Amplitude analyses from incomplete data using fixed-t dispersion relations

1976 ◽  
Vol 54 (4) ◽  
pp. 390-407 ◽  
Author(s):  
A. P. Contogouris
Keyword(s):  
Experimental Data ◽  
Incomplete Data ◽  
Sum Rules ◽  
Finite Energy ◽  
High Energy ◽  
Dispersion Relations ◽  
The Real ◽  
General Method

A general method combining fixed-t dispersion relations with an incomplete set of experimental data and leading to amplitude analyses is presented. Applications to several two-body nondiffractive reactions are considered and certain regularities in the t structure of the resulting amplitudes are pointed out. Finite-energy sum rules (FESR) are also considered and discussed. Confrontation of the high energy solutions with FESR leads to an understanding of the t structure of the real parts of the amplitudes.

scholarly journals Elastic scattering and breakup reactions with light proton- and neutron-rich exotic nuclei

2018 ◽  
Vol 194 ◽  
pp. 07002
Author(s):  
M.K. Gaidarov ◽  
V.K. Lukyanov ◽  
D.N. Kadrev ◽  
E.V. Zemlyanaya ◽  
A.N. Antonov ◽  
...  
Keyword(s):  
Experimental Data ◽  
Elastic Scattering ◽  
Cross Sections ◽  
Cluster Model ◽  
Microscopic Analysis ◽  
High Energy ◽  
The Real ◽  
Optical Potentials ◽  
Generator Coordinate ◽  
Energy Approximation

A microscopic analysis of the optical potentials (OPs) and cross sections of elastic scattering of 8B on 12C, 58Ni, and 208Pb targets at energies 20 < E < 170 MeV and 12,14Be on 12C at 56 MeV/nucleon is carried out. The real part of the OP is calculated by a folding procedure and the imaginary part is obtained on the base of the high-energy approximation (HEA). The density distributions of 8B evaluated within the variational Monte Carlo (VMC) model and the three-cluster model (3CM) are used to construct the potentials. The 14Be densities obtained in the framework of the the generator coordinate method (GCM) are used to calculate the optical potentials, while for the same purpose both the VMC model and GCM densities of 12Be are used. In the hybrid model developed and explored in our previous works, the only free parameters are the depths of the real and imaginary parts of OP obtained by fitting the experimental data. The use of HEA to estimate the imaginary OP at energies just above the Coulomb barrier is discussed. In addition, cluster model, in which 8B consists of a p-halo and the 7Be core, is applied to calculate the breakup cross sections of 8B nucleus on 9Be, 12C, and 197Au targets, as well as momentum distributions of 7Be fragments. A good agreement of the theoretical results with the available experimental data is obtained. It is concluded that the reaction studies performed in this work may provide supplemental information on the internal spatial structure of the proton- and neutron-halo nuclei.

scholarly journals Global parameterization of $$\pi \pi $$ scattering up to 2 $${\mathrm {\,GeV}}$$

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
J. R. Pelaez ◽  
A. Rodas ◽  
J. Ruiz de Elvira
Keyword(s):  
Experimental Data ◽  
Partial Wave ◽  
Real Axis ◽  
Complex Plane ◽  
Dispersion Relations ◽  
The Real ◽  
Partial Waves

AbstractWe provide global parameterizations of $$\pi \pi \rightarrow \pi \pi $$ππ→ππ scattering S0 and P partial waves up to roughly 2 GeV for phenomenological use. These parameterizations describe the output and uncertainties of previous partial-wave dispersive analyses of $$\pi \pi \rightarrow \pi \pi $$ππ→ππ, both in the real axis up to 1.12 $${\mathrm {\,GeV}}$$GeV and in the complex plane within their applicability region, while also fulfilling forward dispersion relations up to 1.43 $${\mathrm {\,GeV}}$$GeV. Above that energy we just describe the available experimental data. Moreover, the analytic continuations of these global parameterizations also describe accurately the dispersive determinations of the $$\sigma /f_0(500)$$σ/f0(500), $$f_0(980)$$f0(980) and $$\rho (770)$$ρ(770) pole parameters.

scholarly journals What is duality?

1970 ◽  
Vol 318 (1534) ◽  
pp. 257-278 ◽  
Keyword(s):  
Sum Rules ◽  
Scattering Amplitude ◽  
Finite Energy ◽  
High Energy ◽  
Low Energy ◽  
Strong Interactions ◽  
High Energies ◽  
Resonance Formation ◽  
Interference Models ◽  
Regge Poles

Duality gives a satisfying connexion between two different areas of strong interaction physics, Regge poles at high energy and resonances at low energy. This interlocking gives powerful bootstrap conditions, and together with the assumption that certain channels do not contain resonances it gives strong restrictions on the hadron spectrum. Since there is some confusion about the term duality, we shall explain what is meant by the various forms of duality (f. e. s. r. (finite energy sum rules) duality, local duality), and what is meant by ‘building up’, and we shall show in what way antidual models (such as the generalized interference model) come into conflict with basic empirical facts. Duality expresses the relation between two descriptions of the hadronic scattering amplitude. At low energy (l. e.) the description by direct-channel resonances is simple and useful (see figure 1). At low energy the data show prominent peaks as a function of energy, and one may try the approximation of resonance saturation, i. e. of neglecting the non-resonating background. The second description is the exchange of Regge poles, and it is useful at high energies (h.e.), where typical features are forward peaks, energy dependence s α , and structure at fixed t (see figure 2). The two descriptions are very different; resonance formation corresponds to poles in the s channel, Regge exchange to poles in the t channel. Duality says that there are direct relations between these two descriptions, that they are equivalent in a certain sense. In complete contrast, the interference models postulate that one must add the two descriptions. (If lowest order perturbation theory was relevant to strong interactions, one would be led to adding the diagrams.)

DERIVATIVE DISPERSION RELATIONS FOR THE AMPLITUDE SLOPES IN pp AND ${\rm \bar{p}p}$ SCATTERING

2007 ◽  
Vol 16 (09) ◽  
pp. 2893-2897 ◽  
Author(s):  
ERASMO FERREIRA
Keyword(s):  
Elastic Scattering ◽  
Forward Direction ◽  
High Energy ◽  
Dispersion Relations ◽  
Energy Data ◽  
The Real

We extend the use of derivative dispersion relations to the study of slopes of the real and imaginary amplitudes in pp and [Formula: see text] elastic scattering. The new relations are tested against the solutions for the amplitudes obtained in the analysis of the high energy data. Extensions beyond the forward direction are investigated.

Study of potential curves by UHF type methods. CH4 molecule and its dissociation products

1986 ◽  
Vol 51 (4) ◽  
pp. 731-737
Author(s):  
Viliam Klimo ◽  
Jozef Tiňo
Keyword(s):  
Experimental Data ◽  
Quantum Chemistry ◽  
High Energy ◽  
Basis Set ◽  
Electronic Correlation ◽  
Exact Methods ◽  
Energy Parameters ◽  
Bond Functions ◽  
The Individual ◽  
Potential Curves

Geometry and energy parameters of the individual dissociation intermediate steps of CH4 molecule, parameters of the barrier to linearity and singlet-triplet separation of the CH2 molecule have been calculated by means of the UMP method in the minimum basis set augmented with the bond functions. The results agree well with experimental data except for the geometry of CH2(1A1) and relatively high energy values of CH(2II) and CH2(1A1) where the existence of two UHF solutions indicates a necessity of description of the electronic correlation by more exact methods of quantum chemistry.

scholarly journals High energy cosmic ray interactions and UHECR composition problem

2019 ◽  
Vol 210 ◽  
pp. 02001
Author(s):  
Sergey Ostapchenko
Keyword(s):  
Experimental Data ◽  
Monte Carlo ◽  
Cosmic Rays ◽  
Cosmic Ray ◽  
High Energy ◽  
Ultra High Energy ◽  
Hadronic Interactions ◽  
High Energy Cosmic Rays ◽  
Cosmic Ray Interactions ◽  
Composition Problem

The differences between contemporary Monte Carlo generators of high energy hadronic interactions are discussed and their impact on the interpretation of experimental data on ultra-high energy cosmic rays (UHECRs) is studied. Key directions for further model improvements are outlined. The prospect for a coherent interpretation of the data in terms of the UHECR composition is investigated.

Finite-energy sum rules and the reactions ee → eeϵ (750) and ee → eef (1260)

1971 ◽  
Vol 36 (5) ◽  
pp. 463-466 ◽  
Author(s):  
B. Schrempp-Otto ◽  
F. Schrempp ◽  
T.F. Walsh
Keyword(s):  
Sum Rules ◽  
Finite Energy

Algorithms for determining the phase of RHEED oscillations

2015 ◽  
Vol 48 (6) ◽  
pp. 1927-1934 ◽  
Author(s):  
Zbigniew Mitura ◽  
Sergei L. Dudarev
Keyword(s):  
Experimental Data ◽  
Direct Method ◽  
Incident Beam ◽  
Diffraction Theory ◽  
High Energy ◽  
Angle Of Incidence ◽  
High Energy Electron ◽  
Dynamical Diffraction ◽  
Glancing Angle ◽  
Low Symmetry

Oscillations of reflection high-energy electron diffraction (RHEED) intensities are computed using dynamical diffraction theory. The phase of the oscillations is determined using two different approaches. In the first, direct, approach, the phase is determined by identifying the time needed to reach the second oscillation minimum. In the second approach, the phase is found using harmonic analysis. The two approaches are tested by applying them to oscillations simulated using dynamical diffraction theory. The phase of RHEED oscillations observed experimentally is also analysed. Experimental data on the variation of the phase as a function of the glancing angle of incidence, derived using the direct method, are compared with the values computed using both the direct and harmonic methods. For incident-beam azimuths corresponding to low-symmetry directions, both approaches produce similar results.

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