Narrow Results

Using new data on pion production in p+p interactions from the NA49 experiment, it is demonstrated that the detailed features of double differential pion cross sections are well reproduced over most of the phase space from the decay of a representative sample of known mesonic and baryonic resonances.

Thirteen resonances reaching up to spin four tensor-mesons and including the newly measured N* states up to the N*(1680) have been used. The p_T integrated Feynman x_F distributions in the high-x_F region 0.4 < x_F < 0.9 are quantitatively reproduced as well as the p_T distributions up to 2 GeV/c and beyond at all x_F.

In both these phase space regions direct effects of parton dynamics such as valence quark fragmentation or parton scattering are generally evoked in order to provide a basis of understanding. The saturation of the measured yields by resonance decay casts a doubt on these assumptions.

The inelastic collisions of positrons with calcium and strontium positive ions are treated for the first time as a three-channel problem within the framework of the improved coupled-static and frozen-core approximations with the assumption that the elastic, ground positronium and excited-positronium formation channels are open. The calculations of the partial and total cross sections are carried out for eight values of the total angular momentum ℓ (0 ≤ ℓ ≤7), at 20 values of the incident energy lying above the excited positronium formation threshold and extending to a wide region above the ionization threshold of the target ion. The total collisional positronium formation cross sections of e⁺–Sr⁺ scattering show a peak around the ionization threshold of Sr⁺ but display a peak at 30 eV for e⁺–Ca⁺ scattering. In both scattering problems the total excited Ps formation cross sections have considerable values in the energy range .

The investigations of the elastic and inelastic collisions of positrons with potassium atoms, K (1s², 2s², 2p⁶, 3s², 3p⁶, 4s), are presented. The potassium target atoms are described using Clementi–Roetti wavefunctions within the framework of the one-valence-electron model. The total cross-sections which correspond to eight partial cross-sections are calculated at 34 values of the incident energy using the coupled-static approximation. The resulting total elastic, ground- and excited-positronium formation cross-sections are compared with experimental results and those calculated by other authors. In the vicinity of 6 eV, and consistent with the measurements of Parikh et al.,² our total cross-section displays a pronounced peak. We support the conclusion of McAlinden et al.¹⁵ and Hewitt et al.¹⁴ that above about 4 eV, positronium formation is mainly into excited states. Good agreement is obtained with the total cross-section measurements of Kwan et al.¹ and Parikh et al.² Positronium formation is not important above about 50 eV.

This paper deals with the presentation of a kinetic model for a suspension of identical hard spheres. Considering that the collisions between particles are instantaneous, binary, inelastic and taking the diameter of the spheres into account, a Boltzmann equation for the dispersed phase is proposed. It allows one to obtain the conservation of mass and momentum as well as, for slightly inelastic collisions, an H-theorem which conveys the irreversibility of the evolution. The problem of the boundary conditions for the Boltzmann equation is then introduced. From an anisotropic law of rebound characterizing the inelastic and non-punctual impact of a particle to the wall, a parietal behavior for the first moments of the kinetic equation is deduced.

In this paper we analyze the linear Boltzmann equation of semiconductor theory with unbounded collision term modelling both elastic and inelastic scattering of electrons on the crystalline lattice (corresponding to scattering on impurities and optical phonons), in both bounded and unbounded domains. We prove the existence of a substochastic semigroup solving this problem and, for a large class of scattering cross-sections, we also characterize the generator of this semigroup as the closure of the formal right-hand side operator showing thus that the semigroup is conservative (stochastic) in this case. On the other hand, we provide an example of a cross-section growing at an exponential rate for which the semigroup is not conservative.

Many features of real granular fluids under rapid flow are exhibited as well by a system of smooth hard spheres with inelastic collisions. For such a system, it is tempting to apply standard methods of kinetic theory and hydrodynamics to calculate properties of interest. The domain of validity for such methods is a priori uncertain due to the inelasticity, but recent systematic studies continue to support the utility of kinetic theory and hydrodynamics as both qualitative and quantitative descriptions for many physical states. The basis for kinetic theory and hydrodynamic descriptions is discussed briefly for the special case of a low density gas.

We are interested in the existence results for second-order differential inclusions, involving finite number of unilateral constraints in an abstract framework. These constraints are described by a set-valued operator, more precisely a proximal normal cone to a time-dependent set. In order to prove these existence results, we study an extension of the numerical scheme introduced in [10] and prove a convergence result for this scheme.

A review of selected theoretical works devoted to the understanding of the rate constants measured by the flow supersonic reactor experiments is presented. This review focuses on the kinetics of reactive and inelastic neutral–neutral collisions at low temperature. Neutral–neutral reactions can show puzzling non-Arrhenius temperature dependence, while most of ion–neutral collisions are well explained by a long-range capture model. First, a short summary of the adiabatic capture method and the variational transition state theory is presented. Then, a variety of reaction mechanisms are detailed, involving spin-orbit effects, short-range potential effects, and quantum tunneling effects, along with the theoretical methods necessary to unveil these mechanisms. In the second part of this chapter, a similar analysis is applied to purely inelastic collisions. The different models available for describing specifically electronic, spin-orbit, vibrational, and rotational transitions are reviewed and compared to the results of Close Coupling calculations.

Many features of real granular fluids under rapid flow are exhibited as well by a system of smooth hard spheres with inelastic collisions. For such a system, it is tempting to apply standard methods of kinetic theory and hydrodynamics to calculate properties of interest. The domain of validity for such methods is a priori uncertain due to the inelasticity, but recent systematic studies continue to support the utility of kinetic theory and hydrodynamics as both qualitative and quantitative descriptions for many physical states. The basis for kinetic theory and hydrodynamic descriptions is discussed briefly for the special case of a low density gas.