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Physics Faculty Research & Creative Works

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Approximation theory

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Full-Text Articles in Physics

(E,2e) Measurements On Xenon: Reexamination Of The Fine-Structure Effect, Radmila Panajotovic, Julian C A Lower, Erich Weigold, A. Prideaux, Don H. Madison May 2006

(E,2e) Measurements On Xenon: Reexamination Of The Fine-Structure Effect, Radmila Panajotovic, Julian C A Lower, Erich Weigold, A. Prideaux, Don H. Madison

Physics Faculty Research & Creative Works

The process of electron scattering from heavy target atoms is of considerable interest due to the enhanced role of relativistic effects and distortion of the electron trajectories resulting from the large value of nuclear charge. Here we present (e,2e) ionization measurements and distorted-wave Born approximation calculations for the scattering of spin-polarized electrons from xenon atoms in which the fine-structure levels of the residual ion are resolved. Comparison of measurements performed using a high-sensitivity toroidal analyzer spectrometer with the predictions of sophisticated calculations provide an improved understanding of the ionization dynamics of heavy target atoms and the treatment of electron exchange …


Kinetics Of Binary Nucleation Of Vapors In Size And Composition Space, Sergey P. Fisenko, Gerald Wilemski Jan 2004

Kinetics Of Binary Nucleation Of Vapors In Size And Composition Space, Sergey P. Fisenko, Gerald Wilemski

Physics Faculty Research & Creative Works

We reformulate the kinetic description of binary nucleation in the gas phase using two natural independent variables: the total number of molecules g and the molar composition x of the cluster. The resulting kinetic equation can be viewed as a two-dimensional Fokker-Planck equation describing the simultaneous Brownian motion of the clusters in size and composition space. Explicit expressions for the Brownian diffusion coefficients in cluster size and composition space are obtained. For characterization of binary nucleation in gases three criteria are established. These criteria establish the relative importance of the rate processes in cluster size and composition space for different …


Probing Scattering Wave Functions Close To The Nucleus, Don H. Madison, Daniel Fischer, Matthew S. Foster, Michael Schulz, Robert Moshammer, Stephenie J. Jones, Joachim Hermann Ullrich Dec 2003

Probing Scattering Wave Functions Close To The Nucleus, Don H. Madison, Daniel Fischer, Matthew S. Foster, Michael Schulz, Robert Moshammer, Stephenie J. Jones, Joachim Hermann Ullrich

Physics Faculty Research & Creative Works

Recently, three-dimensional imaging of the ejected electrons following 100  MeV/amu C6+ single ionization of helium led to the observation of a new structure not predicted by theory [M. Schulz et al., Nature (London) 422, 48 (2003)]. Instead of the usual “recoil lobe” centered on the momentum-transfer axis, a ring-shaped structure centered on the beam axis was observed. New measurements at 2  MeV/amu exhibit a similar structure, which is now predicted by theory. We argue that the same theory failed at 100  MeV/amu because the faster projectiles probe distances much closer to the nucleus, where our multiple-scattering model is expected …


Slow Convergence Of The Born Approximation For Electron-Atom Ionization, Stephenie J. Jones, Don H. Madison Dec 2002

Slow Convergence Of The Born Approximation For Electron-Atom Ionization, Stephenie J. Jones, Don H. Madison

Physics Faculty Research & Creative Works

It is usually assumed that the first-Born approximation for electron-atom ionization becomes valid for the fully differential cross section at sufficiently high impact energies, at least for asymmetric collisions where the projectile suffers only a small energy loss and is scattered by a small angle. Here we investigate this assumption quantitatively for ionization of hydrogen atoms. We find that convergence of the Born approximation to the correct nonrelativistic result is generally achieved only at energies where relativistic effects start to become important. Consequently, the assumption that the Born approximation becomes valid for high energy is inaccurate, since by the time …


Differential Cross Sections And Cross-Section Ratios For The Electron-Impact Excitation Of The Neon 2p⁵3s Configuration, Murtadha A. Khakoo, James M. Wrkich, Mary Lu Larsen, G. Kleiban, Isik Kanik, Sandor Trajmar, Michael J. Brunger, P. J O Teubner, Albert Crowe, Christopher J. Fontes, Robert E H Clark, Vlado Zeman, Klaus Bartschat, Don H. Madison, Rajesh C. Srivastava, Allan Daniel Stauffer Jun 2002

Differential Cross Sections And Cross-Section Ratios For The Electron-Impact Excitation Of The Neon 2p⁵3s Configuration, Murtadha A. Khakoo, James M. Wrkich, Mary Lu Larsen, G. Kleiban, Isik Kanik, Sandor Trajmar, Michael J. Brunger, P. J O Teubner, Albert Crowe, Christopher J. Fontes, Robert E H Clark, Vlado Zeman, Klaus Bartschat, Don H. Madison, Rajesh C. Srivastava, Allan Daniel Stauffer

Physics Faculty Research & Creative Works

Electron-impact differential cross-section measurements for the excitation of the 2p53s configuration of Ne are reported. The Ne cross sections are obtained using experimental differential cross sections for the electron-impact excitation of the n = 2 levels of atomic hydrogen [Khakoo et al., Phys. Rev. A 61, 012701-1 (1999)], and existing experimental helium differential cross-section measurements, as calibration standards. These calibration measurements were made using the method of gas mixtures (Ne and H followed by Ne and He), in which the gas beam profiles of the mixed gases are found to be the same within our experimental errors. We …


Doubly Differential Electron-Emission Spectra In Single And Multiple Ionization Of Noble-Gas Atoms By Fast Highly-Charged-Ion Impact, Tom Kirchner, Laszlo Gulyas, Robert Moshammer, Michael Schulz, Joachim Hermann Ullrich Apr 2002

Doubly Differential Electron-Emission Spectra In Single And Multiple Ionization Of Noble-Gas Atoms By Fast Highly-Charged-Ion Impact, Tom Kirchner, Laszlo Gulyas, Robert Moshammer, Michael Schulz, Joachim Hermann Ullrich

Physics Faculty Research & Creative Works

Low-energy electron emission spectra are studied in collisions of 3.6 MeV/amu Au53+ ions with neon and argon atoms for well-defined degrees of target ionization. We calculate doubly differential cross sections as functions of the recoil-ion charge state in the continuum-distorted-wave with eikonal initial-state approximation using a binomial analysis of the total and differential ionization probabilities, and compare them with the present and with previously published experimental data. Very good agreement is found for the single-ionization spectra and for double ionization of neon, while some discrepancies are observed in the spectra for double and triple ionization of argon.


Three-Body Coulomb Problem Probed By Mapping The Bethe Surface In Ionizing Ion-Atom Collisions, Robert Moshammer, Appathurai N. Perumal, Michael Schulz, V. D. Rodriguez, Holger Kollmus, Rido Mann, Siegbert Hagmann, Joachim Hermann Ullrich Nov 2001

Three-Body Coulomb Problem Probed By Mapping The Bethe Surface In Ionizing Ion-Atom Collisions, Robert Moshammer, Appathurai N. Perumal, Michael Schulz, V. D. Rodriguez, Holger Kollmus, Rido Mann, Siegbert Hagmann, Joachim Hermann Ullrich

Physics Faculty Research & Creative Works

The three-body Coulomb problem has been explored in kinematically complete experiments on single ionization of helium by 100 MeV / u C 6 + and 3.6 MeV / u u 5 3 + impact. Low-energy electron emission (E e < 150 eV ) as a function of the projectile deflection ϑ p (momentum transfer), i.e., the Bethe surface [[15]], has been mapped with Δ ϑ p ± 25 nanoradian resolution at extremely large perturbations (3.6 MeV / uAu53+ ) where single ionization occurs at impact parameters of typically 10 times the He K -shell radius. The experimental data are not in agreement with state-of-the-art continuum distorted wave-eikonal initial state theory.


Strong Enhancement Of Superconducting TC In Ferromagnetic Phases, Theodore R. Kirkpatrick, Dietrich Belitz, Thomas Vojta, Rajesh S. Narayanan Sep 2001

Strong Enhancement Of Superconducting TC In Ferromagnetic Phases, Theodore R. Kirkpatrick, Dietrich Belitz, Thomas Vojta, Rajesh S. Narayanan

Physics Faculty Research & Creative Works

It is shown that the critical temperature for spin-triplet, p-wave superconductivity mediated by spin fluctuations is generically much higher in a Heisenberg ferromagnetic phase than in a paramagnetic one, due to the coupling of the magnons to the longitudinal magnetic susceptibility. Together with the tendency of the low-temperature ferromagnetic transition in very clean Heisenberg magnets to be of first order, this qualitatively explains the phase diagram recently observed in UGe2.


Ionization Of Hydrogen Atoms By Fast Electrons, Sindu P. Jones, Don H. Madison Oct 2000

Ionization Of Hydrogen Atoms By Fast Electrons, Sindu P. Jones, Don H. Madison

Physics Faculty Research & Creative Works

We study ionization of atomic hydrogen by fast electrons using asymptotically correct two-center wave functions to describe the scattering system both initially and finally. For the final state, we employ the well-known product wave function of Redmond, which treats all three two-body Coulomb interactions exactly, albeit independently. This "3C" wave function is the leading term of the exact scattering wave function, regardless of how slow the three particles are, if any two particles have large relative separation [Y.E. Kim and A.L. Zubarev, Phys. Rev. A 56, 521 (1997)]. Here we extend the analysis of Qiu et al. [Phys. Rev. A …


Do Interactions Increase Or Reduce The Conductance Of Disordered Electrons? It Depends!, Thomas Vojta, Frank Epperlein, Michael Schreiber Nov 1998

Do Interactions Increase Or Reduce The Conductance Of Disordered Electrons? It Depends!, Thomas Vojta, Frank Epperlein, Michael Schreiber

Physics Faculty Research & Creative Works

We investigate the influence of electron-electron interactions on the conductance of two-dimensional disordered spinless electrons. We present an efficient numerical method based on diagonalization in a truncated basis of Hartree-Fock states to determine with high accuracy the low-energy properties in the entire parameter space. We find that weak interactions increase the dc conductance in the strongly localized regime while they decrease the dc conductance for weak disorder. Strong interactions always decrease the conductance. We also study the localization of single-particle excitations at the Fermi energy which turns out to be only weakly influenced by the interactions.


Chaotic Behavior And Damage Spreading In The Glauber Ising Model: A Master Equation Approach, Thomas Vojta May 1997

Chaotic Behavior And Damage Spreading In The Glauber Ising Model: A Master Equation Approach, Thomas Vojta

Physics Faculty Research & Creative Works

We investigate the sensitivity of the time evolution of a kinetic Ising model with Glauber dynamics against the initial conditions. To do so we apply the "damage spreading" method, i.e., we study the simultaneous evolution of two identical systems subjected to the same thermal noise. We derive a master equation for the joint probability distribution of the two systems. We then solve this master equation within an effective-field approximation which goes beyond the usual mean-field approximation by retaining the fluctuations though in a quite simplistic manner. The resulting effective-field theory is applied to different physical situations. It is used to …