Optical colours and polarization of a model reflection nebula. III. Composite and mixture of grains in the nebula with the star in the rear

The colour differences between the star and the associated reflection nebula and polarization caused by core mantle grains and mixture of grains have been given. They are based on homogeneous plane-parallel slab-model of the nebula with the star in the rear. The composite particles in the form of concentric spheres consist of homogeneous core of graphite, silicate or SiC and homogeneous mantle of ice. The effect of varying the core and mantle radii has been studied. The mixtures of grains composed of ice, silicate, graphite and SiC in various proportions have also been considered. Each of these grain species has been considered with exp(−a ³) type of size distribution function. The wavelength dependent indices of refraction have been used throughout.     

Optical absorption edge in SnS

Optical absorption in single crystals of tin sulfide has been studied at many temperatures between 100 and 300 °K, in the wavelength range 2·2–0·8 μ. From the interference fringe patterns the absorption coefficient, reflection coefficient and index of refraction as a function of wavelength were determined for two light polarizations (ε∥a and ε∥b). From an analysis of the data, indirect band gaps of 1·142 and 1·095 eV were found for the two directions of polarization. Also it was found that the phonon assisted transitions required the participation of two phonons at different energy thresholds with energies 0·033 or 0·038 eV and 0·082 or 0·113 eV, with reference to the two axis. The temperature dependence of the indirect band gap for each direction of light polarization is linear with a slope ?4·05 × 10^?3eV and ?4·37 × 10^?3 eV respectively.     

Exact solutions to a time-dependent vacuum transport problem

We consider a point source of radiation emitting into an empty spherical volume with a well-defined boundary. This geometry represents, for example, an eruptive variable star at the center of a spherical-shell nebula. The nebula has a fixed albedo. For various time histories of the emission of the central star, we derive solutions for the time dependence of the flux falling on the nebular boundary. This flux has two components: the direct flux from the star and the diffuse flux reemitted by the boundary. Solutions generally involve combinations of hyperbolic sines and cosines and change character abruptly at multiples of t_c, the light-travel time across the nebula.     

Near-infrared polarization study of L1641S

H-band polarimetric images and KS-band images of star formation region L1641S are presented. Two reflection nebulae, Re50N and Re50, are in the north and south of the region, respectively. The polarization maps of two nebulae exhibit high degrees of polarization and centrosymmetric patterns, indicating the single scattering and small dust grains in the nebulae. There are two infrared sources, IRS1 and IRS2, in the nebula Re50N. IRS1 is the illuminating source of the nebulae and the driving source of CO outflow; IRS2 is suggested to provide considerable light at optical wavelengths. The high polarization in Re50N can be interpreted as surface scattering from the outflow at an inclination of 30 degrees. Based on the polarization arc structure, we further identified the bipolar structure of the nebula Re50N. The FU Orionis phenomenon in L1641S is discussed at the end of this paper.     

Symmetry analysis in neutron diffraction studies of magnetic structures: 5. Polarization effects in the scattering of neutrons by magnetic structures

It is shown that both the cross section of elastic scattering by a magnetic structure and the polarization vector of the scattered neutrons beam are described by a set of complex axial vectors M^L. They depend on the vectors of atomic magnetic moments in a primitive cell of the crystal and the wave-vector star of the magnetic structure. Particularly, the intensity of a magnetic Bragg reflection and the polarization vector of the scattered beam of that reflection are determined only by a vector M^L connected with an arm star contribution of the magnetic structure and corresponding to the wave vector k_L of a star {k}. A single magnetic reflection allows one to determinean arm contribution of the magnetic structure if one uses polarization effects and an expansion of the magnetic structure over the basis functions of the irreducible representation of the crystal space group. In the general case minimal number of necessary reflections for the total determination of a magnetic crystal is equal to the arm number of the wave-vector star. All analyses here have been done for the single domain magnetic structure. The polarization phenomena will not be observed for many cases where there is a uniform distribution of domains.     

Algebraic recurrence relations for the finite-order scattering and transmission functions

In preceding papers (cf. Bellmanet al.(^1,2,3,), integral recurrence for the finite-order scattering and transmission functions have been given in connection with integral recurrence relations for the finite order X- and Y-functions with the aid of an initial-value method. In the present paper, it is shown how to find algebraic recurrence relations for the finite-order scattering and transmission functions in terms of finite-order X- and Y-functions without referring to an initial-value method. These recurrence relations are suitable for the numerical computation of the finite-order scattering and transmission functions by use of a digital computer. Furthermore, in Tables 1–3, a numerical example of the finite-order reflection functions for optical thickness 0·2 with albedo = 1 is listed. Table 4 furnishes an example of the cumulative reflection functions for optical thickness 0·2 with three different albedos.     

Microwave cyclotron resonance of hot electrons in p-type GaSb

A microwave photocreated cyclotron resonance signal is observed in p-type GaSb in the temperature range 1–30 K. Circular polarization and other measurements identify the carriers as electrons in the (000) conduction band. The problem of a surface effect on the measured peak position, reported for the first time is avoided by bulk carrier creation. An exponential loss of signal intensity at 27 K is explained by the theory of background plasma effects. The measured ωτ of 1·5–4 yields an electron collision time of τ ～ 10^?11 sec. The scattering mechanism at liquid helium temperatures is identified as being partly due to neutral defect acceptor scattering of hot electrons, with an unidentified residual scattering process. The electron polaron effective mass is measured to be (m *(polaron)/m₀) = 0·0412 ± 0·0012 for hot electrons with an average energy of ～ 14 MeV and is isotropic within 1 per cent. When corrections for conduction-band non-parabolicity and hot polaron effects are applied, the band-edge free electron mass is calculated to be (m₀*(free)/m₀) = 0·0396 ± 0·0021 (±5·2 per cent).     

Lattice vibrations of AsxP1−xIn solid solutions

On the basis of investigations of reflection spectra from As_xP_1?xIn solid solutions, new data have been obtained on the character of the vibrational spectrum for compositions in which x is, 0, 0·2, 0·3, 0·4, 0·5, 0·6, 0·8, 0·9 and 1. The variation of the frequencies and oscillator strengths that characterize As and P atom vibrations has been determined as a function of composition. From the comparison of calculated with experimental reflection spectra, the dispersion of the real part (∈₁) and the imaginary part (∈₂) of the dielectric constants of the substance as well as |∈| have been estimated. The values of the nonlocal and local parts of the effective ion charge of InAs and InP were also determined.     

Untersuchung der Polarisationsebene von Photonen nach Compton-Streuung an polarisierten Elektronen

Two polarization phenomena in Compton scattering by polarized electrons were investigated. In the first experiment, the rotation of the polarization plane of photons passing through magnetized iron and gadolinium was measured. This effect arises from a spin dependence of the Compton forward scattering amplitude. For 228 and 333 keV photons and iron absorbers, the observed rotation angles areφ ₀=(3.90±0.57) ×10^?3 rad · cm^?2 and (4.75±0.58)×10^?3 rad · cm^?2, respectively. Secondly, the orientation of the photon polarization plane after scattering of unpolarized photons by polarized electrons was measured. This experiment tests time reversal invariance in quantum electrodynamics. No dependence of the polarization plane on the direction of the electron spin was found within 2×10^?3.     

Polarisationsmessungen an Elektronenstrahlen nach der Transmission durch magnetisierte Eisenschichten

Magnetized iron foils of a thickness of 500 Å were transmitted by 60 keV electrons. The spin polarization of the electron beam was investigated by Mott scattering after transmission. No polarization effect was found. Since the lowest detectable polarization degree wasP=0·003 the atomic polarization cross section must be assumed to be smaller than 0·8·10^?20cm². This cross section is the sum of the spin exchange cross section and the spin dependent part of the total scattering cross section. If the electron binding energy is neglected, the spin depentend part of the total scattering cross section can be calculated from the theory of Møller scattering. In the case of our conditions-60 keV and an aperture of 10^?3 radian-the calculated cross section is smaller than the experimental upper limit. In further experiments the electron beam was split into the energy spectrum by an electrostatic analyzer placed between the iron foil and the Mott scattering foil. In these measurements only small parts of the energy spectrum were investigated, however, even here no detectable polarization occured.     

Relativmessung der Elektronenpolarisation beimxβ-Zerfall: RaE(Bi210)-P32

An apparatus is described for comparing the longitudinal polarization valuesP ofβ-particles from different emitters by the method of double scattering. For RaE(Bi²¹⁰) and P³² we have measured the ratio of polarization values to be P(RaE)/ P(P³²)=0·757±0·022 at 540 keV. This is in good agreement with previous measurements. Ratios of matrix elements are determined from polarization and spectrum shape data of RaE, but these values are not reliable because the spectrum shape shows a systematic discrepancy between theory and experiment below 200 keV. A discussion of electron polarization and spectrum shape data of P³² shows that deviations of polarization from the allowed value are probably very small.     

Elastische und unelastische Streuung von Elektronen an Gasen

The theoretical differential cross section for the elastic scattering and for the excitation of optical transitions in helium by electron impact has been refined in Born approximation by use of the two parameter Eckart eigenfunction for the ground state and for the excited states. The angular distributions of 25 kev electrons scattered elastically and inelastically by helium were measured in the angular range 2·3·10^?4≦?≦4·10^?2. The intensity distribution of the elastically scattered electrons is in accordance with the theoretical curve for?>7·10^?3 and is disturbed at smaller angles by the primary beam. Normalization of the experimental values to the theoretical elastic differential cross section leads to agreement between the experimental differential cross section for the excitation of the 2¹ P and 3¹ P state and the scattering formulae given in this paper. There are small systematic deviations (<20%) for the 2¹ P differential cross section in the angular range 3·10^?3<?<1·10^?2 only. The oscillator strength of these two transitions has been determined from the scattering measurements:f ₂₁=0·312±0·04 andf ₃₁=0·0898±0·006.     

Messung der longitudinalen Polarisation von Betastrahlen aus RaE (Bi210) und Sb124 mit Hilfe der Møller-Streuung

The electron-electron (Møller) scattering method is used for the determination of the helicity of beta rays from the 1.17 MeV transition of RaE and from the 2.31 MeV transition of Sb¹²⁴. The apparatus is described and the evaluation of the efficiency of polarization detection for this apparatus is given in detail. The depolarization corrections are discussed. The results of the helicity measurements areP = ? (0·77±0·09)v/cfor RaE at a mean energy of 640 keV andP = ? (0·90±0·14)v/c for Sb¹²⁴ at a mean energy of 1550 keV.     

Neutron diffraction study on the hyperfine-induced nuclear spin order in the antiferromagnet PrSn3

At several $\text{(h+}\text{1}\text{2}\text{0 0)}$ reciprocal lattice positions of PrSn₃, we observed Bragg scattering of neutrons which is purely due to the nuclear spin polarization of ¹⁴¹Pr, and could measure the temperature dependence of the polarization between 10 mK and 4.2 K. From the perfectly polarized state of the nuclear spins, the difference between the spin-dependent nuclear scattering lengths b⁺ and b^- has been determined to be b⁺ - b^- = -0.110 ± 0.006 × 10^-12 cm, which is significantly larger in magnitude than the previously reported value. An additional electronic polarization which is linearly proportional to the nuclear spin polarization has also been observed.     

A fast linearized pseudo-spherical two orders of scattering model to account for polarization in vertically inhomogeneous scattering-absorbing media

We calculate the reflection matrix for the first two orders of scattering in a vertically inhomogeneous, scattering-absorbing medium. We take full account of polarization and perform a complete linearization (analytic differentiation) of the reflection matrix with respect to both the inherent optical properties of the medium and the surface reflection condition. Further, we compute a scalar-vector correction to the total intensity due to the effect of polarization; this correction is also fully linearized. The solar beam attenuation has been computed for a pseudo-spherical atmosphere.Results from the two orders of scattering (2OS) model have been tested against scalar intensities for an inhomogeneous atmosphere, and against Stokes vector results for a homogeneous atmosphere. We have also performed backscatter simulations of reflected sunlight in the O₂A band for a variety of geometries, and compared our results with those from a full vector multiple scattering code. Our results are exact in the center of strong lines and most inaccurate in the continuum, where polarization is least significant. The s- and p-polarized radiances are always computed very accurately. The effect of gas absorption optical depth, solar zenith angle, viewing geometry, surface albedo and wind speed (in the case of ocean glint) on the intensity, polarization and corresponding weighting functions have been investigated. It is shown that the 2OS model provides fast and reliably accurate polarization corrections to the scalar-model radiance and weighting function fields. The model can be implemented in operational retrieval algorithms as an adjunct radiative transfer code to deal with polarization effects.     

Measurement of the angular distribution of the polarization of the recoil proton from the photoproduction of neutral pions on hydrogen at a photon energy of 360 MeV. II

The angular distribution of the polarization of the recoil protons from the reactionγ+p→π ⁰+p has been measured at a photon energy of 360 MeV and at pion CM angles of 58°, 75°, 96° and 105°. The polarization of the protons has been determined by the left to right ratio in scattering on a helium gas target. The trajectory of each scattered proton has been measured by a system of spark chambers.     

Elastic constants of solid krypton at T = 77 K determined by inelastic neutron scattering

Long-wavelength acoustic phonons have been studied for each of the [ζ00]T, [ζ00]L, [ζζ0]L and [ζζ0]T₁ branches in solid Kr at T = 77 K by means of inelastic neutron scattering utilizing ‘cold neutrons’ as they are available in the long-wave length tail of the pile spectrum. The raw data have been corrected for resolution effects taking into account the curvature of the dispersion surface and variation of mode eigenvectors. It has turned out, that this yields appreciable shifts of the raw data. The results of our experiment give c₁₁ = 4·25 ± 0·10, c₄₄ = 2·04 ± 0·03, c₁₂ = 2·82 ± 0·12 and a value for B = (c₁₁ + 2c₁₂)/3 = 3·30 ± 0·09 × 10¹⁰ dyne/cm². Available thermodynamic data for Kr gives a derived value for B^ad = 2·58 ± 0·06 × 10¹⁰ dyne/cm² indicating a large difference between zero sound and first sound in solid Kr at high temperatures.     

Delbrück-Streuung von 17 MeV-Photonen

Differential cross sections have been measured for the small angle scattering ofγ-rays by iron, silver, tantalum, lead and uranium with 17 MeV photons from Li⁷ (p, γ) Be⁸ at mean four momentum transfersq of 0·5mc and 1·3mc and with 7 MeV photons from F¹⁹(p, αγ)O¹⁶ at mean four momentum transfer of 0·5mc. Under these experimental conditions only Compton, Rayleigh and possibly Delbrück scattering are of importance. Extrapolation of known theoretical results to higher energies shows, that Rayleigh and Compton scattering from bound electrons should depend only onq for small angles, smallq and fixedZ. Using this it follows, that at 17 MeV andq≈0·5mc an additional scattering process must be present, which increases with growingZ and which is negligible in the measurements at 17 MeV withq≈1·3mc and at 7 MeV withq≈0·5mc. These results are in qualitative agreement with the approximate theory for Delbrück scattering ofBethe andRohrlich, however experimental cross sections at 17 MeV andq≈0·5mc are about a factor of 1·6 lower than those predicted by this theory. This discrepancy is not unexpected, since exact calculations of Delbrück scattering amplitude fromKessler andZernik at 2·62 MeV and 6·14 MeV show even greater deviations in the same sense.     

Critical behaviour of the two-dimensional ising antiferromagnets K2CoF4 and Rb2CoF4

The studies have been performed by means of neutron scattering. We report here the first experimental verification of the theoretical predictions concerning temperature dependence of the long range order parameter of two-dimensional Ising systems, giving the values B = 1·16±0·03 and β = 0·119±0·008 for the critical parameters. Also the parameters for the inverse correlation length and the staggered susceptibility were determined, with exponents v = 0·89±0·1 and γ = 1·34±0·22. It was discovered that frozen-in states of stacking of the two-dimensional planes appeared upon quick cooling through the ordering temperature.     

Polarization in charge exchange reaction π−+p→π0+n at 40 GeV/c for the 4-momentum transfer range 0<|t|<2 (GeV/c)2

The results on measuring polarization in charge exchange reaction π^?+p→π⁰+n at 40 GeV/c are presented for the 4-momentum transfer range from 0 up to 2 (GeV/c)². At |t|≦0.4 (GeV/c)² the polarization has a positive sign. In the “crossover” region of π^± elastic scattering a possible minimum in the polarization behaviour has been seen for the first time. the polarization is zero within the statistical accuracy near this point. In the “deep” region of the charge-exchange differential cross-section the polarization has a negative sign. The presented data are not in agreement with the modern theoretical models.