Confining potential in momentum space

A method is presented for the solution in momentum space of the bound state problem with a linear potential in r space. The potential is unbounded at large r leading to a singularity at small q. The singularity is integrable, when regulated by exponentially screening the r-space potential, and is removed by a subtraction technique. The limit of zero screening is taken analytically, and the numerical solution of the subtracted integral equation gives eigenvalues and wave functions in good agreement with position space calculations

Solution of two-body relativistic bound state equations with confining plus Coulomb interactions

Studies of meson spectroscopy have often employed a nonrelativistic Coulomb plus Linear Confining potential in position space. However, because the quarks in mesons move at an appreciable fraction of the speed of light, it is necessary to use a relativistic treatment of the bound state problem. Such a treatment is most easily carried out in momentum space. However, the position space Linear and Coulomb potentials lead to singular kernels in momentum space. Using a subtraction procedure we show how to remove these singularities exactly and thereby solve the Schroedinger equation in momentum space for all partial waves. Furthermore, we generalize the Linear and Coulomb potentials to relativistic kernels in four dimensional momentum space. Again we use a subtraction procedure to remove the relativistic singularities exactly for all partial waves. This enables us to solve three dimensional reductions of the Bethe-Salpeter equation. We solve six such equations for Coulomb plus Confining interactions for all partial waves

Integrating knowledge management into business processes

University of Technology Sydney. Faculty of Information Technology.The 'new economy' enterprises, this thesis explains why knowledge management can fail and how the risk of such failures may be minimised. The key proposal is that knowledge management should be integrated into business processes and software agents should be used to facilitate knowledge management in business processes. The problem then is how such integration of the methodology can be applied to a concrete knowledge model. The Evolving Knowledge Process (EKP) Model The proposed approach includes these features: firstly, a method for developing a knowledge model; secondly, how the proposed knowledge model can be integrated into business processes; and thirdly, the use of a software agent to facilitate the integration of knowledge management into the business process; and finally, we implemented the EKP model using the Java programming language to demonstrate our system on the computer and to facilitate the use of agents. Agents to Facilitate the Process This thesis suggests how knowledge agents can facilitate the knowledge process. One solution is to develop a multiagent system based on the Evolving Knowledge Process (EKP) model. We defined each agent in the knowledge process to support and facilitate the process. Each agent has its own goals, plans and actions, and communicates with the other agents

Instantaneous Bethe-Salpeter Equation: Analytic Approach for Nonvanishing Masses of the Bound-State Constituents

The instantaneous Bethe-Salpeter equation, derived from the general Bethe-Salpeter formalism by assuming that the involved interaction kernel is instantaneous, represents the most promising framework for the description of hadrons as bound states of quarks from first quantum-field-theoretic principles, that is, quantum chromodynamics. Here, by extending a previous analysis confined to the case of bound-state constituents with vanishing masses, we demonstrate that the instantaneous Bethe-Salpeter equation for bound-state constituents with (definitely) nonvanishing masses may be converted into an eigenvalue problem for an explicitly - more precisely, algebraically - known matrix, at least, for a rather wide class of interactions between these bound-state constituents. The advantages of the explicit knowledge of this matrix representation are self-evident.Comment: 12 Pages, LaTeX, 1 figur

Relativistic Multiple Scattering Theory and the Relativistic Impulse Approximation

It is shown that a relativistic multiple scattering theory for hadron-nucleus scattering can be consistently formulated in four-dimensions in the context of meson exchange. We give a multiple scattering series for the optical potential and discuss the differences between the relativistic and non-relativistic versions. We develop the relativistic multiple scattering series by separating out the one boson exchange term from the rest of the Feynman series. However this particular separation is not absolutely necessary and we discuss how to include other terms. We then show how to make a three-dimensional reduction for hadron-nucleus scattering calculations and we find that the relative energy prescription used in the elastic scattering equation should be consistent with the one used in the free two-body t-matrix involved in the optical potential. We also discuss what assumptions are involved in making a Dirac Relativistic Impulse Approximation (RIA).Comment: 20 pages, 9 figures, Accepted for publication in Journal of Physics

Relativistic Elastic Differential Cross Sections for Equal Mass Nuclei

The effects of relativistic kinematics are studied for nuclear collisions of equal mass nuclei. It is found that the relativistic and non-relativistic elastic scattering amplitudes are nearly indistinguishable, and, hence, the relativistic and non-relativistic differential cross sections become indistinguishable. These results are explained by analyzing the Lippmann-Schwinger equation with the first order optical potential that was employed in the calculatio

Relativistic Multiple Scattering Theory and the Relativistic Impulse Approximation

It is shown that a relativistic multiple scattering theory for hadron - nucleus scattering can be consistently formulated in four dimensions in the context of meson exchange. We give a multiple scattering series for the optical potential and discuss the differences between the relativistic and non- relativistic versions. We develop the relativistic multiple scattering series by separating out the one-boson exchange term from the rest of the Feynman series. However, this particular separation is not absolutely necessary and we discuss how to include other terms. We then show how to make a three- dimensional reduction for hadron - nucleus scattering calculations and we find that the relative energy prescription used in the elastic scattering equation should be consistent with that used in the free two- body t- matrix involved in the optical potential. We also discuss what assumptions are involved in making a Dirac relativistic impulse approximation ( RIA)

Kaon-nucleus scattering

Two kinds of number density distributions of the nucleus, harmonic well and Woods-Saxon models, are used with the t-matrix that is taken from the scattering experiments to find a simple optical potential. The parameterized two body inputs, which are kaon-nucleon total cross sections, elastic slope parameters, and the ratio of the real to imaginary part of the forward elastic scattering amplitude, are shown. The eikonal approximation was chosen as the solution method to estimate the total and absorptive cross sections for the kaon-nucleus scattering

Electromagnetic Dissociation and Space Radiation

Relativistic nucleus-nucleus reactions occur mainly through the Strong or Electromagnetic (EM) interactions. Transport codes often neglect the latter. This work shows the importance of including EM interactions for space radiation applications.Comment: 11 page

Optical Potential for Light Nuclei and Momentum-Space Eikonal Phase Function

One way of predicting nuclear cross sections is to use the Eikonal method, a high energy (small scattering angle) approximation that depends on the nucleus-nucleus optical potential. In the position-space representation, the optical potential is a 6-dimensional integral over projectile and target densities and the nucleon-nucleon transition amplitude. The integration is often performed numerically and is inefficient, especially when the task is to compute large numbers of nuclear cross sections for various projectile-target reactions. The aim of the current work is to present two efficient methods for the computation of the Eikonal phase shift function. Analytic formulas of the optical potential are presented in the position-space representation for nuclei that are well-represented by harmonic-well nuclear matter densities (A < 20), which reduces the Eikonal phase factor to an integration over a single dimension. Next, the Eikonal phase function is presented in the momentum-space representation, which is particularly useful when the Fourier transform of the position-space optical potential is known. These new methods increase the computational efficiency by three orders of magnitude and allow for rapid prediction of elastic differential, total, elastic, and reaction cross sections in the Eikonal approximation