Prof.Hafez M Abdel Radi | Modern Science and Arts (MSA) university (original) (raw)

Uploads

Papers by Prof.Hafez M Abdel Radi

Physical Review A, 1975

Nonrelativistic wave functions and energy values for the ground state of helium are calculated ac... more Nonrelativistic wave functions and energy values for the ground state of helium are calculated accurately by using the conventional Rayleigh-Ritz technique. However, the trial wave functions used are more general than those used by Hylleraas and others. They contain interelectronic separation coordinates in the exponential function beside the variational parameters. Groups of threeand four-parameter wave functions are obtained with comparatively smaller energies. Also, improved wave functions and energies have been obtained by solving determinants of orders 7, 13, 22, 34, 50, 70, 95, and 125, using a simple model. The last determinant yields an energy value of-2.903 724 371 a.u. as compared with-2.903 724 370 a.u. obtained by Pekeris by solving a determinant of order 715. The first determinant (ten parameters) yields an energy value of ,-2.903425 858 a.u. , as compared with the recent value of-2.9022 a.u. computed by Tweed with the use of a 41-parameter wave function.

Journal of Physics B: Atomic and Molecular Physics, 1974

The Kohn variational method has been applied to the zero energy positron-helium collisions. Resul... more The Kohn variational method has been applied to the zero energy positron-helium collisions. Results show that singularity persists in scattering length values, for variant IV of Peterkop and Rabik (1971), which may suggest that this method is not, after all, reliable.

Physics Letters A, 1973

A variational calculation with a trial wave function including up to 17 parameters has been used ... more A variational calculation with a trial wave function including up to 17 parameters has been used to investigate the existence of a positron-helium bound state. The resulting binding energy was found to be greater than the helium binding energy, and thus it is believed that the positron does not get bound to a helium atom. The calculations provide also values of ground state helium energy and the corresponding wave functions.

Physical Review C, 1983

Monte Carlo studies of pion distributions from heavy ion collisions

Physical Review C, 1982

To compare with the wealth of new data on alpha-accompanied fission of 236U* we have made new tra... more To compare with the wealth of new data on alpha-accompanied fission of 236U* we have made new trajectory calculations. Initial conditions for several parameters were selected from Gaussian distributions by the Monte Carlo method and about 15,000 trajectories were run for alpha source at the electrostatic saddle point. Momentum and energy are fully conserved in the three-body problem, though the usual point charge approximation without nuclear forces was used. The main calculations center the alpha source at the electrostatic saddle. General agreement with experiment is remarkable including even the appearance of low-energy secondary peaks at large angles. Effects of shiftingthe source from the saddle point toward either fragment are studied, running an additional 15,000 trajectories for each of two shifts. Both the satellite peak phenomena and the angular distribution indicate the need for a small shift of source toward the light fragment.-Keyword abstract: NUCLEAR REACTIONS. Alpha accompanied thermal neutron ternary fission 235 U(n,f). Monte Carlo theory; trajectory calculations; ct-particle angular-and energy distributions.

Physical Review C, 1982

Coulomb effects on heavy-ion pion production cross sections are formulated in terms of weighted a... more Coulomb effects on heavy-ion pion production cross sections are formulated in terms of weighted averaging over various projectile fragments. Satisfactory fits to zero-degree pion data are found for Ar + C and Ne + C systems. The fragment distributions of excited compound nuclei, before nucleon evaporation, must be used, and the fragment velocity dispersion parameter needed is smaller than that measured for fragments after nucleon evaporation. Average charge Zeff values are determined and compared with those from an experimental paper. In the heavy-ion energy range of the Oo pion studies (300 MeV~ E/A ~ 600 MeV), it is inferred that target-projectile factorization for fragmentation cross sections does not hold.

Computer Physics Communications, 1984

ABSTRACT

Physical Review C, 1989

Lorentz-invariant cross sections for the production of ..pi..°, ..pi../sup +/, and ..pi..⁻ hav... more Lorentz-invariant cross sections for the production of ..pi..°, ..pi../sup +/, and ..pi..⁻ have been investigated, for the pion c.m. momentum range 0--0.5 GeV/c at angles 0°⁻⁻⁹°sup 0/, by Monte Carlo methods for grazing nuclear collisions of ²°⁷Pb+²°⁷Pb at 0.4 GeV/nucleon. Pions are considered to be produced isotropically at the center of mass at closest approach at random from a Gaussian momentum distribution. The pion equations of motion are solved including the electromagnetic effects due to the projectile and target ²°⁷Pb nuclei. The trajectory calculations differ from some earlier theoretical work in that pions are considered to scatter from the surface of, and propagate within, a spectator fragment. After surface scattering, the trajectory calculations continue but are weighted by the pion reflectivity. For that purpose, a model developed by Mehrem et al., for the relativistic oblique incidence of pions on nuclear matter represented by a uniform complex nuclear potential, has been used to evaluate the pion reflectivity for the three types of pions.

In the simplest model of an ideal gas, which was presented in the previous chapter, we consider e... more In the simplest model of an ideal gas, which was presented in the previous chapter, we consider each atom/molecule to be a hard sphere that collides elastically with other atoms/molecules or with the walls of the container holding the gas.

We find it possible to obtain a formal complex refractive index that depends on r, k 0 , and k•r ... more We find it possible to obtain a formal complex refractive index that depends on r, k 0 , and k•r for the pion-nucleus interaction in terms of a full pion-nucleus optical potential operator including the Lorentz-Lorenz effect and p 2 (r) terms. The proton. and neutron densities are taken as Woods-Saxon form. Numerical calculations are made for a radial propagation of a pion approaching a lanthanum (A=139, Z=57) with different energies. The real and imaginary refractive index (which are related to the complex pion wave number), the optical potential, and the absorption probability density are displayed as a function of r.

Part 1: Fundamental Basics.- Units and Dimensions.- Vectors.- Part 2: Mechanics.- Motion in One D... more Part 1: Fundamental Basics.- Units and Dimensions.- Vectors.- Part 2: Mechanics.- Motion in One Dimension.- Motion in Two Dimensions.- Force and Motion.- Work, Energy, Momentum, Power, Gravitation.- Mechanical Properties of Matter.- Part 3: Thermodynamics.- Heat and the Laws of Thermodynamics.- Thermal Properties of Matter.- Kinetic Theory of Gases.- Part 4: Sound and Light Waves.- Oscillations and Wave Motion.- Sound Waves.- Superposition of Sound Waves.- Light Waves and Optics.- Interference, Diffraction, and Polarization of Light.- Part 5: Electricity.- Electric Force and Fields.- Gauss's Law.- Electric Potential.- Capacitors and Capacitance.- Electric Circuits.- Part 6: Magnetism.- Magnetic Field.- Sources of the Magnetic Field.- Faraday's Law.- Inductance.

Applied Mathematics & Information Sciences

This article proves that speed of light in all uniformly moving inertial reference frames is abso... more This article proves that speed of light in all uniformly moving inertial reference frames is absolute as postulated by Einstein. This is first done by considering light propagating with a speed c in all directions in an inertial frame of reference. If that frame is moving uniformly with a speed v relative to a second stationary inertial frame, we assume that light in the second frame is propagating in all directions with a different speed c= c. Consequently, modified transformation Equations are formed. The established Poincaré ellipsoidal light waves are then used to find the Equation that governs the relation of  at any speed v. The analytical solution and numerical calculations to this equation yield a value  =1. This proves that speed of light propagates through empty space with speed c independent of the speed of the light source or the observer.

It has been known for over two years now that the ..pi../sup -/ spectrum from heavy ion collision... more It has been known for over two years now that the ..pi../sup -/ spectrum from heavy ion collisions peaks near beam velocity and that the ..pi../sup +/ spectrum has a corresponding depression. It has been guessed that these features are Coulomb effects of projectile fragments. A theoretical treatment of this phenomena is given, and results are compared with experimental data. (WHK)

Journal of Physics B: Atomic and Molecular Physics

ABSTRACT

Physical Review C

Numerical semi-classical calculations are carried out to study the angular distribution of deuter... more Numerical semi-classical calculations are carried out to study the angular distribution of deuterons from the p,d pickup reaction of 25 MeV protons incident on the nucleus 156 Gd and also its proton elastic scattering. It is found that, due to the rapid fall of the real optical potential in the vicinity of the target nucleus, the classical trajectories are very sensitive to the proton impact parameters. A selection of 276,983 trajectories is used for protons with impact parameters p b satisfying p 7.23018 f m 10 f m b ≤ ≤ with steps of 5 10 f m −. Using the imaginary part of the optical potential for protons, a simple quantum approach is constructed to evaluate the probability of a surviving proton throughout its path. In addition, a simple three-body quantum approach is developed to calculate the probability of a neutron transfer by a surviving proton at closest approach. The formed deuteron is then allowed to start its trajectory while keeping its identity until detected. Throughout this journey, the deuteron trajectory is under the influence of its Coulomb and real optical potential, while its absorption is determined by the imaginary optical potential component. Within estimated uncertainties, the resulting theoretical angular distribution achieves a comparable fit with experimental results for the angular momentum transfer L=0 compared to other theoretical models, and concludes that the strong p,d cross sections are due to the dominant s 1/2 component of the Nilsson 1 2 + [400] level in 155 Gd.

Undergraduate Lecture Notes in Physics, 2012

ABSTRACT

Undergraduate Lecture Notes in Physics, 2012

Physical Review A, 1975

Nonrelativistic wave functions and energy values for the ground state of helium are calculated ac... more Nonrelativistic wave functions and energy values for the ground state of helium are calculated accurately by using the conventional Rayleigh-Ritz technique. However, the trial wave functions used are more general than those used by Hylleraas and others. They contain interelectronic separation coordinates in the exponential function beside the variational parameters. Groups of threeand four-parameter wave functions are obtained with comparatively smaller energies. Also, improved wave functions and energies have been obtained by solving determinants of orders 7, 13, 22, 34, 50, 70, 95, and 125, using a simple model. The last determinant yields an energy value of-2.903 724 371 a.u. as compared with-2.903 724 370 a.u. obtained by Pekeris by solving a determinant of order 715. The first determinant (ten parameters) yields an energy value of ,-2.903425 858 a.u. , as compared with the recent value of-2.9022 a.u. computed by Tweed with the use of a 41-parameter wave function.

Journal of Physics B: Atomic and Molecular Physics, 1974

The Kohn variational method has been applied to the zero energy positron-helium collisions. Resul... more The Kohn variational method has been applied to the zero energy positron-helium collisions. Results show that singularity persists in scattering length values, for variant IV of Peterkop and Rabik (1971), which may suggest that this method is not, after all, reliable.

Physics Letters A, 1973

A variational calculation with a trial wave function including up to 17 parameters has been used ... more A variational calculation with a trial wave function including up to 17 parameters has been used to investigate the existence of a positron-helium bound state. The resulting binding energy was found to be greater than the helium binding energy, and thus it is believed that the positron does not get bound to a helium atom. The calculations provide also values of ground state helium energy and the corresponding wave functions.

Physical Review C, 1983

Monte Carlo studies of pion distributions from heavy ion collisions

Physical Review C, 1982

To compare with the wealth of new data on alpha-accompanied fission of 236U* we have made new tra... more To compare with the wealth of new data on alpha-accompanied fission of 236U* we have made new trajectory calculations. Initial conditions for several parameters were selected from Gaussian distributions by the Monte Carlo method and about 15,000 trajectories were run for alpha source at the electrostatic saddle point. Momentum and energy are fully conserved in the three-body problem, though the usual point charge approximation without nuclear forces was used. The main calculations center the alpha source at the electrostatic saddle. General agreement with experiment is remarkable including even the appearance of low-energy secondary peaks at large angles. Effects of shiftingthe source from the saddle point toward either fragment are studied, running an additional 15,000 trajectories for each of two shifts. Both the satellite peak phenomena and the angular distribution indicate the need for a small shift of source toward the light fragment.-Keyword abstract: NUCLEAR REACTIONS. Alpha accompanied thermal neutron ternary fission 235 U(n,f). Monte Carlo theory; trajectory calculations; ct-particle angular-and energy distributions.

Physical Review C, 1982

Coulomb effects on heavy-ion pion production cross sections are formulated in terms of weighted a... more Coulomb effects on heavy-ion pion production cross sections are formulated in terms of weighted averaging over various projectile fragments. Satisfactory fits to zero-degree pion data are found for Ar + C and Ne + C systems. The fragment distributions of excited compound nuclei, before nucleon evaporation, must be used, and the fragment velocity dispersion parameter needed is smaller than that measured for fragments after nucleon evaporation. Average charge Zeff values are determined and compared with those from an experimental paper. In the heavy-ion energy range of the Oo pion studies (300 MeV~ E/A ~ 600 MeV), it is inferred that target-projectile factorization for fragmentation cross sections does not hold.

Computer Physics Communications, 1984

ABSTRACT

Physical Review C, 1989

Lorentz-invariant cross sections for the production of ..pi..°, ..pi../sup +/, and ..pi..⁻ hav... more Lorentz-invariant cross sections for the production of ..pi..°, ..pi../sup +/, and ..pi..⁻ have been investigated, for the pion c.m. momentum range 0--0.5 GeV/c at angles 0°⁻⁻⁹°sup 0/, by Monte Carlo methods for grazing nuclear collisions of ²°⁷Pb+²°⁷Pb at 0.4 GeV/nucleon. Pions are considered to be produced isotropically at the center of mass at closest approach at random from a Gaussian momentum distribution. The pion equations of motion are solved including the electromagnetic effects due to the projectile and target ²°⁷Pb nuclei. The trajectory calculations differ from some earlier theoretical work in that pions are considered to scatter from the surface of, and propagate within, a spectator fragment. After surface scattering, the trajectory calculations continue but are weighted by the pion reflectivity. For that purpose, a model developed by Mehrem et al., for the relativistic oblique incidence of pions on nuclear matter represented by a uniform complex nuclear potential, has been used to evaluate the pion reflectivity for the three types of pions.

In the simplest model of an ideal gas, which was presented in the previous chapter, we consider e... more In the simplest model of an ideal gas, which was presented in the previous chapter, we consider each atom/molecule to be a hard sphere that collides elastically with other atoms/molecules or with the walls of the container holding the gas.

We find it possible to obtain a formal complex refractive index that depends on r, k 0 , and k•r ... more We find it possible to obtain a formal complex refractive index that depends on r, k 0 , and k•r for the pion-nucleus interaction in terms of a full pion-nucleus optical potential operator including the Lorentz-Lorenz effect and p 2 (r) terms. The proton. and neutron densities are taken as Woods-Saxon form. Numerical calculations are made for a radial propagation of a pion approaching a lanthanum (A=139, Z=57) with different energies. The real and imaginary refractive index (which are related to the complex pion wave number), the optical potential, and the absorption probability density are displayed as a function of r.

Part 1: Fundamental Basics.- Units and Dimensions.- Vectors.- Part 2: Mechanics.- Motion in One D... more Part 1: Fundamental Basics.- Units and Dimensions.- Vectors.- Part 2: Mechanics.- Motion in One Dimension.- Motion in Two Dimensions.- Force and Motion.- Work, Energy, Momentum, Power, Gravitation.- Mechanical Properties of Matter.- Part 3: Thermodynamics.- Heat and the Laws of Thermodynamics.- Thermal Properties of Matter.- Kinetic Theory of Gases.- Part 4: Sound and Light Waves.- Oscillations and Wave Motion.- Sound Waves.- Superposition of Sound Waves.- Light Waves and Optics.- Interference, Diffraction, and Polarization of Light.- Part 5: Electricity.- Electric Force and Fields.- Gauss's Law.- Electric Potential.- Capacitors and Capacitance.- Electric Circuits.- Part 6: Magnetism.- Magnetic Field.- Sources of the Magnetic Field.- Faraday's Law.- Inductance.

Applied Mathematics & Information Sciences

This article proves that speed of light in all uniformly moving inertial reference frames is abso... more This article proves that speed of light in all uniformly moving inertial reference frames is absolute as postulated by Einstein. This is first done by considering light propagating with a speed c in all directions in an inertial frame of reference. If that frame is moving uniformly with a speed v relative to a second stationary inertial frame, we assume that light in the second frame is propagating in all directions with a different speed c= c. Consequently, modified transformation Equations are formed. The established Poincaré ellipsoidal light waves are then used to find the Equation that governs the relation of  at any speed v. The analytical solution and numerical calculations to this equation yield a value  =1. This proves that speed of light propagates through empty space with speed c independent of the speed of the light source or the observer.

It has been known for over two years now that the ..pi../sup -/ spectrum from heavy ion collision... more It has been known for over two years now that the ..pi../sup -/ spectrum from heavy ion collisions peaks near beam velocity and that the ..pi../sup +/ spectrum has a corresponding depression. It has been guessed that these features are Coulomb effects of projectile fragments. A theoretical treatment of this phenomena is given, and results are compared with experimental data. (WHK)

Journal of Physics B: Atomic and Molecular Physics

ABSTRACT

Physical Review C

Numerical semi-classical calculations are carried out to study the angular distribution of deuter... more Numerical semi-classical calculations are carried out to study the angular distribution of deuterons from the p,d pickup reaction of 25 MeV protons incident on the nucleus 156 Gd and also its proton elastic scattering. It is found that, due to the rapid fall of the real optical potential in the vicinity of the target nucleus, the classical trajectories are very sensitive to the proton impact parameters. A selection of 276,983 trajectories is used for protons with impact parameters p b satisfying p 7.23018 f m 10 f m b ≤ ≤ with steps of 5 10 f m −. Using the imaginary part of the optical potential for protons, a simple quantum approach is constructed to evaluate the probability of a surviving proton throughout its path. In addition, a simple three-body quantum approach is developed to calculate the probability of a neutron transfer by a surviving proton at closest approach. The formed deuteron is then allowed to start its trajectory while keeping its identity until detected. Throughout this journey, the deuteron trajectory is under the influence of its Coulomb and real optical potential, while its absorption is determined by the imaginary optical potential component. Within estimated uncertainties, the resulting theoretical angular distribution achieves a comparable fit with experimental results for the angular momentum transfer L=0 compared to other theoretical models, and concludes that the strong p,d cross sections are due to the dominant s 1/2 component of the Nilsson 1 2 + [400] level in 155 Gd.

Undergraduate Lecture Notes in Physics, 2012

ABSTRACT

Undergraduate Lecture Notes in Physics, 2012