Adding and invariant imbedding equations in matrix notation for all the scattering functions

Previous work by the author introduced a radiative formulation, containing a delta interior illumination, that allowed scattering solutions driven by internal sources to be handled in complete analogy to those for the standard problem (external delta illumination scattering through a medium). This analogy was made explicit by defining the three levels of scattering functions, S_s-level, $\text{S}$_s- and S_F-level, and $\text{S}$_F-level, that characterize scattering through, into and out of, and within a finite medium, respectively. For an inhomogeneous medium the invariant imbedding method was employed to solve for these functions. This paper continues the work by showing that: (1) Adding equations can be derived for all the scattering functions using one superposition formula. (2) Adding and invariant imbedding computational methods are closely related and should be used in combination for efficient calculations. (3) A new set of functions can be defined that represent scattering out of a medium driven by thermal sources. (4) All scattering functions can be converted to represent a planetary problem by one adding step. References are given for numerical results using this formulation.     

Nonmagnetic impurity effects and neutron scattering spectrum in iron pnictides

We study the effect of local impurity and the neutron scattering spectrum based on the five-orbital model obtained by the first principle calculation for iron pnictides. We find that the interband impurity scattering is induced by the complex multiorbital structure. This fact means that the fully-gapped sign-reversing s-wave state, which is predicted by spin-fluctuation theories, is very fragile against impurities. The result suggests a reasonable possibility that the fully-gapped s-wave state without sign reversal (s₊₊-wave) would be realized in dirty iron pnictides. We also find that broad peak structure observed in the neutron scattering measurements can be explained by the s₊₊-wave state.     

Multichannel scattering of a particle in a quantum wire of cylindrical symmetry

The Schrödinger equation for a scattering particle in a quantum wire is considered. We discuss two geometrical forms of cross-section of the wire: the rectangular section and the cylindrical one. It is shown that scattering of the particle on an arbitrary potential V = V (x, y, z,), given in the wire, can be considered as a multichannel scattering, where the index of the channel coincides with the index which determines energy levels of the confined transverse motion of the particle. A method for determination of the amplitudes of transmission T _i and reflection R _i in the case of multichannel scattering is proposed. The case of two-channel scattering is considered in detail and a method for determination of the scattering amplitudes T ₁, T ₂ and R ₁, R ₂ is proposed.     

Scattering length and effective range in closed form for the Coulomb plus Yamaguchi potential

From the known expression for the off-shell T-matrix corresponding to the potential consisting of the sum of the Coulomb potential and the Yamaguchi potential, the physical scattering amplitude can be derived in a satisfactory way. We derive simple exact closed formulae for the scattering length a_cs and the effective range r_cs from this amplitude. These are compared with approximate formulae derived by Harrington. Also a few numerical calculations are reported and compared with results obtained by Harrington and by Ali et al.     

NegativeP′-pole parameters and vanishing total cross sections in high energy πN scattering

In πN forward scattering the conventionalP′-pole can be simulated by two vacuum poles with α(0)<0 and different signs of the residues. In the regions ?0.3≦ α _p ′(0)≦?0.1 and ?0.8≦α _p ′'(0)≦?0.4 the practically identical fits to the πN scattering data from 8 to 65 GeV/c yield 0.98≦α _p (0)<1. The dispersion theoretical sum rule for the scattering lengtha ⁽⁺⁾ is fulfilled because of the negativeP′ residue; it is used as a finite-energy sum rule withN=8 GeV/c.     

Theory of resonant forbidden Raman scattering in semiconductors

The Raman tensors for the electric field-induced and wavevector dependent scattering from LO phonons in semiconductors have been calculated near critical points using a perturbation treatment. The resulting expressions have analytic closed forms such that the dependence of the forbidden scattering intensity on the incident photon energy and the applied d.c. electric field can be evaluated from available energy band parameters. The forbidden LO scattering intensity of GaAs in the back scattering configuration has been numerically calculated near the e₁ and E₁ gaps as functions of the incident photon energy and the dc electric field. The result shows strong interference between the two scattering processes. The allowed TO and LO Raman scattering intensities of GaAs were also calculated at a wavelength of 1.06 μm from the SHG and Faust-Henry coefficients, and compared with the forbidden LO intensity.     

Comparison of the amplification coefficients of conjugate and non-conjugate waves in stimulated light scattering

The energies of conjugate and non-conjugate waves in stimulated light scattering were experimentally measured simultaneously. The level of spontaneous scattered light was measured with the same setup. These data allow to compare amplification coefficients of conjugate and non-conjugate waves. The coefficient for the conjugate wave proved to be two times greater then for the non-conjugate wave, assuming that ～√N_m modes are excited inside the light guide with carbondisulfide, which was used as scattering medium. N_m is the maximal number of light guide modes which can propogate within a solid angle occupied by scattering light.     

N-point functions and low-energy scattering by N centres

The scattering of a low-energy particle by a potential of a small range is known to be described satisfactorily by the s-wave alone. In the present paper we give a method of describing low-energy scattering by N potentials with the aid of N waves. For this purpose, a special system of Laplacian eigenfunctions is suggested. The scattering amplitude depends on only N parameters, irrespective of overlapping of potentials. The physical significance of these parameters δ_λ, λ=1,2,…N, is shown by exp (2iδ_λ)=S_λ where S_λ is the eigenvalue of the S matrix. The parameters δ_λ may be obtained by direct methods and perturbation theory.The low-energy scattering by an arbitrary configuration of N centres is discussed. The differential cross-section is averaged over all orientations of the configuration and radially about the direct beam, giving it as a function of the scattering angle. This formula may be used for the phase shift analysis.     

CO2 laser induced compton effect in underdense hydrogen plasma

Recent experimental observation of induced scattering of CO₂ laser radiation by an underdense hydrogen plasma can be explained theoretically by non-linear and Compton scattering from ions in the highly cooperative plasma conditions prevailing (kλ_D? 1).     

High frequency Brillouin scattering in metals and gaseous plasmas

Spontaneous and stimulated Brillouin scattering are studied in metals and gaseous plasmas, for an incident laser frequencyω ₁ greater than the corresponding plasma frequencyω _plin the medium. The calculation of threshold powers for the stimulated scattering in aluminium metal and non-degenerate Al-plasmas shows that their values become quite small asω ₁ approachesω _plFor the case of backward wave scattering we also estimate the critical power above which a temporal instability sets in such media. It is argued that this instability may be one of the factors for anomalously large absorption of high power laser beams in laser-induced plasmas.     

Electronic thermal conductivity in suspended and supported bilayer graphene

Electronic thermal conductivity κ_e is investigated, using Boltzmann transport equation approach, in a suspended and supported bilayer graphene (BLG) as a function of temperature and electron concentration. The electron scattering due to screened charged impurity, short-range disorder and acoustic phonon via deformation potential are considered for both suspended and supported BLG. Additionally, scattering due to surface polar phonons, is considered in supported BLG. In suspended BLG, calculated κ_e is compared with the experimental data leaving the phonon thermal conductivity. It is emphasized that κ_e is important in samples with very high electron concentration and reduced phonon thermal conductivity. κ_e is found to be about two times smaller in supported BLG compared to that in suspended BLG. With the reduced extrinsic disorders, in principle, the intrinsic scattering by acoustic phonons can set a fundamental limit on possible intrinsic κ_e.     

Jahn-Teller phase transition in CsCuCl3 and CsCrCl3: A neutron scattering study

The diffuse scattering above T_c was studied in CsCuCl₃ and CsCrCl₃ by neutron scattering technique. These compounds undergo phase transitions associated with the Jahn-Teller effect. Their structures are characterized by isolated chains of face sharing CuCl₆ and CrCl₆ octahedra, respectively. The diffuse scattering shows two main features: it does not occur at the superllatice points of the low temperature phase, but is centred around the strong Bragg points, and its shape changes from one Bragg point to another. This behaviour, which is incompatible with critical scattering from intra-chain correlations of Jahn-Teller distorted octahedra, can be interpreted as “dense impurity” Huang scattering.     

Determination by polarization analysis of the scattering amplitudes a+ and a- and of the degree of orientation of nuclei polarized by hyperfine fields in magnetically ordered substances

Improvements of the Ito-Shull techniques are suggested for measuring the scattering amplitudes a₊ and a_- associated with the compound states $\text{I +}\text{1}\text{2}$ and $\text{I -}\text{1}\text{2}$ which are formed by the nucleus of spin I and the incident neutron. In ferro- and ferri-magnets one can increase the sensitivity by suppressing the electronic part of the magnetic scattering when polarizing the neutrons along the scattering vector. In anti-ferromagnets one can separate the nuclear magnetic part by substracting the electronic magnetic scattering with unpolarized neutrons from the total magnetic scattering (electronic + nuclear) obtained by measuring the spin-flip amplitudes U^+- or U^-+.     

Direct-inelastic and trapping-desorption scattering of N2 and CH4 from Pt(111)

Angle and velocity distributions for supersonic chopped beams of N₂ and CH₄ scattered from clean close-packed Pt(111) surfaces are reported. For specular direct-inelastic scattering N₂ and CH₄ velocity distributions can be characterized by empirical relationships used for Ar scattering. For instance, for specular scattering the following relation is found for Ar, N₂ and CH₄: 〈KE_f〉 = A(KE_i) + B(2kT_s), where 〈KE_f〉 is the average final kinetic energy, KE_i is the incident kinetic energy and T_s is the surface temperature. The beam and surface temperature independent coefficients A and B are, respectively: Ar 0.87, 0.17; N₂ 0.79, 0.19 and CH₄ 0.84, 0.25. Unlike Ar, N₂ desorbs from Pt with a Maxwell-Boltzmann velocity distribution near the surface temperature. Qualitatively the trapping probabilities for these molecules on Pt(111) are ordered: Xe > N₂ > CH₄> Ar.     

Extension of Yafet's theory of spin relaxation to ferromagnets

By making use of Kramer's degeneracy of the electronic states in a nonmagnetic material, Yafet has derived an expression for the spin relaxation time T₁ due to scattering of electrons at phonons which involves the properties of electronic and phononic states and the matrix elements for the scattering. It is shown that an analogous expression for T₁ can be derived for ferromagnets (where Kramer's degeneracy does not hold) when taking into account the conservation of the total number of electrons. This expression can be used as a starting point for the ab initio calculation of T₁, and this quantity is required for an interpretation of the ultrafast demagnetization of ferromagnets after excitation with a femtosecond laser pulse.     

On spectral invariance of single scattering albedo for water droplets and ice crystals at weakly absorbing wavelengths

The single scattering albedo ω_0λ in atmospheric radiative transfer is the ratio of the scattering coefficient to the extinction coefficient. For cloud water droplets both the scattering and absorption coefficients, thus the single scattering albedo, are functions of wavelength λ and droplet size r. This note shows that for water droplets at weakly absorbing wavelengths, the ratio ω_0λ(r)/ω_0λ(r₀) of two single scattering albedo spectra is a linear function of ω_0λ(r). The slope and intercept of the linear function are wavelength independent and sum to unity. This relationship allows for a representation of any single scattering albedo spectrum ω_0λ(r) via one known spectrum ω_0λ(r₀). We provide a simple physical explanation of the discovered relationship. Similar linear relationships were found for the single scattering albedo spectra of non-spherical ice crystals.     

Noneikonal approach to the scattering of hadrons from nuclei. II. Proton and pion scattering from D, 3He and 4He (kL ≳ 1 GeV/c)

A previously formulated noneikonal theory for hadron-nucleus scattering valid for all angles is applied to p and π scattering on the lightest targets (k_L ? 1 GeV/c). When the required input is known, calculated differential cross sections agree well with experiments out to medium angles, far beyond the region of previous analyses. In the case of pA scattering at k_L = 1.2 GeV/c at which momentum some parameters in the elementary amplitudes F_xN are badly known, limits on their values have been obtained by demanding simultaneous agreement between theory and data for several targets. Generally speaking the agreement evidences the existence of some major corrections to the eikonal amplitude, namely, propagator off-shell and nucleon recoil effects. Inclusion of the latter primarily affects the single scattering amplitude, which may dominate the large-q² cross section if F_xN (like F_pp) itself rises with q². The calculation of pD and p⁴He cross sections requires knowledge of body form factors S_A often unknown for large q². Consistency requirements for angular distributions at several k_L lead to a conjectured large-q² behavior of S_A(q). In the case of the D the conjecture has been largely confirmed by a recent measurement of the electric form factor. The agreement leaves little room for $\text{NN}{}^1$ components in the D as heretofore derived from pD scattering. We speculate that in general, reasonable estimates for nuclear form factors out to very large q² may be obtained from hadron-nucleus scattering data with existing facilities. Since higher q² values can be reached in hadron-nucleus than in eA scattering, the former may well provide the first tests for predicted scaling of nuclear form factors.     

Light scattering by a “soft” layered sphere: Analysis by the method of spectral expansion in Kotel’nikov-Shannon choice functions

Light scattering by a two-layer “soft” sphere is studied. The analysis is made by the method of expansion in the spatial spectrum in Kotel’nikov-Shannon choice functions. In the case where changes of relative refractive indices of the first (Δn ₁ and the second ((Δn ₂) layers have the same sign, the scattering indicatrices are found to be close to the indicatrices for a homogeneous sphere with averaged effective parameters, and the integrated cross sections should be close as well. However, in the case where Δn ₁ and Δn ₂ have opposite signs, changes in the indicatrix are stronger. The major lobe becomes weaker and, in certain cases, even vanishes, whereas the side lobes and backward scattering increase in intensity. The physical interpretation of the results that can be used for the analysis of experimental data is given.     

Spin dynamics and four-photon mixing in InSb

The spin flip Raman interaction can be used to excite coherent spin precession in semiconductors. Resonant, four-photon mixing is shown to be equivalent to Raman scattering from this coherent state. Studies of the four-photon intensity give information concerning spin dynamics (T₁ and T₂) in n-InSb.     

Scattering theory with different state spaces of perturbed and free system

A new method of the time-dependent approach to the scattering problem is presented. For the main initial objects we take a pair of nonnegative bilinear functionals β_j (j = 1,2) (instead of a pair of selfadjoint operators H_j). In the particular case β_j and H_j are connected by the Green's functions of the corresponding Schrödinger equations. In the general case β₂ may be rather arbitrary. The method proposed here can apply to the scattering problem with a non-operator perturbation. This method essentially uses a pair of different state spaces for the free and perturbed physical system respectively.