Physical Sciences and Mathematics Commons^™

Progenitors, Symmetric Presentations, And Related Topics, Joana Viridiana Luna

Electronic Theses, Projects, and Dissertations

Abstract

A progenitor developed by Robert T. Curtis is a type of infinite groups formed by the semi-direct product of a free group m∗n and a transitive permutation group of degree n. To produce finite homomorphic images we had to add relations to the progenitor of the form 2∗n : N. In this thesis we have investigated several permutations progenitors and monomials, 2∗12 : S4, 2∗12 : S4 × 2, 2∗13 : (13 : 4), 2∗30 : ((2• : 3) : 5), 2∗13 :13,2∗13 :(13:2),2∗13 :(13:S3),53∗2 :m (13:4),7∗8 :m (32 :8 ...

Progenitors, Symmetric Presentations And Constructions, Diana Aguirre

Electronic Theses, Projects, and Dissertations

Abstract

In this project, we searched for new constructions and symmetric presentations of important groups, nonabelian simple groups, their automorphism groups, or groups that have these as their factor groups. My target nonabelian simple groups included sporadic groups, linear groups, and alternating groups. In addition, we discovered finite groups as homomorphic images of progenitors and proved some of their isomorphism type and original symmetric presentations. In this thesis we found original symmeric presentations of M12, J1 and the simplectic groups S(4,4) and S(3,4) on various con- trol groups. Using the technique of double coset enumeration we ...

Theoretical And Experimental Study Of (E,2e) Ionization Of The Co2 (1ΠG) Molecule At 250 Ev, Mevlut Dogan, Zehra Nur Ozer, Murat Yavuz, Osman Alwan, Adnan Naja, Boghos B. Joulakian, Esam S M Ali, Chuangang Ning, Don H. Madison

Don H. Madison

Triple differential cross sections (TDCSs) of the electron-impact ionization of carbon dioxide are measured in the coplanar asymmetric geometry, with incident electron energy value of 250eV, and ejected electron of 37eV. We will report the experimental results in comparison with the theoretical calculations of the M3DW and TCC (type 5) calculations.

Strong-Field Nonsequential Double Ionization Of Ar And Ne, Zhangjin Chen, Yaqiu Liang, Don H. Madison, Chiidong Lin

Don H. Madison

We investigate the nonsequential double ionization (NSDI) of Ar and Ne based on quantitative rescattering theory (QRS). According to QRS theory, each elementary NSDI process can be calculated by multiplying the returning electron wave packet with appropriate differential electron-ion scattering cross sections. We include (e, 2e) and electron-impact excitation cross sections of Ar+ to obtain the correlated electron momentum spectra for the NSDI of Ar by few-cycle pulses to check the dependence of NSDI on the carrier-envelope phase. The results are compared to the ion momentum spectra from the recent experiment of Johnson [Phys. Rev. APLRAAN1050-294710.1103/ PhysRevA.83.013412 ...

Theoretical Fully Differential Cross Sections For Double-Charge-Transfer Collisions, Allison L. Harris, Jerry Peacher, Don H. Madison

Don H. Madison

We present a four-body model for double charge transfer, called the four-body double-capture model. This model explicitly treats all four particles in the collision, and we apply it here to fully differential cross sections (FDCSs) for proton+helium collisions. The effects of initial- and final-state electron correlations are studied, as well as the role of the projectile-nucleus interaction. We also present results for proton+helium single capture, as well as single-capture:double-capture ratios of FDCSs.

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

Don H. Madison

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 ...

Recent Theoretical Progress In Treating Electron Impact Ionization Of Molecules, Ola A. Al-Hagan, Chuangang Ning, Kate L. Nixon, Andrew James Murray, Christopher J. Colyer, Mark A. Stevenson, B. Lohmann, Don H. Madison

Don H. Madison

(e,2e) ionization differential cross sections are presented for several molecules. We will compare experimental results with theoretical calculations using the molecular three body distorted wave (M3DW) approximations for H 2, N2, H2O and Formic Acid (FA) using better wave-function for the molecules than we had in previous works. Generally, good agreement is found between the M3DW approach and experiments.

Low Energy (E,2e) Coincidence Studies Of Nh3: Results From Experiment And Theory, Kate L. Nixon, Andrew James Murray, Hari Chaluvadi, Chuangang Ning, James Colgan, Don H. Madison

Don H. Madison

Experimental and theoretical triple differential cross sections (TDCS) from ammonia are presented in the low energy regime with outgoing electron energies from 20 eV down to 1.5 eV. Ionization measurements from the 3a1, 1e1, and 2a1 molecular orbitals were taken in a coplanar geometry. Data from the 3a1 and 1e1 orbitals were also obtained in a perpendicular plane geometry. The data are compared to predictions from the distorted wave Born approximation and molecular-three-body distorted wave models. The cross sections for the 3a1 and 1e1 orbitals that have p-like character were found to be similar, and were different to that ...

Low Energy (E, 2e) Study From The 1t2 Orbital Of Ch4, Shenyue Xu, Hari Chaluvadi, Xueguang Ren, Thomas Pfluger, Arne Senftleben, Chuangang Ning, Shuncheng Yan, Peng Zhang, Jie Yang, Xinwen Ma, Joachim Hermann Ullrich, Don H. Madison, Alexander Dorn

Don H. Madison

Single ionization of the methane (CH4) 1t2 orbital by 54 eV electron impact has been studied experimentally and theoretically. The measured triple differential cross sections cover nearly a 4π solid angle for the emission of low energy electrons and a range of projectile scattering angles. Experimental data are compared with theoretical calculations from the distorted wave Born approximation and the molecular three-body distorted wave models. It is found that theory can give a proper description of the main features of experimental cross section only at smaller scattering angles. For larger scattering angles, significant discrepancies between experiment and theory are observed ...

Electron-Impact Excitation To The 4p55s And 4p55p Levels Of Kr | Using Different Distorted-Wave And Close-Coupling Methods, Arati K. Dasgupta, Klaus Bartschat, D. Vaid, Alexei N. Grum-Grzhimailo, Don H. Madison, Milan Blaha, John L. Giuliani

Don H. Madison

Electron-impact excitation of the 4p55s and 4p55p levels of Kr I has been investigated in detail by calculating cross sections using distorted-wave and close-coupling approaches. The results are presented from the excitation thresholds up to 50 eV incident energy. They are contrasted among the different calculations and compared with other theoretical predictions and experimental data. Significant disagreement is found with many of the recent experimental data of Chilton et al. [Phys. Rev. A 62, 032714 (2000)].

Energy And Angular Distribution Of Electrons Ejected From Helium By Fast Protons And Electrons: Theory And Experiment, Steven Trent Manson, Larry H. Toburen, Don H. Madison, Nikolaus Stolterfoht

Don H. Madison

A comprehensive study of the angular and energy distributions of electrons ejected in collisions of fast electrons and protons with He is presented. New experimental results for 300-keV, 1-MeV, and 5-MeV proton impact are reported along with theoretical results for 2-keV electron impact and 100-keV, 300-keV, 1-MeV, and 5-MeV proton impact. The theoretical results, based upon Born approximation with Hartree-Slater initial discrete and final continuum wave functions, show excellent agreement with experimental electron-impact results. Serious discrepancies are found between theory and experiment in the angular distribution of ejected electrons for forward angles for 100- and 300-keV proton impact; the discrepancies ...

Effect Of Polarization And Absorption On Differential Cross Sections And Angular Correlation Parameters For Electron Excitation Of Helium, M. E. Stewart, Don H. Madison

Don H. Madison

The effects of local polarization and absorption potentials on differential cross sections and angular correlation parameters are studied within the distorted-wave approximation for electron excitation of the 2 1P state of helium. For examining the effect of local polarization, we have compared a recent numerical self-consistent adiabatic polarization potential for helium with the commonly used hydrogenic adiabatic polarization potential. Different radial regions for the polarization potential were studied to determine their contribution to the overall effect of polarization. Calculations are also presented which show the effects of different strengths for a local absorption potential.

Electron-Impact-Ionization Cross Sections Of H2 For Low Outgoing Electron Energies From 1 To 10 Ev, Ola A. Al-Hagan, Andrew James Murray, Christian V. Kaiser, James Colgan, Don H. Madison

Don H. Madison

Theoretical and experimental fully differential cross sections are presented for electron-impact ionization of molecular hydrogen in a plane perpendicular to the incident beam direction. The experimental data exhibit a maximum for 1-eV electrons detected 180° apart and a minimum for 10-eV electrons. We investigate the different physical effects which cause back-to-back scattering and demonstrate that, over the energy range from 10 to 1 eV, a direct transition is observed from a region where Wannier threshold physics is essentially unimportant to where it completely dominates.

Effect Of Projectile Coherence On Atomic Fragmentation Processes, Michael Schulz, Kisra N. Egodapitiya, Sachin D. Sharma, Aaron C. Laforge, Robert Moshammer, A. A. Hasan, Don H. Madison

Don H. Madison

We demonstrate that the projectile coherence can have a major impact on atomic fragmentation processes. This has been overlooked for decades in formal scattering theory and may explain puzzling discrepancies between theoretical and experimental fully differential cross sections for single ionization.

Doubly Differential Cross Sections For Proton-Impact Ionization Of Argon, Don H. Madison, Steven Trent Manson

Don H. Madison

Proton-impact-ionization cross sections for argon which are differential in the energy and angle of the ejected electron have been calculated within the framework of the Born approximation using both Hartree-Slater and Hartree-Fock wave functions for the ejected electron. Results of the two types of calculations are compared with each other and with experiment. Differential cross sections for all five sub shells of argon are examined and particular attention is given to some interesting features of the K-shell cross sections. The range of applicability of the theoretical models is discussed.

Dynamical (E, 2e) Studies Using Tetrahydrofuran As A Dna Analog, Christopher J. Colyer, Susan M. Bellm, B. Lohmann, G. Friedrich Hanne, Ola A. Al-Hagan, Don H. Madison, Chuangang Ning

Don H. Madison

Triple differential cross sections for the electron-impact ionization of the outer valence orbital of tetrahydrofuran have been measured using the (e, 2e) technique. The measurements have been performed with coplanar asymmetric kinematics, at an incident electron energy of 250 eV and at an ejected electron energy of 10 eV, over a range of momentum transfers. The experimental results are compared with theoretical calculations carried out using the molecular three-body distorted wave model. The results obtained are important for gaining an understanding of electron driven processes at a molecular level and for modeling energy deposition in living tissue.

Dynamical (E, 2e) Studies Using Tetrahydrofuran As A Dna Analogue, Christopher J. Colyer, Susan M. Bellm, G. Friedrich Hanne, Ola A. Al-Hagan, Don H. Madison, Chuangang Ning, B. Lohmann

Don H. Madison

We present dynamical (e, 2e) measurements for the electron impact ionization of formic acid and tetrahydrofuran molecules performed under similar kinematics. The experiments have been performed in the coplanar asymmetric geometry for a range of momentum transfers, at an incident electron energy of 250 eV and with an ejected electron energy of 10eV. The experimental results are compared with theoretical calculations carried out using the molecular 3-body distorted wave (M3DW) model.

Differential Cross Sections For Single Ionization Of H2 By 75kev Proton Impact, Ujjal Chowdhury, Michael Schulz, Don H. Madison

Don H. Madison

We have calculated Triply differential cross sections (TDCS) and doubly differential cross sections (DDCS) for single ionization of H2 by 75 keV proton impact using the molecular 3 body distorted wave Eikonal initial state (M3DW-EIS) approach. Previously published measured DDCS-P (differential in the projectile scattering angle and integrated over the ejected electron angles) found pronounced structures at relatively large angles which were interpreted as an interference resulting from the two-centered potential of the molecule.

Differential Cross Sections For The Ionization Of Oriented H2 Molecules By Electron Impact, James Colgan, Michael S. Pindzola, Francis J. Robicheaux, Christian V. Kaiser, Andrew James Murray, Don H. Madison

Don H. Madison

A nonperturbative close-coupling technique is used to calculate differential cross sections for the electron-impact ionization of H2 at an energy of 35.4 eV. Our approach allows cross sections for any orientation of the molecule with respect to the incident electron beam to be analyzed. New features in the resulting cross sections are found compared with the case where the molecular orientation is averaged, and also with cross sections for He at equivalent electron kinematics. When averaged over all possible molecular orientations, good agreement is found with recent experimental results.

Differential Cross Sections For Single Ionization Of H2 By 75-Kev Proton Impact, Ujjal Chowdhury, Michael Schulz, Don H. Madison

Don H. Madison

We have calculated triply differential cross sections (TDCS) and doubly differential cross sections (DDCS) for single ionization of H2 by 75-keV proton impact using the molecular three-body distorted-wave-eikonal initial-state (M3DW-EIS) approach. Previously published measured DDCS (differential in the projectile scattering angle and integrated over the ejected electron angles) found pronounced structures at relatively large angles that were interpreted as an interference resulting from the two-centered potential of the molecule. Theory treating H2 as atomic H multiplied by a molecular interference factor only predicts the observed structure when assumptions are made about the molecular orientation. Here we apply the M3DW-EIS method ...