248 research outputs found
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
Pion Generalized Dipole Polarizabilities by Virtual Compton Scattering
We present a calculation of the cross section and the event generator of the
reaction . This reaction is sensitive to the pion
generalized dipole polarizabilities, namely, the longitudinal electric
, the transverse electric , and the magnetic
which, in the real-photon limit, reduce to the ordinary electric
and magnetic polarizabilities and , respectively.
The calculation of the cross section is done in the framework of chiral
perturbation theory at . 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.
Meson exchange and nucleon polarizabilities in the quark model
Modifications to the nucleon electric polarizability induced by pion and
sigma exchange in the q-q potentials are studied by means of sum rule
techniques within a non-relativistic quark model. Contributions from meson
exchange interactions are found to be small and in general reduce the quark
core polarizability for a number of hybrid and one-boson-exchange q-q models.
These results can be explained by the constraints that the baryonic spectrum
impose on the short range behavior of the mesonic interactions.Comment: 11 pages, 1 figure added, expanded discussio
- …