75 research outputs found
Low-energy Compton scattering on the nucleon and sum rules
The Gerasimov-Drell-Hearn and Baldin-Lapidus sum rules are evaluated in the
dressed K-matrix model for photon-induced reactions on the nucleon. For the
first time the sum of the electric and magnetic polarisabilities
and the forward spin polarisability are explicitly calculated in two
alternative ways -- from the sum rules and from the low-energy expansion of the
real Compton scattering amplitude -- within the {\em same} framework. The two
methods yield compatible values for but differ somewhat for
. Consistency between the two ways of determining the
polarisabilities is a measure of the extent to which basic symmetries of the
model are obeyed.Comment: 9 pages, 4 figures, using REVTeX. More concise version, results
unchanged. To appear in Phys. Rev.
Exclusive measurement of coherent eta photoproduction from the deuteron
Coherent photoproduction of eta mesons from the deuteron has been measured
from threshold up to incident photon energies of 750 MeV using the photon
spectrometer TAPS at the tagged photon facility at the Mainz microtron MAMI.
For the first time, differential coherent cross sections have been deduced from
the coincident detection of the eta meson and the recoil deuteron. A missing
energy analysis was used for the suppression of background events so that a
very clean identification of coherent eta-photoproduction was achieved. The
resulting cross sections agree with previous experimental results except for
angles around 90 deg in the photon-deuteron cm-system where they are smaller.
They are compared to various model calculations.Comment: 4 pages, 4 figure
Higher order forward spin polarizability
As a guideline for future experiments to extract the four (leading) spin
polarizabilities of the nucleon, we have constructed the forward amplitude for
polarized Compton scattering by dispersion integrals. These integrals have been
saturated by recently measured helicity-dependent photoabsorption cross
sections as well as predictions for pion photoproduction multipoles from
several phenomenological descriptions and chiral perturbation theory. The
comparison of these results corroborates the strategy to extract the spin
polarizabilities by fitting them to polarized Compton data and fixing all
higher order spin effects by dispersion relations based on pion photoproduction
multipoles.Comment: 21 pages, 6 figures, 3 Tables; version to appear in Phys. Lett.
Quasi-free Compton Scattering and the Polarizabilities of the Neutron
Differential cross sections for quasi-free Compton scattering from the proton
and neutron bound in the deuteron have been measured using the Glasgow/Mainz
tagging spectrometer at the Mainz MAMI accelerator together with the Mainz 48
cm 64 cm NaI(Tl) photon detector and the G\"ottingen SENECA
recoil detector. The data cover photon energies ranging from 200 MeV to 400 MeV
at . Liquid deuterium and hydrogen targets
allowed direct comparison of free and quasi-free scattering from the proton.
The neutron detection efficiency of the SENECA detector was measured via the
reaction . The "free" proton Compton scattering cross
sections extracted from the bound proton data are in reasonable agreement with
those for the free proton which gives confidence in the method to extract the
differential cross section for free scattering from quasi-free data.
Differential cross sections on the free neutron have been extracted and the
difference of the electromagnetic polarizabilities of the neutron have been
obtained to be
in units . In combination with the polarizability sum deduced from photoabsorption data, the neutron electric and
magnetic polarizabilities, and
are obtained. The backward spin polarizability of the neutron was determined to
be
Dispersion Effects in Nucleon Polarisabilities
We present a formalism to extract the dynamical nucleon polarisabilities
defined via a multipole expansion of the structure amplitudes in nucleon
Compton scattering. In contradistinction to the static polarisabilities,
dynamical polarisabilities gauge the response of the internal degrees of
freedom of a composed object to an external, real photon field of arbitrary
energy. Being energy dependent, they therefore contain additional information
about dispersive effects induced by internal relaxation mechanisms, baryonic
resonances and meson production thresholds of the nucleon. We give explicit
formulae to extract the dynamical electric and magnetic dipole as well as
quadrupole polarisabilities from low energy nucleon Compton scattering up to
the one pion production threshold and discuss the connection to the definition
of static nucleon polarisabilities. As a concrete example, we examine the
results of leading order Heavy Baryon Chiral Perturbation Theory for the four
leading spin independent iso-scalar polarisabilities of the nucleon. Finally,
we consider the possible r{\^o}le of energy dependent effects in low energy
extractions of the iso-scalar dipole polarisabilities from Compton scattering
on the deuteron.Comment: 17 pages LaTeX2e with 2 figures, using includegraphicx (5 .eps
files). Minor corrections, references updated. Contents identical to version
to appear in Phys. Rev. C 65, spelling differen
Electroweak Matrix Elements in the Two-Nucleon Sector from Lattice QCD
We demonstrate how to make rigorous predictions for electroweak matrix
elements in nuclear systems directly from QCD. More precisely, we show how to
determine the short-distance contributions to low-momentum transfer electroweak
matrix elements in the two-nucleon sector from lattice QCD. In potential model
descriptions of multi-nucleon systems, this is equivalent to uniquely
determining the meson-exchange currents, while in the context of nuclear
effective field theory, this translates into determining the coefficients of
local, gauge-invariant, multi-nucleon-electroweak current operators. The
energies of the lowest-lying states of two nucleons on a finite volume lattice
with periodic boundary conditions in the presence of a background magnetic
field are sufficient to determine the local four-nucleon operators that
contribute to the deuteron magnetic moment and to the threshold cross-section
of n + p -> d + gamma. Similarly, the energy-levels of two nucleons immersed in
a background isovector axial weak field can be used to determine the
coefficient of the leading local four-nucleon operator contributing to the
neutral- and charged-current break-up of the deuteron. This is required for the
extraction of solar neutrino fluxes at SNO and future neutrino experiments.Comment: 22 pages, 4 figure
Analyzing the Effects of Neutron Polarizabilities in Elastic Compton Scattering off He
Motivated by the fact that a polarized He nucleus behaves as an
`effective' neutron target, we examine manifestations of neutron
electromagnetic polarizabilities in elastic Compton scattering from the
Helium-3 nucleus. We calculate both unpolarized and double-polarization
observables using chiral perturbation theory to next-to-leading order
() at energies, , where is
the pion mass. Our results show that the unpolarized differential cross section
can be used to measure neutron electric and magnetic polarizabilities, while
two double-polarization observables are sensitive to different linear
combinations of the four neutron spin polarizabilities.
[Note added in 2018] The qualitative conclusions and analytic formulae
presented in this paper are correct, but several of the numerical results are
wrong: see the erratum posted as arXiv:1804.01206 for further details. A full
suite of corrected numerical results for cross sections and asymmetries can be
found in Margaryan et al., arXiv:1804.00956. They can also be obtained as an
interactive Mathematica notebook by emailing [email protected]: 40 pages, 16 figure
Cluster Transformation Coefficients for Structure and Dynamics Calculations in n-Particle Systems: Atoms, Nuclei, and Quarks
The structure and dynamics of an n-particle system are described with coupled
nonlinear Heisenberg's commutator equations where the nonlinear terms are
generated by the two-body interaction that excites the reference vacuum via
particle-particle and particle-hole excitations. Nonperturbative solutions of
the system are obtained with the use of dynamic linearization approximation and
cluster transformation coefficients. The dynamic linearization approximation
converts the commutator chain into an eigenvalue problem. The cluster
coefficients factorize the matrix elements of the (n)-particles or
particle-hole systems in terms of the matrix elements of the (n-1)-systems
coupled to a particle-particle, particle-hole, and hole-hole boson. Group
properties of the particle-particle, particle-hole, and hole-hole permutation
groups simplify the calculation of these coefficients. The particle-particle
vacuum-excitations generate superconductive diagrams in the dynamics of
3-quarks systems. Applications of the model to fermionic and bosonic systems
are discussed.Comment: 13 pages, 5 figures, Wigner Proceedings for Conference Wigner
Centenial Pecs, July 8-12, 200
Photon- and pion-nucleon interactions in a unitary and causal effective field theory based on the chiral Lagrangian
We present and apply a novel scheme for studying photon- and pion-nucleon
scattering beyond the threshold region. Partial-wave amplitudes for the
and states are obtained by an analytic extrapolation of
subthreshold reaction amplitudes computed in chiral perturbation theory, where
the constraints set by electromagnetic-gauge invariance, causality and
unitarity are used to stabilize the extrapolation. Based on the chiral
Lagrangian we recover the empirical s- and p-wave amplitudes up to energies
MeV in terms of the parameters relevant at order .Comment: 76 pages, 23 figures, one additional figure, Tables 4,5 and Figure 4
are corrected, a few references and comments are added. The role of higher
partial waves in pion photoproduction is clarifie
Nucleon Polarizabilities from Deuteron Compton Scattering within a Green's-Function Hybrid Approach
We examine elastic Compton scattering from the deuteron for photon energies
ranging from zero to 100 MeV, using state-of-the-art deuteron wave functions
and NN-potentials. Nucleon-nucleon rescattering between emission and absorption
of the two photons is treated by Green's functions in order to ensure gauge
invariance and the correct Thomson limit. With this Green's-function hybrid
approach, we fulfill the low-energy theorem of deuteron Compton scattering and
there is no significant dependence on the deuteron wave function used.
Concerning the nucleon structure, we use Chiral Effective Field Theory with
explicit \Delta(1232) degrees of freedom within the Small Scale Expansion up to
leading-one-loop order. Agreement with available data is good at all energies.
Our 2-parameter fit to all elastic data leads to values for the
static isoscalar dipole polarizabilities which are in excellent agreement with
the isoscalar Baldin sum rule. Taking this value as additional input, we find
\alpha_E^s= (11.3+-0.7(stat)+-0.6(Baldin)) x 10^{-4} fm^3 and \beta_M^s =
(3.2-+0.7(stat)+-0.6(Baldin)) x 10^{-4} fm^3 and conclude by comparison to the
proton numbers that neutron and proton polarizabilities are essentially the
same.Comment: 47 pages LaTeX2e with 20 figures in 59 .eps files, using graphicx.
Minor modifications; extended discussion of theoretical uncertainties of
polarisabilities extraction. Version accepted for publication in EPJ
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