Khin Maung | University of Southern Mississippi (original) (raw)
Papers by Khin Maung
Life sciences in space research, Aug 1, 2019
The space radiation environment is a complex mixture of particle types and energies originating f... more The space radiation environment is a complex mixture of particle types and energies originating from sources inside and outside of the galaxy. These environments may be modified by the heliospheric and geomagnetic conditions as well as planetary bodies and vehicle or habitat mass shielding. In low Earth orbit (LEO), the geomagnetic field deflects a portion of the galactic cosmic rays (GCR) and all but the most intense solar particle events (SPE). There are also dynamic belts of trapped electrons and protons with low to medium energy and intense particle count rates. In deep space, the GCR exposure is more severe than in LEO and varies inversely with solar activity. Unpredictable solar storms also present an acute risk to astronauts if adequate shielding is not provided. Near planetary surfaces such as the Earth, moon or Mars, secondary particles are produced when the ambient deep space radiation environment interacts with these surfaces and/or atmospheres. These secondary particles further complicate the local radiation environment and modify the associated health risks. Characterizing the radiation fields in this vast array of scenarios and environments is a challenging task and is currently accomplished with a combination of computational models and dosimetry. The computational tools include models for the ambient space radiation environment, mass shielding geometry, and atomic and nuclear interaction parameters. These models are then coupled to a radiation transport code to describe the radiation field at the location of interest within a vehicle or habitat. Many new advances in these models have been made in the last decade, and the present review article focuses on the progress and contributions made by workers and collaborators at NASA Langley Research Center in the same time frame. Although great progress has been made, and models continue to improve, significant gaps remain and are discussed in the context of planned future missions. Of particular interest is the juxtaposition of various review committee findings regarding the accuracy and gaps of combined space radiation environment, physics, and transport models with the progress achieved over the past decade. While current models are now fully capable of characterizing radiation environments in the broad range of forecasted mission scenarios, it should be remembered that uncertainties still remain and need to be addressed.
Using split‐quaternions, we find explicit SDYM SU(1,1) instanton solutions in S2- × S2+ which is ... more 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
The Bethe–Salpeter equation for bound states of a fermion–antifermion pair in the instantaneous a... more The Bethe–Salpeter equation for bound states of a fermion–antifermion pair in the instantaneous approximation for the involved interaction kernel is converted into an equivalent matrix eigenvalue problem with explicitly (algebraically) given matrices.
Bulletin of the American Physical Society, 2015
Mississippi-One of the many potentially limiting factors for extraterrestrial operations involvin... more Mississippi-One of the many potentially limiting factors for extraterrestrial operations involving manned missions is the dose received by crew in the harsh space radiation environment. In order to sufficiently understand the radiation dose delivered to astronauts behind shielding, the radiation transport codes used to calculate these doses require accurate nuclear fragmentation cross sections. The fragmentation process can be divided in to two steps: a fast step (abrasion), and a slower evaporation step (ablation). This talk will focus on the ablation cross section, which is calculated by a Monte Carlo process via the updated evaporation code EVA based on Dostrovsky et. al. Phys. Rev. 116, 683 (1959). The code has been updated and completely modernized. Efforts are under way for potential improvements to the model and preliminary results will be presented.
Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 2021
Abstract Astronauts are exposed to ionizing radiation that may pose significant health risks from... more Abstract Astronauts are exposed to ionizing radiation that may pose significant health risks from missions to low Earth orbit (LEO) and beyond. The National Aeronautics and Space Administration (NASA) uses the deterministic radiation transport code, High charge (Z) and Energy TRaNsport (HZETRN), to estimate particle fluxes inside shielded vehicles to evaluate risk of radiation exposure to crew members. Highly efficient radiation transport algorithms and cross section models are needed to perform calculations in realistic vehicles with complex geometrical configurations. The HZETRN code uses the NUClear FRaGmentation (NUCFRG) model to evaluate fragmentation cross section products from nucleus–nucleus collisions. Although highly efficient, the NUCFRG model has some limitations that are based on its unique implementation of the abrasion–ablation formalism. NUCFRG performs well in predicting fragmentation cross sections on the average when compared to experimental data; however, even–odd nuclear structure effects observed in laboratory measurements are absent. The aim of the present work is to formulate a self-consistent theory that produces accurate nuclear fragmentation cross sections while maintaining numerical efficiency. To that end, the Relativistic Abrasion–Ablation FRaGmentation (RAADFRG) model has been developed. The theoretical framework for nuclear interaction is multiple scattering theory (MST), where relativistic kinematics may be included in the momentum–space representation of the Lippmann–Schwinger equation. The nuclear abrasion model employs the Eikonal (Eik) approximation and is used to predict prefragment cross sections. A novel approach is utilized for the excitation energy of prefragment, where in addition to differences of binding energies between two nuclei, energy is transferred to the prefragment from subsequent multiple scattering of abraded nucleons with the spectator nucleon constituents of the prefragment. Next, the excited prefragment liberates particles through the nuclear ablation process, and a nuclear coalescence model that forms aggregate particles for each prefragment channel is included in the yield. The ElectroMagnetic Dissociation FRaGmentation (EMDFRG) model is also included for peripheral interactions that stimulates particle emission via nuclear-photon field interactions. When compared to NUCFRG3, uncertainty quantification analysis shows that RAADFRG is better able to predict experimental nuclear fragmentation cross sections. RAADFRG is also shown to produce the even–odd nuclear structure effects, which is achieved by modification of isospin pairing correction in the prefragment excitation energy model.
Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 2017
Radiation transport codes require accurate nuclear cross sections to compute particle fluences in... more Radiation transport codes require accurate nuclear cross sections to compute particle fluences inside shielding materials. The Tripathi semi-empirical reaction cross section, which includes over 60 parameters tuned to nucleon-nucleus (NA) and nucleus-nucleus (AA) data, has been used in many of the world's best-known transport codes. Although this parameterization fits well to reaction cross section data, the predictive capability of any parameterization is questionable when it is used beyond the range of the data to which it was tuned. Using uncertainty analysis, it is shown that a relativistic Three-Dimensional Lippmann-Schwinger (LS3D) equation model based on Multiple Scattering Theory (MST) that uses 5 parameterizations-3 fundamental parameterizations to nucleon-nucleon (NN) data and 2 nuclear charge density parameterizations-predicts NA and AA reaction cross sections as well as the Tripathi cross section parameterization for reactions in which the kinetic energy of the projectile in the laboratory frame (T Lab) is greater than 220 MeV/n. The relativistic LS3D model has the additional advantage of being able to predict highly accurate total and elastic cross sections. Consequently, it is recommended that the relativistic LS3D model be used for space radiation applications in which T Lab > 220 MeV/n.
Physics Letters B, 2015
The effects of relativistic kinematics are studied for nuclear collisions of equal mass nuclei. I... more 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 calculation.
Eprint Arxiv Hep Ph 0302228, Feb 25, 2003
We consider the correspondence between solutions of non-gravitational field theories formulated i... more We consider the correspondence between solutions of non-gravitational field theories formulated in Euclidean space-time and Minkowski spacetime. Infinitely many "Euclidean" spaces can be obtained from M 4 via a group of transformations in which the Wick rotation is a special case.
![Research paper thumbnail of Split-quaternionic representation of SDYM SU(1,1) instantons in S[sub −][sup 2] × S[sub +][sup 2]](https://attachments.academia-assets.com/115622342/thumbnails/1.jpg)
](AIP Conference Proceedings, 2007
Using split-quaternions, we find explicit SDYM SU(1, 1) instanton solutions in S 2 − ×S 2 + which... more Using split-quaternions, we find explicit SDYM SU(1, 1) instanton solutions in S 2 − ×S 2 + which is the conformal compactification of the semi-Euclidean 4-spacetime R 2+2 of split-signature (−, −, +, +). The noncompact Lie group SU(1, 1) is naturally introduced as an appropriate gauge group for SDYM instantons in S 2 − × S 2 +. It is shown that SDYM and ASDYM SU(1, 1) instanton solutions in S 2 − × S 2 + lead to the absolute minima of Yang-Mills action and that Yang-Mills action satisfies the same quantization as in SU(2) non-abelian gauge theories in S 4. It is also shown that SDYM and ASDYM field equations in S 2 − × S 2 + can be described as simple split-quaternionic 2-forms.
Two kinds of number density distributions of the nucleus, harmonic well and Woods-Saxon models, a... more 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
The Bethe-Salpeter equation for bound states of a fermion-antifermion pair in the instantaneous a... more The Bethe-Salpeter equation for bound states of a fermion-antifermion pair in the instantaneous approximation for the involved interaction kernel is converted into an equivalent matrix eigenvalue problem with explicitly (algebraically) given matrices.
Unknown, 1988
Methods of solution are presented for the Eikonal form of the nucleus-nucleus coupled-channel sca... more Methods of solution are presented for the Eikonal form of the nucleus-nucleus coupled-channel scattering amplitudes. Analytic solutions are obtained for the second-order optical potential for elastic scattering. A numerical comparison is made between the first ...
Radiation Measurements, 2014
The quality factor is the largest source of uncertainty in space radiation risk assessment. Corre... more The quality factor is the largest source of uncertainty in space radiation risk assessment. Correlated uncertainties reduce uncertainty in the difference of distributions. Correlated quality factors are used to reduce uncertainty in shielding risk assessment.
Physical Review D, 2001
The instantaneous Bethe-Salpeter equation, derived from the general Bethe-Salpeter formalism by a... more 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.
Physical Review D, 2001
The Bethe-Salpeter formalism in the instantaneous approximation for the interaction kernel enteri... more The Bethe-Salpeter formalism in the instantaneous approximation for the interaction kernel entering into the Bethe-Salpeter equation represents a reasonable framework for the description of bound states within relativistic quantum field theory. In contrast to its further simplifications (like, for instance, the so-called reduced Salpeter equation), it allows also the consideration of bound states composed of "light" constituents. Every eigenvalue equation with solutions in some linear space may be (approximately) solved by conversion into an equivalent matrix eigenvalue problem. We demonstrate that the matrices arising in these representations of the instantaneous Bethe-Salpeter equation may be found, at least for a wide class of interactions, in an entirely algebraic manner. The advantages of having the involved matrices explicitly, i.e., not "contaminated" by errors induced by numerical computations, at one's disposal are obvious: problems like, for instance, questions of the stability of eigenvalues may be analyzed more rigorously; furthermore, for small matrix sizes the eigenvalues may even be calculated analytically.
Physical Review D, 1993
Solutions of two-body, bound-state equations have recently been developed for quark-antiquark bou... more Solutions of two-body, bound-state equations have recently been developed for quark-antiquark bound-state pairs. These solutions use a confining potential in momentum space as input into threedimensional reductions of the Bethe-Salpeter equation using special subtraction procedures. Regge trajectories are calculated for the Schrodinger equation which display the well-known unphysical behavior where lower mass trajectories overlap higher mass ones and also display nonlinearity. Both of these features contradict experiment. Regge trajectories obtained from the Thompson equation, which is relativistic in origin, avoid both of these problems.
Physical Review D, 1993
Studies of meson spectroscopy have often employed a non-relativisticCoulomb plus Linear Confining... more Studies of meson spectroscopy have often employed a non-relativisticCoulomb plus Linear Confining potential in position space. However because the quarks in mesons move at an appreciable fractionof the speed of light,itisnecessary 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 singularitiesezactly and thereby solve the Schr_dinger equation in momentum space for all partial waves. Furthermore, we generalize the Linear and Coulomb potentials to relativistickernels in 4-dimensional momentum space. Again we use a subtraction procedure to remove the relativistic singularities exactly for allpartial waves. This enables us to solve 3-dimensional reductions of the Bethe-Salpeter equation. We solve six such equations for Coulomb plus Confining interactionsfor allpartialwaves.
Physical Review C, 1990
(SURA) operates the Continuous Electron Beam Accelerator Facility for the United States Departmen... more (SURA) operates the Continuous Electron Beam Accelerator Facility for the United States Department of Energy under contract DE-AC05-84ER40150. DISCLAIMER This report was prepared as an account of work sponsored by the United States government. Neither the United States nor the United States Department of Energy, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, mark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or any agency thereof.
Physical Review A, 1994
The Lande subtraction method is a technique for removing the singularity which arises when one so... more The Lande subtraction method is a technique for removing the singularity which arises when one solves the Schrodinger equation in momentum space for the Coulomb potential. Using this technique, numerical solutions for eigenvalues and eigenfunctions are presented and compared to exact results. Approximately 50 eigenvalues can be calculated very accurately for various values of the angular momentum. Numerous eigenfunctions can a1so be found very accurately. In addition, it is shown how to implement the Lande subtraction method for potentials which are a linear combination of the Coulomb potential and some other potential. Using a basis-function expansion technique, it is shown how to obtain solutions in those cases where the momentum integrals must be evaluated explicitly.
Canadian Journal of Physics, 1992
A method is presented for the solution in momentum space of the bound-state problem with a linear... more 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.
Life sciences in space research, Aug 1, 2019
The space radiation environment is a complex mixture of particle types and energies originating f... more The space radiation environment is a complex mixture of particle types and energies originating from sources inside and outside of the galaxy. These environments may be modified by the heliospheric and geomagnetic conditions as well as planetary bodies and vehicle or habitat mass shielding. In low Earth orbit (LEO), the geomagnetic field deflects a portion of the galactic cosmic rays (GCR) and all but the most intense solar particle events (SPE). There are also dynamic belts of trapped electrons and protons with low to medium energy and intense particle count rates. In deep space, the GCR exposure is more severe than in LEO and varies inversely with solar activity. Unpredictable solar storms also present an acute risk to astronauts if adequate shielding is not provided. Near planetary surfaces such as the Earth, moon or Mars, secondary particles are produced when the ambient deep space radiation environment interacts with these surfaces and/or atmospheres. These secondary particles further complicate the local radiation environment and modify the associated health risks. Characterizing the radiation fields in this vast array of scenarios and environments is a challenging task and is currently accomplished with a combination of computational models and dosimetry. The computational tools include models for the ambient space radiation environment, mass shielding geometry, and atomic and nuclear interaction parameters. These models are then coupled to a radiation transport code to describe the radiation field at the location of interest within a vehicle or habitat. Many new advances in these models have been made in the last decade, and the present review article focuses on the progress and contributions made by workers and collaborators at NASA Langley Research Center in the same time frame. Although great progress has been made, and models continue to improve, significant gaps remain and are discussed in the context of planned future missions. Of particular interest is the juxtaposition of various review committee findings regarding the accuracy and gaps of combined space radiation environment, physics, and transport models with the progress achieved over the past decade. While current models are now fully capable of characterizing radiation environments in the broad range of forecasted mission scenarios, it should be remembered that uncertainties still remain and need to be addressed.
Using split‐quaternions, we find explicit SDYM SU(1,1) instanton solutions in S2- × S2+ which is ... more 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
The Bethe–Salpeter equation for bound states of a fermion–antifermion pair in the instantaneous a... more The Bethe–Salpeter equation for bound states of a fermion–antifermion pair in the instantaneous approximation for the involved interaction kernel is converted into an equivalent matrix eigenvalue problem with explicitly (algebraically) given matrices.
Bulletin of the American Physical Society, 2015
Mississippi-One of the many potentially limiting factors for extraterrestrial operations involvin... more Mississippi-One of the many potentially limiting factors for extraterrestrial operations involving manned missions is the dose received by crew in the harsh space radiation environment. In order to sufficiently understand the radiation dose delivered to astronauts behind shielding, the radiation transport codes used to calculate these doses require accurate nuclear fragmentation cross sections. The fragmentation process can be divided in to two steps: a fast step (abrasion), and a slower evaporation step (ablation). This talk will focus on the ablation cross section, which is calculated by a Monte Carlo process via the updated evaporation code EVA based on Dostrovsky et. al. Phys. Rev. 116, 683 (1959). The code has been updated and completely modernized. Efforts are under way for potential improvements to the model and preliminary results will be presented.
Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 2021
Abstract Astronauts are exposed to ionizing radiation that may pose significant health risks from... more Abstract Astronauts are exposed to ionizing radiation that may pose significant health risks from missions to low Earth orbit (LEO) and beyond. The National Aeronautics and Space Administration (NASA) uses the deterministic radiation transport code, High charge (Z) and Energy TRaNsport (HZETRN), to estimate particle fluxes inside shielded vehicles to evaluate risk of radiation exposure to crew members. Highly efficient radiation transport algorithms and cross section models are needed to perform calculations in realistic vehicles with complex geometrical configurations. The HZETRN code uses the NUClear FRaGmentation (NUCFRG) model to evaluate fragmentation cross section products from nucleus–nucleus collisions. Although highly efficient, the NUCFRG model has some limitations that are based on its unique implementation of the abrasion–ablation formalism. NUCFRG performs well in predicting fragmentation cross sections on the average when compared to experimental data; however, even–odd nuclear structure effects observed in laboratory measurements are absent. The aim of the present work is to formulate a self-consistent theory that produces accurate nuclear fragmentation cross sections while maintaining numerical efficiency. To that end, the Relativistic Abrasion–Ablation FRaGmentation (RAADFRG) model has been developed. The theoretical framework for nuclear interaction is multiple scattering theory (MST), where relativistic kinematics may be included in the momentum–space representation of the Lippmann–Schwinger equation. The nuclear abrasion model employs the Eikonal (Eik) approximation and is used to predict prefragment cross sections. A novel approach is utilized for the excitation energy of prefragment, where in addition to differences of binding energies between two nuclei, energy is transferred to the prefragment from subsequent multiple scattering of abraded nucleons with the spectator nucleon constituents of the prefragment. Next, the excited prefragment liberates particles through the nuclear ablation process, and a nuclear coalescence model that forms aggregate particles for each prefragment channel is included in the yield. The ElectroMagnetic Dissociation FRaGmentation (EMDFRG) model is also included for peripheral interactions that stimulates particle emission via nuclear-photon field interactions. When compared to NUCFRG3, uncertainty quantification analysis shows that RAADFRG is better able to predict experimental nuclear fragmentation cross sections. RAADFRG is also shown to produce the even–odd nuclear structure effects, which is achieved by modification of isospin pairing correction in the prefragment excitation energy model.
Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 2017
Radiation transport codes require accurate nuclear cross sections to compute particle fluences in... more Radiation transport codes require accurate nuclear cross sections to compute particle fluences inside shielding materials. The Tripathi semi-empirical reaction cross section, which includes over 60 parameters tuned to nucleon-nucleus (NA) and nucleus-nucleus (AA) data, has been used in many of the world's best-known transport codes. Although this parameterization fits well to reaction cross section data, the predictive capability of any parameterization is questionable when it is used beyond the range of the data to which it was tuned. Using uncertainty analysis, it is shown that a relativistic Three-Dimensional Lippmann-Schwinger (LS3D) equation model based on Multiple Scattering Theory (MST) that uses 5 parameterizations-3 fundamental parameterizations to nucleon-nucleon (NN) data and 2 nuclear charge density parameterizations-predicts NA and AA reaction cross sections as well as the Tripathi cross section parameterization for reactions in which the kinetic energy of the projectile in the laboratory frame (T Lab) is greater than 220 MeV/n. The relativistic LS3D model has the additional advantage of being able to predict highly accurate total and elastic cross sections. Consequently, it is recommended that the relativistic LS3D model be used for space radiation applications in which T Lab > 220 MeV/n.
Physics Letters B, 2015
The effects of relativistic kinematics are studied for nuclear collisions of equal mass nuclei. I... more 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 calculation.
Eprint Arxiv Hep Ph 0302228, Feb 25, 2003
We consider the correspondence between solutions of non-gravitational field theories formulated i... more We consider the correspondence between solutions of non-gravitational field theories formulated in Euclidean space-time and Minkowski spacetime. Infinitely many "Euclidean" spaces can be obtained from M 4 via a group of transformations in which the Wick rotation is a special case.
AIP Conference Proceedings, 2007
Using split-quaternions, we find explicit SDYM SU(1, 1) instanton solutions in S 2 − ×S 2 + which... more Using split-quaternions, we find explicit SDYM SU(1, 1) instanton solutions in S 2 − ×S 2 + which is the conformal compactification of the semi-Euclidean 4-spacetime R 2+2 of split-signature (−, −, +, +). The noncompact Lie group SU(1, 1) is naturally introduced as an appropriate gauge group for SDYM instantons in S 2 − × S 2 +. It is shown that SDYM and ASDYM SU(1, 1) instanton solutions in S 2 − × S 2 + lead to the absolute minima of Yang-Mills action and that Yang-Mills action satisfies the same quantization as in SU(2) non-abelian gauge theories in S 4. It is also shown that SDYM and ASDYM field equations in S 2 − × S 2 + can be described as simple split-quaternionic 2-forms.
Two kinds of number density distributions of the nucleus, harmonic well and Woods-Saxon models, a... more 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
The Bethe-Salpeter equation for bound states of a fermion-antifermion pair in the instantaneous a... more The Bethe-Salpeter equation for bound states of a fermion-antifermion pair in the instantaneous approximation for the involved interaction kernel is converted into an equivalent matrix eigenvalue problem with explicitly (algebraically) given matrices.
Unknown, 1988
Methods of solution are presented for the Eikonal form of the nucleus-nucleus coupled-channel sca... more Methods of solution are presented for the Eikonal form of the nucleus-nucleus coupled-channel scattering amplitudes. Analytic solutions are obtained for the second-order optical potential for elastic scattering. A numerical comparison is made between the first ...
Radiation Measurements, 2014
The quality factor is the largest source of uncertainty in space radiation risk assessment. Corre... more The quality factor is the largest source of uncertainty in space radiation risk assessment. Correlated uncertainties reduce uncertainty in the difference of distributions. Correlated quality factors are used to reduce uncertainty in shielding risk assessment.
Physical Review D, 2001
The instantaneous Bethe-Salpeter equation, derived from the general Bethe-Salpeter formalism by a... more 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.
Physical Review D, 2001
The Bethe-Salpeter formalism in the instantaneous approximation for the interaction kernel enteri... more The Bethe-Salpeter formalism in the instantaneous approximation for the interaction kernel entering into the Bethe-Salpeter equation represents a reasonable framework for the description of bound states within relativistic quantum field theory. In contrast to its further simplifications (like, for instance, the so-called reduced Salpeter equation), it allows also the consideration of bound states composed of "light" constituents. Every eigenvalue equation with solutions in some linear space may be (approximately) solved by conversion into an equivalent matrix eigenvalue problem. We demonstrate that the matrices arising in these representations of the instantaneous Bethe-Salpeter equation may be found, at least for a wide class of interactions, in an entirely algebraic manner. The advantages of having the involved matrices explicitly, i.e., not "contaminated" by errors induced by numerical computations, at one's disposal are obvious: problems like, for instance, questions of the stability of eigenvalues may be analyzed more rigorously; furthermore, for small matrix sizes the eigenvalues may even be calculated analytically.
Physical Review D, 1993
Solutions of two-body, bound-state equations have recently been developed for quark-antiquark bou... more Solutions of two-body, bound-state equations have recently been developed for quark-antiquark bound-state pairs. These solutions use a confining potential in momentum space as input into threedimensional reductions of the Bethe-Salpeter equation using special subtraction procedures. Regge trajectories are calculated for the Schrodinger equation which display the well-known unphysical behavior where lower mass trajectories overlap higher mass ones and also display nonlinearity. Both of these features contradict experiment. Regge trajectories obtained from the Thompson equation, which is relativistic in origin, avoid both of these problems.
Physical Review D, 1993
Studies of meson spectroscopy have often employed a non-relativisticCoulomb plus Linear Confining... more Studies of meson spectroscopy have often employed a non-relativisticCoulomb plus Linear Confining potential in position space. However because the quarks in mesons move at an appreciable fractionof the speed of light,itisnecessary 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 singularitiesezactly and thereby solve the Schr_dinger equation in momentum space for all partial waves. Furthermore, we generalize the Linear and Coulomb potentials to relativistickernels in 4-dimensional momentum space. Again we use a subtraction procedure to remove the relativistic singularities exactly for allpartial waves. This enables us to solve 3-dimensional reductions of the Bethe-Salpeter equation. We solve six such equations for Coulomb plus Confining interactionsfor allpartialwaves.
Physical Review C, 1990
(SURA) operates the Continuous Electron Beam Accelerator Facility for the United States Departmen... more (SURA) operates the Continuous Electron Beam Accelerator Facility for the United States Department of Energy under contract DE-AC05-84ER40150. DISCLAIMER This report was prepared as an account of work sponsored by the United States government. Neither the United States nor the United States Department of Energy, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, mark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or any agency thereof.
Physical Review A, 1994
The Lande subtraction method is a technique for removing the singularity which arises when one so... more The Lande subtraction method is a technique for removing the singularity which arises when one solves the Schrodinger equation in momentum space for the Coulomb potential. Using this technique, numerical solutions for eigenvalues and eigenfunctions are presented and compared to exact results. Approximately 50 eigenvalues can be calculated very accurately for various values of the angular momentum. Numerous eigenfunctions can a1so be found very accurately. In addition, it is shown how to implement the Lande subtraction method for potentials which are a linear combination of the Coulomb potential and some other potential. Using a basis-function expansion technique, it is shown how to obtain solutions in those cases where the momentum integrals must be evaluated explicitly.
Canadian Journal of Physics, 1992
A method is presented for the solution in momentum space of the bound-state problem with a linear... more 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.