvents.

The optical properties of solids

1—The theory of the optical constants of metals remained in the state in which it was left by Drude until Kronig applied the modern theory of metals to the problem. Since the appearance of Kronig's first paper many authors have tried to extend the theory so as to bring the finer effects within its scope, and we may sum up the present position as follows. In the infra-red the optical constants of metals vary with temperature, and are therefore very much influenced by the thermal vibrations of the solid. For frequencies in this region the existing theory is effectively the Drude theory which relates the optical constants to the conductivity in static fields and to the inertia of the electrons. This theory is satisfactory in the far infra-red, but fails in the near infra-red. In the visible and ultra-violet the optical constants are approximately independent of temperature, which means that the effect of the theory to be reasonably accurate, and we might hope to obtain useful information about the internal state of a metal. It must, however, be admitted that there is no really consistent theory extant, and, since our means of investigating the interior of a metal are very limited indeed, it seems desirable that the theory should be put upon as sound a basis as possible. It is the main object of this paper to give a critical discussion of the phenomenon in the visible and ultra-violet, the effect of the lattice vibrations being entirely neglected. In 2 the fundamental formula, which is a generalization of the Kramers-Heisenberg dispersion formula, is derived, and it shown that it is quite unnecessary to make the wave-length. In fact the problem becomes clarified if we do not make this assumption. It is also shown that there is no Lorentz-Lorenz correction to be introduced.