Relativistic Coulomb Problem: Analytic Upper Bounds on Energy Levels

The spinless relativistic Coulomb problem is the bound-state problem for the spinless Salpeter equation (a standard approximation to the Bethe--Salpeter formalism as well as the most simple generalization of the nonrelativistic Schr\"odinger formalism towards incorporation of relativistic effects) with the Coulomb interaction potential (the static limit of the exchange of some massless bosons, as present in unbroken gauge theories). The nonlocal nature of the Hamiltonian encountered here, however, renders extremely difficult to obtain rigorous analytic statements on the corresponding solutions. In view of this rather unsatisfactory state of affairs, we derive (sets of) analytic upper bounds on the involved energy eigenvalues.Comment: 12 pages, LaTe

Relativistic Harmonic Oscillator

We study the semirelativistic Hamiltonian operator composed of the relativistic kinetic energy and a static harmonic-oscillator potential in three spatial dimensions and construct, for bound states with vanishing orbital angular momentum, its eigenfunctions in compact form, i. e., as power series, with expansion coefficients determined by an explicitly given recurrence relation. The corresponding eigenvalues are fixed by the requirement of normalizability of the solutions.Comment: 14 pages, extended discussion of result

A Variational Approach to the Spinless Relativistic Coulomb Problem

By application of a straightforward variational procedure we derive a simple, analytic upper bound on the ground-state energy eigenvalue of a semirelativistic Hamiltonian for (one or two) spinless particles which experience some Coulomb-type interaction.Comment: 7 pages, HEPHY-PUB 606/9

Stability in the instantaneous Bethe-Salpeter formalism: harmonic-oscillator reduced Salpeter equation

A popular three-dimensional reduction of the Bethe-Salpeter formalism for the description of bound states in quantum field theory is the Salpeter equation, derived by assuming both instantaneous interactions and free propagation of all bound-state constituents. Numerical (variational) studies of the Salpeter equation with confining interaction, however, observed specific instabilities of the solutions, likely related to the Klein paradox and rendering (part of the) bound states unstable. An analytic investigation of this problem by a comprehensive spectral analysis is feasible for the reduced Salpeter equation with only harmonic-oscillator confining interactions. There we are able to prove rigorously that the bound-state solutions correspond to real discrete energy spectra bounded from below and are thus free of any instabilities.Comment: 23 pages, 3 figures, extended conclusions, version to appear in Phys. Rev.

Casus

Ecvet Şeci'nin Saadet'te tefrika edilen Casus adlı romanıTefrikanın devamına rastlanmamış, tefrika yarım kalmıştır

Characterization of the airborne aerosol inlet and transport system used during the A-LIFE aircraft field experiment

Atmospheric aerosol particles have a profound impact on Earth's climate by scattering and absorbing solar and terrestrial radiation and by impacting the properties of clouds. Research aircraft such as the Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR) Falcon are widely used to study aerosol particles in the troposphere and lower stratosphere. However, transporting a representative sample to the instrumentation inside the aircraft remains a challenge due to high airspeeds and changing ambient conditions. In particular, for high-quality coarse-mode aerosol measurements, knowledge about losses or enhancements in the aerosol sampling system is crucial. In this study, the sampling efficiency of the aerosol inlet aboard the Falcon research aircraft is characterized for the first time with state-of-the art in situ measurements including sizing instruments operated behind the Falcon aerosol inlet and mounted at the aircraft wing not affected by the aerosol inlet. Sampling efficiencies were derived for different true airspeed ranges by comparing the in-cabin and ”full”-size-range particle number size distributions during 174 flight sequences with a major contribution of mineral dust particles during the ”Absorbing aerosol layers in a changing climate: aging, lifetime and dynamics” project (A-LIFE). Additionally, experimentally derived Stokes numbers were used to calculate the cutoff diameter of the aerosol sampling system for different particle densities as a function of true airspeed. As expected, the results show that the velocity of the research aircraft has a major impact on the sampling of coarse-mode aerosol particles with in-cabin instruments. For true airspeeds up to about 190 m s−1, aerosol particles larger than about 1 µm are depleted in the sampling system of the Falcon during the A-LIFE project. In contrast, for true airspeeds higher than 190 m s−1, an enhancement of particles up to a diameter of 4 µm is observed. For even larger particles, the enhancement effect at the inlet is still present, but inertial and gravitational particle losses in the transport system get more and more pronounced, which leads to a decreasing overall sampling efficiency. In summary, aerosol particles are either depleted or enhanced in the Falcon aerosol inlet, whereas transport in sampling lines always leads to a loss of particles. Here, we have considered both effects and determined the cutoff diameter for the A-LIFE transport system (i.e., the sampling lines only), the cutoff diameter of the Falcon aerosol inlet (i.e., the effect of the inlet only), and the combined effect of the inlet and sampling lines.</p

Pion Generalized Dipole Polarizabilities by Virtual Compton Scattering πe→πeγ\pi e \to \pi e\gamma

We present a calculation of the cross section and the event generator of the reaction $\pi e\to \pi e \gamma$. This reaction is sensitive to the pion generalized dipole polarizabilities, namely, the longitudinal electric $\alpha_L(q^2)$, the transverse electric $\alpha_T(q^2)$, and the magnetic $\beta(q^2)$ which, in the real-photon limit, reduce to the ordinary electric and magnetic polarizabilities $\bar{\alpha}$ and $\bar{\beta}$, respectively. The calculation of the cross section is done in the framework of chiral perturbation theory at ${\cal O}(p^4)$. A pion VCS event generator has been written which is ready for implementation in GEANT simulation codes or for independent use.Comment: 33 pages, Revtex, 15 figure

Semi-Relativistic Hamiltonians of Apparently Nonrelativistic Form

We construct effective Hamiltonians which despite their apparently nonrelativistic form incorporate relativistic effects by involving parameters which depend on the relevant momentum. For some potentials the corresponding energy eigenvalues may be determined analytically. Applied to two-particle bound states, it turns out that in this way a nonrelativistic treatment may indeed be able to simulate relativistic effects. Within the framework of hadron spectroscopy, this lucky circumstance may be an explanation for the sometimes extremely good predictions of nonrelativistic potential models even in relativistic regions.Comment: 20 pages, LaTeX, no figure

Variational Estimation of the Wave Function at Origin for Heavy Quarkonium

The wave function at the origin (WFO) is an important quantity in studying many physical problems concerning heavy quarkonia. However, when one used the variational method with fewer parameters, in general, the deviation of resultant WFO from the "accurate" solution was not well estimated. In this paper, we discuss this issue by employing several potential forms and trial wave functions in detail and study the relation between WFO and the reduced mass.Comment: 17 pages, .zip file of the LATEX2

Instantaneous Bethe-Salpeter equation: utmost analytic approach

The Bethe-Salpeter formalism in the instantaneous approximation for the interaction kernel entering into the Bethe-Salpeter equation represents a reasonable framework for the description of bound states within relativistic quantum field theory. In contrast to its further simplifications (like, for instance, the so-called reduced Salpeter equation), it allows also the consideration of bound states composed of "light" constituents. Every eigenvalue equation with solutions in some linear space may be (approximately) solved by conversion into an equivalent matrix eigenvalue problem. We demonstrate that the matrices arising in these representations of the instantaneous Bethe-Salpeter equation may be found, at least for a wide class of interactions, in an entirely algebraic manner. The advantages of having the involved matrices explicitly, i.e., not "contaminated" by errors induced by numerical computations, at one's disposal are obvious: problems like, for instance, questions of the stability of eigenvalues may be analyzed more rigorously; furthermore, for small matrix sizes the eigenvalues may even be calculated analytically.Comment: LaTeX, 23 pages, 2 figures, version to appear in Phys. Rev.