102 research outputs found
An exactly solvable three-particle problem with three-body interaction
The energy spectrum of the three-particle Hamiltonian obtained by replacing
the two-body trigonometric potential of the Sutherland problem by a three-body
one of a similar form is derived. When expressed in appropriate variables, the
corresponding wave functions are shown to be expressible in terms of Jack
polynomials. The exact solvability of the problem with three-body interaction
is explained by a hidden sl(3,\R) symmetry.Comment: LaTeX, 15 pages, no figures, slightly shortened version to appear in
Phys. Rev. A, one error correcte
G(2)-Calogero-Moser Lax operators from reduction
We construct a Lax operator for the -Calogero-Moser model by means of a
double reduction procedure. In the first reduction step we reduce the
-model to a -model with the help of an embedding of the -root
system into the -root system together with the specification of certain
coupling constants. The -Lax operator is obtained thereafter by means of
an additional reduction by exploiting the embedding of the -system into
the -system. The degree of algebraically independent and non-vanishing
charges is found to be equal to the degrees of the corresponding Lie algebra.Comment: 12 pages, Late
A new measurement of the neutron detection efficiency for the NaI Crystal Ball detector
We report on a measurement of the neutron detection efficiency in NaI
crystals in the Crystal Ball detector obtained from a study of single p0
photoproduction on deuterium using the tagged photon beam at the Mainz
Microtron. The results were obtained up to a neutron energy of 400 MeV. They
are compared to previous measurements made more than 15 years ago at the pion
beam at the BNL AGS
Measurement of the transverse target and beam-target asymmetries in meson photoproduction at MAMI
We present new data for the transverse target asymmetry T and the very first
data for the beam-target asymmetry F in the
reaction up to a center-of-mass energy of W=1.9 GeV. The data were obtained
with the Crystal-Ball/TAPS detector setup at the Glasgow tagged photon facility
of the Mainz Microtron MAMI. All existing model predictions fail to reproduce
the new data indicating a significant impact on our understanding of the
underlying dynamics of meson photoproduction. The peculiar nodal
structure observed in existing T data close to threshold is not confirmed.Comment: 5 pages, 3 figures, accepted for publication in PR
T and F asymmetries in π0 photoproduction on the proton
The γp→π0p reaction was studied at laboratory photon energies from 425 to 1445 MeV with a transversely polarized target and a longitudinally polarized beam. The beam-target asymmetry F was measured for the first time and new high precision data for the target asymmetry T were obtained. The experiment was performed at the photon tagging facility of the Mainz Microtron (MAMI) using the Crystal Ball and TAPS photon spectrometers. The polarized cross sections were expanded in terms of associated Legendre functions and compared to recent predictions from several partial-wave analyses. The impact of the new data on our understanding of the underlying partial-wave amplitudes and baryon resonance contributions is discussed
Quantum Calogero-Moser Models: Integrability for all Root Systems
The issues related to the integrability of quantum Calogero-Moser models
based on any root systems are addressed. For the models with degenerate
potentials, i.e. the rational with/without the harmonic confining force, the
hyperbolic and the trigonometric, we demonstrate the following for all the root
systems: (i) Construction of a complete set of quantum conserved quantities in
terms of a total sum of the Lax matrix (L), i.e. (\sum_{\mu,\nu\in{\cal
R}}(L^n)_{\mu\nu}), in which ({\cal R}) is a representation space of the
Coxeter group. (ii) Proof of Liouville integrability. (iii) Triangularity of
the quantum Hamiltonian and the entire discrete spectrum. Generalised Jack
polynomials are defined for all root systems as unique eigenfunctions of the
Hamiltonian. (iv) Equivalence of the Lax operator and the Dunkl operator. (v)
Algebraic construction of all excited states in terms of creation operators.
These are mainly generalisations of the results known for the models based on
the (A) series, i.e. (su(N)) type, root systems.Comment: 45 pages, LaTeX2e, no figure
Measurements of double-polarized compton scattering asymmetries and extraction of the proton spin polarizabilities
The spin polarizabilities of the nucleon describe how the spin of the nucleon responds to an incident polarized photon. The most model-independent way to extract the nucleon spin polarizabilities is through polarized Compton scattering. Double-polarized Compton scattering asymmetries on the proton were measured in the Δ(1232) region using circularly polarized incident photons and a transversely polarized proton target at the Mainz Microtron. Fits to asymmetry data were performed using a dispersion model calculation and a baryon chiral perturbation theory calculation, and a separation of all four proton spin polarizabilities in the multipole basis was achieved. The analysis based on a dispersion model calculation yields γE1E1=−3.5±1.2, γM1M1=3.16±0.85, γE1M2=−0.7±1.2, and γM1E2=1.99±0.29, in units of 10−4 fm4
Determination of the scalar polarizabilities of the proton using beam asymmetry in Compton scattering
The scalar dipole polarizabilities, and , are
fundamental properties related to the internal dynamics of the nucleon. The
currently accepted values of the proton polarizabilities were determined by
fitting to unpolarized proton Compton scattering cross section data. The
measurement of the beam asymmetry in a certain kinematical range
provides an alternative approach to the extraction of the scalar
polarizabilities. At the Mainz Microtron (MAMI) the beam asymmetry was measured
for Compton scattering below pion photoproduction threshold for the first time.
The results are compared with model calculations and the influence of the
experimental data on the extraction of the scalar polarizabilities is
determined.Comment: 6 pages, 5 figure
Helicity-dependent cross sections and double-polarization observable E in η photoproduction from quasifree protons and neutrons
Precise helicity-dependent cross sections and the double-polarization observable E were measured for η
photoproduction from quasifree protons and neutrons bound in the deuteron. The η → 2γ and η → 3π0 → 6γ
decay modes were used to optimize the statistical quality of the data and to estimate systematic uncertainties. The
measurement used the A2 detector setup at the tagged photon beam of the electron accelerator MAMI in Mainz.
A longitudinally polarized deuterated butanol target was used in combination with a circularly polarized photon
beam from bremsstrahlung of a longitudinally polarized electron beam. The reaction products were detected with
the electromagnetic calorimeters Crystal Ball and TAPS, which covered 98% of the full solid angle. The results
show that the narrow structure observed earlier in the unpolarized excitation function of η photoproduction off
the neutron appears only in reactions with antiparallel photon and nucleon spin (σ1/2). It is absent for reactions
with parallel spin orientation (σ3/2) and thus very probably related to partial waves with total spin 1/2. The
behavior of the angular distributions of the helicity-dependent cross sections was analyzed by fitting them with Legendre polynomials. The results are in good agreement with a model from the Bonn-Gatchina group, which
uses an interference of P11 and S11 partial waves to explain the narrow structure
Measurement of pi^0 photoproduction on the proton at MAMI C
Differential cross sections for the gamma p -> pi^0 p reaction have been
measured with the A2 tagged-photon facilities at the Mainz Microtron, MAMI C,
up to the center-of-mass energy W=1.9 GeV. The new results, obtained with a
fine energy and angular binning, increase the existing quantity of pi^0
photoproduction data by ~47%. Owing to the unprecedented statistical accuracy
and the full angular coverage, the results are sensitive to high partial-wave
amplitudes. This is demonstrated by the decomposition of the differential cross
sections in terms of Legendre polynomials and by further comparison to model
predictions. A new solution of the SAID partial-wave analysis obtained after
adding the new data into the fit is presented.Comment: 13 pages, 12 figures, 1 tabl
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