Comparing some nucleon-nucleon potentials

The aim is to compare a few Nucleon-Nucleon (NN) potentials especially Reid68, Reid68-Day, Reid93, UrbanaV14, ArgonneV18, Nijmegen 93, Nijmegen I and Nijmegen II. Although these potentials have some likenesses and are almost phenomenological, they include in general different structures and their own characteristics. The potentials are constructed in a manner that fit NN scattering data or phase shifts and are compared in this way. A high-quality scale of a potential is that it fits the data with χ²/N _data ≈ 1, describes well the deuteron properties and gives satisfactory results in nuclear-structure calculations. However, these scales have some failures. Here, we first compare many potentials by confronting them with the data. Then, we try to compare the potential forms by considering the potential structures directly and therefore regarding their substantial bases somehow. To do so, we note that since the potentials are written in different schemas, it is necessary to write them in a unique schema. On the other hand, because three major terms in the NN interaction are central, tensor and spin-orbit terms; so, to perform a reduction plan and arrive at a common structure, we choose the Reid’s potential form. Next, we compare the potentials for some states and address some other related issues as well.     

Equivalent nonlocal nucleon-nucleon potentials

The local nucleon-nucleon potential which contains a strong repulsive core is often replaced by an equivalent weak but non-local potential. Such potentials can be obtained by unitary transformations of the two-body Hamiltonian. Necessary and sufficient conditions are derived which must be fulfilled by the unitary transformations in order to give equivalent potentials. Special examples of unitary transformations with this property are investigated.     

Modern nucleon-nucleon potentials and symmetry energy in infinite matter

We study the symmetry energy in infinite nuclear matter employing a non-relativistic Brueckner-Hartree-Fock approach and using various new nucleon-nucleon (NN) potentials, which fit np and pp scattering data very accurately. The potential models we employ are the recent versions of the Nijmegen group, Nijm-I, Nijm-II, and Reid93, the Argonne V₁₈ potential and the CD-Bonn potential. All these potentials yield a symmetry energy which increases with density, resolving a discrepancy that existed for older NN potentials. The origin of remaining differences is discussed.     

Bag-model inspired nucleon-nucleon potentials and the three-nucleon system

Several examples of short-range energy-dependentN-N potentials derived in the quark-compound-bag (QCB) model are presented. They all satisfy the classical causality condition. We show that for radii of theN-N interactions ofb1.4 fm thes-wave QCB potentials reproduce fairly well the trinucleon binding energy and other three-nucleon observables.     

Optical potentials in relativistic meson-nucleon model

The relativistic microscopic optical potentials (RMOP) at E < 300 MeV have been derived and investigated based on Walecka's meson-nucleon model. An effective lagrangian including nucleon, σ- and ω-mesons, which is required to reproduce the nuclear matter saturation properties, has been introduced and used to calculate the self-energy of a nucleon in the nuclear medium. Systematical analyses of the scattering data are performed with the RMOP. Finally, several effects, such as the meson-nucleon vertex form factor, isovector meson exchanges, non-linear σ-model are studied.     

Bridge between bound state and reaction effective nucleon-nucleon potentials

It has been a long standing problem to find the connection between the realistic nucleon-nucleon interaction and the interaction between two nucleons when they are embedded inside a nuclear medium, the so-called ‘effective interaction’. On the one hand various many-body approaches have been employed, while on the other hand, information is sought on the basis of static nuclear properties. Both provide partial information. An attempt is made to understand if there is an inherent link, a bridge, which connects all these informations, through the study of heavy ion fusion reactions.     

Semiclassical approximation for relativistic potentials

We consider the application of semiclassical approximation to relativistic potentials for massless particles where the kinetic energy is a nontrivial, nonlocal operator. Quantization rules are derived for an arbitrary confining potential and compared to some exact results forS-waves. These results admit of a partial generalization to smalll values.     

Two and three pion-cut contributions to nucleon-nucleon scattering

Examining information from NN forward scattering in terms of discrepancy functions, we show that the 2π cut contributions as calculated via dispersion methods from πN scattering are in perfect agreement with NN scattering. Furthermore, we demonstrate the need for 3π cut contributions which are quantitatively well described by a nucleon exchange model. Finally, in addition to the 2π and 3π cut contributions, we determine the coupling constants of the ω and A₁ to be: g_Vω²/4π = 8.1 ± 1.5, g_Tω/g_Vω = 0.14 ± 0.20 and g_A1²/4π = 7.3 ± 3.0. The coupling of the η turns out to be zero.     

Diffraction in three dimensions

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Quantization of Gauge Systems . By M. Henneaux and C. Teitelboim. 1994, US$29.95, £25.00 (pbk) pp. xxii + 520. Princeton, ISBN 0 691 03769 8. Scope: textbook. Level: postgraduate and specialist.

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Electronic Structure of Refractory Carbides and Nitrides . Edited by V. A. Gubanov, A.L. Ivanovsky and V. P. Zhukov. 1994, $79.95 (hbk) pp. xiv + 256. Cambridge University Press, ISBN 0 521 41885 2. Scope: monograph. Level: postgraduate and specialist.

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Shape invariant potentials in higher dimensions

In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended to arrive at a large class of new shape invariant potentials in arbitrary dimensions. A reformulation of the shape invariance property and possible generalizations are proposed. These may lead to an important extension of the shape invariance property to Hamiltonians that are related to standard potential problems via space time transformations, which are found useful in path integral formulation of quantum mechanics.     

Comparison of bound-state properties of self-consistent Thomas-Fermi potentials for neutral systems in two and three dimensions

It is pointed out that self-consistent Thomas-Fermi potentials for neutral systems in two dimensions must possess at least one bound state. In contrast, it was recently argued that some non-zero attractive strength is required for bound states in three dimensions.     

Electromagnetic properties of relativistic quarks in confining potentials

We investigate electromagnetic properties of the quark core of nucleons in a model with massless quarks in confining potentials. We find quark core rms radii of 0.6 fm or smaller to be compatible with form factor data corrected for pion cloud effects. Relations between the magnetic form factor and the axial vector or pseudoscalar form factors will also be discussed.     

Rearrangement term with relativistic density-dependenthyperon potentials

An appropriate density dependence of hyperon potentials is important for the stiffening of the equation of state and massive neutron stars. To persist in covariance and thermodynamic consistency, the rearrangement term is indispensable. In this work, we derive the rearrangement term for hyperon potentials with arbitrary density-dependence. The importance of the rearrangement term is also exhibited in numerical instances.     

Continuous freezing in three dimensions

We analyze the freezing transition in a system of hard particles with a very long-ranged repulsion. The long-range repulsion makes first-order freezing transitions continuous, but leaves the initial stages of the crystallization unchanged: the crystal phase must still nucleate. The coexistence between bulk phases is replaced by microphase separation.