Nonperturbative dressing of nucleons by mesons

Following Feynman's treatment of the polaron problem we present an approximate non-perturbative method of dressing nucleons by scalar and vector mesons: after integrating out the meson fields in the path integral we perform a variational calculation for the effective two-time action of the nucleon by using the same ansatz as Feynman did for the polaron. New features arise from the vector mesons which lead to velocity-dependent terms. We obtain numerical results for the radius and the mean number of the mesons of the dressed particle and derive the effective action in theA nucleon case.     

Subthreshold production ofK + mesons and the fragmentation of the target nucleus

The interplay between subthresholdK ⁺-production and the fragmentation of the target nucleus is considered in proton-nucleus interactions at projectile energies between 0.8 and 1 GeV. Inclusive data for the production ofK ⁺ mesons and of fragments are well described in the framework of the modified phase space model. For a coincidence measurement betweenK ⁺ mesons and fragments the model predicts a decrease of the relative yield of intermediate mass fragments by about four orders of magnitude. This strong decrease is a consequence of energy-momentum conservation, because at subthreshold energies a second endothermic process like multifragmentation can hardly proceed simultaneously with theK ⁺ production. AK ⁺ meson is, therefore, expected to be accompanied by a heavy target residue, which is so weakly excited that it may evaporate a few nucleons but cannot decay into fragments. Due to the large energy and momentum transfer in this process the strength of the predicted effect is supposed to be sensitive to the details of the reaction dynamics.The authors would like to thank H.W. Barz, F. Dönau and O. Schult for many valuable comments and discussions.     

Strangeness production in proton—proton and proton—nucleus collisions

We discuss the investigation of the strange meson production in proton-proton (pp) and proton-nucleus (pA) reactions within an effective Lagrangian model. The kaon production proceeds mainly via excitations ofN*(1650),N*(1710), andN* (1720) resonant intermediate nucleonic states, in the collision of two initial state nucleons. Therefore, the strangeness production is expected to provide information about the resonances lying at higher excitation energies. For beam energies very close to the kaon production threshold the hyperon-proton final state interaction effects are quite important. Thus, these studies provide a check on the models of hyperon-nucleon interactions. The inmedium production of kaons shows strong sensitivity to the self-energies of the intermediate mesons     

Protonium annihilation into two mesons

The available branching ratios for protonium annihilation into two mesons are analyzed in terms of a hadronic picture. We start from protonium wave functions calculated using a realistic OBE potential, a phenomenological part to account for the annihilation, and a particularly simple transition operatorV(N¯N meson _a + meson _b ). Flavour effects, sensitivity to tensor mixing and to isospin mixing are investigated.Work supported in part by German BMFT grant 06 OR 762, and by European Community project SC1-0233-C     

Mass spectra of light and heavy mesons in the-Dirac equation with power-law potential

The mass spectra of both light and heavy mesons are studied in the Dirac equation with an equally mixed 4-vector and scalar power-law potential model. This potential provides an excellent fit not only to the mass spectra ofp°, ϕ, Ψ and υ families but also to those ofD, F andB mesons. The light quark masses inp° and ϕ as well as in atom-like mesons are very close to the current quark masses.     

The NN → NNη reaction close to threshold

The pp → ppη and np → npη reactions at energies near the η production threshold are studied in a non-relativistic one boson exchange model, where the (1535 MeV) S11 resonance is excited through the exchange of π, η, ? and ω mesons and subsequently decays into an ηN pair. Energy integrated cross sections and energy spectra of the out going η's are reported. Providing NN and ηN final state interactions are taken into account coherently, the model reproduces both the scale and energy dependence of the cross section for the pp → ppη reactions up to 100 MeV. Final state interaction corrections due to the nucleon-nucleon and meson-nucleon forces influence strongly the scale and shape of the cross sections. The shape of the energy spectra of the outgoing η's provides a clear signature of the ηN force.     

Is energy increasing with angular momentum?

We submit to the community of physicists and mathematical physicists the following problem: prove that the ground-state energy of a system ofN particles without spin, without statistics, and interacting by central forces increases with angular momentum. For two particles, this is obvious. For more than two we give a number of arguments which support our conjecture.     

A discrete model exhibiting successive bifurcations leading to the onset of turbulence

A simple discrete model which consists ofN limit-cycle oscillators interacting with a linear coupling is numerically investigated in order to study the sequence of oscillatory states leading to the onset of turbulence. The systems withN=2 and 3 are studied. The system ofN=2 does not exhibit a nonperiodic motion, whereas the system ofN=3 does exhibit a nonperiodic motion. It is shown that, as an external parameter changes, the system ofN=3 undergoes a sequence of bifurcations, exhibiting the singly periodic, doubly periodic and nonperiodic motions, successively. This is similar to the bifurcation scheme for the onset of turbulence proposed by Ruelle and Takens and experimentally shown by Gollub and Swinny in a rotating Couette flow. The successive bifurcations are investigated in details and new features are reported.     

Absence of discrete spectrum in highly negative ions

LetH _N be the Hamiltonian for the Coulomb system consisting ofN particles of like charge in the field of a fixed point chargeZ. We show that if the particles are bosons, thenH _N has no discrete spectrum whenNN ₀=cZ ² for some constantc. If the particles are fermions, thenH _N is bounded below uniformly inN. These results can be extended to molecules and to other power law potentials.Research supported by the National Science Foundation, MCS78 -20455 USAOn leave from Department of Mathematics, University of Lowell, Lowell, MA O1854 USA     

Equilibrium of charged,spinning, magnetic particles

An unsymmetrical, stationary solution of the Einstein-Maxwell equations is given. The solution corresponds to the exterior field of two massive, charged, magnetised, spinning particles. In general line singularities are present in the solution. The field ofN such particles is then considered and necessary and sufficient conditions for the equilibrium of the system are given.     

Weak violation of universality for polyelectrolyte chains: Variational theory and simulations

A variational approach is considered to calculate the free energy and the conformational properties of a polyelectrolyte chain in d dimensions. We consider in detail the case of pure Coulombic interactions between the monomers, when screening is not present, in order to compute the end-to-end distance and the asymptotic properties of the chain as a function of the polymer chain length N. We find R≃N ^ν(log N)^γ, where ν = and λ is the exponent which characterizes the long-range interaction U∝ 1/r ^λ. The exponent γ is shown to be non-universal, depending on the strength of the Coulomb interaction. We check our findings by a direct numerical minimization of the variational energy for chains of increasing size 2⁴ < N < 2¹⁵. The electrostatic blob picture, expected for small enough values of the interaction strength, is quantitatively described by the variational approach. We perform a Monte Carlo simulation for chains of length 2⁴ < N < 2¹⁰. The non-universal behavior of the exponent γ previously derived within the variational method is also confirmed by the simulation results. Non-universal behavior is found for a polyelectrolyte chain in d = 3 dimension. Particular attention is devoted to the homopolymer chain problem, when short-range contact interactions are present. Received 8 August 2000 and Received in final form 19 December 2000     

Species segregation in one-dimensional granular-system simulations

We present one-dimensional molecular dynamics simulations of a two-species, initially uniform, freely evolving granular system. Colliding particles swap their relative position with a 50% probability allowing for the initial spatial ordering of the particles to evolve in time and frictional forces to operate. Unlike one-dimensional systems of identical particles, two-species one-dimensional systems of quasi-elastic particles are ergodic and the particles' velocity distributions tend to evolve towards Maxwell-Boltzmann distributions. Under such conditions, standard fluid equations with merely an additional sink term in the energy equation, reflecting the non-elasticity of the interparticle collisions, provide an excellent means to investigate the system's evolution. According to the predictions of fluid theory we find that the clustering instability is dominated by a non-propagating mode at a wavelength of the order 10πL/Nɛ , where N is the total number of particles, L the spatial extent of the system and ɛ the inelasticity coefficient. The typical fluid velocities at the time of inelastic collapse are seen to be supersonic, unless Nɛ ≲ 10π . Species segregation, driven by the frictional force occurs as a result of the strong temperature gradients within clusters which pushes the light particles towards the clusters' edges and the heavy particles towards the center. Segregation within clusters is complete at the time of inelastic collapse.     

Some particular solutions of theN-body problem on the line obtained from supersymmetry

An inverse technique based on supersymmetry is used to construct a class ofN-body bosonic Hamiltonians in one spatial dimension, for which the ground-state energy is fixed at a certain value. The corresponding interaction among particles is described by non-singularN-body potentials. The ground-state wave function can also be obtained explicitly.     

Neutral meson production in relativistic heavy ion collisions

The production of ⁰ and mesons has been studied in the reactions²⁰Ne +Al at 350 MeV/u and⁴⁰Ar + Ca at 1.0 GeV/u. Rapidity distributions and transverse momentum spectra have been measured and are compared to thermal distributions.Dedicated to Prof. Dr. P. Kienle on the occasion of his 60th birthday     

ISO(3,1¦N) andOSp(N¦4) supergravities

We advance anISO(3,1¦N) extended Poincaré supergravity and anOSp(N¦4) de Sitter supergravity by using the supergauge action mechanisms of supergroups on the superspaces and by treating the gravitational parts of these two supergravities as the gauge theories of gravity, give a new matrix representation ofISO(3,1¦N) generators and a new one ofOSp(N¦4) ones, obtain the commutation and anticommutation relations ofiso(3, 1¦N) andosp(N¦4) superalgebras, construct the actions of these Supergravities and discuss some other problems. A particle multiplets method based on the supersymmetry transformation is used and the probable numbers of particles of different helicities in the two supergravities are given.     

Invariants and radiation of some nonstationary systems

In this paper formulas are obtained by means of the coherent-state method for calculating the radiation power of a nonstationary quantum system ofN charged particles whose Hamiltonian is a general quadratic form with respect to coordinates and momenta. The transitions between the coherent states and the Fock states of this system are discussed. The radiation is calculated both in the dipole approximation and strictly. As an example, the radiation of a charge in homogeneous varying electric and magnetic fields is found. The classical limit is considered.