Richard R. Silbar

Nucleon-nucleon dynamics at medium energies: (I). Unitary model for elastic and inelastic scattering

Abstract A framework is presented for a unified theory of elastic nucleon-nucleon scattering and single-pion production at medium energies. The model is relativistic, unitary, and takes into account all spin complications. In the simplest version of the theory the driving mechanism is one-pion exchange but the model can be extended to include short-range forces. The resulting set of coupled linear integral equations have the structure of three-body equations and can be solved exactly. The method of solution is discussed.

Melting as a dislocation-mediated phase transition

We present a theory of the melting of elements as a dislocation-mediated phase transition. We model dislocations near the melt as noninteracting closed loops on a lattice. In this framework we derive simple expressions for the melting temperature and latent heat of fusion that depend on the dislocation density at melt. We use experimental data for more than half the elements in the periodic table to determine the dislocation density from both relations. Melting temperatures yield a dislocation density of (0.61{+-}0.20)b{sup -2}, in good agreement with the density obtained from latent heats, (0.66{+-}0.11)b{sup -2}, where b is the length of the smallest perfect-dislocation Burgers vector. Melting corresponds to the situation where, on average, half of the atoms are within a dislocation core. (c) 2000 The American Physical Society.

Analysis of dislocation mechanism for melting of elements: Pressure dependence

In the framework of melting as a dislocation-mediated phase transition we derive an equation for the pressure dependence of the melting temperatures of the elements valid up to pressures of order their ambient bulk moduli. Melting curves are calculated for Al, Mg, Ni, Pb, the iron group (Fe, Ru, Os), the chromium group (Cr, Mo, W), the copper group (Cu, Ag, Au), noble gases (Ne, Ar, Kr, Xe, Rn), and six actinides (Am, Cm, Np, Pa, Th, U). These calculated melting curves are in good agreement with existing data. We also discuss the apparent equivalence of our melting relation and the Lindemann criterion, and the lack of the rigorous proof of their equivalence. We show that the would-be mathematical equivalence of both formulas must manifest itself in a new relation between the Gruneisen constant, bulk and shear moduli, and the pressure derivative of the shear modulus.

Neutron stars for undergraduates

The calculation of the structure of white dwarf and neutron stars is a suitable topic for an undergraduate thesis or an advanced special topics or independent study course. The subject is rich in many different areas of physics, ranging from thermodynamics to quantum statistics to nuclear physics to special and general relativity. The computations for solving the coupled structure differential equations (both Newtonian and general relativistic) can be done using a symbolic computational package. In doing so, students will develop computational skills and learn how to deal with units. Along the way they also will learn some of the physics of equations of state and of degenerate stars.

Nucleon-nucleon dynamics at medium energies (III). I = 1 spin-dependent total cross sections

Abstract We present I = 1 spin-dependent total cross section predictions of a unitary, relativistic three-body model, described in earlier papers in this series, for the NN → NN and NN → NNπ coupled reactions. The spin-averaged NN → NNπ cross section is quite peripheral and is in good agreement with experiment from 500 to 2000 MeV. The elastic cross section is non-peripheral and does not agree with experiment. This is probably because of the neglect, so far, of short-range forces in the model. There are very large spin-dependent effects in both the elastic and NN → NNπ cross sections, even though this is a model without dibaryon resonances.

Pseudo resonance behavior in nucleon-nucleon scattering

Abstract In a relativistic unitary model for intermediate energy nucleon-nucleon scattering there are strong indications that the resonance-like looping behavior of the 3 F 3 and 1 D 2 amplitudes is not due to a resonance pole but to the coupling with the inelastic NNπ channel. In its most simple form the looping behavior is caused by a square root branch cut.

Nucleon-nucleon dynamics at medium energies (II). Results for NN phase parameters

Abstract We present predictions for nucleon-nucleon elastic scattering phase parameters based on a unitary, relativistic, one-pion-exchange model, which takes single-pion-production inelasticity into account. The agreement of the high-L phase shifts with data is considerably improved at intermediate energies by inclusion of the NΔ inelastic channel. Our predicted inelasticities are in generally good agreement with the data, but are smaller than the predictions of Green and Sainio. The Argand plots of the 1D2, 3F3, 3P1, and 1G4 all show counterclockwise motion resulting from the onset of inelastic channels.

Exclusive spin-dependent pion production in medium-energy nucleon-nucleon collisions: The role of unitarity

Abstract Polarization asymmetries are calculated for the reaction p↑ + p → p + π + + n at 800 MeV. The dynamics are treated in a relativistic model that preserves two- and three-body unitarity. These calculations, when compared to recent data taken at LAMPF, show marked improvement over simple Born approximation predictions.

Absence of attraction in the NN central potential derived from skyrmions

Abstract The nucleon-nucleon potential is studied using a skyrmion lagrangian containing terms of second, fourth, and sixth order in the field derivatives; the fourth-order pieces contain both an antisymmetric (repulsive) form and a symmetric (attractive) one. No attraction is found in the central NN potential VC when the full structure of the sixth-order term is retained. As yet another candidate for the source of attraction in VC, admixtures of ΔΔ components in the two-baryon wave function are considered. These slightly lower the values of VC for 1 ⩽ R ⩽ 2 fm, but by no means sufficiently to bring about a net attraction there. Thus the challenge of finding sources of attraction in the skyrmion approach remains.

NN → NNπ at intermediate energies: Predictions of a unitary model

Abstract We explore the NN → NN π reaction in detail within the context of a unified model which satisfies two- and three-body unitary. Predictions for differential cross sections and spin observables are examined and compared with experimental data, where available, for a variety of exclusive [pp → p(n) π + , pp → pp( π 0 ), and np → p(p) π − ] and inclusive [pp → p(X) and pp → n(X)] reactions. Based on predictions of the model, further experiments are suggested to shed additional light on the NN → NN π process. Due to dynamical symmetries the np → p(p) π − observables are strikingly different from the more familiar pp → p(n) π + observables, and we urge that this reaction be investigated experimentally. Experimental tests for the existence of dibaryons are also briefly discussed.