On Lennard–Jones Type Potentials and Hard-Core Potentials with an Attractive Tail

We revisit an old tree graph formula, namely the Brydges–Federbush tree identity, and use it to get new bounds for the convergence radius of the Mayer series for gases of continuous particles interacting via non-absolutely summable pair potentials with an attractive tail including Lennard–Jones type pair potentials.     

Charmonium and Meson–Molecule Hybrid Tetraquarks

In the X (3872) decay, both of the ${{J/{\psi\pi\pi}}}$ and ${{J/{\psi\pi\pi\pi}}}$ branching fractions are observed experimentally, and their sizes are comparable to each other. In order to clarify the mechanism to cause such a large isospin violation, we investigate X(3872) employing a model of coupled-channel two-meson scattering with a ${{\rm c}\bar{c}}$ core. The two-meson states consist of ${{D^0\overline{D}^{*0}}}$ , D ⁺ D ^*?, ${{J/{\psi\rho}}}$ , and ${{J/{\psi\omega}}}$ . The effects of the ρ and ω meson width are also taken into account. We calculate the transfer strength from the ${{{\rm c}\bar{c}}}$ core to the final two-meson states. It is found that very narrow ${{J/{\psi\rho}}}$ and ${{J/{\psi\omega}}}$ peaks appear very close to the ${{D^0\overline{D}^{*0}}}$ threshold for a wide range of variation in the parameter sets. The size of the ${{J/{\psi\rho}}}$ peak is almost the same as that of ${{J/{\psi\omega}}}$ , which is consistent with the experiments. The large width of the ρ meson makes the originally small isospin violation by about five times larger.     

Potentials with Convergent Schwinger–DeWitt Expansion

Convergence of the Schwinger–DeWittexpansion for the evolution operator kernel for specialclass of potentials is studied. It is shown that thisexpansion, which is in the general case asymptotic,converges for the potentials considered (widely used, inparticular, in one-dimensional many-body problems), andthat convergence takes place only for definite discretevalues of the coupling constant. For other values of the charge, a divergent expansiondetermines the kernels having essential singularity atthe origin (beyond the usual -function). If oneconsiders only this class of potentials, then one can avoid many problems connected withasymptotic expansions, and one gets a theory withdiscrete values of the coupling constant that is incorrespondence with the discreteness of charge innature. This approach can be applied to quantum fieldtheory.     

Energy Density and Production Ratios of Baryon from QGP with Diquarks

At a very high temperature, the quark matter is a hot and dense matter under the colour deconfinement condition, and quarks can coalescent diquarks. Energy density of this system is figured out. A way to calculate baryon ratios produced from quark gluon plasma with diquarks in relativistic heavy ion collisions is presented.     

Ratio of Baryon to Meson and Baryon Antibaryon Correlation in e+e－ Annihilation under Two Kinds of Color Connections

The ratio of final baryon to meson and baryon antibaryon correlation in e⁺e^－ annihilation are considered as sensitive observables to test the hadronizition models,because among the results obtainted in different popular hadronizition models,only those from JETSET event generator can fit experimental data by adjusting extra ad hoc parameters. We replace the color neutral flow connection,which is the results in large N_c limit and is used in JETSET,with the color separate connection,which is allowed by PQCD,and calculate these observables. We compare the obtained results with those from the standard JETSET7.4 code and the available experimental data. We find that the results and the relevant properties are consistent with data. This shows that the consistency of the data with the results from the standard JETSET7.4 code for these properties does not mean that the traditional color neutral flow is the only color connection selected by NPQCD. The 100% color separate connection is also possible.     

Nonautonomous Breather and Rogue Wave in Spinor Bose–Einstein Condensates with Space-Time Modulated Potentials

To study controlled evolution of nonautonomous matter-wave breathers and rogue waves in spinor Bose–Einstein condensates with spatiotemporal modulation,we focus on a system of three coupled Gross–Pitaevskii equations with spacetime-dependent external potentials and temporally modulated gain-loss distributions.With different external potentials and gain-loss distributions,various solutions for controlled nonautonomous matterwave breathers and rogue waves are derived by the Darboux transformation ...     

Potentials and phase shifts for nucleon–light nuclei systems

The technique proposed to enhance the resolution of the point spread function (PSF) of an optical system underneath defocussing and spherical aberrations. The method of approach is based on the amplitude and phase masking in a ring aperture for modifying the light intensity distribution in the Gaussian focal plane (\(Y_{D} = 0\)) and in the defocussed planes (\(Y_{D}= \pi \) and \(Y_{D}= 2\pi \)). The width of the annulus modifies the distribution of the light intensity in the side lobes of the resultant PSF. In the presence of an asymmetry in the phase of the annulus, the Hanning amplitude apodizer [cos(\(\pi \beta \rho \))] employed in the pupil function can modify the spatial distribution of light in the maximum defocussed plane (\({Y}_{D} = 2\pi \)), results in PSF with improved resolution.     

Self Duality Equations for Ginzburg–Landau¶and Seiberg–Witten Type Functionals¶with 6th Order Potentials

The abelian Chern–Simons–Higgs model of Hong-Kim-Pac and Jackiw–Weinberg leads to a Ginzburg–Landau type functional with a 6^th order potential on a compact Riemann surface. We derive the existence of two solutions with different asymptotic behavior as the coupling parameter tends to 0, for any number of prescribed vortices. We also introduce a Seiberg–Witten type functional with a 6^th order potential and again show the existence of two asymptotically different solutions on a compact K?hler surface. The analysis is based on maximum principle arguments and applies to a general class of scalar equations. Received: 13 October 1998 / Accepted: 21 October 2000     

Testing Nucleon–nucleon Potentials in Three- and Four-nucleon Scattering Observables

We present a theoretical study of three- and four-nucleon continuum within the hyperspherical harmonics method, using a representative variety of realistic nucleon–nucleon potential models, i.e. one of phenomenological type, the Argonne v ₁₈ (AV18), one obtained within chiral effective field theory up to next-to-next-to-next-leading order, the Idaho N3LO (I-N3LO), and a “low-k” model derived from the CD-Bonn potential. In particular, the convergence pattern for the four-nucleon system is found to be problematic for the P-waves phase-shifts in the case of the AV18 potential at higher energies. An extrapolation procedure is presented and discussed. Finally, we present the theoretical results for p?d and p?³ scattering observables at two selected energies, and we compare these with the available experimental data. In particular, some spread in the unpolarized cross section and in some polarization observables has been observed using the three potential models, in particular for A =  4. Furthermore the well known discrepancy in the vector polarization observables remains for the three potential models.     

Darboux Transformations for Energy-Dependent Potentials and the Klein–Gordon Equation

We construct explicit Darboux transformations for a generalized Schrödinger-type equation with energy-dependent potential, a special case of which is the stationary Klein–Gordon equation. Our results complement and generalize former findings (Lin et al., Phys Lett A 362:212–214, 2007).     

The Lagnese–Stellmacher Potentials Revisited

We give a new proof of a classical result of Lagnese and Stellmacher, characterizing all Huygens’ operators of the form , where q(x) depends on only one variable. The proof amounts to characterize the Schrödinger operators with a finite heat kernel expansion.     

Exact Solutions of the Klein–Gordon Equation with Position-Dependent Mass for Mixed Vector and Scalar Kink-Like Potentials

The relativistic problem of spinless particles with position-dependent mass subject to kink-like potentials (~tanh αx) is investigated. By using the basic concepts of the supersymmetric quantum mechanics formalism and the functional analysis method, we solve exactly the position-dependent effective mass Klein–Gordon equation with the vector and scalar kink-like potential coupling, and obtain the bound state solutions in the closed form. It is found that in the presence of position-dependent mass there exists the symmetry that the discrete positive energy spectra and negative energy spectra are symmetric about zero energy for the case of a mixed vector and scalar kink-like potential coupling, and in the presence of constant mass this symmetry only appears for the cases of a pure scalar kink-like potential coupling or massless particles.     

Pion–Rho Meson Lagrangian in Nuclear Matter

We present an in-medium modified pion and rho meson Lagrangian which describes the pion, rho meson and the corresponding soliton properties in nuclear matter. Within the present approach pion properties in nuclear matter is closely related to the low-energy pion-nucleus scattering phenomenology. We discuss the possible modifications of rho meson properties in nuclear matter.     

Short-Range and Medium-Range Order in Liquid Cu-Ni Alloy

The liquid structure of the Cu70Ni30 alloy has been investigated using a θ-θ high-temperature x-ray diffractometer.At all temperatures above its liquidus,a distinct pre-peak has been found around a scattering vector magnitude of 13.5nm^-1.The height of the pre-peak decreases gradually with increasing temperature but it clearly exists up to a temperature of 1400℃.This behaviour indicates that stable medium-range order atomic clusters exist in the melt.It is concluded that the short-range order atomic clusters of the liquid Cu70Ni30 alloy mainly consist of Cu atoms with centred Ni atoms.The appearance of the pre-peak in the structure factor of the liquid Cu70Ni30 alloy is caused by the interaction between centred Ni atoms locating in the neighbouring atomic clusters.     

Exact Solutions of Klein-Gordon Equation with Exponential Scalar and Vector Potentials

We obtain the exact analytical solution of the Klein-Gordon equation for the exponential vector and scalar potentials by using the asymptotic iteration method. For the scalar potential greater than the vector potential case, the exact bound state energy eigenvalues and corresponding eigenfunctions are presented. The bound state eigenfunction solutions are obtained in terms of the confluent hypergeometric functions.     

Structural-Phase Transformations and Short-Range Order Evolution in the Fe–Cr System during Mechanical Alloying

Physics of the Solid State - Using Mössbauer spectroscopy on 57Fe nuclei and X-ray diffraction, the mechanism of mechanical alloying in a planetary ball mill of the Fe–Cr nanocrystalline...