Properties of alpha-particle solutions to the many-nucleon problem

A class of A-nucleon (for even N = Z) Hamiltonians is found such that they admit, among others, solutions that can be exactly related to solutions to the problem of A/4 alpha particles in the sense that the respective eigenvalues of the two problems coincide and that the A-nucleon solutions can be constructed from the alpha-particle solutions within a procedure that follows from the resonating-group model. It is shown that an effective nuclear Hamiltonian close to a realistic one possesses these properties, the alpha-particle states in nuclei having basic properties of an alpha condensate and, frequently, a normal nuclear density. The statistics of alpha particles (and other composite bosons) proves to be different from Bose-Einstein and Fermi-Dirac statistics and from parastatistics.     

On the possibility of an analytic solution of the three-body problem

Three-body Faddeev equations in the Noyes-Fiedeldey form are rewritten as a matrix analog of a one-dimensional nonrelativistic Schrödinger equation. Unlike the method of K-harmonics, where a similar equation was obtained by expansion of a three-body Schrödinger equation wavefunction into the orthogonal set of functions of two variables (K-harmonics), the use of the Noyes-Fiedeldey form of Faddeev equations allows us to limit ourselves to the expansion in functions of one variable only. The solutions of the above mentioned matrix equation are obtained. These solutions converge uniformly within every interval of continuity of the matrix, which corresponds to the potential of that equation. Their asymptotic behavior for large interparticle distances is discussed. The solutions for the harmonic oscillator, inverse-square, and Coulomb-Kepler potentials are found. It is shown that energy levels in the last case may be calculated from a simple formula which is very similar to the corresponding formula for the two-body Coulomb-Kepler problem. This formula can be easily generalized to the case of n particles interacting with inverse distance potentials.     

A theorem on the existence of dyon solutions

We prove the existence of finite energy dyon solutions to Yang-Mills-Higgs equations satisfying the Julia-Zee ansatz, and the generalization to SU(N) gauge groups. This rigorously establishes the existence of a model for the particles having electric and magnetic charge conjectured by Schwinger. We also prove that the solutions are real analytic on (0, ∞) and C^∞ at r = 0. To establish our result we prove a new abstract theorem that allows one to study singular constrained minimization problems without the introduction of Lagrange multipliers.     

A program for simulation experiments to study reactions with three particles in the final state

The results from the kinematic simulation of experiments to study two-stage A + B → C + D* → C + (E + F) reactions that proceed through a decaying intermediate state D* with three particles in the final state are presented, and the program used in this modeling is described. The program allows us to determine an experiment’s geometry, calculate the time-of-flight times and energies for all secondary particles within the chosen geometry, and optimize the setup parameters (detector size and time and energy resolution) so as to obtain the proper excitation energy resolution of intermediate state D*. The results obtained in simulating an experiment to study the d + ³H → ³He + ²n, ²n → n + n reaction are detailed.     

Application of RTDF to particles with curved surfaces

The applicability of the ray tracing with diffraction on facets model is extended to particles with curved surfaces. This allows tests against T-matrix calculations for larger size parameters and modelling of light scattering by more realistic particle shapes, such as ice crystals with rounded edges.     

Finite field theories in three dimensions with and without supersymmetry

Necessary and sufficient conditions are derived for the finiteness of theS-matrix and vacuum stress of theories with Yukawa,? ³, and? ⁴ couplings in three spacetime dimensions, and general supersymmetric solutions to these conditions are given. The requirement of a finiteS-matrix allows many non-supersymmetric solutions, but with two bosons and two fermions the additional constraint of a finite vacuum stress allows only one simple alternative to supersymmetry.     

Analysis of the pion form factor in the space-like and time-like region

We discuss an analytic parametrization of the pion form factor which is only weakly model dependent. Its model dependence comes from a preference of those analytic functions that are smooth in a certain well-defined sense. Different solutions for different values ofχ ² corresponding to different degrees of smoothness can be constructed. All available space-like and time-like data are taken into account simultaneously. Our approach allows conclusions on an incompatibility of space-like with time-like data sets and on the significance of the occurrence of higher coupled resonances. We discuss the asymptotic behaviour which is consistent with QCD and give the relevant low energy and resonance parameters.     

General N-solitons and their dynamics in several nonlocal nonlinear Schrödinger equations

General N-solitons in three recently-proposed nonlocal nonlinear Schrödinger equations are presented. These nonlocal equations include the reverse-space, reverse-time, and reverse-space–time nonlinear Schrödinger equations, which are nonlocal reductions of the Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy. It is shown that general N-solitons in these different equations can be derived from the same Riemann–Hilbert solutions of the AKNS hierarchy, except that symmetry relations on the scattering data are different for these equations. This Riemann–Hilbert framework allows us to identify new types of solitons with novel eigenvalue configurations in the spectral plane. Dynamics of N-solitons in these equations is also explored. In all the three nonlocal equations, their solutions often collapse repeatedly, but can remain bounded or nonsingular for wide ranges of soliton parameters as well. In addition, it is found that multi-solitons can behave very differently from fundamental solitons and may not correspond to a nonlinear superposition of fundamental solitons.     

Influence of corrugation on light-scattering properties of capsule and finite-cylinder particles: Analytic solution using Sh-matrices

We use the Sh-matrices to derive an analytic T-matrix solution for the light scattering from capsule and finite-cylinder particles with corrugated surfaces. The solution is tested by comparison with discrete-dipole-approximation (DDA) calculations. We present results from finite circular cylinders and capsules whose diameter/length ratio is 1/2. Such particles have interest as simulants of aerosolized spores. We analyze and compare their two-dimensional scattering patterns. The effect of corrugated surfaces of relatively small amplitude is quite significant on the resulting scattering patterns.     

πℓ2, Kℓ3and K0−K0 constraints on leptoquarks and supersymmetric particles

Mass bounds from different processes for charged Higgs particles, for pseudoscalar leptoquarks occurring in dynamically broken theories, for vector leptoquarks occurring in the Pati-Salam type of grand unified theories and for the exotic particles of supersymmetric theories are studied. The processes considered are the π → eν to π → μν branching ratio, the CP-violating K?3 decay parameters, and the CP-violating part of the K_L ? K_S mass difference. The π → eν to π → μν branching ratio sets the most stringent bounds, 0.5 TeV for charged Higgs particles, 1 TeV for pseudoscalar leptoquarks, 125 TeV for vector leptoquarks and 0.1–1 TeV for the supersymmetric partners of ordinary particles. The π?2 branching ratio should be sensitive at the present experimental accuracy to the effects of pseudoscalar leptoquarks.     

(1+1)-Dirac bound states in one dimension, with position-dependent Fermi velocity and mass

We extend Panella and Roy’s [17] work for massless Dirac particles with position-dependent (PD) velocity. We consider Dirac particles where the mass and velocity are both position-dependent. Bound states in the continuum (BIC)-like and discrete bound state solutions are reported. It is observed that BIC-like solutions are not only feasible for the ultra-relativistic (massless) Dirac particles but also for Dirac particles with PDmass and PD-velocity that satisfy the condition m(x) v _F ² (x) = A, where A ≥ 0 is constant. Dirac Pöschl-Teller and harmonic oscillator models are also reported.     

Dynamics of Two- and Four-Boson Interactions in Dressed Vacuum States

We analyze the spatial and temporal dynamics of virtual particles in the vacuum states of the one-dimensional ? ²- and ? ⁴-model systems. The properties of the vacuum state for the ? ²-system can be found analytically, which allows us to compute all spatial and temporal correlations exactly. For large spatial and temporal separations, the correlation functions approach a non-vanishing finite constant associated with the occurrence of multiple vacuum bubbles, in contradiction to lowest-order perturbation theory. Long-range inter-bubble correlations suggest that virtual particles can actually enhance the occurrence of another bubble due to stimulated emission. We argue that many of the vacuum’s properties can be explained in the usual particles terms.     

Speed of particles and a relativity of locality in κ-Minkowski quantum spacetime

The last decade of research on κ-Minkowski noncommutative spacetime has been strongly characterized by a controversy concerning the speed of propagation of massless particles. Most arguments suggested that this speed should depend on the momentum of the particle strongly enough to be of interest for some ongoing experimental studies. But the only explicit derivations of worldlines in κ-Minkowski predicted no momentum dependence for the speed of massless particles. We return to this controversy equipped with the recent understanding that in some quantum spacetimes coincidences of events assessed by an observer who is distant from the events can be artifactual. We therefore set up our investigation in such a way that we never rely on the assessment of coincidences of events by distant observers. This allows us to verify explicitly that in κ-Minkowski simultaneously-emitted massless particles of different momentum are detected at different times, and establish a linear dependence of the detection times on momentum.     

Synthesis and characterization of cobalt–manganese oxides

Cobalt doped/un-doped manganese oxides materials were synthesized at various doping rates by soft chemical reactions, oxidation-reduction method, which allows generating a metal-mixed oxide. The synthesized materials were characterized using several techniques including chemical analysis, X-rays diffraction (XRD), scanning electron microscopy (SEM), thermogravimetric analysis (TGA), and vibrating sample magnetometer (VSM). The chemical analysis confirmed the presence of cobalt in the samples. XRD patterns reveal mainly a spinel-like structure and SEM micrographs exhibited morphology with fine aggregate of particles. TGA profiles showed weight loss due to loss of water in a first step, followed by a loss of oxygen from the lattice associated with partial reduction of Mn⁴⁺ to Mn³⁺. VSM was used to measure the magnetization as a function of the applied magnetic field at temperatures T=50 and 300 K. Different magnetic behaviors were observed when cobalt percentage changed in the samples. These behaviors are considered to be related to the size of the particles and composition of the materials. Higher coercive field and lesser magnetization were observed for the sample with higher cobalt content.     

Limitations on retrieval of complex refractive index of spherical particles from scattering measurements

On the base of a lookup table approach we performed sensitivity tests of dual-polarization polar nephelometer (D2PN) data to optical and microphysical parameters of ensembles of spherical particles. Measurement errors were modeled as Gaussian random variables. It is shown that D2PN data enable to retrieve some microphysical parameters (depending on the case) along with the assessment of the complex refractive index. In the case of the low absorbing particles, measurement errors substantially reduce the sensitivity to the imaginary part of the refractive index and only the range of the imaginary part can be estimated, whereas the real part of the refractive index and the microphysical parameters can be retrieved. When the absorption of spherical particles is moderate, i.e., 10⁻⁴?χ?0.5, the real n and imaginary χ parts of the refractive index can be deduced along with the microphysical parameters. In the case when the absorption of spherical particles is high, only the microphysical characteristics and the imaginary part can be retrieved. These limitations on retrieval should be valid for data of other instruments measuring the same magnitudes as D2PN with the same errors, at least for aerosols made of spherical particles.