A covariant multiple scattering series for elastic projectile-target scattering

A covariant formulation of the multiple scattering series for the optical potential is presented. The case of a scalar nucleon interacting with a spin zero isospin zero A-body target through meson exchange, is considered. It is shown that a covariant equation for the projectile-target t-matrix can be obtained which sums the ladder and crossed ladder diagrams efficiently. From this equation, a multiple scattering series for the optical potential is derived, and it is shown that in the impulse approximation, the two-body t-matrix associated with the first order optical potential is the one in which one particle is kept on mass-shell. The meaning of various terms in the multiple scattering series is given. The construction of the first-order optical potential for elastic scattering calculations is described

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

Split Quaterionic Representation of SDYM (SU(1,1) Instantons in \u3ci\u3eS\u3c/i\u3e\u3csup\u3e2-\u3c/sup\u3e × \u3ci\u3eS\u3c/i\u3e\u3csup\u3e2+\u3c/sup\u3e

Using split‐quaternions, we find explicit SDYM SU(1,1) instanton solutions in S2- × S2+ which is the conformal compactification of the semi‐Euclidean 4‐spacetime R2+2 of split signature (-,-,+,+). It is also shows that SDYM and ASDYM fields in S2- × S2+ can be described as simple split-quaternionic 2-forms

Why Do I Write the Way I Write

Panel: Why I Write The Way I D

The design of semi-submersibles for minimum vertical motion

Summary available: p. [1

Radiation Transport and Shielding for Space Exploration and High Speed Flight Transportation

Transportation of ions and neutrons in matter is of direct interest in several technologically important and scientific areas, including space radiation, cosmic ray propagation studies in galactic medium, nuclear power plants and radiological effects that impact industrial and public health. For the proper assessment of radiation exposure, both reliable transport codes and accurate data are needed. Nuclear cross section data is one of the essential inputs into the transport codes. In order to obtain an accurate parametrization of cross section data, theoretical input is indispensable especially for processes where there is little or no experimental data available. In this grant period work has been done on the studies of the use of relativistic equations and their one-body limits. The results will be useful in choosing appropriate effective one-body equation for reaction calculations. Work has also been done to improve upon the data base needed for the transport codes used in the studies of radiation transport and shielding for space exploration and high speed flight transportation. A phenomenological model was developed for the total absorption cross sections valid for any system of charged and/or uncharged collision pairs for the entire energy range. The success of the model is gratifying. It is being used by other federal agencies, national labs and universities. A list of publications based on the work during the grant period is given below and copies are enclosed with this report

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)