Two-body scattering without angular-momentum decomposition

Rodríguez‐Gallardo, M.; Deltuva, A.; Cravo, E.; Crespo, R.; Fonseca, A. C.

doi:10.1103/physrevc.78.034602

Cited by 21 publications

(42 citation statements)

References 27 publications

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“…The spectator equation for relativistic NN scattering has been successfully solved in [7] using a helicity formulation. Aside from NN scattering, 3D formulations for the scattering of pions off nucleons [8] and protons off light nuclei [9] have recently been successfully carried out.…”

Section: Introductionmentioning

confidence: 99%

Two-nucleon systems in three dimensions

et al. 2010

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A recently developed formulation for treating two-and three-nucleon bound states in a threedimensional formulation based on spin-momentum operators is extended to nucleon-nucleon scattering. Here the nucleon-nucleon t-matrix is represented by six spin-momentum operators accompanied by six scalar functions of momentum vectors. We present the formulation and provide numerical examples for the deuteron and nucleon-nucleon scattering observables. A comparison to results from a standard partial wave decomposition establishes the reliability of this new formulation. 21.45.Bc

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Section: Introductionmentioning

confidence: 99%

Two-nucleon systems in three dimensions

et al. 2010

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“…The three-dimensional Lippmann-Schwinger (LS3D) solution method avoids the numerical difficulties associated with the PW method and has been used for relatively low energy reactions [21][22][23][24][25]. This section outlines the LS3D equation and the solution methods.…”

Section: B Lippmann-schwinger 3d Solution Methodsmentioning

confidence: 99%

“…The incoming momentum, k, is taken to be in the direction of the z-axis, and the azimuthal angle between k and k ′ is set to zero: φ ′ = 0; therefore, y may be expressed as a function of x ′ , x ′′ , and φ ′′ [21,23],…”

Section: B Lippmann-schwinger 3d Solution Methodsmentioning

confidence: 99%

“…Although there are numerical limitations associated with the PW method, the full threedimensional Lippmann-Schwinger (LS3D) solution method circumvents the necessity of using highly oscillating Legendre polynomials [21][22][23][24][25]. Most of the LS3D studies have consisted of NN interactions [21,22,24] with the exception of Rodriguez-Gallardo et al [23] who studied NA and AA reactions at relatively low energies and Liu et al [25] who studied three-body reactions.…”

Section: Introductionmentioning

confidence: 99%

“…Most of the LS3D studies have consisted of NN interactions [21,22,24] with the exception of Rodriguez-Gallardo et al [23] who studied NA and AA reactions at relatively low energies and Liu et al [25] who studied three-body reactions. This demonstrates the validity of the method and can be compared to results generated with the PW method since few partial waves are needed for such reactions.…”

Section: Introductionmentioning

confidence: 99%

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Elastic differential cross sections for space radiation applications

et al. 2014

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The eikonal, partial wave (PW) Lippmann-Schwinger, and three-dimensional LippmannSchwinger (LS3D) methods are compared for nuclear reactions that are relevant for space radiation applications. Numerical convergence of the eikonal method is readily achieved when exact formulas of the optical potential are used for light nuclei (A ≤ 16), and the momentum-space representation of the optical potential is used for heavier nuclei. The PW solution method is known to be numerically unstable for systems that require a large number of partial waves, and, as a result, the LS3D method is employed. The effect of relativistic kinematics is studied with the PW and LS3D methods and is compared to eikonal results. It is recommended that the LS3D method be used for high energy nucleon-nucleus reactions and nucleus-nucleus reactions at all energies because of its rapid numerical convergence and stability.

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Different Methods for the Two-Nucleon T-Matrix in the Operator Form

et al. 2012

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We compare three methods to calculate the nucleon-nucleon t-matrix based on the three-dimensional formulation of J. Golak et al., Phys. Rev. C 81, 034006, (2010). In the first place we solve a system of complex linear inhomogeneous equations directly for the t-matrix. Our second method is based on iterations and a variant of the Lanczos algorithm. In the third case we obtain the t-matrix in two steps, solving a system of real linear equations for the k-matrix expansion coefficients and then solving an on-shell equation, which connects the scalar coefficients of the k- and t-matrices. A very good agreement among the three methods is demonstrated for selected nucleon-nucleon scattering observables using a chiral next-to-next-to-leading-order neutron-proton potential. We also apply our three-dimensional framework to the demanding problem of proton-proton scattering, using a corresponding version of the nucleon-nucleon potential and supplementing it with the (screened) Coulomb force, taken also in the three-dimensional form. We show converged results for two different screening functions and find a very good agreement with other methods dealing with proton-proton scattering.Comment: 18 pages, 10 figures (54 eps files

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Two-body scattering without angular-momentum decomposition

Cited by 21 publications

References 27 publications

Two-nucleon systems in three dimensions

Two-nucleon systems in three dimensions

Elastic differential cross sections for space radiation applications

Different Methods for the Two-Nucleon T-Matrix in the Operator Form

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