Impact-Parameter Representations and the Coordinate-Space Description of a Scattering Amplitude

1969 ◽  
Vol 181 (5) ◽  
pp. 2048-2055 ◽  
Author(s):  
N. P. Chang ◽  
K. Raman
Keyword(s):  
Impact Parameter ◽  
Scattering Amplitude ◽  
Coordinate Space ◽  
Space Description

Impact Parameter Representations

1972 ◽  
Vol 50 (16) ◽  
pp. 1862-1875 ◽  
Author(s):  
A. N. Kamal
Keyword(s):  
Wave Function ◽  
Impact Parameter ◽  
Momentum Space ◽  
Scattering Amplitude ◽  
Function Approach ◽  
Coordinate Space ◽  
Energy Shell ◽  
Parameter Representation ◽  
The Relationship

A discussion of the Glauber and Blankenbecler–Goldberger impact parameter representation for the scattering amplitude is presented with emphasis on the wave function approach. The treatment makes clear the relationship between the approximations made to derive either of the two amplitudes. Both on-energy-shell and off-energy-shell scatterings are treated. A derivation of the two representations in momentum space is presented bringing out the relationship between the approximations in a coordinate space treatment and the momentum space treatment.

On the possibility of gluon number fluctuations in diffractive deep inelastic scattering data with impact parameter

2016 ◽  
Vol 31 (33) ◽  
pp. 1650186
Author(s):  
Z. Hu ◽  
W. Xiang ◽  
S. Cai
Keyword(s):  
Inelastic Scattering ◽  
Deep Inelastic Scattering ◽  
Impact Parameter ◽  
Scattering Amplitude ◽  
Global Analysis ◽  
High Energy ◽  
Scattering Data ◽  
Deep Inelastic Scattering Data ◽  
Saturation Exponent ◽  
The Impact

A global analysis of the latest diffractive deep inelastic scattering (DIS) data with gluon number fluctuations and impact parameter is performed. The impact parameter is introduced into the scattering amplitude by saturation scale with a Gaussian b-dependence. The results show that the description of the diffractive DIS data is improved once the gluon number fluctuations and impact parameter are included, with [Formula: see text]/d.o.f = 0.878, [Formula: see text]/d.o.f = 0.928 and [Formula: see text]/d.o.f = 0.897 in different sets of free parameters. Moreover, we find that the impact parameter ([Formula: see text] 0.1) is possibly compressed by the gluon number fluctuations, which leads to the value of saturation exponent returning to [Formula: see text] 0.2. This outcome is compatible with the prediction that the saturation exponent is dominated by the fluctuations at sufficiently high energy, which may indicate the possibility of gluon number fluctuations in diffractive DIS data.

Real part of scattering amplitude at ultrahigh energies

2015 ◽  
Vol 30 (30) ◽  
pp. 1550188 ◽  
Author(s):  
V. V. Anisovich ◽  
V. A. Nikonov ◽  
J. Nyiri
Keyword(s):  
Impact Parameter ◽  
Parameter Space ◽  
Scattering Amplitude ◽  
Black Disk ◽  
Asymptotic Regime ◽  
The Real ◽  
Impact Parameter Space ◽  
The Impact

On the basis of requirements of unitarity and analyticity we analyze the real and imaginary parts of the scattering amplitude at recent ultrahigh energies, [Formula: see text]. The predictions for the region [Formula: see text] and [Formula: see text] are given supposing the black disk asymptotic regime. It turns out that the real part of the amplitude is concentrated in the impact parameter space at the border of the black disk.

Impact Parameter Representation of the Scattering Amplitude

1971 ◽  
Vol 49 (14) ◽  
pp. 1885-1898 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Elastic Scattering ◽  
Phase Shift ◽  
Differential Cross Section ◽  
Cross Section ◽  
Impact Parameter ◽  
Differential Cross ◽  
Scattering Amplitude ◽  
Potential Methods ◽  
Energy Dependent ◽  
The Impact

From the Lippmann–Schwinger equation, the exact and different approximate relations for the impact parameter form of the total scattering amplitude on- and off-the-energy shell are derived. The relation between the impact parameter phase shift and the range of potential is studied, and several methods of determining the potential from the impact parameter phase shift for local, nonlocal, and energy dependent interactions are obtained in Blankenbecler and Goldberger's approximation. By considering solvable examples it is shown that the Glauber's approximation, in certain cases, may be valid for all scattering angles. Finally for completely elastic scattering or for a purely absorptive potential, methods of finding the impact parameter phase shift from the differential cross section for scattering are given.

scholarly journals ONE-DIMENSIONAL MODEL FOR QCD AT HIGH ENERGY

2007 ◽  
Vol 16 (09) ◽  
pp. 2814-2817
Author(s):  
J. T. DE SANTANA AMARAL
Keyword(s):  
Impact Parameter ◽  
Evolution Equations ◽  
Scattering Amplitude ◽  
Mean Field ◽  
Reaction Diffusion ◽  
Universality Class ◽  
High Energy ◽  
Natural Generalization ◽  
Dimensional Model ◽  
Structural Aspects

In these proceedings a stochastic particle (1+1)-dimensional model which mimics high energy evolution and scattering in QCD at fixed impact parameter is presented. The model exhibits a saturation mechanism similar to gluon saturation in QCD as well as all the qualitative features expected in QCD at fixed impact parameter, concerning both the mean-field aspects and the effects of fluctuations, and appears to be in the universality class of the reaction-diffusion process, as also expected for QCD. The evolution equations for the scattering amplitude generated by this model appear as a natural generalization of the Balitsky-JIMWLK equations in which both target and projectile are symmetrically treated. The structural aspects of the model may inspire future searches for corresponding structures in QCD.

scholarly journals Cul-De-Sac of the Spatial Image of Proton Interactions

Physics ◽  
2019 ◽  
Vol 1 (1) ◽  
pp. 33-39 ◽  
Author(s):  
Igor Dremin
Keyword(s):  
Elastic Scattering ◽  
Impact Parameter ◽  
Imaginary Part ◽  
Parameter Space ◽  
Scattering Amplitude ◽  
Unitarity Condition ◽  
Spatial Image ◽  
Elastic Scattering Amplitude ◽  
Impact Parameter Space ◽  
The Impact

The unitarity condition in the impact parameter space is used to obtain some information about the shape of the interaction region of colliding protons. It is shown that, strictly speaking, a reliable conclusion can be gained only if the behavior of the elastic scattering amplitude (especially, its imaginary part) at all transferred momenta is known. This information is currently impossible to obtain from experimentation. In practice, several assumptions and models are used. They lead to different results as shown below.

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