Phase of the Elastic Scattering Amplitude and the Rate of Decrease of the Total Cross Section at High but Finite Energy

1969 ◽  
Vol 186 (5) ◽  
pp. 1695-1697
Author(s):  
Franklin F. K. Cheung
Keyword(s):  
Elastic Scattering ◽  
Total Cross Section ◽  
Cross Section ◽  
Scattering Amplitude ◽  
Finite Energy ◽  
Elastic Scattering Amplitude

scholarly journals First determination of the $${\rho }$$ parameter at $${\sqrt{s} = 13}$$ TeV: probing the existence of a colourless C-odd three-gluon compound state

2019 ◽  
Vol 79 (9) ◽  
Author(s):  
G. Antchev ◽  
P. Aspell ◽  
I. Atanassov ◽  
V. Avati ◽  
J. Baechler ◽  
...  
Keyword(s):  
Elastic Scattering ◽  
Total Cross Section ◽  
Cross Section ◽  
Scattering Amplitude ◽  
Theoretical Models ◽  
Proton Proton ◽  
Slowing Down ◽  
Proton Elastic Scattering ◽  
Compound State ◽  
Elastic Scattering Amplitude

Abstract The TOTEM experiment at the LHC has performed the first measurement at $$\sqrt{s} = 13\,\mathrm{TeV}$$s=13TeV of the $$\rho $$ρ parameter, the real to imaginary ratio of the nuclear elastic scattering amplitude at $$t=0$$t=0, obtaining the following results: $$\rho = 0.09 \pm 0.01$$ρ=0.09±0.01 and $$\rho = 0.10 \pm 0.01$$ρ=0.10±0.01, depending on different physics assumptions and mathematical modelling. The unprecedented precision of the $$\rho $$ρ measurement, combined with the TOTEM total cross-section measurements in an energy range larger than $$10\,\mathrm{TeV}$$10TeV (from 2.76 to $$13\,\mathrm{TeV}$$13TeV), has implied the exclusion of all the models classified and published by COMPETE. The $$\rho $$ρ results obtained by TOTEM are compatible with the predictions, from other theoretical models both in the Regge-like framework and in the QCD framework, of a crossing-odd colourless 3-gluon compound state exchange in the t-channel of the proton–proton elastic scattering. On the contrary, if shown that the crossing-odd 3-gluon compound state t-channel exchange is not of importance for the description of elastic scattering, the $$\rho $$ρ value determined by TOTEM would represent a first evidence of a slowing down of the total cross-section growth at higher energies. The very low-|t| reach allowed also to determine the absolute normalisation using the Coulomb amplitude for the first time at the LHC and obtain a new total proton–proton cross-section measurement $$\sigma _{\mathrm{tot}} = (110.3 \pm 3.5)\,\mathrm{mb}$$σtot=(110.3±3.5)mb, completely independent from the previous TOTEM determination. Combining the two TOTEM results yields $$\sigma _{\mathrm{tot}} = (110.5 \pm 2.4)\,\mathrm{mb}$$σtot=(110.5±2.4)mb.

Diffractive results from CDF

2015 ◽  
Vol 30 (08) ◽  
pp. 1542003 ◽  
Author(s):  
Konstantin Goulianos
Keyword(s):  
Elastic Scattering ◽  
Total Cross Section ◽  
Cross Section ◽  
Imaginary Part ◽  
Scattering Amplitude ◽  
Pomeron Exchange ◽  
Optical Theorem ◽  
Double Dissociation ◽  
Elastic Scattering Amplitude ◽  
Theoretical Predictions

We present a reference review of diffractive results from CDF for [Formula: see text] collisions at [Formula: see text], 630, 1800, and 1960 GeV at the Tevatron, published in 19 PRL/PRD papers from 1994 to 2012. Both soft and hard diffractive results are included for single and/or double dissociation, central diffraction or double Pomeron exchange (where both the proton and antiproton remain intact), multi-gap diffraction (a combination of single and double dissociation), elastic scattering, and the total cross-section, which through the optical theorem is related to the imaginary part of the forward elastic scattering amplitude. In each review, we include the comparisons made by CDF with theoretical predictions.

scholarly journals ELASTIC SCATTERING OF PROTONS FROM $\sqrt{s} = 23.5~{\rm GeV}$ to 7 TeV FROM A GENERALIZED BIALAS–BZDAK MODEL

2014 ◽  
Vol 29 (02) ◽  
pp. 1450019 ◽  
Author(s):  
T. CSÖRGŐ ◽  
F. NEMES
Keyword(s):  
Elastic Scattering ◽  
Total Cross Section ◽  
Cross Section ◽  
Scattering Amplitude ◽  
Elastic Cross Section ◽  
Forward Scattering Amplitude ◽  
Proton Proton ◽  
Elastic Proton ◽  
Model Independent ◽  
Total P

The Bialas–Bzdak model of elastic proton–proton scattering is generalized to the case when the real part of the parton–parton level forward scattering amplitude is nonvanishing. Such a generalization enables the model to describe well the dip region of the differential cross-section of elastic scattering at the intersecting storage rings (ISR) energies, and improves significantly the ability of the model to describe also the recent TOTEM data at [Formula: see text] LHC energy. Within this framework, both the increase of the total cross-section, as well as the decrease of the location of the dip with increasing colliding energies, is related to the increase of the quark–diquark distance and to the increase of the "fragility" of the protons with increasing energies. In addition, we present and test the validity of two new phenomenological relations: one of them relates the total p+p cross-section to an effective, model-independent proton radius, while the other relates the position of the dip in the differential elastic cross-section to the measured value of the total cross-section.

Study of p-4Hetotal reaction cross-section using Glauber and Coulomb-modified Glauber models

2014 ◽  
Vol 23 (03) ◽  
pp. 1450010 ◽  
Author(s):  
Ibrahim M. A. Tag El-Din ◽  
M. M. Taha ◽  
Samia S. A. Hassan
Keyword(s):  
Elastic Scattering ◽  
Energy Range ◽  
Cross Section ◽  
Reaction Cross Section ◽  
Scattering Amplitude ◽  
Phase Variation ◽  
Nucleon Nucleon ◽  
Reaction Cross ◽  
Pauli Blocking ◽  
Elastic Scattering Amplitude

The total nuclear reaction cross-section σRfor p-4He in the energy range from 25 MeV to 1000 MeV is calculated within Glauber and Coulomb-modified Glauber models. The Coulomb-modified Glauber model (CMGM) is introduced via modification of the Coulomb trajectory of the projectile from a straight line, and calculation of the effective radius of interaction. The effects of in-medium nucleon–nucleon (NN) total cross-section, phase variation, high order momentum transfer component of nucleon–nucleon elastic scattering amplitude and Pauli blocking are studied. It is pointed out that the phase variation of the nucleon–nucleon amplitude plays a significant role in describing σRwith γ = -1.6 fm2at in-medium nuclear density ϱ = 0 and γ = -2 fm2at ϱ = 0.17 fm-3in the whole energy range. A remarkable fit to the available experimental data is obtained by invoking Pauli blocking and high order momentum transfer of nucleon–nucleon (NN) elastic scattering amplitude for Ep< 100 MeV.

scholarly journals REAL PART OF THE $\bar pp$ ELASTIC SCATTERING AMPLITUDE AT $\sqrt{s} = 546\, {\rm GeV}$

1991 ◽  
Vol 06 (32) ◽  
pp. 2973-2975 ◽  
Author(s):  
CLAUDE BOURRELY ◽  
JACQUES SOFFER ◽  
TAI TSUN WU
Keyword(s):  
Experimental Data ◽  
Elastic Scattering ◽  
Cross Section ◽  
Scattering Amplitude ◽  
Accurate Determination ◽  
The Real ◽  
Interference Region ◽  
Elastic Scattering Amplitude ◽  
Theoretical Predictions

In order to get an accurate determination of the real part of the [Formula: see text] elastic scattering amplitude at [Formula: see text], the Genoa–Palaiseau–Roma–Valencia collaboration plans to take experimental data on dσ/dt in the Coulomb interference region. We present detailed theoretical predictions for this cross-section. These predictions can be compared directly with the forthcoming data.

Phase Variation Effect on Proton - Nucleus Elastic Scattering

1996 ◽  
Vol 49 (3) ◽  
pp. 655 ◽  
Author(s):  
Mohamed A Hassan ◽  
Hamed EA Awd-Allah ◽  
Samia SA Hassan ◽  
Ibrahim MA Tag El-Din
Keyword(s):  
Experimental Data ◽  
Elastic Scattering ◽  
Cross Section ◽  
Scattering Amplitude ◽  
Phase Variation ◽  
Nucleon Nucleon ◽  
Free Nucleon ◽  
High Energies ◽  
Elastic Scattering Amplitude ◽  
Variation Parameter

Proton–deuteron elastic scattering at intermediate and high energies illustrates the importance of the phase variation of the nucleon–nucleon elastic scattering amplitude as in previous work. Two kinds of phase variation are examined. The first is the usual one which is related to free nucleon-free nucleon collisions as suggested by Franco. The second is assumed to be related to the time ordering of multi-scattering processes. The two kinds play similar roles in improving the results. The contributions of both kinds lead to a good fit to the experimental data at the energies considered. The value of the phase variation parameter in each kind (where they are considered together), which gives a good fit to the experimental data, are approximately the same and of order 4 (GeV / c)‾ 2. Also, with relatively small values of the phase variation parameter, the phase variation effect improves the agreement with the experimental data for the p–4He elastic scattering differential cross section at the minimum region in the energy range 97–393 GeV.

Soluble model of a break-up process

1961 ◽  
Vol 264 (1318) ◽  
pp. 408-430 ◽  
Keyword(s):  
Elastic Scattering ◽  
Cross Section ◽  
Cross Sections ◽  
Scattering Amplitude ◽  
Impulse Approximation ◽  
Branch Points ◽  
Elastic Scattering Amplitude ◽  
Break Up ◽  
Analytic Behaviour ◽  
Dominant Peak

The exact solution of a one-dimensional problem, representing the scattering of a particle by another particle which is bound to a fixed centre of force, is given. All the interactions have zero range and are described by boundary conditions. The possible processes are elastic scattering and break-up of the bound system. The elastic scattering and break-up amplitudes are explicitly determined, and the behaviour of the corresponding cross-sections is discussed. At high energies, the incident particle tends to transfer its whole momentum to the bound one, giving rise to a strong peak in the break-up cross-section. The analytic behaviour of the amplitudes is examined. The Riemann surface of the elastic scattering amplitude has three sheets. The break-up threshold gives rise to cubic-root branch points. The remaining singularities are a finite number of poles. The exact amplitudes are compared with those given by the impulse approximation (in first and second order) and by Born’s approximation. It is found that these approximations are reliable only at high incident energies and within the width of the dominant peak of the break-up cross-section.

Glaubere−- Li elastic scattering amplitude

1976 ◽  
Vol 14 (1) ◽  
pp. 189-192 ◽  
Author(s):  
F. T. Chan ◽  
C. H. Chang
Keyword(s):  
Elastic Scattering ◽  
Scattering Amplitude ◽  
Elastic Scattering Amplitude
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