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.
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.
120238308
Subshell branching ratios of partial photoionization cross sections
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
120365252
Massless composite particles and space-time description of gauge transformations
Space-time symmetries for massless composite particles are studied within the kinematical framework of the relativistic harmonic-oscillator formalism. It is noted first that the Lorentz-invariant harmonic-oscillator equation is separable in the Kalnins-Miller coordinate system in which the helicity and gauge transformation parameters can be separated from other space-time variables. It is shown then that this separation procedure leads to the representations of the Poincare group which display the same space-time symmetry as those for photons and gravitons. The gauge transformation parameters are shown to be internal space-time parameters in the case of massless composite particles. It is shown in particular that the spin in this case is associated with an orbitlike motion on the plane perpendicular to the momentum of the composite particle.
37376282
Finite-temperature corrections in the dilated chiral quark model
We calculate the finite-temperature corrections in the dilated chiral quark model using the effective potential formalism. Assuming that the dilaton limit is applicable at some short length scale, we interpret the results to represent the behavior of hadrons in dense and hot matter. We obtain the scaling law, f{sub {pi}}(T)/f{sub {pi}} = m{sub Q}(T)/m{sub Q} {approx_equal} m{sub {sigma}}(T)/m{sub {sigma}}while we argue, using PCAC, that pion mass does not scale within the temperature range involved in our Lagrangian. It is found that the hadron masses and the pion decay constant drop faster with temperature in the dilated chiral quark model than in the conventional linear sigma model that does not take into account the QCD scale anomaly. We attribute the difference in scaling in heat bath to the effect of baryonic medium on thermal properties of the hadrons. Our finding would imply that the AGS experiments (dense and hot matter) and the RHIC experiments (hot and dilute matter) will ``see`` different hadron properties in the hadronization exit phase.
119443823
Squeezed states and thermally excited states in the wigner phase-space picture of quantum mechanics
Abstract The phase-space picture of thermal excitations is presented starting from the formalism of two-mode coherent and squeezed states. It is shown that the thermal degree of freedom can be augmented into the existing formalism of coherent and squeezed states. It is shown further that the thermal excitation leads to a diametric expansion of the Wigner phase-space distribution function.
120211993
Space-time symmetries of confined quarks
The first paragraph of Rotbart's recent paper is amplified. It is shown that the minimum symmetry for the spacetime separation of the confined quarks is that of the O(3)-like little group of the Poincare group for massive hadrons. It is then pointed out that the existence of additional coordinate dependences is determined from the way in which specific models are constructed.
123143192
Three‐particle symmetry classifications according to the method of Dirac
It is shown that the method of Dirac is an effective way of teaching three‐particle symmetry classifications to students in the first‐year quantum mechanics class, who wish to understand the symmetry properties associated with elementary particles before or without learning group theory. According to the method spelled out for the N‐particle case by Dirac in Secs. 55 and 56 of his classic book Principles of Quantum Mechanics, explicit calculations are carried out for three particles. It is shown that this method leads to the three‐particle wave functions and their symmetric combinations as given by Feynman et al. In the following paper, the general principles derived here are applied to the quark model of hadrons.