Phenomenological Non-Local Nucleon-Nucleon Interactions and the Neutron-Deuteron Elastic Scattering

Phenomenological “inside non-local, outside Yukawa-tail”N-N interactions, which fit the N-N data and produce the correct triton binding energy, are tested for elastic n-d scattering observables in the energy range of –22.7 MeV. The sensitivity of the different measurable quantities to the type and to the different components of the N-N interaction is investigated. Some of the possible modifications of the triplet P-wave interactions necessary to reproduce the neutron vector analyzing power are found. The new INOY and - interactions together with appropriate parametrizations of the higher partial waves seem to reproduce the experimental data better than the corresponding components of the Argonne potential. Received February 12, 1997; revised October 3, 1997; accepted for publication October 8, 1997     

Neutron Skin Thickness of Nuclei and Effective Nucleon-Nucleon Interactions

The Skyrme energy density functional is applied to study the ground state properties of a series of finite nuclei. The charge rms radii, neutron rms radii, and the neutron skin thickness for some nuclei are calculated and compared with the experimental data. The constraint on the effective interactions, especially, the density dependence of the isospin-dependent. part of Skyrme interactions is extracted by the data of neutron skin thicknesses of ^208Pb and isotopes of Sn.     

Froth-like Minimizers of a Non-Local Free Energy Functional with Competing Interactions

We investigate the ground and low energy states of a one dimensional non-local free energy functional describing at a mean field level a spin system with both ferromagnetic and antiferromagnetic interactions. In particular, the antiferromagnetic interaction is assumed to have a range much larger than the ferromagnetic one. The competition between these two effects is expected to lead to the spontaneous emergence of a regular alternation of long intervals on which the spin profile is magnetized either up or down, with an oscillation scale intermediate between the range of the ferromagnetic and that of the antiferromagnetic interaction. In this sense, the optimal or quasi-optimal profiles are “froth-like”: if seen on the scale of the antiferromagnetic potential they look neutral, but if seen at the microscope they actually consist of big bubbles of two different phases alternating among each other. In this paper we prove the validity of this picture, we compute the oscillation scale of the quasi-optimal profiles and we quantify their distance in norm from a reference periodic profile. The proof consists of two main steps: we first coarse grain the system on a scale intermediate between the range of the ferromagnetic potential and the expected optimal oscillation scale; in this way we reduce the original functional to an effective “sharp interface” one. Next, we study the latter by reflection positivity methods, which require as a key ingredient the exact locality of the short range term. Our proof has the conceptual interest of combining coarse graining with reflection positivity methods, an idea that is presumably useful in much more general contexts than the one studied here.     

Nucleon-Nucleon Interaction and the Mixing of Scalar Meson

Whether the mixing of scalar meson exists or not is an interesting question. We consider the mixing of scalar meson and further study the nucleon-nucleon interaction in the chiral SU（3） quark model by solving the resonating group method equation. The results are analyzed and compared with no mixing, ideal mixing and general mixing. It seems that the nucleon-nucleon interaction and binding energy of deuteron can be reasonably described with the different mixing of scalar meson.     

Polarized Proton Targets and Low-Energy Nucleon-Nucleon Experiments

The possible use of a polarized proton target in the investigation of low-energy nucleon-nucleon interactions is reviewed. The reconstruction of the scattering matrix and verification of P-, T-and isotopical invariances are briefly discussed. Possible sources and detectors of polarized particles are considered. The problem of phase-shift analysis and nucleon-nucleon potentials are treated in the appendices. Tables of experimental values are given for the polarization of nucleons scattered on nucleons. Experimental quantities determined from the phase-shift analysis are given in graphs for the energies 14.5 and 23.1 MeV.     

Non-Local Scattering Kernel and the Hydrodynamic Limit

In this paper we study the interaction of a fluid with a wall in the framework of the kinetic theory. We consider the possibility that the fluid molecules can penetrate the wall to be reflected by the inner layers of the wall. This results in a scattering kernel which is a non-local generalization of the classical Maxwell scattering kernel. The proposed scattering kernel satisfies a global mass conservation law and a generalized reciprocity relation. We study the hydrodynamic limit performing a Knudsen layer analysis, and derive a new class of (weakly) nonlocal boundary conditions to be imposed to the Navier–Stokes equations.     

Pade Expansion and Nucleon-Nucleon Scattering in Coupled Channels

We extend our Pade-aided analysis of the nonperturbative renormalization of nucleon-nucleon scattering to the case of coupled channels.     

基于平移不变壳模型的轻核(A≤6)基态特性

包含中心力、张量力、自旋-轨道力和四级自旋-轨道力且具有高斯型径向关系的唯象核子-核子相互作用被构造并通过调节有关参数来得到氘核结合能、均方根半径、D态几率、磁偶极矩和电四极矩的理论值和实验值之间的最好拟合.氘核基态波函数用对应主量子数0≤N≤1 0的平移不变壳模型基函数来展开.另外,用新的相互作用还计算了³H ,⁴He,⁵He和⁶Li核的结合能、均方根半径和磁偶极矩.这些核的波函数也是用平移不变壳模型基函数来展开,只是对前两个核,N=10;对⁵He,N=7;对⁶Li,N=6.对氘核,进一步研究了三体力的作用.所得结果与相应的实验数据符合甚好.     

Non-Local Realistic Theories and the Scope of the Bell Theorem

According to a widespread view, the Bell theorem establishes the untenability of so-called ‘local realism’. On the basis of this view, recent proposals by Leggett, Zeilinger and others have been developed according to which it can be proved that even some non-local realistic theories have to be ruled out. As a consequence, within this view the Bell theorem allows one to establish that no reasonable form of realism, be it local or non-local, can be made compatible with the (experimentally tested) predictions of quantum mechanics. In the present paper it is argued that the Bell theorem has demonstrably nothing to do with the ‘realism’ as defined by these authors and that, as a consequence, their conclusions about the foundational significance of the Bell theorem are unjustified.     

Phase Shifts and Mixing Parameters for Elastic Neutron-Deuteron Scattering Above Breakup Threshold

Complex eigenphases and mixing parameters for elastic n-d scattering above the breakup threshold are calculated. Faddeev equations are solved precisely using the Bonn-B NN potential. We point out defects in existing N-d phase-shift analyses. Peculiar energy variations in the mixing parameter η^3/2− are shown to have no effect on observables and are simply an artifact of the S-matrix parametrization. It is shown, that the n-d analyzing power A _y depends most sensitively on the three eigenphases δ^1/2 _3/2/1, δ^2/3 _3/2/1, and δ^5/2 _3/2/1, which again are predominantly generated by the ³ P _j NN force components. Therefore a determination of those eigenphases from experimental data would help to constrain the ³ P _j NN forces. Received September 26, 1994; accepted for publication December 15, 1994     

Local and Non-Local Aspects of Quantum Gravity

The analysis of the measurement of gravitational fields leads to the Rosenfeld inequalities. They say that, as an implication of the equivalence of the inertial and passive gravitational masses of the test body, the metric cannot be attributed to an operator that is defined in the frame of a local canonical quantum field theory. This is true for any theory containing a metric, independently of the geometric framework under consideration and the way one introduces the metric in it. Thus, to establish a local quantum field theory of gravity one has to transit to non-Riemann geometry that contains (beside or instead of the metric) other geometric quantities. From this view, we discuss a Riemann–Cartan and an affine model of gravity and show them to be promising candidates of a theory of canonical quantum gravity.     

Resonances and Gamow States in Non-Local Potentials

For a large class of non-local, non separable potentials with non-compact support, the solution of the radial integrodifferential equation may be reduced to the solution of a homogeneous linear integral equation of Fredholm type with a quadratically integrable kernel. In this way we derive expansions of the wave functions and the Green's function of the Schrödinger equation with a non-local potential in terms of bound states, resonant states and a continuum of scattering functions with complex wave number. The rules of normalization, orthogonality and completeness satisfied by the eigenstates of the Schrödinger equation belonging to complex eigenvalues with Im E_n < 0, (Gamow or resonant states) are also derived. Finally, by means of a realistic example, it is shown how to use these expansions to exhibit the resonant behaviour of the differential cross section. Explicit expressions for the transition amplitudes and the partial widths in terms of expectation values of operators computed with Gamow functions are given.     

Extraction of the Neutron-Neutron Scattering Length a nn from Kinematically Complete Neutron-Deuteron Breakup Experiments

Data for the neutron-neutron final-state-interaction cross section obtained recently in a kinematically complete neutron-deuteron breakup experiment have been reanalyzed using rigorous solutions of the three-nucleon Faddeev equations with realistic nucleon-nucleon interactions. A discrepancy was found with respect to a recent analysis based on the W-matrix approximation to the Paris potential. We also estimate theoretical uncertainties in extracting the neutron-neutron scattering length resulting from the use of different nucleon-nucleon interactions and the possible action of the two-pion-exchange three-nucleon force. We find that there exists a certain production angle for the interacting neutron-neutron pair where the uncertainties become minimal. Received August 27, 1994; revised February 13, 1995; accepted for publication March 21, 1995     

Energy Conditions and Constraints on the Generalized Non-Local Gravity Model

We study and derive the energy conditions in generalized non-local gravity, which is the modified theory of general relativity obtained by adding a term m~(2 n-2)R□~(-n)nR to the Einstein-Hilbert action. Moreover, to obtain some insight on the meaning of the energy conditions, we illustrate the evolutions of four energy conditions with the model parameter ε for different n. By analysis we give the constraints on the model parameters ε.     

Studies of In-Medium Nucleon-Nucleon Collision Cross Section in the Nonrelativistic Energy Region

At nonrelativistic energy region, by using Skyrme interaction, nucleon-nucleon collision cross sections in medium and their relations with densities and energies have been studied. It is found that under PauLi correction, nucleon-nucleon collision cross section in medium is larger than free nucieon-nucleon collision cross section.     

Sensitivity of the Low-Energy p-d Capture Observables to the Nucleon-Nucleon Force Components

 Polarization observables in low-energy proton-deuteron radiative capture have been calculated using the Bonn-B nucleon-nucleon potential. Their sensitivity to the changes of the nucleon-nucleon force components has been studied. Modifications of these forces, which drastically diminished the permanent discrepancy between the data and theory for the vector-analyzing power in low-energy nucleon-deuteron elastic scattering, have only small effects on the pd capture observables. Received May 26, 1999; accepted for publication June 30, 1999     

Non-Local Coupling and Partial Synchronization in Chaotic Systems

Partial synchronization （PaS） on regular networks with a few non-local couplings are studied. The criterion that PaS can emerge in any given network and some relevant phenomena about Lyapunov exponents are found. Theoretical and numerical analysis show that the non-local coupling is the key mechanism of the emergence of PaS.