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At least 19 records

A T-matrix theory of galactic heavy-ion fragmentation

The theory of galactic heavy ion fragmentation is furthered by incorporating a T matrix approach into the description of the three step process of abrasion, ablation, and final state interations. The connection between this T matrix and the interaction potential is derived. For resonant states, the substitution of complex energies for real energies in the transition rate is formerly justified for up to third order processes. The previously developed abrasion-ablation fragmentation theory is rederived from first principles and is shown to result from time ordering, classical probability, and zero width resonance approximations. Improvements in the accuracy of the total fragmentation cross sections require an alternative to the latter two approximations. A Lorentz invariant differential abrasion-ablation cross section is derived which explicitly includes the previously derived abrasion total cross sections. It is demonstrated that spectral and angular distributions can be obtained from the general Lorentz invariant form.

Norbury, J. W.↗

A complex T-matrix derivation of a resonance amplitude

Time-dependent perturbation-theory techniques are used to derive a compact expression, valid to arbitrary order and displaying time dependence explicitly, for a quantum-mechanical transition amplitude applicable to the description of resonances. A solution representing a complex-energy generalization of the usual real-energy (nonresonant) amplitude is obtained and generalized to all orders by introducing a complex-energy T matrix. Applications to physical problems such as the extension of the Fermi golden rules to resonances (Norbury and Deutchman, 1984); pion production in relativistic nucleus-nucleus collisions (Norbury et al., 1985); and the determination of resonant cross sections for nuclear, atomic, or molecular processes involving the formation and decay of intermediate discrete or continuum states are indicated.

Norbury, J. W.↗

Doubly differential cross sections for galactic heavy-ion fragmentation

An abrasion-ablation T-matrix formulation is applied to the calculation of double differential-cross sections in projectile fragmentation of 2.1 GeV/nucleon O-16 on Be-9 and 86 MeV/nucleon C-12 on C-12 and Ag-108. An exponential parameterization of the ablation T-matrix is used and the total width of the intermediate states is taken as a parameter. Fitted values of the total width to experimental results are used to predict the lifetime of the ablation stage and indicate a decay time on the order of 10 to the -19th power sec.

Cucinotta, Francis A.↗

A covariant multiple scattering series for elastic projectile-target scattering

A covariant formulation of the multiple scattering series for the optical potential is presented. The case of a scalar nucleon interacting with a spin zero isospin zero A-body target through meson exchange, is considered. It is shown that a covariant equation for the projectile-target t-matrix can be obtained which sums the ladder and crossed ladder diagrams efficiently. From this equation, a multiple scattering series for the optical potential is derived, and it is shown that in the impulse approximation, the two-body t-matrix associated with the first order optical potential is the one in which one particle is kept on mass-shell. The meaning of various terms in the multiple scattering series is given. The construction of the first-order optical potential for elastic scattering calculations is described.

Gross, Franz↗

Solidification in neutron star cores

A mathematical computation based on the t-matrix approach shows that a system of strongly interacting baryons under sufficiently high pressure (approximately 10 to the 30th power atm) and densities greater than 10 to the 15th power g/cu cm minimizes the energy by arranging the constituents in a lattice structure rather than in a fluid phase. The solution is given assuming an optimum spin arrangement, although all other possible arrangements would also satisfy the conditions for crystallization to occur.

Canuto, V.↗

Crystallization of dense neutron matter

The equation of state for cold neutron matter at high density is studied in the t-matrix formulation, and it is shown that energetically it is convenient to have neutrons in a crystalline configuration rather than in a liquid state for values of the density exceeding 1600 Tg/cu cm. The study of the mechanical properties indicates that the system is stable against shearing stresses. A solid core in the deep interior of heavy neutron stars appears to offer the most plausible explanation of speed-ups observed in the Vela pulsar.

Canuto, V.↗

A distorted-wave methodology for electron-ion impact excitation - Calculation for two-electron ions

A distorted-wave program is being developed for calculating the excitation of few-electron ions by electron impact. It uses the exchange approximation to represent the exact initial-state wavefunction in the T-matrix expression for the excitation amplitude. The program has been implemented for excitation of the 2/1,3/(S,P) states of two-electron ions. Some of the astrophysical applications of these cross sections as well as the motivation and requirements of the calculational methodology are discussed.

Bhatia, A. K.↗

On the factorization and fitting of molecular scattering information

The reported analysis is based on the factored IOS T-matrix. It is shown that line shape measurements may be used over a range of temperatures to evaluate inelastic scattering cross sections. Basic factorization or parameterization relations are derived by considering the wavefunction equations. The parameterization of cross sections is considered, taking into account the differential scattering amplitude and cross section, integral cross sections, phenomenological cross sections for general relaxation processes, and viscosity and diffusion cross sections. Thermal averages and rates are discussed, giving attention to integral cross sections and rates, and general phenomenological cross sections. The results of computational studies are also presented.

Goldflam, R.↗

Derivation of the chemical-equilibrium rate coefficient using scattering theory

Scattering theory is applied to derive the equilibrium rate coefficient for a general homogeneous chemical reaction involving ideal gases. The reaction rate is expressed in terms of the product of a number of normalized momentum distribution functions, the product of the number of molecules with a given internal energy state, and the spin-averaged T-matrix elements. An expression for momentum distribution at equilibrium for an arbitrary molecule is presented, and the number of molecules with a given internal-energy state is represented by an expression which includes the partition function.

Mickens, R. E.↗

Absorption and scattering of light by nonspherical particles

Using the example of the polarization of scattered light, it is shown that the scattering matrices for identical, randomly ordered particles and for spherical particles are unequal. The spherical assumptions of Mie theory are therefore inconsistent with the random shapes and sizes of atmospheric particulates. The implications for corrections made to extinction measurements of forward scattering light are discussed. Several analytical methods are examined as potential bases for developing more accurate models, including Rayleigh theory, Fraunhoffer Diffraction theory, anomalous diffraction theory, Rayleigh-Gans theory, the separation of variables technique, the Purcell-Pennypacker method, the T-matrix method, and finite difference calculations.

Bohren, C. F.↗

Kaon-nucleus scattering

The derivations of the Lippmann-Schwinger equation and Watson multiple scattering are given. A simple optical potential is found to be the first term of that series. The number density distribution models of the nucleus, harmonic well, and Woods-Saxon are used without t-matrix taken from the scattering experiments. The parameterized two-body inputs, which are kaon-nucleon total cross sections, elastic slope parameters, and the ratio of the real to the imaginary part of the forward elastic scattering amplitude, are presented. The eikonal approximation was chosen as our solution method to estimate the total and absorptive cross sections for the kaon-nucleus scattering.

Hong, Byungsik↗

The normal modes of a resonant cavity containing discrete inhomogeneities - The influence of fibril magnetic fields on the solar acoustic oscillations

Motivated by considerations of the interaction between fibril magnetic fields and solar p-modes, the acoustic spectrum of a cylindrical cavity filled with ideal gas in which a number of magnetic flux tubes are embedded is studied. A formalism, based on the T-matrix approach to acoustic scattering, is developed which can be used to determine the eigenfrequencies and eigenfunctions for any arbitrary distribution of flux tubes. For weak scatterers, the frequency shifts and velocity eigenfunctions are calculated using perturbation theory for the cases of a single flux tube and a random distribution of up to 100 flux tubes. The results of this 'exact' approach are used to give a critical appraisal of the predictions of theories based on some form of averaging, such as the one discussed recently by Bogdan and Zweibel (1987).

Bogdan, Thomas J.↗

The prediction of pseudo-resonance positions in the Schwinger variational principle

The Schwinger Variational Principle is appled to s-wave electron-hydrogen atom scattering. It is shown computationally, that, consistent with a paper by B. Apagyi, P. Levay, and K. Ladanyi, there are pseudo-resonances at the static exchange level of approximation, but not at the static level. The T-matrix was employed, as well as, the K-matrix version of the Schwinger Principle, with a real Slater basis, and obtained the same results in both. The origin of the pseudo-resonances as resulting from singularities in the separable potential that is effectively employed in the Lippmann-Schwinger equation from which the Schwinger Variational Principle can be derived. The determination of the pseudo-resonance parameters from the separable potential is computationally inexpensive and may be used to predict the pseudo-resonance parameters for the scattering calculations so that they may be avoided.

Weatherford, Charles A.↗

Kaon-nucleus scattering

Two kinds of number density distributions of the nucleus, harmonic well and Woods-Saxon models, are used with the t-matrix that is taken from the scattering experiments to find a simple optical potential. The parameterized two body inputs, which are kaon-nucleon total cross sections, elastic slope parameters, and the ratio of the real to imaginary part of the forward elastic scattering amplitude, are shown. The eikonal approximation was chosen as the solution method to estimate the total and absorptive cross sections for the kaon-nucleus scattering.

Hong, Byungsik↗

A study of pseudoresonances in the application of the Schwinger variational principle to electron scattering from atomic hydrogen

The Schwinger variational principle is applied to s-wave electron-hydrogen atom scattering. Computationally, consistent with a recent paper by Apagyi et al. (1988), there are pseudoresonances at the static exchange level of approximation, but not at the static level. The T-matrix as well as the K-matrix version of the Schwinger principle is used with a real Slater basis, and the same results are obtained in both. The origin of the pseudoresonances from singularities in the separable potential that is effectively employed in the Lippman-Schwinger equation from which the Schwinger variational principle can be derived. The determination of the pseudoresonance parameters from the separable potential is computationally inexpensive and may be used to predict the pseudoresonance parameters for the scattering calculations so as to avoid them.

Weatherford, Charles A.↗

Ab initio method for calculating total cross sections

A method for calculating total cross sections without formally including nonelastic channels is presented. The idea is to use a one channel T-matrix variational principle with a complex correlation function. The derived T matrix is therefore not unitary. Elastic scattering is calculated from T-parallel-squared, but total scattering is derived from the imaginary part of T using the optical theorem. The method is applied to the spherically symmetric model of electron-hydrogen scattering. No spurious structure arises; results for sigma(el) and sigma(total) are in excellent agreement with calculations of Callaway and Oza (1984). The method has wide potential applicability.

Bhatia, A. K.↗

Light scattering by size-shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength

Rigorously light scattering by size-shape distributions of randomly oriented axially symmetric particles are calculated by the T-matrix method, as extended to randomly oriented scatterers. The computational scheme is described along with a newly developed convergence procedure that makes it possible to substantially reduce computer time and storage requirements. The elements of the Stokes scattering matrix for a power-law size distribution of randomly oriented moderately aspherical spheroids are shown to be much smoother than and differ substantially from those of equivalent monodisperse spheroids; averaging over orientations does not eliminate the necessity of averaging over particle sizes. The angular-scattering behavior of the ensembles of nonspherical particles is found to be significantly different from that of the equivalent polydisperse spheres.

Mishchenko, Michael I.↗

Intensity and polarization of light scattered by size distributions of randomly oriented nonspherical particles

Calculations of light scattering by small particles are important in many diverse fields of science and engineering. In many cases of practical interest, scattering particles are nonspherical and are distributed over sizes and orientations. However, accurate light scattering computations for ensembles of nonspherical particles are difficult and time-consuming, and the literature in which such calculations are reported is rather scarce. In this paper, the T-matrix approach, as extended recently to randomly oriented particles, is used to calculate rigorously light scattering by size distributions of randomly oriented axially symmetric particles. To model the variation of particle sizes in real ensembles, we use a power law distribution typical of some terrestrial aerosols. Contour plots of intensity and degree of linear polarization for polydisperse prolate and oblate spheroids of different aspect ratios and effective equivalent-sphere size parameters from 0 to 10 are calculated and compared with calculations for equivalent spheres. The angular scattering behavior of nonspherical polydispersions is found to be greatly different from that of spheres, while the scattering properties of oblate and prolate spheroids of the same aspect ratio are similar. With increasing particle size, both intensity and polarization become more shape-dependent. In general, nonspherical particles are stronger side scatterers and weaker backscatterers than equivalent spheres. With increasing aspect ratio of nonspherical particles polarization tends to be predominantly positive. Possible effects of particle nonsphericity on optical remote sensing of atmospheric aerosols are discussed.

Mishchenko, M. I.↗