13,917 research outputs found
Normalization of the covariant three-body bound state vertex function
The normalization condition for the relativistic three nucleon Bethe-Salpeter
and Gross bound state vertex functions is derived, for the first time, directly
from the three body wave equations. It is also shown that the relativistic
normalization condition for the two body Gross bound state vertex function is
identical to the requirement that the bound state charge be conserved, proving
that charge is automatically conserved by this equation.Comment: 24 pages, 9 figures, published version, minor typos correcte
Two-pion exchange potential and the amplitude
We discuss the two-pion exchange potential which emerges from a box diagram
with one nucleon (the spectator) restricted to its mass shell, and the other
nucleon line replaced by a subtracted, covariant scattering amplitude
which includes , Roper, and isobars, as well as contact terms
and off-shell (non-pole) dressed nucleon terms. The amplitude satisfies
chiral symmetry constraints and fits data below 700 MeV pion
energy. We find that this TPE potential can be well approximated by the
exchange of an effective sigma and delta meson, with parameters close to the
ones used in one-boson-exchange models that fit data below the pion
production threshold.Comment: 9 pages (RevTex) and 7 postscript figures, in one uuencoded gzipped
tar fil
Gauging the three-nucleon spectator equation
We derive relativistic three-dimensional integral equations describing the
interaction of the three-nucleon system with an external electromagnetic field.
Our equations are unitary, gauge invariant, and they conserve charge. This has
been achieved by applying the recently introduced gauging of equations method
to the three-nucleon spectator equations where spectator nucleons are always on
mass shell. As a result, the external photon is attached to all possible places
in the strong interaction model, so that current and charge conservation are
implemented in the theoretically correct fashion. Explicit expressions are
given for the three-nucleon bound state electromagnetic current, as well as the
transition currents for the scattering processes
\gamma He3 -> NNN, Nd -> \gamma Nd, and \gamma He3 -> Nd. As a result, a
unified covariant three-dimensional description of the NNN-\gamma NNN system is
achieved.Comment: 23 pages, REVTeX, epsf, 4 Postscript figure
Formation of nanosized strontium substituted hydroxyapatites
Incorporation of specific elements into calcium phosphates offers the combination of a bioactive material and a therapeutic effect. This is important for improving the integration of implants as well as treating medical conditions. Strontium is a suitable candidate and displays the ability to stimulate bone growth and reducing bone resorption. This study investigated the formation of strontium carbonated hydroxyapatite nanoparticles from an amorphous phase. Crystallization of carbonated hydroxyapatite occurred at 585 oC, but samples with an intended 25% and 75% replacement of calcium with strontium crystallized at 624 oC. Heat treatment at the crystallization temperature revealed that strontium free apatite does not crystallize in 5 minutes, but an increasing strontium concentration leads to a higher rate of crystallization. X-ray diffraction patterns suggest that it may be difficult to include strontium, but higher strontium concentrations are possibly included with ease in the lattice. This work has produced a nanosized apatite accompanied by an amorphous phase after a short heat-treatment time. This offers a range of features that collectively show great promise for significantly enhancing the release of strontium for improved bone therapeutic effects
A study of 2 GHz electromagnetic wave propagation over optical paths in three geographical regions of the United States
Statistical correlation between optical microwave propagation reliability, fade margin, path length, and geographic locatio
Scalar-particle self-energy amplitudes and confinement in Minkowski space
We analyze the analytic structure of the Covariant Spectator Theory (CST)
contribution to the self-energy amplitude for a scalar particle in a \phi^2
\chi-theory. To this end we derive dispersion relations in 1+1 and in 3+1
dimensional Minkowski space. The divergent loop integrals in 3+1 dimensions are
regularized using dimensional regularization. We find that the CST dispersion
relations exhibit, in addition to the usual right-hand branch cut, also a
left-hand cut. The origin of this "spectator" left-hand cut can be understood
in the context of scattering for a scalar \phi^2 \chi^2-type theory. If the
interaction kernel contains a linear confining component, its contribution to
the self-energy vanishes exactly.Comment: 19 pages, 11 figures; one paragraph added and some typos corrected;
version published in Few-Body System
Enumerative aspects of the Gross-Siebert program
We present enumerative aspects of the Gross-Siebert program in this
introductory survey. After sketching the program's main themes and goals, we
review the basic definitions and results of logarithmic and tropical geometry.
We give examples and a proof for counting algebraic curves via tropical curves.
To illustrate an application of tropical geometry and the Gross-Siebert program
to mirror symmetry, we discuss the mirror symmetry of the projective plane.Comment: A version of these notes will appear as a chapter in an upcoming
Fields Institute volume. 81 page
Spontaneous emission from large quantum dots in nanostructures: exciton-photon interaction beyond the dipole approximation
We derive a rigorous theory of the interaction between photons and spatially
extended excitons confined in quantum dots in inhomogeneous photonic materials.
We show that, beyond the dipole approximation, the radiative decay rate is
proportional to a non-local interaction function, which describes the
interaction between light and spatially extended excitons. In this regime,
light and matter degrees of freedom cannot be separated and a complex interplay
between the nanostructured optical environment and the exciton envelope
function emerges. We illustrate this by specific examples and derive a series
of important analytical relations, which are useful for applying the formalism
to practical problems. In the dipole limit, the decay rate is proportional to
the projected local density of optical states and we obtain the strong and weak
confinement regimes as special cases.Comment: 14 pages, 4 figure
Gauging the spectator equations
We show how to derive relativistic, unitary, gauge invariant, and charge
conserving three-dimensional scattering equations for a system of hadrons
interacting with an electromagnetic field. In the method proposed, the
spectator equations describing the strong interactions of the hadrons are
gauged using our recently introduced gauging of equations method. A key
ingredient in our model is the on-mass-shell particle propagator. We discuss
how to gauge this on-mass-shell propagator so that both the Ward-Takahashi and
Ward identities are satisfied. We then demonstrate our gauging procedure by
deriving the gauge-invariant three-dimensional expression for the deuteron
photodisintegration amplitude within the spectator approach.Comment: 17 pages, REVTeX, epsf, 1 Postscript figur
Separable Structure of Many-Body Ground-State Wave Function
We have investigated a general structure of the ground-state wave function
for the Schr\"odinger equation for identical interacting particles (bosons
or fermions) confined in a harmonic anisotropic trap in the limit of large .
It is shown that the ground-state wave function can be written in a separable
form. As an example of its applications, this form is used to obtain the
ground-state wave function describing collective dynamics for trapped
bosons interacting via contact forces.Comment: J. Phys. B: At. Mol. Opt. Phys. 33 (2000) (accepted for publication
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