Non-coherent scattering in subordinate line—V: Solutions of the transfer problem

We present several examples of the numerical solution of the radiative transfer in subordinate lines. Using a simplified physical model that yields the line source function analogous to the usual two-level-atom form modified by the presence of the redistribution function R_v in the scattering integral, we have solved the transfer problem for isothermal, plane-parallel atmospheres, both finite and semi-infinite. For finite atmospheres, we have found substantial differences between the solutions with R_v and those with complete redistribution. On the other hand, for semi-infinite atmospheres the complete redistribution appears to be a good approximation, at least for a_l?a_u (damping parameters for the lower and upper levels, respectively). It is shown that the effect of R_v becomes more pronounced with increasing ratio a_u/a_l. Finally, it is demonstrated that an approximate form for R_v analogous to that of Kneer for R_II serves as a very good approximation for computing the line profiles, particularly in the line wings.     

Phase-function method for elasticα-α scattering

The phase-function method is adapted to deal with scattering on Coulomb plus nonlocal separable potentials. The Coulomb effect is included rigorously and a closed form expression is obtained for the scattering phase shiftδ _l (k). Based on the expression forδ _l (k) we present results forα-α elastic scattering phases which compare very well with more detailed calculations.     

Amplitudes of multichannel scattering on the barrier with a constant height in the scattering direction

The immersing method is applied to solve the N-channel scattering problem. In particular, we consider the particle scattering on a multidimensional potential barrier, which is constant in the scattering direction and arbitrary in the lateral direction. For this case the scattering amplitudes t _m and r _m (m = 1, 2, …, N) are determined. Transition from the obtained formulas to the case of thin potential is performed. For this case analytical expressions of transmission amplitudes t _m and reflection amplitudes r _m are obtained. We show that the product of transmission and reflection amplitudes in the channel m does not depend on the scattering channel. It is assumed that the scattering particle falls on the potential with the longitudinal wave vector k _l corresponding to the channel l.     

On the unitary pole expansion of the potentials I and III of Malfliet and Tjon

The unitary pole expansion for the local soft-core potentials I and III of Malfliet and Tjon is obtained, and the Faddeev-Lovelace equations are solved for the separable potentials. The energyE _T of the triton and the doublet scattering length² a have been obtained. The results are ?8.59 MeV ≦E_T≦ ?8.57 MeV and 0.89 fm≦² a≦0.91 fm. For the quartet scattering length a value₄ a = 6.39 fm has been found.     

New determination of the neutron-proton scattering amplitude and precise measurements of the scattering amplitudes on carbon,chlorine, fluorine and bromine

After an improvement on the theory of the neutron-gravity-refractometer and after refinements of the experimental procedure we have performed new measurements of the absolute value of the neutron-proton scattering amplitude at low neutron energies. In order to obtain and to confirm a very high accuracy we carried out neutron-reflection experiments on 18 various liquids of 11 different organic substances containing the elements carbon, hydrogen and/or chlorine. Compounds with fluorine and bromine were used to measure the scattering amplitudes of these elements. We found the coherent scattering amplitudes of the bound atoms to be:a _H=?3.7409(1l)fm,a _c=6.6484(13)fm,a _c1=9.5792(8)fm,a _F=5.66(2)fm anda _Br=6.79(2)fm. The low energy (n, p)-parametersa _t anda _s were calculated with the presenta _H and a new value of the (n, p) scattering cross-sectionσ ₀. By comparing the measureda _C with values obtained from precise transmission experiments we could determine the gravitational accelerationg _f of the free neutron in terms of the local value g. We found the two values to be equal:g _f =0.9996(7)g.     

Transport cross sections for charged particle scattering in (dense-) cesium plasma; electrical conductivity

Transport cross sections for the electron-ion and electron-electron scattering in (dense) cesium plasmas is determined with the partial wave method. The scattering phase shifts δ_l(k) are calculated numerically by means of the usual Numerov method and the advantageous amplitude — phase method for energies E = 10^-4··· 5 ryd and for Debye screening lengths R_D = (10···10³)a₀. Besides the usual Debye potential, also a Thomas-Fermi potential is applied for the cesium electron-ion interaction. The resulting transport cross sections are compared with the Born and quasi-classical approximations. Furthermore, the electrical conductivity of fully ionized cesium plasmas is determined and compared with respective Spitzer results.     

Correlation between the properties of the deuteron and the low-energy triplet parameters of neutron-proton scattering

The correlation between the asymptotic normalization constant for the deuteron, A_S, and the neutron-proton scattering length for the triplet case, a_t, is investigated. It is found that 99.7% of the asymptotic constant A_S is determined by the scattering length a_t. It is shown that the linear correlation between the quantities A _S ^?2 and 1/a_t provides a good test of correctness of various models of nucleon-nucleon interaction. It is revealed that, for the normalization constant A_S and for the root-mean-square deuteron radius r_d, the results obtained with the experimental value recommended at present for the triplet scattering length a_t are exaggerated with respect to their experimental counterparts. By using the latest experimental data obtained for phase shifts by the group headed by Arndt, it proved to be possible to derive, for the low-energy parameters of scattering (a_t, r_t, P_t) and for the properties of the deuteron (A_S, r_d) results that comply well with experimental data.     

Neutron scattering in argon and <Emphasis Type="Italic">ne</Emphasis> interaction

As a preparation for the new experiment to measure the ne scattering length a_ne the total neutron cross section of gaseous argon has been obtained by the time-of-flight method at the Dubna booster IBR-30 in the energy range from ～5 eV to ～30 keV. A combined one-level analysis of the newly obtained and other known data on cross sections of Ar and ³⁶Ar has made it possible to improve some neutron parameters and calculate the scattering cross section σ_s and the scattering length a separately for ³⁶Ar and ⁴⁰Ar at any energy.     

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^-+.     

Anisotropy in the length change of gallium single crystals at their superconducting transition

The magnetostriction of gallium single crystals has been measured for the three principal axes between 0.3K and 1.1 K. It is found that the length change at the transition from the superconducting to the normal state is given approximately by (Δl/l)_a = − 3.10⁻⁹, (Δl/l)_b = + 4.4 · 10⁻⁹ and (Δl/l)_c = + 1.8 · 10⁻⁹, for the a, b and c axes at T = 0 K. A short discussion of the results with respect to microscopic theory is presented.     

Stimulated Raman scattering of an extraordinary mode in a solid state plasma

This paper presents an investigation of stimulated Raman scattering of an extraordinary mode in a solid state plasma, n In Sb. As the pump wave (w₀, k₀) propagates in the semiconductor the electrons acquire an oscillatory drift velocity and the magnetic field of the pump interacts with a low frequency perturbation (w_l, k_l) to give rise to high frequency side bands (w_l ± w₀, k_l ± k₀). The side band (w_l − w₀, k_l − k₀) interacts with the pump to produce a low frequency ponderomotive force responsible for driving the original density perturbation. The expressions for the growth rate and threshold for the instability have been obtained. For typical plasma parameters of n In Sb and laser radiation of frequency 1.778 × 10¹⁴s⁻¹, the growth rate turns out to be ~ 10¹¹s⁻¹ for the scattering angle θ = 0°. The growth rate is found to reduce with increasing values of scattering angle. A magnetic field enhances the growth rate and tends to reduce the threshold for the instability. The present investigation may be used to obtain useful information about the nature of elementary excitations in solid state plasmas, and the estimate of the growth rate may help in diagnostics and in the characterization of semiconductors.     

Final-state summation in photoelectron diffraction

A formula was derived to perform the summation over the l_c±1 final states of the dipole transition matrix element and the scattering path operator. This formula shows that often it seems more convenient to speak about l_c+1 and l_c±1 channels instead of the l_c+1 and the l_c−1 channel. Using this formula and restricting the considerations on the first order scattering and the plane wave approximation, explicit formulas were given for the photoelectron intensity, the circular dichroism and the spin polarization in terms of products of the vectors involved in the problem: photon wavevector, photon polarization, magnetization, electron wave vector, and orientation of the spin detector. Additionally the scattering part contains the position vectors of the scatterers with respect to the emitter. These formulas are discussed as well for magnetic as for nonmagnetic samples and for s, p, d and f core states. General expressions are given for the peak rotation. Also it is possible to write down explicitly the dependence on absolute value and the phases of the complex radial matrix elements.     

Experimental study of resistivity of metallic materials with dynamic disorder

As a result of strong electron-phonon interaction, the enhancement of scattering with increasing temperature may decrease the mean free pathl in crystals down to interatomic distances:l≈a. This means that with respect to the electron wave the degree of the atomic disorder in these crystals is approximately the same as in amorphous metal. Because of a high electron velocity the dynamic character of the disorder seems to be unimportant. At the same time, the degree of disorder can be easily changed by varying the temperature. This makes it possible to simulate and study the transport properties of the disordered media on highquality crystals with strong phonon scattering. The sign that indicates the fitness of a crystalline metallic material for such studies is the saturation of its resistivityρ that ceases to grow as the temperature is increased. The saturation of resistivity was investigated experimentally on (i) Cu-Zr alloys in the crystalline state, (ii) single crystals of WO₂, which is a metal with well-defined Fermi surface. The samples of Cu-Zr were produced by the recrystallization of amorphous ribbon. Some of these samples reveal resistivity saturation. With further increase ofT a maximum in theρ(T) dependence was observed at those compositions which slightly decreased theirρ value under recrystallization. This unusual dependence can be explained in terms of the two-band model assuming that thed-electrons reach the minimal free path,l≈a, while thes-electrons do not. The WO₂ crystals were used to study the anisotropy of (T). In the directions, whereρ is high, there is a tendency to saturation. Whereρ is low, no tendency to saturation is observed. The quantitative analysis of the curves has shown that not only the absolute value but also the relative value of the deviation from the Boltzmann lawρ～T decreases down as the resistivity decreases.     

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.     

Determination of the ππ scattering lengths from data on πN → ππN reactions by the method of Roy equations

Fitted phase-shift curves from the threshold to the dipion mass, which is equal to 1 GeV, are constructed on the basis of all available experimental values of the S-and P-wave phase shifts for five charged channels of pion-pion scattering. The resulting phase-shift curves are introduced in the Roy equations in order to obtain the subtraction constants λ _l ^I (s). By using these subtraction-constant values as functions of the dipion mass, the S ₀-and S ₂-wave pion-pion scattering lengths are found to be a ₀ ⁰ = (0.240 ± 0.023)m _π ^?1 and a ₀ ² = (?0.034 ± 0.013)m _π ^?1 . A strong correlation of the S-wave scattering lengths is demonstrated.     

Effects of Field Fluctuations,Losses, and Aberrations on the Sensitivity of a Michelson GW Antenna Using Squeezed Radiation

The sensitivity of an interferometric gravitational wave (GW) antenna operating above a few hundred Hertz is shot-noise limited. Sub-shot-noise sensitivity can be achieved by superimposing squeezed light on the laser field. The benefits of this approach are reduced in nonideal interferometers having fringe visibility less than unity, as pointed out by Gea-Banacloche and Leuchs and recently discussed by Chickarmane. Here, we consider an interferometer described by a set of coefficients V_l^(k), V_sq^(k), V_lsq^(k) depending on the misalignment, mismatching, and aberrations of the optical systems, as well as on the asymmetry of the beam splitter and the two-arm losses. Due to the presence of terms proportional to the product of laser times squeezed fields, we have taken into account the amplitude fluctuations of a_l. A simple model of the squeezed vacuum light, produced by a degenerate optical parametric oscillator (OPO), is used for calculating the dependence of the spectral density of the output of a GW antenna on the fluctuations of the OPO-cavity resonance frequency, the pump amplitude fluctuation, and the nonlinear-crystal-temperature drift. A set of figures η_sq± and r_lsq±⁽²⁾ are introduced for describing the effects of the amplitude fluctuations and the relative line width γ_la on the spectral density of the quadrature phase operator X = a_la_sq⁺ h.c.     

Intracellular potential relief and size effects in the lattice of a LaF3 superionic conductor

The potential relief in the lattice of a LaF₃ crystal is calculated by quantum-mechanical methods for clusters containing from 24 to 1200 ions. For the dielectric phase, formation energy E _a for defects of the vacancy-interstitial fluorine ion type and potential barrier E _d preventing the motion of fluorine ions are found to grow from minimal values E _a = 0.12 eV and E _d = 0.22 eV for a cluster of 24 ions to maximal values E _a = 0.16 eV and E _d = 0.26 eV for clusters of 576 and 1200 ions. The values of E _a and E _d obtained in quasi-mechanical calculations are in good agreement with those obtained from Raman and quasi-elastic light scattering data.     

The I = 0, s-wave ππ scattering length

Interior dispersion relations are applied to πN scattering amplitudes to extract the I = 0, s-wave ππ scattering length, a₀⁰. Two methods are used, the second of which also incorporates known ππ scattering phase shifts. We have used the πN amplitude analysis of Pietarinen and obtained values of a₀⁰: (0.28 ± 0.09)μ^? and (0.25 ± 0.08)μ^? for the two methods respectively, consistent with other recent determinations from K_e4 and πN → ππN data. The 1971 πN phase-shift analysis of Ahmehed and Lovelace was also used successfully in the first method to obtain the value a₀⁰: (0.15 ± 0.14)μ^?, consistent with the above. The second method was found to be ineffective in the face of relatively unsmooth discrepancy functions obtained from the Ahmehed-Lovelace phase shifts.