122939851
Nonstatistical behavior of photoeffect subshell branching ratios at high energies
121020837
Observation of zeros and amplification of quadrupole-matrix-element contributions to photoelectron angular distributions
123462298
Overlap of shape resonance and Cooper-minimum structure in photoionization
Examples of a Cooper minimum inside the range of a shape-resonance maximum of a photoionization cross section have been found in numerical calculations within a single-electron model in a relativistic Hartree-Fock-Slater potential. In these model calculations for the photoionization of tin and uranium we find relatively broad shape resonances in all the $d$ and $f$ subshells. In addition a Cooper minimum occurs in the outer subshells of these high-angular-momentum states within the region of the shape-resonance maximum. We examine the matrix elements for these subshells and the resulting cross sections and angular distributions.
119962841
Photoelectron angular distributions from the subshells of high-Z elements
Numerical predictions are obtained, within a relativistic multipole central-field approximation calculation, for the radial matrix elements and resulting angular distributions of photoelectrons ejected from inner through outer subshells of uranium and for photoelectron energies from near threshold (1 eV) to 100 keV. Some data are also presented for outer subshells of mercury. We confirm that for inner shells higher-multipole effects persist to low energies, while we find that for outer shells such effects become small. For uranium inner ns subshells the asymmetry parameter ..beta../sub n/s differs from its nonrelativistic value 2, but not more than 30% (for n .. epsilonp/sub 1/2/ and ns ..-->.. epsilonp/sub 3/2/ transitions for these inner shells are similar). For outer s subshells relativistic spin-orbit splittings cause large deviations from the nonrelativistic predictions which can be understood from the magnitudes, zeros, and splittings of the two radial matrix elements. For U 6p/sub 1/2/ and 6p/sub 3/2/, ..beta../sub 6p/ has the same qualitative features found in nonrelativistic calculations for outer p shells of other high-Z elements, but the angular distributions from the two states do differ in detail. Such differences in angular distributions of themore » photoelectrons from the two j substates of given l become smaller for inner p shells. For outer d and f subshells the asymmetry parameter oscillates with photoelectron energy in a manner similar to that found by Manson in nonrelativistic dipole d-subshell calculations, and no qualitatively important relativistic effects have been identified; this is due to the decrease of the fine-structure-splitting interval with increasing angular momentum.« less
121398906
Generalized Fermi-Segrè formula
119495662
Direct radiative recombination of electrons with atomic ions: Cross sections and rate coefficients
Simple expressions are obtained which permit systematic estimates of the rate coefficients for direct radiative recombination (DRR) of fast electrons with atomic ions of various ionic species. The analysis utilizes a set of cross sections obtained through numerical calculations combined with the use of an interpolation scheme to smoothly connect reduced cross sections (apart from normalizations) of the bremsstrahlung tip region and the low-lying DRR region. It is shown that these numerical cross sections can be reproduced by the predictions of a modified semiclassical Kramers formula with an appropriate effective charge Z/sub eff/, which is larger than the effective charge which reproduces the energy levels of the states into which capture occurs. In accord with this modified Kramers formula, the numerically obtained total cross sections are shown to scale with Z/sub eff//sup 2//K for each isoelectronic sequence, and with a parameter (n/sub 0/)/sub eff/ which characterizes each isoelectronic sequence. Using these scaling properties, simple analytic expressions are obtained for recombination rate coefficients, for the rate of electron kinetic-energy loss, and for the rate of radiated power loss, assuming a classical Maxwell-Boltzmann thermal distribution of continuum electrons.
118236132
Group contractions and the E(2)-like little group for massless particles as an infinite-momentum/zero-mass limit of the 0(3)-like little group for massive particles
17539164
Is the concept of quantum probability consistent with Lorentz covariance
Lorentz-covariant harmonic oscillator wave functions are constructed from the Lorentz-invariant oscillator differential equation of Feynman, Kislinger, and Ravndal for a two-body bound state. The wave functions are not invariant but covariant. As the differential equation contains the time-separation variable, the wave functions contain the same time-separation variable which does not exist in Schrodinger wave functions. This time-separation variable can be shown to belong to Feynman's rest of the universe, and can thus be eliminated from the density matrix. The covariant probability interpretation is given. This oscillator formalism explains Feynman's decoherence mechanism which is exhibited in Feynman's parton picture.
8523168
Fixed-Point Analysis of the Low-Energy Constants in the Pion-Nucleon Chiral Lagrangian
In the framework of heavy-baryon chiral perturbation theory, we investigate the fixed point structure of renormalization group equations (RGE) for the ratios of the renormalized low energy constants (LECs) that feature in the pion-nucleon chiral Lagrangian. The ratios of the LECs deduced from our RGE analysis are found to be in semi-quantitative agreement with those obtained from direct fit to the experimental data. The naturalness of this agreement is discussed using a simple dimensional analysis combined with Wilsonian RGEs.
119099546
Quark number susceptibility with finite chemical potential in holographic QCD
We study the quark number susceptibility in holographic QCD with a finite chemical potential or under an external magnetic field at finite temperature. We first consider the quark number susceptibility with the chemical potential. We observe that approaching Tc from high temperature regime, χq/T2 develops a peak as we increase the chemical potential, which confirms recent lattice QCD results. We discuss this behavior in connection with the existence of the critical end point in the QCD phase diagram. We also consider the quark number susceptibility under the external magnetic field. We predict that the quark number susceptibility exhibits a blow-up behavior at low temperature as we raise the value of the magnetic field. We finally spell out some limitations of our study.
117540013
Theory and applications of the Poincaré group
I: Elements of Group Theory.- 1. Definition of a Group.- 2. Subgroups, Cosets, and Invariant Subgroups.- 3. Equivalence Classes, Orbits, and Little Groups.- 4. Representations and Representation Spaces.- 5. Properties of Matrices.- 6. Schur's Lemma.- 7. Exercises and Problems.- II: Lie Groups and Lie Algebras.- 1. Basic Concepts of Lie Groups.- 2. Basic Theorems Concerning Lie Groups.- 3. Properties of Lie Algebras.- 4. Properties of Lie Groups.- 5. Further Theorems of Lie Groups.- 6. Exercises and Problems.- III: Theory of the Poincare Group.- 1. Group of Lorentz Transformations.- 2. Orbits and Little Groups of the Proper Lorentz Group.- 3. Representations of the Poincare Group.- 4. Lorentz Transformations of Wave Functions.- 5. Lorentz Transformations of Free Fields.- 6. Discrete Symmetry Operations.- 7. Exercises and Problems.- IV: Theory of Spinors.- 1. SL(2, c) as the Covering Group of the Lorentz Group.- 2. Subgroups of SL(2, c).- 3. SU (2).- 4. 5L(2, c) Spinors and Four-Vectors.- 5. Symmetries of the Dirac Equation.- 6. Exercises and Problems.- V: Covariant Harmonic Oscillator Formalism.- 1. Covariant Harmonic Oscillator Differential Equations.- 2. Normalizable Solutions of the Relativistic Oscillator Equation.- 3. Irreducible Unitary Representations of the Poincare Group.- 4. Transformation Properties of Harmonic Oscillator Wave Functions.- 5. Harmonic Oscillators in the Four-Dimensional Euclidean Space.- 6. Moving O(4) Coordinate System.- 7. Exercises and Problems.- VI: Dirac's Form of Relativistic Quantum Mechanics.- 1. C-Number Time-Energy Uncertainty Relation.- 2. Dirac's Form of Relativistic Theory of "Atom ".- 3. Dirac's Light-Cone Coordinate System.- 4. Harmonic Oscillators in the Light-Cone Coordinate System.- 5. Lorentz-Invariant Uncertainty Relations.- 6. Exercises and Problems.- VII: Massless Particles.- 1. What is the E(2) Group?.- 2. E(2)-like Little Group for Photons.- 3. Transformation Properties of Photon Polarization Vectors.- 4. Unitary Transformation of Photon Polarization Vectors.- 5. Massless Particles with Spin 1/2.- 6. Harmonic Oscillator Wave Functions for Massless Composite Particles.- 7. Exercises and Problems.- VIII: Group Contractions.- 1. SE(2) Group as a Contraction of SO(3).- 2. E(2)-like Little Group as an Infinite-momentum/zero-mass Limit of the O(3)-like Little Group for Massive Particles.- 3. Large-momentum/zero-mass Limit of the Dirac Equation.- 4. Finite-dimensional Non-unitary Representations of the SE(2) Group.- 5. Polarization Vectors for Massless Particles with Integer Spin.- 6. Lorentz and Galilei Transformations.- 7. Group Contractions and Unitary Representations of SE(2).- 8. Exercises and Problems.- IX: SO(2, 1) and SU(1, 1).- 1. Geometry of SL(2, r) and Sp(2).- 2. Finite-dimensional Representations of SO(2, 1).- 3. Complex Angular Momentum.- 4. Unitary Representations of SU(1, 1).- 5. Exercises and Problems.- X: Homogeneous Lorentz Group.- 1. Statement of the Problem.- 2. Finite-dimensional Representations of the Homogeneous Lorentz Group.- 3. Transformation Properties of Electric and Magnetic Fields.- 4. Pseudo-unitary Representations for Dirac Spinors.- 5. Harmonic Oscillator Wave Functions in the Lorentz Coordinate System.- 6. Further Properties of the Homogeneous Lorentz Group.- 7. Concluding Remarks.- XI: Hadronic Mass Spectra.- 1. Quark Model.- 2. Three-particle Symmetry Classifications According to the Method of Dirac.- 3. Construction of Symmetrized Wave Functions.- 4. Symmetrized Products of Symmetrized Wave Functions.- 5. Spin Wave Functions for the Three-Quark System.- 6. Three-quark Unitary Spin and SU(6) Wave Functions.- 7. Three-body Spatial Wave Functions.- 8. Totally Symmetric Baryonic Wave Functions.- 9. Baryonic Mass Spectra.- 10. Mesons.- 11. Exercises and Problems.- XII: Lorentz-Dirac Deformation in High-Energy Physics.- 1. Lorentz-Dirac Deformation of Hadronic Wave Functions.- 2. Form Factors of Nucleons.- 3. Calculation of the Form Factors.- 4. Scaling Phenomenon and the Parton Picture.- 5. Covariant Harmonic Oscillators and the Parton Picture.- 6. Calculation of the Parton Distribution Function for the Proton.- 7. Jet Phenomenon.- 8. Exercises and Problems.- References.