Scattering amplitudes and integral equations for the collision of two charged composite particles

Alt, E. O.; Sandhas, W.

doi:10.1103/physrevc.21.1733

Cited by 108 publications

(126 citation statements)

References 20 publications

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“…The channel states |ψ γ for γ = 1, 2, 3 are the eigenstates of the corresponding channel Hamiltonian H γ = H 0 + v γ with the energy eigenvalue E; thus, |ψ γ is a product of the bound state wave function for pair γ and a plane wave with fixed on-shell momentum corresponding to the relative motion of particle γ and pair γ in the initial or final state. The Coulomb interaction is an additional complication in the AGS method; nevertheless, when only two particles are charged and charge numbers Z are not too large, the Coulomb interaction has been successfully included [19,20] using the method of screening and renormalization [23,24].…”

Section: Theoretical Descriptionmentioning

confidence: 99%

Adiabatic approximation versus exact Faddeev method for (d,p) and (p,d) reactions

Nunes

Deltuva

2011

Phys. Rev. C

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The finite range adiabatic wave approximation provides a practical method to analyze (d,p) ≈ 5% for a range of beam energies (E d ≈ 20 − 40 MeV) but differences increase significantly for very low energies and for the highest energies. Our tests show that ADWA agrees best with Faddeev when the angular momentum transfer is small ∆l = 0 and when the neutron-nucleus system is loosely bound.

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Section: Theoretical Descriptionmentioning

confidence: 99%

Adiabatic approximation versus exact Faddeev method for (d,p) and (p,d) reactions

Nunes

Deltuva

2011

Phys. Rev. C

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“…The pp Coulomb force is included using the method of screening and renormalization [11,12] where the screening radius R = 10 to 12 fm is found to be sufficient to get convergence for the Coulomb-distorted short-range part of the amplitude. The obtained results are well converged with respect to the partial-wave expansion.…”

Section: Theorymentioning

confidence: 99%

Four-body calculation of elastic deuteron-deuteron scattering

Deltuva

Fonseca

2015

Phys. Rev. C

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Fully converged calculations of deuteron-deuteron elastic scattering observables are performed at energies above three-and four-body breakup threshold. Differential cross sections and analyzing powers are obtained using realistic nucleon-nucleon force models together with the Coulomb repulsion between protons. For all observables we find a very reasonable agreement with the available experimental data limited to deuteron beam energies up to 25.3 MeV.

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“…Applying the renormalization procedure, i.e., multiplying both sides of Eq. (5) by the renormalization factor Z −1 R [15,20], in the R → ∞ limit, yields the full 1 + 3 → 1 + 3 transition amplitude in the presence of Coulomb…”

mentioning

confidence: 99%

“…system to the pion production threshold. The work is based on the solution of the momentum-space Alt, Grassberger and Sandhas (AGS) equations [17] together with the screening and renormalization approach [18,19,20] for the Coulomb interaction leading to the results of observables that are independent of the screening radius, provided it is sufficiently large.In the present manuscript for the first time we extend the method of Refs. [15,16] to the p-3 He elastic scattering using the four-body AGS equations [21].…”

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confidence: 99%

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Four-Body Calculation of Proton-He3Scattering

2007

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The four-body equations of Alt, Grassberger and Sandhas are solved, for the first time, for proton-3 He scattering including the Coulomb interaction between the three protons using the method of screening and renormalization as it was done recently for proton-deuteron scattering. Various realistic two-nucleon potentials are used. Large Coulomb effects are seen on all observables. Comparison with data at different energies shows large deviations in the proton analyzing power but quite reasonable agreement in other observables. The effect of nucleon-nucleon magnetic moment interaction and correlations between p-d and p-3 He analyzing powers are studied.PACS numbers: 21.30. -x, 21.45.+v, 24.70.+s, 25.10.+s Modern calculations of light nuclear systems A ≤ 12 are essential to our understanding of the force models that have been developed to describe how nucleons interact at low energies [1,2]. Of these nuclear systems, the four-nucleon (4N ) system is particularly important because it gives rise, experimentally, to the simplest set of nuclear reactions that shows the complexity of heavier systems and the Coulomb interaction manifest itself in new ways relative to what is observed in the threenucleon (3N ) system. Theoretically it is also important because with powerful numerical techniques and fast computers one can calculate not only bound state properties [3] but also scattering observables [4,5,6,7,8,9, 10] for a number of elastic, transfer and breakup reactions that place new challenges to our understanding of the underlying force models. The importance of scattering calculations also has to do with the possibility to probe states in the continuum associated with specific resonances, states of higher angular momentum than corresponding bound states, effects that depend on the spin orientation of the projectile and/or target, and threshold effects on the observables, among others.While the three-nucleon system has been extensively studied [11,12] through neutron-deuteron (nd) and proton-deuteron (pd) elastic scattering and breakup experiments, exact calculations using realistic force models as well as interactions derived from Effective Field Theory were restricted, for a long time, to the nd system due to limitations in including the Coulomb force in the description of pd scattering beyond low energy pd → pd and pd ↔ γ 3 He calculations [13,14] in the framework of the variational hyperspherical approach. The situation has now changed due to the work of Refs. [15,16] where calculations of pd → pd, pd → ppn, pd ↔ γ 3 He, γ 3 He → ppn, e 3 He → e ′ pd, and e 3 He → e ′ ppn were performed at energies ranging from 1 MeV in the center of mass (c.m.) system to the pion production threshold. The work is based on the solution of the momentum-space Alt, Grassberger and Sandhas (AGS) equations [17] together with the screening and renormalization approach [18,19,20] for the Coulomb interaction leading to the results of observables that are independent of the screening radius, provided it is sufficiently large.In the prese...

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Scattering amplitudes and integral equations for the collision of two charged composite particles

Cited by 108 publications

References 20 publications

Adiabatic approximation versus exact Faddeev method for (d,p) and (p,d) reactions

Adiabatic approximation versus exact Faddeev method for (d,p) and (p,d) reactions

Four-body calculation of elastic deuteron-deuteron scattering

Four-Body Calculation of Proton-He3Scattering

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