Michael Haftel - Academia.edu (original) (raw)

Papers by Michael Haftel

Research paper thumbnail of VII International Conference on “Few Body Problems in Nuclear and Particle Physics” December 29, 1975 – January 3, 1976

Research paper thumbnail of Potential-harmonic expansion for atomic wave functions

Research paper thumbnail of THE N-P FSI ANGULAR DISTRIBUTION IN DEUTERON BREAKUP AT 45 MeV

Few Body Dynamics, 1976

Publisher Summary This chapter reviews the N–P Final State Interaction (FSI) angular distribution... more Publisher Summary This chapter reviews the N–P Final State Interaction (FSI) angular distribution in deuteron breakup at 45 MeV. An experiment described in the chapter was performed to provide an FSI angular distribution at energy higher than previously available. The experiment was performed with the NRL Sector Focusing Cyclotron using standard coincidence electronics for kinematically complete experiments. The chapter presents a comparison of the data with the results of calculations using several S-wave separable potentials tailored to test for sensitivity to off-shell and on-shell effects. These potentials have been described previously. The potentials have two different form factors A and B: A has off-shell behavior similar to that of the Reid soft core potential while B has off-shell behavior resembling the softer Yamaguchi. The potentials fit two different sets of phase shifts: set 1 corresponds nearly to experimental p–p 90° cross sections and set 2 corresponds to cross sections less than the p–p experimental values at energies above 10 MeV. The results, when put in the context of previous experiments and calculations, emphasize that there are still some basic factors not being considered in deuteron breakup calculations.

Research paper thumbnail of Approximate Coulomb effects in the three-body scattering problem

Research paper thumbnail of Application of the three-body model to the reactions ⁶Li(³He,t ³He)³He and ⁶Li(³He,³He³He)³H

Experimental and theoretical cross sections are presented for the ⁶Li(³He,³He³He)³H and ⁶... more Experimental and theoretical cross sections are presented for the ⁶Li(³He,³He³He)³H and ⁶Li(³He,t³He)³He reactions for the symmetric angle pairs 20°⁻²°sup 0/, 28.3°-28.3°, and 35°⁻³⁵sup 0/. The theoretical cross sections are calculated in a three-body model where the trions (i.e., mass-3 nuclei) are treated as elementary particles with ⁶Li being a ³He-³H bound state. The trion-trion interaction is represented by S wave

Research paper thumbnail of Three trion breakup of 6Li + 3He at 132 MeV

Lecture Notes in Physics

Without Abstract

Research paper thumbnail of Reply: What Can We Learn from Three-Body Reactions?

Physical Review Letters, 1975

Research paper thumbnail of H2(p,pp)nreaction as a probe of the short-range nuclear force

Research paper thumbnail of p,2p Reactions With Divers Potentials

Physical Review C, 1972

The pp cross sections relevant to a factorized-impulse-approximation treatment of (p, 2p) reactio... more The pp cross sections relevant to a factorized-impulse-approximation treatment of (p, 2p) reactions from 150to 350 MeV are calculated. Several on-shell prescriptions are used and compared with the half-off-shell prescription suggestedby the Faddeev-Watson multiplescattering series. Four phenomenological potentials, Hamada-Johnston, Bryan-Scott III, Reid hard core, and Reid soft core, are investigated as well as three potentials which are phase-shift equivalent to the Reid soft-core potential. We find significant differences ...

Research paper thumbnail of Application of the three-body model to the reactions ^{6}Li(^{3}He,t^{3}He)^{3}He and ^{6}Li(^{3}He, ^{3}He^{3}He)^{3}H

Physical Review C, 1977

Experimental and theoretical cross sections are presented for the 6Li(3He, 3He3He)3H and 6Li(3He,... more Experimental and theoretical cross sections are presented for the 6Li(3He, 3He3He)3H and 6Li(3He,t3He)3He reactions for the symmetric angle pairs 20°-20°, 28.3°-28.3°, and 35°-35°. The theoretical cross sections are calculated in a three-body model where the trions (i.e., mass-3 nuclei) are treated as elementary particles with 6Li being a 3He-3H bound state. The trion-trion interaction is represented by S wave separable

Research paper thumbnail of Off-shell effects in 16O

Nuclear Physics A, 1972

We calculate the binding energy of 16O for a set of phase-shift-equivalent potentials previously ... more We calculate the binding energy of 16O for a set of phase-shift-equivalent potentials previously studied in nuclear matter. Off-shell variations of up to 2.8 MeV per particle occur compared with about a 10 MeV per particle variation in nuclear matter. As in nuclear matter calculations a nearly linear relation exists between the variations in the binding-energy results and the wound integral k. We compare the 16O results with a nuclear matter calculation at the ``equivalent'' nuclear matter density of kF = 1.13 fm-1. This ``equivalent'' density reflects the fact that 16O has a surface and hence a lower average density than nuclear matter. The 16O and nuclear matter off-shell variations are comparable once one takes into account the lower average density of 16O and the suppression of the relative D-wave interaction - also a surface effect. We present a method of computing the correlated wave functions of finite nuclear systems and display such wave functions for 16O. The correlated wave functions of 16O and of nuclear matter are strikingly similar for all of the potentials studied. Supported in part by the Atomic Energy Commission under Contract AT(30-1) 2098.

Research paper thumbnail of The 2H(p, 2p)n reaction at Einc = 45 MeV and its sensitivity to various separable S-wave N-N potentials

Nuclear Physics A, 1976

This paper presents and analyses the data for the 2H(p, pp)n reaction at Einc = 44.9 MeV. Kinemat... more This paper presents and analyses the data for the 2H(p, pp)n reaction at Einc = 44.9 MeV. Kinematic conditions including the quasi-free scattering region and the regions far from quasi-two-body processes are considered. The experimental results are compared with the predictions of several separable S-wave models of the N-N interaction. Potential models that differ only off-shell, as well as models

Research paper thumbnail of Atom–diatom processes in helium: The multiple-scattering description of elastic and dissociative collisions

The Journal of Chemical Physics, 1982

Elastic and dissociative scattering of He on He2 are studied for an incident laboratory energy of... more Elastic and dissociative scattering of He on He2 are studied for an incident laboratory energy of 1 K. We apply Faddeev-AGS multiple-scattering theory in momentum space to the analysis. We show that this leads to a simple justification for the importance of the ‘‘complex-formation mechanism’’ in termolecular recombination, the time reverse of collision-induced dissociation. Our work, in which separable expansions of two phenomenological He–He potentials are used, predicts significant magnitude differences in the cross sections derived from the interactions and also verifies the validity of the ‘‘peaking approximation’’ for hyperthermal-energy elastic collisions.

Research paper thumbnail of The role of vibrational excitations in collision-induced dissociation using Faddeev–AGS theory

The Journal of Chemical Physics, 1986

This paper examines the role of vibrational (and rotational) excitations in collision-induced dis... more This paper examines the role of vibrational (and rotational) excitations in collision-induced dissociation in atom–diatom reactions. We treat a model system of identical, bosonic hydrogen atoms and investigate the total H+H2→H+H+H cross section as functions of total center-of-mass (c.m.) energy and vibrational–rotational quantum numbers v, j. The investigations are based on Faddeev–AGS theory and both three-dimensional (3D) and collinear (one-dimensional, 1D) geometries are considered. We derive both low- and high-energy relations between the total dissociation cross section, c.m. energy, and the vibrational–rotational wave functions, employing the single-scattering approximation of Faddeev theory. We apply these relations to the spectrum of the Kolos–Wolniewicz potential, both in three dimensions and one dimension. For collisions with a fixed total c.m. energy, our investigations predict considerable vibrational enhancement of the total cross section in the low-energy limit, with t...

Research paper thumbnail of Termolecular recombination rate, microscopic reversibility and faddeev theory

Chemical Physics Letters, 1981

ABSTRACT Exact Faddeev theory and microscopic reversibility are applied to the description of ter... more ABSTRACT Exact Faddeev theory and microscopic reversibility are applied to the description of termolecular recombination in a model system of three helium-like atoms. Our results indicate that experimentally determined values of k3(T) can be reproduced.

Research paper thumbnail of Fully converged three-dimensional collision-induced dissociation calculations with Faddeev—AGS theory

Chemical Physics Letters, 1982

Research paper thumbnail of (p, 2p) REACTIONS WITH DIVERS POTENTIALS. Technical Report No. 73-002

Please see Document Availability for additional information on obtaining the full-text document. ... more Please see Document Availability for additional information on obtaining the full-text document. Library patrons may search WorldCat to identify libraries that may hold this item. Keep in mind that many technical reports are not cataloged in WorldCat. ... Select a citation type above to copy/paste or download the reference. ... Some links on this page may take you to non-federal websites. Their policies may differ from this site.

Research paper thumbnail of Off - Shell Effects in Triton Binding - Energy and Form - Factor Calculations

Research paper thumbnail of Electron-deuteron tensor polarization and the two-nucleon force

Physical Review C, 1980

Electron-deuteron scattering observables, including the tensor polarizations T,o, T,+"T,+"are cal... more Electron-deuteron scattering observables, including the tensor polarizations T,o, T,+"T,+"are calculated for a variety of S-N potential models. The main goal is to determine how the tensor polarization experiments can help distinguish competing potential models with respect to off-shell behavior and tensor force strength. The pair meson-exchange-current correction of Gari and Hyuga is included in the analysis as well as a correction suggested by Friar for energy-dependent potentials. It is found that whereas electrondeuteron elastic scattering cross sections do not readily distinguish different potentials, the tensor polarizations do. The tensor polarization T,o mainly distinguishes potentials with different deuteron s-wave momentum distributions, but does not distinguish potentials with different d-state probabilities (PD). The tensor polarization T,+"since it factors essentially into a product of the magnetic and quadrupole form factors, allows for the extraction of the quadrupole form factor which is closely related to the tensor force strength and PD. The tensor polarization T, +, is completely determined by the elastic scattering cross sections and magnetic form factor, and yields no additional information on the N-lV force unobtainable from elastic scattering measurements. The tensor polarizations T,o and T» have maximum values of order unity in the region q = 2 to 5 fm '; The calculations indicate that measurements of T,o for 2&q & 5 fm and T, +, for 3&q &5 fm ' could yield important information on the off-shell behavior and tensor force strength. The meson-exchange-current and energy-dependence corrections are important and must be taken into account to extract potential properties from such experiments. NUCLEAR STHUCTURK H: form factors, tensor polarization calculated: dependence on of'f-shell behavior and &z, seven potential models; pair currents included.

Research paper thumbnail of Fast Convergent Hyperspherical Expansion and Its Application to Precise Nonvariational Atomic Calculations

An efficient method of solving the three-body Schroedinger equation is presented. The wave functi... more An efficient method of solving the three-body Schroedinger equation is presented. The wave function is decomposed into the product of a correlation factor describing the singularity and clustering structure, and a smooth factor expanded in hyperspherical harmonics. The application to the Helium atom yields a ground state energy of 2.9037244 (2.9033052) au for infinite (finite) nuclear mass. The convergence pattern shows that the accuracy of these values is better than a few parts in 14/1

Research paper thumbnail of VII International Conference on “Few Body Problems in Nuclear and Particle Physics” December 29, 1975 – January 3, 1976

Research paper thumbnail of Potential-harmonic expansion for atomic wave functions

Research paper thumbnail of THE N-P FSI ANGULAR DISTRIBUTION IN DEUTERON BREAKUP AT 45 MeV

Few Body Dynamics, 1976

Publisher Summary This chapter reviews the N–P Final State Interaction (FSI) angular distribution... more Publisher Summary This chapter reviews the N–P Final State Interaction (FSI) angular distribution in deuteron breakup at 45 MeV. An experiment described in the chapter was performed to provide an FSI angular distribution at energy higher than previously available. The experiment was performed with the NRL Sector Focusing Cyclotron using standard coincidence electronics for kinematically complete experiments. The chapter presents a comparison of the data with the results of calculations using several S-wave separable potentials tailored to test for sensitivity to off-shell and on-shell effects. These potentials have been described previously. The potentials have two different form factors A and B: A has off-shell behavior similar to that of the Reid soft core potential while B has off-shell behavior resembling the softer Yamaguchi. The potentials fit two different sets of phase shifts: set 1 corresponds nearly to experimental p–p 90° cross sections and set 2 corresponds to cross sections less than the p–p experimental values at energies above 10 MeV. The results, when put in the context of previous experiments and calculations, emphasize that there are still some basic factors not being considered in deuteron breakup calculations.

Research paper thumbnail of Approximate Coulomb effects in the three-body scattering problem

Research paper thumbnail of Application of the three-body model to the reactions ⁶Li(³He,t ³He)³He and ⁶Li(³He,³He³He)³H

Experimental and theoretical cross sections are presented for the ⁶Li(³He,³He³He)³H and ⁶... more Experimental and theoretical cross sections are presented for the ⁶Li(³He,³He³He)³H and ⁶Li(³He,t³He)³He reactions for the symmetric angle pairs 20°⁻²°sup 0/, 28.3°-28.3°, and 35°⁻³⁵sup 0/. The theoretical cross sections are calculated in a three-body model where the trions (i.e., mass-3 nuclei) are treated as elementary particles with ⁶Li being a ³He-³H bound state. The trion-trion interaction is represented by S wave

Research paper thumbnail of Three trion breakup of 6Li + 3He at 132 MeV

Lecture Notes in Physics

Without Abstract

Research paper thumbnail of Reply: What Can We Learn from Three-Body Reactions?

Physical Review Letters, 1975

Research paper thumbnail of H2(p,pp)nreaction as a probe of the short-range nuclear force

Research paper thumbnail of p,2p Reactions With Divers Potentials

Physical Review C, 1972

The pp cross sections relevant to a factorized-impulse-approximation treatment of (p, 2p) reactio... more The pp cross sections relevant to a factorized-impulse-approximation treatment of (p, 2p) reactions from 150to 350 MeV are calculated. Several on-shell prescriptions are used and compared with the half-off-shell prescription suggestedby the Faddeev-Watson multiplescattering series. Four phenomenological potentials, Hamada-Johnston, Bryan-Scott III, Reid hard core, and Reid soft core, are investigated as well as three potentials which are phase-shift equivalent to the Reid soft-core potential. We find significant differences ...

Research paper thumbnail of Application of the three-body model to the reactions ^{6}Li(^{3}He,t^{3}He)^{3}He and ^{6}Li(^{3}He, ^{3}He^{3}He)^{3}H

Physical Review C, 1977

Experimental and theoretical cross sections are presented for the 6Li(3He, 3He3He)3H and 6Li(3He,... more Experimental and theoretical cross sections are presented for the 6Li(3He, 3He3He)3H and 6Li(3He,t3He)3He reactions for the symmetric angle pairs 20°-20°, 28.3°-28.3°, and 35°-35°. The theoretical cross sections are calculated in a three-body model where the trions (i.e., mass-3 nuclei) are treated as elementary particles with 6Li being a 3He-3H bound state. The trion-trion interaction is represented by S wave separable

Research paper thumbnail of Off-shell effects in 16O

Nuclear Physics A, 1972

We calculate the binding energy of 16O for a set of phase-shift-equivalent potentials previously ... more We calculate the binding energy of 16O for a set of phase-shift-equivalent potentials previously studied in nuclear matter. Off-shell variations of up to 2.8 MeV per particle occur compared with about a 10 MeV per particle variation in nuclear matter. As in nuclear matter calculations a nearly linear relation exists between the variations in the binding-energy results and the wound integral k. We compare the 16O results with a nuclear matter calculation at the ``equivalent'' nuclear matter density of kF = 1.13 fm-1. This ``equivalent'' density reflects the fact that 16O has a surface and hence a lower average density than nuclear matter. The 16O and nuclear matter off-shell variations are comparable once one takes into account the lower average density of 16O and the suppression of the relative D-wave interaction - also a surface effect. We present a method of computing the correlated wave functions of finite nuclear systems and display such wave functions for 16O. The correlated wave functions of 16O and of nuclear matter are strikingly similar for all of the potentials studied. Supported in part by the Atomic Energy Commission under Contract AT(30-1) 2098.

Research paper thumbnail of The 2H(p, 2p)n reaction at Einc = 45 MeV and its sensitivity to various separable S-wave N-N potentials

Nuclear Physics A, 1976

This paper presents and analyses the data for the 2H(p, pp)n reaction at Einc = 44.9 MeV. Kinemat... more This paper presents and analyses the data for the 2H(p, pp)n reaction at Einc = 44.9 MeV. Kinematic conditions including the quasi-free scattering region and the regions far from quasi-two-body processes are considered. The experimental results are compared with the predictions of several separable S-wave models of the N-N interaction. Potential models that differ only off-shell, as well as models

Research paper thumbnail of Atom–diatom processes in helium: The multiple-scattering description of elastic and dissociative collisions

The Journal of Chemical Physics, 1982

Elastic and dissociative scattering of He on He2 are studied for an incident laboratory energy of... more Elastic and dissociative scattering of He on He2 are studied for an incident laboratory energy of 1 K. We apply Faddeev-AGS multiple-scattering theory in momentum space to the analysis. We show that this leads to a simple justification for the importance of the ‘‘complex-formation mechanism’’ in termolecular recombination, the time reverse of collision-induced dissociation. Our work, in which separable expansions of two phenomenological He–He potentials are used, predicts significant magnitude differences in the cross sections derived from the interactions and also verifies the validity of the ‘‘peaking approximation’’ for hyperthermal-energy elastic collisions.

Research paper thumbnail of The role of vibrational excitations in collision-induced dissociation using Faddeev–AGS theory

The Journal of Chemical Physics, 1986

This paper examines the role of vibrational (and rotational) excitations in collision-induced dis... more This paper examines the role of vibrational (and rotational) excitations in collision-induced dissociation in atom–diatom reactions. We treat a model system of identical, bosonic hydrogen atoms and investigate the total H+H2→H+H+H cross section as functions of total center-of-mass (c.m.) energy and vibrational–rotational quantum numbers v, j. The investigations are based on Faddeev–AGS theory and both three-dimensional (3D) and collinear (one-dimensional, 1D) geometries are considered. We derive both low- and high-energy relations between the total dissociation cross section, c.m. energy, and the vibrational–rotational wave functions, employing the single-scattering approximation of Faddeev theory. We apply these relations to the spectrum of the Kolos–Wolniewicz potential, both in three dimensions and one dimension. For collisions with a fixed total c.m. energy, our investigations predict considerable vibrational enhancement of the total cross section in the low-energy limit, with t...

Research paper thumbnail of Termolecular recombination rate, microscopic reversibility and faddeev theory

Chemical Physics Letters, 1981

ABSTRACT Exact Faddeev theory and microscopic reversibility are applied to the description of ter... more ABSTRACT Exact Faddeev theory and microscopic reversibility are applied to the description of termolecular recombination in a model system of three helium-like atoms. Our results indicate that experimentally determined values of k3(T) can be reproduced.

Research paper thumbnail of Fully converged three-dimensional collision-induced dissociation calculations with Faddeev—AGS theory

Chemical Physics Letters, 1982

Research paper thumbnail of (p, 2p) REACTIONS WITH DIVERS POTENTIALS. Technical Report No. 73-002

Please see Document Availability for additional information on obtaining the full-text document. ... more Please see Document Availability for additional information on obtaining the full-text document. Library patrons may search WorldCat to identify libraries that may hold this item. Keep in mind that many technical reports are not cataloged in WorldCat. ... Select a citation type above to copy/paste or download the reference. ... Some links on this page may take you to non-federal websites. Their policies may differ from this site.

Research paper thumbnail of Off - Shell Effects in Triton Binding - Energy and Form - Factor Calculations

Research paper thumbnail of Electron-deuteron tensor polarization and the two-nucleon force

Physical Review C, 1980

Electron-deuteron scattering observables, including the tensor polarizations T,o, T,+"T,+"are cal... more Electron-deuteron scattering observables, including the tensor polarizations T,o, T,+"T,+"are calculated for a variety of S-N potential models. The main goal is to determine how the tensor polarization experiments can help distinguish competing potential models with respect to off-shell behavior and tensor force strength. The pair meson-exchange-current correction of Gari and Hyuga is included in the analysis as well as a correction suggested by Friar for energy-dependent potentials. It is found that whereas electrondeuteron elastic scattering cross sections do not readily distinguish different potentials, the tensor polarizations do. The tensor polarization T,o mainly distinguishes potentials with different deuteron s-wave momentum distributions, but does not distinguish potentials with different d-state probabilities (PD). The tensor polarization T,+"since it factors essentially into a product of the magnetic and quadrupole form factors, allows for the extraction of the quadrupole form factor which is closely related to the tensor force strength and PD. The tensor polarization T, +, is completely determined by the elastic scattering cross sections and magnetic form factor, and yields no additional information on the N-lV force unobtainable from elastic scattering measurements. The tensor polarizations T,o and T» have maximum values of order unity in the region q = 2 to 5 fm '; The calculations indicate that measurements of T,o for 2&q & 5 fm and T, +, for 3&q &5 fm ' could yield important information on the off-shell behavior and tensor force strength. The meson-exchange-current and energy-dependence corrections are important and must be taken into account to extract potential properties from such experiments. NUCLEAR STHUCTURK H: form factors, tensor polarization calculated: dependence on of'f-shell behavior and &z, seven potential models; pair currents included.

Research paper thumbnail of Fast Convergent Hyperspherical Expansion and Its Application to Precise Nonvariational Atomic Calculations

An efficient method of solving the three-body Schroedinger equation is presented. The wave functi... more An efficient method of solving the three-body Schroedinger equation is presented. The wave function is decomposed into the product of a correlation factor describing the singularity and clustering structure, and a smooth factor expanded in hyperspherical harmonics. The application to the Helium atom yields a ground state energy of 2.9037244 (2.9033052) au for infinite (finite) nuclear mass. The convergence pattern shows that the accuracy of these values is better than a few parts in 14/1