Soft-core Models Research Articles

Bayesian Estimation of Soft-Core Potential Models for Spatial Point Patterns

For a spatial pattern of points interacting with a repulsive potential in a given finite region of the plane, Bayesian estimation of parametric interaction potential functions between individuals (the Soft-Core models) is proposed.The computations are performed by the use of MCMC (Markov Chain Monte Carlo) methods.We consider two prior distributions with the jumping distributions within Markov chain simulations.Simulated marginal posterior densities of model parameters are fitted to the generalized gamma distribution.We compare marginal posterior modes with the maximum likelihood estimates of the model parameters.The validity of our procedure is graphically demonstrated by the L-statistics.As illustrations, the application to several real data is presented.

Faddeev–Yakubovsky calculations for [formula omitted] hypernuclear systems

We present results for the Λ separation energies of the four-body hypernuclei 4 ΛHe and 4 ΛH based on solutions of the Yakubovsky equations for these systems. Our results show that none of the Nijmegen soft-core models or the Jülich A ˜ model correctly binds all four-body hypernuclei states simultaneously. We discuss the possibilities to constrain hyperon–nucleon interactions using the charge-dependence of the four-body Λ separation energies.

S-matrix poles near theΛNandΣNthresholds in the coupledΛN−ΣNsystem

We search t-matrix poles for $\ensuremath{\Lambda}N\ensuremath{-}\ensuremath{\Sigma}N$ coupling interactions using two soft core models of the Nijmegen group which bind the hypertriton at the correct binding energy, and hard core models which are still influential in hypernuclear physics. To treat the hard core potentials, a useful method for calculating the off-shell t-matrix is proposed. We find poles close to the $\ensuremath{\Sigma}N$ threshold in the second or third quadrant of the complex plane of the $\ensuremath{\Sigma}N$ relative momentum. The relation between the poles and the shape of the $\ensuremath{\Lambda}N$ elastic total cross section is discussed based on a so-called uniformization by which two-channel t-matrices become single-valued on a complex valuable. We also find poles near the $\ensuremath{\Lambda}N$ threshold. These are correlated to the S-wave $\ensuremath{\Lambda}N$ scattering lengths, the values of which have yet to be determined.

Soft-core hyperon-nucleon potentials

A new Nijmegen soft-core OBE potential model is presented for the low-energy $\mathrm{YN}$ interactions. Besides the results for the fit to the scattering data, which largely defines the model, we also present some applications to hypernuclear systems using the G-matrix method. The potentials are generated by the exchange of nonets of pseudoscalar, vector, and scalar mesons. As is standard in the Nijmegen soft-core models, we also include the $J=0$ contributions from the tensor ${f}_{2}{,f}_{2}^{\ensuremath{'}}{,a}_{2},$ and pomeron Regge trajectories, and use Gaussian form factors to guarantee that the potentials have a soft behavior near the origin. An important innovation with respect to the original soft-core potential is the assignment of the cutoff masses for the baryon-baryon-meson (BBM) vertices in accordance with broken $\mathrm{SU}{(3)}_{F},$ which serves to connect the $\mathrm{NN}$ and the $\mathrm{YN}$ channels. As a novel feature, we allow for medium strong breaking of the coupling constants, using the ${}^{3}{P}_{0}$ model with a Gell-Mann--Okubo hypercharge breaking for the BBM coupling. Charge-symmetry breaking in the $\ensuremath{\Lambda}p$ and $\ensuremath{\Lambda}n$ channels is included as well. We present six hyperon-nucleon potentials which describe the available $\mathrm{YN}$ cross section data equally well, but which exhibit some differences on a more detailed level. The differences are constructed such that the models encompass a range of scattering lengths in the $\ensuremath{\Sigma}N$ and $\ensuremath{\Lambda}N$ channels. In all cases, we obtained ${\ensuremath{\chi}}^{2}{/N}_{\mathrm{data}}\ensuremath{\approx}0.55$ for 35 $\mathrm{YN}$ data. In particular, we were able to fit the precise experimental datum ${r}_{R}=0.468\ifmmode\pm\else\textpm\fi{}0.010$ for the inelastic capture ratio at rest. For the scalar-meson mixing angle we obtained values ${\ensuremath{\theta}}_{S}=37\ifmmode^\circ\else\textdegree\fi{}--40\ifmmode^\circ\else\textdegree\fi{},$ which points to almost ideal mixing angles for the scalar $q\overline{q}$ states. The G-matrix results indicate that the remarkably different spin-spin terms of the six potentials appear specifically in the energy spectra of $\ensuremath{\Lambda}$ hypernuclei.

The Nijmegen hyperon-nucleon and hyperon-hyperon interactions

After a brief general introduction, we first review the Nijmegen interactions and the treatment of mesons, emphasizing the important role of the scalar-meson nonet. Then, we discuss the very recent new soft-core models: (i) one-boson-exchange model NSC97, and (ii) the extended-soft-core model. Stressed is the simultaneous description of all baryon-baryon channels. Results are discussed for YN and YY systems.

Simulation of site-site soft-core liquid crystal models

Suggested mechanisms responsible for liquid-crystalline ordering include non-spherical excluded volume effects, anisotropic attraction forces and flexibility. It has been shown using hard-core models that non-spherical excluded volume effects are the essential factor and can qualitatively explain the phenomenology of the problem. However, the simulation of hard-core models is technically demanding. A simpler and more direct alternative is to use a model with a soft-core site-site potential. We employ here a system of molecules composed of a few (11) atoms, constrained to form a multilinear molecule, and in mutual interaction via a continuous repulsive site-site potential of the form r -12. Our results show that such a model is capable of exhibiting nematic and smectic liquid-crystal phases.

Muon capture in deuterium and the meson exchange current effect

One-meson exchange current effect in reaction μ − + d → 2 n + v μ is calculated by using the weak axial current operator which satisfies the nuclear continuity equation up to the order 1 M 2 ( M is the nucleon mass). In the vector part of the weak nuclear interaction the vector-isovector pion exchange currents are also included. Their contribution is found to be non-negligible. The nuclear wave functions are generated from the Paris, Reid soft-core and Bonn potential models. Our result is compatible with the previous one, obtained with only the static axial exchange currents included.

Structural characterization of soft-core and hard-core glasses by Delaunay tessellation

Methods of the Delaunay and Voronoi tessellation are applied to investigate significant structures and structural differences among liquids, glasses, and crystals of the soft-core (inverse 12th power potential) and hard-core models for which molecular dynamics (MD) techniques are used. With particle configurations obtained by MD simulations the Delaunay tessellation for the three dimensional systems defines uniquely a network of tetrahedra. Density dependent properties of the irregularity distribution which measures the magnitude of distortion of each Delaunay tetrahedron (DT) from regular shape (equal edge lengths) and of the length of edges of DT are examined in detail for both models. Clear differences between the hard-core and soft-core systems are observed. Short range correlation of DT is calculated on the pair distribution function of center-to-center distances of the circumspheres of DT, which turns out to be useful to distinguish the short range order of glasses from that of crystals or liquids. It is also shown that there are no clear differences in the distribution of various types of Voronoi polyhedron (VP) between liquids and glasses. However, among various types of polygons (i-edged faces) of VP, the contribution from i=5 increases rather rapidly with increasing density around the glass transition point.