Multiple-scattering Model Research Articles

Analysis of backward $$\pi \mathcal{N}$$ scattering using a multiple-scattering modelscattering using a multiple-scattering model

A multiple-scattering model is used to analyse the experimental data of the backward\(\pi \mathcal{N}\) scattering at 6 GeV/c. The elementary backward collisions π+p and π−p are described by a Regge-pole model with the\(\Delta _\delta \) and\(\mathcal{N}_\alpha \) linear trajectories while the multiple-scattering correction terms are convolution products of the Regge-pole terms and the amplitudes corresponding to the forward scattering. Thes helicity amplitudesΔ andN respectively associated to isospin 3/2 and 1/2 in theu-channel are deduced and compared with the results of other models.

MS-Xα calculations on boron trihalides and comparison with their photoelectron spectra

The multiple-scattering Xα model has been applied to the sequence of boron trihalides BX 3 where X = F.C1. Br, and I. Transition state calculations show good agreement with the experimental ionization potentials measured by photoelectron spectra.

Shape Resonances inK-Shell Photoionization of Diatomic Molecules

We show that $K$-shell photoionization spectra of diatomic molecules can exhibit strong shape resonances near threshold. The molecular field is decisive in this phenomenon. It induces the resonant contraction of high-$l$ components of the ionization channels, and it couples these components with low-$l$ components produced in the atomic cores by $K$-shell photoionization. We demonstrate the effect for ${\mathrm{N}}_{2}$ by using the multiple-scattering model. Clear evidence for this phenomenon exists for ${\mathrm{N}}_{2}$, CO, and NO.

Evidence for an Elemental Sulfur Component of the Clouds from Venus Spectrophotometry

The decrease in the reflectivity of Venus in the near UV can be explained if the clouds contain particles of elemental sulfur in addition to sulfuric acid. The low-resolution McDonald-Pittsburgh spectrum can be fitted by two sulfur-containing, multiple-scattering cloud models: 1) a mixed cloud consisting of one particle of elemental sulfur of radius 10 µm for every 670 particles of sulfuric acid of radius 1 µm, and 2) a layered cloud of optical thickness τ = 1.0 consisting of 1 µm particles of sulfuric acid overlying a thick cloud of elemental sulfur particles of radius 3.6 µm: Some of the sulfur is incompletely polymerized. The source of the sulfur is photo-dissociation of COS, although some may also be recycled from the lower atmosphere. The sulfur plays a crucial role in the planetary meteorology of Venus since it is responsible for the bulk of the absorption of solar energy.

Limb darkening of two latitudes of Jupiter at phase angles of 34° and 109°

The imaging photopolarimeter aboard Pioneer 10 produced hundreds of red and blue images of Jupiter covering a wide range of phase angles and having good linearity and signal-to-noise characteristics. In this preliminary analysis the limb darkening across two of the red images (at phase angles of about 34° and 109°) in both a prominent dark belt and a bright zone are compared with multiple-scattering models. Of the simple models tried, the smallest deviations from the observations result for ones consisting of a thin absorbing layer above a semi-infinite atmosphere of particles scattering according to the Henyey-Greenstein phase function. The asymmetry parameter for the best fits to both the belt and the zone data is in the range g = 0–0.25, corresponding to particles small in comparison with the wavelength of red light. The phase integral derived from the models lies in the range of about 1.5–1.6, implying a substantial internal heat source for Jupiter.

On a multiple-scattering model for molecules and crystals

Starting from very simple physical arguments, the general structure of a multiple-scattering theory for calculating electronic properties of molecules and solids is derived in a concise way. Results of some recent mathematical investigations are used to put the general formulas into final and practical form.

Strong resonance L-absorption of sulphur fluorine molecule

It is pointed out that the prominent feature in L-absorption spectra of SF 6-molecule may be explained by means of the multiple-scattering model. Some preliminary conclusions about the nature of the effective potential barriers are presented.

Explanation of Rising Multiplicity with Increasing Perpendicular Momentum Transferred to the Leading Proton, Using the Quark Multiple-Scattering Model

It is shown that the rise in multiplicity with increasing perpendicular momentum transferred to the leading proton seen in recent experiments can be simply explained as due to double quark-quark scattering in the Glauber quark multiple-scattering model. The quark-quark inelastic-scattering amplitude is entirely consistent with the quark-quark elastic amplitudes obtained previously for elastic proton-proton scattering.

Absorption cross sections for pions, kaons, protons and antiprotons on complex nuclei in the 6 to 60 GeV/ c momentum range

Absorption cross sections for π ±, K ± mesons, protons and antiprotons on Li, Be, C, Al, Cu, Sn, Pb and U in the momentum range from 6.65 to 60 GeV/ c are measured at the 70 GeV IHEP accelerator. The cross sections are compared with calculations using the Glauber multiple-scattering model. Nucleus radii are found to be described by a power dependence on atomic weight R = r 0 A 1 3 , where r 0 = 1.05 ± 0.02 fm.

Optical spectra of some octahedral transition metal fluorides as calculated by multiple scattering method

The electronic spectra of the octahedral clusters TiF 3− 6, CrF 3− 6, MnF 2− 6, NiF 2− 6, and NiF 4− 6 are calculated using the multiple-scattering model with statistical exchange. The agreement is satisfactory, indicating that this simple method can be used for detailed investigations of the electronic structure of transition metal complexes.

A multiple-scattering model of the diffuse component of lunar radar echoes

We propose that the average diffuse component of lunar radar echoes results from the cumulative effect of multiple scattering within the ejecta blanket of fresh young craters. Using a multiple-scattering polarization computer program, we compare our model with a variety of observations of the diffuse component and find a general agreement between the two. We show that multiple scattering makes a significant contribution to the partial depolarization of incident completely polarized radar signals, although single scattering may also be important. Mean indices of refraction of 1.3 and 1.6 are inferred for the ejecta blanket at wavelengths of 3.8 and 23 cm, respectively. These values are consistent with measurements made on an Apollo 11 fine sample and indicate an increasing density with depth below the surface. We hypothesize that the difference between the diffuse reflectivities of mare and highland areas is due chiefly to differences between the microwave absorption properties of rocks and dust in the two regions. If that is so, radar maps, properly prepared to display such differences, can serve as geological maps of the mineral or minerals (perhaps ilmenite) that are the principal microwave absorbers.

Intensites experimentales et theoriques en diffraction d'électrons lents sur la face (001) de l'aluminium

We present some experimental and theoretical LEED results obtained from the (001) surface of aluminum. The experimental curves were obtained with a new goniometer which allows us to set any incidence conditions, and to measure all the diffracted beams. We show that rotation diagrams are more interesting than energy profiles for studying the dynamical interactions and testing various LEED theories. We use several models to compute such diagrams. As a first step, we compare the results obtained in the S-wave approximation with the three following models: One Dimensional Multiple Scattering Model, Inelastic Collision Model, and the Kambe-McRae Multiple Scattering approach. As a second step, we use more elaborate potentials to calculate LEED intensities according to the Kambe-McRae Multiple Scattering approach, and the Band Structure-Matching formalism; the results are discussed and compared with experiment.

Duality-breaking effects in a model for meson-baryon scattering

Duality-violating effects are examined in the context of an exchange-degenerate multiple-scattering model incorporating strong EXD for poles,SU3 at the vertices ands-u crossing. Ten parameters. includingd/f ratios, are used to simultaneously fit cross-sections for K−p→π−Σ+, π+p→K+Σ+,\(K^ - p \to \bar K^0 n\), K+n→K0p, π−p→π0n and π−p→ηn. The qualitatively different energy dependences of the HCEX and CEX line-reversed cross-section differences arise naturally from the fact that the model requires equal absorption in CEX line-reversed reactions and unequal absorption in the HCEX reactions. The cross-section fits are excellent for the HCEX and reasonable for the CEX reactions; polarizations are correct in sign. Thed/f ratios obtained are close to the quark-modelSU6 values. The model is compared with other multireaction fits and their differences and relative successes are discussed.

Dechanneling of protons in copper single crystals. I

Abstract The dechanneling of 150 keV protons impinging along the <110> direction in nearly perfect copper crystals has been investigated by measurements of the 135° backscattered protons and of the yields of the characteristic Cu(L) X-rays, as a function of the crystal temperature (300 °K, 485 °K, and 645 °K) and the incident beam direction relative to the <110> channel. The data are analyzed and interpreted in a two step procedure. First, the data are reduced in terms of the energies of the observed backscattered protons taking into account the contributions of dechanneled protons and of the protons knocked onto random trajectories by the surface atoms. Second, model backscattering spectra and X-ray yields are constructed by assuming various trial functions for the dependence of the dechanneling rate, on penetration depth. Two trial functions are tested. One is based on a small-angle multiplescattering model of dechanneling. The other assumes an exponential decay of the number of channeled protons, characterized by a mean free path until dechanneling. The data support the latter. The shortening of the mean free path with rising crystal temperature suggests that scattering on the thermally displaced lattice atoms is the primary cause for dechanneling.

Deuteron Alignment in Deuteron-Proton Elastic Scattering at 3.6GeVc

We have performed a deuteron-proton double-scattering experiment with a 3.6-$\frac{\mathrm{GeV}}{c}$ deuteron beam to study the spin alignment of the elastically scattered deuterons. We observed scattered beams of polarized deuterons and have measured the spin alignment and vector polarization in the four-momentum-transfer interval of ${\ensuremath{\Delta}}^{2}=0.13 \mathrm{to} 0.54 {(\frac{\mathrm{GeV}}{c})}^{2}$. Multiple-scattering model fits are presented to our alignment and polarization data as well as to existing differential-cross-section data.

Multiple-Scattering Model for Light Transmission through Optically Thick Clouds*†

A linear-system model has been developed to predict irradiance distributions of visible light below an idealized optically thick atmospheric cloud, which is illuminated from above in an arbitrary manner. The model offers elegant mathematical simplicity at the expense of some precision. As such, it is applicable to a broad class of problems in which correct functional forms are required, but levels of accuracy better than a factor of 2 are not necessary. Optical thicknesses can range from about 5 to 32. One example of a problem in this class, the design of a laser communication system to operate through clouds, provided the original motivation for development of the light-transmission model. The optical effects of the cloud are calculated by means of a four-dimensional linear superposition integral, which takes account of multiple scattering. Two illustrations of the method are given in detail, with incident illumination represented by a tightly collimated beam and by a sum of infinite plane waves, respectively.

Calculation of the ionization energies of the sulphur hexafluoride molecule by the multiple scattering method

The multiple-scattering (or scattered-wave) model has been applied to the sulphur hexafluoride molecule, using an approximate Hartree-Fock potential of the Xα type. The calculated ionization energies are compared with the data from the X-ray photoelectron spectroscopy (ESCA) experiments, and found to be in better agreement than either the ab initio (SCF MO LCAO) or semi-empirical (CNDO) results.

Multiple-quark-scattering analysis of hadron charge-exchange scattering

We investigate the hadron charge-exchange (CEX) scattering processes in terms of the multiple-quark-scattering formalism. We extend the Glauber formalism to include the spin and isospin effects of the constituent particles, and the nucleons and mesons are assumed to belong to 56- and 35-dimensional representations of the nonrelativisticSU6 group. The fundamental quark-scattering amplitudes are expressed as Regge-pole exchange amplitudes. We explain the energy and momentum transfer dependences of the π−p, np and\(\bar p\)p CEX scattering differential cross-sections and polarization data of π−p CEX scattering. The multiple-scattering picture provides natural explanations of the π−p CEX scattering polarization effect and the forward peak in np CEX scattering differential cross-section without invoking the extra ϱ′ and pion-conspirator trajectories. New understandings of the connections of the multiple-scattering model, the absorptive-correction model and the Regge-pole model are discussed.

Pion-Nucleon Scattering from 50 to500GeVc

We show the general features to be expected in scattering at energies high enough that the scattering amplitude consists of only the Pomeranchuk Regge pole and the two-Pomeranchuk-cut terms. The predictions of the Reggeized multiple-scattering quark model for pion-nucleon scattering at lab momenta up to $500\frac{\mathrm{GeV}}{c}$ are given as a specific example.

Models for High-Energy Processes

Recent developments in the concepts and models used to describe high-energy collisions of fundamental particles are reviewed. The areas of appreciable activity in research in high-energy physics are surveyed briefly and the general framework for the description of processes at high energies is outlined. There follows a sampling of recent experimental data designed to show the extent and detail of present-day experimental results. Recent applications of Regge pole models are reviewed with emphasis on the difficulties as well as the successes of models employing only Regge poles. The various multiple-scattering models are then discussed and correlated by means of the methods of Glauber. The connection of these models with amplitudes having branch cuts in the angular-momentum plane (Regge cuts) is described, as well as some comparisons with experiment. Finite energy sum rules as a means of relating the low-energy and high-energy domains are discussed in some detail. Next, the far-reaching concept of duality whereby the direct-channel resonances are (in some sense) the crossed-channel Regge exchanges is described, along with the related ideas of exchange degeneracy, the special role of the Pomeranchon Regge pole, and duality diagrams. An explicit realization of duality is achieved in the Veneziano model. This model is discussed in some detail for the relatively simple and interesting example of pion-pion scattering. Brief mention is also made of the extensions of the Veneziano model to the $n$-particle amplitude, attempts at unitarization, and various applications. The topic of multiparticle final states is covered relatively briefly with emphasis on the applications of double Regge pole exchange to three-body final states, the calculation of proton and pion energy and angular distributions in proton-proton collisions by means of the multi-Regge exchange model, and the generation of self-consistent Regge singularities with the multi-Regge exchange model and unitarity. The final section of the review concerns recent results on pion-pion scattering phase shifts and also $K\ensuremath{-}\ensuremath{\pi}$ phase shifts, and some remarks on theorems connecting decay correlations of resonances with the mechanism of production. The literature survey ended, with a few exceptions, in May 1969.