Multiple scattering theory for pion-nucleus elastic scattering and the in-medium piN amplitude

Abstract

Elastic scattering of positive and/or negative pions (π + and/or π − ) by nuclei has been studied by means of Glauber's multiple scattering theory (GMST). The differential, total and total elastic cross sections using both the full series expansion and the first order correction (called optical limit results, OLA) of the Glauber amplitude, have been calculated. The in-medium πN amplitude (σ e f f . , σ e f f . ) as well as the free πN one (σ f ree , σ f ree ) are invoked into the full series calculations of the Glauber amplitude and our results were compared with the corresponding experimental data. These calculations are carried out for the elastic collisions, π − − 2 He 4 at incident energy 180 MeV, π ± − 3 Li 6 at 240 MeV, π − − 6 C 12 at incident energies 180, 200 and 260 MeV, π + − 8 O 16 at 240 and 270 MeV and π ± − 20 Ca 40 at energy 292.5 MeV. The comparisons reflect that, except around the minima, the full series calculations with the in-medium πN amplitude are better in describing the scattering data than those using the free πN one and both are better than the optical limit results.

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

“…Both the two figures display a very good agreement with the available experimental data by the negative values of γ. This result is Study of α-α 51 and d-nucleus 52 showed that for a given value of the ratio between real and imaginary forward NN elastic scattering amplitude, NN , the variation of γ leads to either overall increase or decrease in the estimated values of elastic scattering differential cross-sections. Indeed, they found such changes depending on the sign of both NN and γ.…”

“…Working within the full multiple scattering series of GMSM different values of γ covering the range from −0.311 fm 2 to −1.09 fm 2 are used to describe the scattering of deuteron from nuclei with 6 < A < 72 at different energies. 52 On the other hand, many efforts are made to calculate the phase variation parameter from effective NN potentials. Ahmed and Alvi 56 estimated that γ is positive and equal to 0.03115 fm 2 at P = 1.75 GeV/c using both Gaussian and Yukawa NN potentials.…”

“…The total reaction cross-section is calculated by introducing the phase variation parameter, γ = ±2.0 fm 2 with = 0 = 0.17 fm −3 .compatible with the study of phase variation of hadronic amplitude 51 and phase variation enhancement on deuteron nucleus scattering 52. A conspicuous difference is clear between the results with positive and negative values of γ.…”

Analysis of elastic scattering data below, atop and above the delta resonance using inverse scattering theory

“…In the Δ-resonance region, also several theories, theoretical models and approximations as, but not restricted to, the multiple scattering theory (Eisenberg and Koltun, 1980) including both Watson's multiple scattering theory and Glauber's multiple scattering theory (Shalaby et al, 2007), the  -hole formalism (Hirata et al, 1979;Kisslinger and Wang, 1976), eikonal approximation with the interacting boson model (Zhang, 1993), strong absorption model (Begum et al, 2003;Rahman and Sen Gupta, 1991), the single folding  -cluster model (ElAzabFarid and Ebrahim 2015), equivalent local Kisslinger optical potential with analytical distorted wave approximation (Safari, 2005), a density dependent optical pion-nuclear potential (Gmitro et al, 1987), local and equivalent local optical potentials (Satchler, 1992;Johnson and Satchler, 1996;Khallaf and Ebrahim, 2000;Ebrahim and Khallaf, 2005;Khallaf and Ebrahim, 2005;Akhter et al, 2001;Hong and Kim, 1999) have been used with varying degrees of success. The deficiencies of these theories are alluded to 1) fail in reproducing backward elastic scattering data for both pion charges 2) difficulty in calculation due to non-localities 3) true quantitative description of the scattering process 4) disagreement between theory and experiment especially around maximum and minimum 5) unphysical meaning for some used parameters and 6) uncertainties in the data.…”

Study of elastic and inelastic pion-nucleus scattering using the microscopic model of optical potential

“…Later on in practice, many applications were made using the joint isospin-averaged 3-parameter πN -amplitude (see, e.g., Ref. 9 and references therein). However, in such approach problems arise to account for the meson trajectory distortions by the external nuclear and Coulomb potentials when calculating eikonal phases.…”