Non-coherent scattering in subordinate lines: A unified approach to redistribution functions

Within the scope of the quantum-mechanical result of Omont, Smith and Cooper, we have derived a laboratory-frame redistribution function for the scattering of radiation in subordinate lines where both atomic levels are radiatively broadened. This new function, denoted as R_V(x′, n′; x, n), is the correct counterpart of Hummer's redistribution function R_IV. Moreover, it follows from the formalism developed here that R_V contains all known redistributions R_i(i=I, II, III, IV) as special cases and we may therefore speak in some sense of a unified redistribution function. A simple method has been tested for the evaluation of R_V and our numerical examinations of the properties of R_V served, among others, as an independent verification of the results obtained by Reichel and Vardavas for R_III and R_IV. Finally, it is shown in the conclusion to this paper that the function R_V, discussed here, can be applied not only to the radiative redistribution, but also to a more general case of a collisional redistribution in subordinate lines.     

Non-coherent scattering in subordinate lines: IV. Angle-averaged redistribution functions

It is demonstrated that a simple Gaussian quadrature over the scattering angles provides a sufficiently accurate and stable method for evaluating all the angle-averaged redistribution functions R_i(x′, x) (i = I–V). We display graphically the functions R_II,III,V and discuss in detail the behaviour of the newly calculated redistribution R_V(x′, x). It is shown that this function exhibits important coherence peaks in the line-wing region which can affect the formation of subordinate lines. An approximate form of R_V, analogous to that of Jefferies and White, is briefly discussed.     

Resonant raman scattering at the E1 energy gap of semiconductor crystals

We present a discussion of resonant Raman scattering by optical phonons at the E₁ energy gap of group IV and groups III–V compound semiconductor crystals (e.g., Ge and InSb). For allowed scattering by TO and LO phonons, the q-dependent “double resonant” two-band calculation of the Raman tensor may display destructive interference effects when the intermediate electron-hole pairs are uncorrelated. We also discuss the Franz-Keldysh mechanism of resonant electric field induced Raman scattering by LO phonons. The double resonance terms due to this mechanism will, for large electric fields, broaden and have its largest resonance enhancement at the energy gap.     

Absorption and emission line profile coefficients of multilevel atoms—IV. Velocity-averaged generalized redistribution functions for three-photon processes

The atomic generalized redistribution functions for three-photon processes, derived in the previous paper of this series, are formulated in terms of linear superpositions of newly introduced auxiliary functions q_I−q_VI, thus extending the traditional formalism of redistribution functions for two-photon processes. The corresponding velocity-averaged laboratory functions Q_I−Q_VI of these auxiliary functions are derived in both their angle-dependent and angle-averaged forms. Since the expressions found for Q_I−Q_VI are quite complicated, the so-called disentangled approximation is employed that uses the representative values of the generalized redistribution function at an orthogonal triad of photon directions rather than the angle-averaged function itself. This approximation yields relatively simple expressions which can be used in radiative transfer calculations.     

The redistribution function for scattering by relativistic electrons

The frequency redistribution function r(ν_i, ν_f) for scattering by relativistic electrons is derived, when this scattering is isotropic in the electron rest frame and recoil effects are neglected. Unlike previous derivations, we obtain for r(ν_i, ν_f) an expression which reduces exactly to its classical value for a non-relativistic gas.     

Maximum entropy principle and power-law tailed distributions

In ordinary statistical mechanics the Boltzmann-Shannon entropy is related to the Maxwell-Bolzmann distribution p_i by means of a twofold link. The first link is differential and is offered by the Jaynes Maximum Entropy Principle. Indeed, the Maxwell-Boltzmann distribution is obtained by maximizing the Boltzmann-Shannon entropy under proper constraints. The second link is algebraic and imposes that both the entropy and the distribution must be expressed in terms of the same function in direct and inverse form. Indeed, the Maxwell-Boltzmann distribution p_i is expressed in terms of the exponential function, while the Boltzmann-Shannon entropy is defined as the mean value of -ln (p_i). In generalized statistical mechanics the second link is customarily relaxed. Of course, the generalized exponential function defining the probability distribution function after inversion, produces a generalized logarithm Λ(p_i). But, in general, the mean value of -Λ(p_i) is not the entropy of the system. Here we reconsider the question first posed in [Phys. Rev. E 66, 056125 (2002) and 72, 036108 (2005)], if and how is it possible to select generalized statistical theories in which the above mentioned twofold link between entropy and the distribution function continues to hold, such as in the case of ordinary statistical mechanics. Within this scenario, apart from the standard logarithmic-exponential functions that define ordinary statistical mechanics, there emerge other new couples of direct-inverse functions, i.e. generalized logarithms Λ(x) and generalized exponentials Λ^-1(x), defining coherent and self-consistent generalized statistical theories. Interestingly, all these theories preserve the main features of ordinary statistical mechanics, and predict distribution functions presenting power-law tails. Furthermore, the obtained generalized entropies are both thermodynamically and Lesche stable.     

Non-coherent scattering in subordinate lines: II. Collisional redistribution

A suitable form of the laboratory-frame redistribution function for the resonance scattering in subordinate lines, allowing for the radiative as well as collisional broadening of both atomic levels involved, is derived. Starting from the quantum-mechanical atomic-frame redistribution of Omont et al., we rewrite it in the form of a linear combination of two redistribution functions r_V and r_III, discussed in the preceding paper. This form, which is a direct generalization of that for resonance lines, permits both a simple physical interpretation and an effective numerical evaluation of the corresponding laboratory-frame redistribution. The case of spatial degeneracy is also discussed. Considerable attention is drawn to a discussion of the basic physical assumptions used, namely, the impact approximation and the Maxwellian velocity-distribution for the lower state atoms. It is shown that both of these assumptions are reasonably well satisfied for a variety of cases of astrophysical interest. Finally, in the Appendix we try to clarify the question of the normalization of the redistribution functions (with respect to inelastic collisions), as well as the question of practical equivalence between the astrophysical applications of the results of Omont et al. and those obtained by Yelnik and Voslamber.     

Dark DC conductivity and spectroscopy of clean and gas doped thin films of organic semiconductors

The dark DC conductivity of thin films of phthalocyanine (I), meso-tetra(p-methylphenyl)porphin (II), meso-tetraphenylporphin (III), hemiporphyrazine (IV), dihydrodibenzo [b,i][1,4,8,11] tetra-azacyclotetradecine (V) and three derivatives of V have been studied in vacuo and in the presence of a wide range of gases. The only gases to produce marked increases in the conductivity were electron acceptors; however, IV was unaffected even by these. The interactions of I, II, III and V and its derivatives with $\text{NO}{}_2\text{N}{}_2\text{O}{}_4$ (NOX) were of particular interest and were studied by conductivity measurements, UV/VIS and IR transmission spectroscopy and IR reflectance spectroscopy. The material most sensitive to NOX and other electron acceptors was I; however, V has a favourable combination of sensitivity coupled with reversibility at room temperature. The Interactions of NOX with I, II and HI are complex, and there is spectroscopic evidence for the generation of NO₂ and the organic radical cations.     

Exclusive processes in QCD:: Two-photon physics involving baryons

Exclusive two-photon processes involving baryons have been calculated within the framework of perturbative QCD. In particular, the angular dependence of the process $\text{γγ →}\text{p}\text{p}$ is predicted as a function of the universal baryonic distribution amplitudes φ(x_i). The overall normalization is then found by a comparison with the process $\text{Ψ →}\text{p}\text{p}$, so that we can present a unique, absolutely normalized QCD prediction for the two-photon processes. We argue that these predictions, based on the $\text{Ψ →}\text{p}\text{p}$ decay rate, should be more reliable than those based on baryonic form factors. Presently not enough data exist to give a meaningful differential cross section for the process $\text{γγ →}\text{p}\text{p}$. Nevertheless, a total cross section has been obtained. Excluding the region close to threshold, quite good agreement between our predictions and experimental data is found. The analysis in this paper is trivially generalized to other baryons as well.     

Effect of two-photon saturation on ordinary Raman scattering

The excitation profile of ordinary Raman scattering under steady-state excitation conditions and the time-resolved emission spectrum of ordinary Raman scattering under transient excitation conditions undergo considerable changes when the excitation frequency ω approaches $\text{1}\text{2}$ ω_mn, where ω_mn is the resonance frequency of a two-photon transition from the ground state |n to an excited state |m of a molecule. The appearance of ghost peaks, dips or dispersion-like features centred at ω ? $\text{1}\text{2}$ ω_mn in the excitation profile and of coherence effects such as Rabi nutations with unusual time-dependence in the time-resolved spectrum are predicted.     

Bäcklund transformation and N-soliton solutions for stimulated Raman scattering and resonant two-photon propagation

The N-fold Bäcklund transformation for equations describing both stimulated Raman scattering and resonant two-photon propagation is derived. As a particular result explicit N-soliton solutions are obtained.     

Nonlinearity in Intensity versus Concentration Dependence for the Deep UV Resonance Raman Spectra of Toluene and Heptane

Abstract: The relation between Raman scattering, resonance Raman scattering, and absorption is reviewed to determine to what extent quantitative analysis can be applied in resonance Raman spectroscopy. In addition, it is demonstrated experimentally that normal Raman spectra can be dramatically inhibited by absorption and resonance Raman effects. Raman spectra of toluene and heptane mixtures—with progressively increasing concentrations of heptane—were measured using 229-nm laser excitation. The results show that the characteristic band intensities are not directly proportional to the relative concentrations of the compounds and deviate due to absorption resonance effects. An approximated mathematical model is developed to demonstrate that the intensities of the normal Raman scattering bands are suppressed. An inhibition coefficient K_i is introduced to describe the situation and determine the penetration depth. Most remarkably, it is shown that the intensity of the resonance Raman scattering bands can be constant even when the concentration ratios differ substantially in the sampled mixtures.     

Relationships in Raman intensity theories,in particular the Mayants-Averbukh theory

Brief surveys are given of the Mayants-Averbukh Raman intensity theory, and of the polar tensor Raman intensity theory recently presented by Bogaard and Haines. It was found that these intensity theories in essence are equivalent. In addition, the appearances of the symmetry invariant parameter matrices F_n⁰ of the Mayants-Averbukh theory were derived and tabulated for various symmetries of bond n. These matrices, and a single bond coordinate system, can be used as a convenient alternative to the Mayants-Averbukh treatment of bonds which have some kind of symmetry with respect to the midpoint of the bond. A modification of the Mayants-Averbukh treatment is also suggested. The rotational mode equations of the Mayants-Averbukh theory have been investigated to elecudate the constraints which they impose on Raman intensity theories based on the bond polarizability model. It was found that the valenceoptical theory is in conformity with the rotational modes only if all electrooptical parameters $\text{?α}{}_{\mathrm{ii}}{}^{\mathrm{(n)}}\text{?γ}{}_{\mathrm{p}}$ are neglected, where α_ii⁽ⁿ⁾ (i = 1, 2, 3) are the diagonal components of the polarizability α⁽ⁿ⁾ of bond n, and γ_p is the pth internal angular coordinate. Furthermore, the valence-optical theory was found to be strictly applicable only for cylindrical bond symmetry, C_mv (m ≥ 4). A generalized valence-optical Raman intensity theory, allowing also for non-zero off-diagonal components α_ij⁽ⁿ⁾, was found to be incompatible with the rotational mode equations of the Mayants-Averbukh theory. However, its basic polarizability equation was useful for suggesting a unique interpretation of a set of f parameters (elements of F_n⁰) in terms of components of the anisotropic part of a symmetric bond polarizability.     

Variation of Br quadrupole coupling with isotopic substitution in methyl bromide

The J = 0 ← 1 transitions in CH₃⁷⁹Br (I), CH₃⁸¹Br (II), CD₃⁷⁹Br (III), and CD₃⁸¹Br (IV) were measured using a Stark-cell spectrometer constructed from C-band waveguide. High-resolution spectra yielded precise values for the bromine quadrupole coupling strength. Values obtained were eqQ(I) = ?577.08 ± 0.15 MHz, eqQ(II) = ?482.18 ± 0.15 MHz, eqQ(III) = ?575.66 ± 0.15 MHz, and eqQ(IV) = ?480.89 ± 0.15 MHz. The observed center frequencies for the J = 0 ← 1 transitions are ν₀(I) = 19136.35 ± 0.03 MHz, ν₀(II) = 19063.62 ± 0.03 MHz, ν₀(III) = 15429.23 ± 0.03 MHz, and ν₀(IV) = 15362.41 ± 0.03 MHz. A 0.26 ± 0.02% decrease in bromine quadrupole coupling is observed when the methyl group is fully deuterated. This is in agreement with, and supports interpretations given for, previous results on methyl chloride.     

Vibrational spectroscopy at very high pressures. part 34.1 Raman spectra of polymorphs of mercuric cyanide

Phase transitions have been observed in mercuric cyanide near 2.5, 8, 19 and 60 kbar. The first four phases have been characterized by Raman spectroscopy. Phase II is closely related to the molecular parent phase I. The coordination at mercury appears to increase to four on entering phase III and phase IV has a spectrum consistent with the cubic structure related to anti-cuprite adopted at s.t.p. by Cd(CN)₂. Above 60 kbar deep brown Hg(CH)₂ V is formed irreversibly: it contains C =N rather than C≡N bonds.     

Spin asymmetries for large-pt jet production in two-photon processes

Relying on the hard scattering formalism we estimate cross sections and spin asymmetries for large-p_t jet production from two-photon processes in collisions of electrons and positrons of definite helicity states. We use distribution functions of polarized partons in polarized electrons obtained in a modified leading logarithmic approximation as well as spin-dependent parton cross sections according to lowest-order QCD calculations. Detecting at least one forward or backward hadronic jet, topologies of jets can be observed different from the 2 large p_t production.     

The generalized exponential-integral V(x,y)=∫1∞ exp(−xt)ln(t+y)dtt and computer algorithms for y = 0, 1

The generalized exponential-integral function V(x, y) defined here includes as special cases the function E⁽²⁾₁(x) = V(x, 0) introduced by van de Hulst and functions M₀(x) = V(x, 1) and N₀(x) = V(x, -1) introduced by Kourganoff in connection with integrals of the form ∫ E_n)t)E_m(t±x), which play an important role in the theory of monochromatic radiative transfer. Series and asymptotic expressions are derived and, for the most important special cases, y = 0 and y = 1, Chebyshev expansions and rational approximations are obtained that permit the function to be evaluated to at least 10 sf on 0<x<∞ using 16 sf arithmetic.     

The scattering of line radiation—III. The source function

After discussing the problems encountered in any attempt to interpret frequency-dependent source functions in terms of the population numbers, a method is developed for doing this to a certain class of frequency-dependent source functions. It is pointed out that, unlike the frequency-independent source functions, an analysis of this nature on the frequency-dependent source functions is not generally practicable and can be done in this case only by virtue of the particular form assumed for the absorption coefficient. Solutions in the form of source functions are presented and discussed for a semi-infinite uniform atmosphere for five different forms of frequency redistribution during the scattering event. The function ∫^∞₀S(ν)φ(ν) dν is then calculated and subsequently is used to obtain the departure parameters of the populations of the energy states. The different population distributions through the atmosphere, that can be deduced from these quantities, are compared for the different cases of frequency redistribution used. Because of the nature of the results obtained, the feasibility of setting up iterative schemes to obtain frequency-dependent source functions for more complex problems is also considered.     

Raman spectra of TiO2-II,TiO2-III,SnO2, and GeO2 at high pressure

Raman spectra of the orthorhombic (II) and high pressure (III) phases of titanium dioxide at pressures to 372 kbar and effects of temperature and hydrostatic pressure on Raman spectra of the tetagonal cassiterite-like phases of TiO₂, GeO₂ and SnO₂ are described. At room temperature, the TiO₂ II–III transition is sluggish, and metastable coexistence was observed from 200 to 300 kbar. The Raman spectra of TiO₂-III imply that its primitive cell contains at least four formula units; however, the structure could not be established from the Raman spectra and available powder X-ray diffraction patterns.The temperature and pressure dependences of the spectrum of the tetragonal MO₂ phases together with bulk moduli and thermal expansion data were used to evaluate the pure-volume and pure-temperature contributions to the isobaric temperature dependence of the Raman frequencies. Large anharmonicities in TiO₂ are attributed to hybridization of the oxygen p states with the d states of the Ti ion. GeO₂, where p-electron bonding is involved, is much less Enharmonic.     

Investigations of EPR g Factors and Rhombic Distortion for the Rhombic Cu2+ Centers in K2Zn1?x Cu x F4 Crystals at Low Temperature

The electron paramagnetic resonance g factors g _i (i?=?x, y, z) of two rhombic Cu²⁺ centers, Cu²⁺(II) and Cu²⁺(III), in K₂Zn_1?x Cu _x F₄ crystals found at low temperature are calculated from the complete diagonalization (of energy matrix) method based on the cluster approach. The calculations show that the ground state wave function of the two rhombically compressed Cu²⁺ centers is $ | {d_{{z^{2} }} }\!\!> $ with a small admixture of $ | {d_{{x^{2} - y^{2} }} } \!\!> $ . The rhombic distortions for both Cu²⁺ centers are obtained from the calculations. The results are discussed.