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Bayegan, S.; Shalchi, M. A.; Hadizadeh, M. R.

doi:10.1103/physrevc.79.057001

Cited by 14 publications

(14 citation statements)

References 29 publications

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“…The helicity formalism of Ref. [5] was employed in 3N calculations in [11,12,13]. Recently we proposed a 3D framework for 3N bound [14,15] and 3N scattering states [16], where spin-momentum operators are introduced and treated analytically so the Faddeev equations turn into a finite set of coupled equations for scalar functions depending only on momentum vectors.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

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

et al. 2012

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“…Consequently, 3D representation avoids the very involved angular momentum algebra for permutations, transformations, and few-nucleon forces, and in contrast to the PW approach, the number of equations in the 3D representation is energy independent. The 3D scheme is successfully implemented in a series of few-body bound and scattering states calculations by different few-body groups, from Ohio-Bochum collaboration 4,5,7,[13][14][15][16][17][18][19][20][21][22][23][24][25] to Tehran [26][27][28][29][30][31][32] and Kraków [33][34][35][36][37][38][39][40][41] groups.…”

Section: Introductionmentioning

confidence: 99%

Relativistic nucleon-nucleon potentials in a spin-dependent three-dimensional approach

Hadizadeh,

Radin,

Nazari

2021

Preprint

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The matrix elements of relativistic nucleon-nucleon (NN) potentials are calculated directly from the nonrelativistic potentials as a function of relative NN momentum vectors, without using a partial wave decomposition. To this aim, the quadratic operator relation between the relativistic and nonrelativistic NN potentials is formulated in momentum-helicity basis states. It leads to a single integral equation for the two-nucleon (2N) spin-singlet state and four coupled integral equations for two-nucleon spin-triplet states, which are solved by an iterative method. Our numerical analysis indicates that the relativistic NN potential obtained using CD-Bonn potential reproduces the deuteron binding energy and neutron-proton elastic scattering differential and total cross-sections with high accuracy.

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“…In this paper we have attempted to formulate the full breakup and the elastic scattering of nucleon-deuteron (Nd) by including directly the spin-isospin degrees of freedom. To this end we have formulated the Faddeev equation for the 3N scattering with the advantage of using the helicity representation of NN forces such as the AV18, Bonn-B and the Chiral potentials [4], [17]. This manuscript is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

A spin-isospin-dependent 3N scattering formalism in a 3D Faddeev scheme

Harzchi

Bayegan

2010

Eur. Phys. J. A

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We have introduced a spin-isospin dependent three-dimensional approach for formulation of the three-nucleon scattering. Faddeev equation is expressed in terms of vector Jacobi momenta and spin-isospin quantum numbers of each nucleon. Our formalism is based on connecting the transition amplitude T to momentum-helicity representations of the two-body t-matrix and the deuteron wave function. Finally the expressions for nucleon-deuteron elastic scattering and full breakup process amplitudes are presented.

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Three dimensional calculations ofNNbound and scattering states with a chiral potential up toNLO3

Abstract: The recently developed chiral nucleon-nucleon

Cited by 14 publications

References 29 publications

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

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

Relativistic nucleon-nucleon potentials in a spin-dependent three-dimensional approach

A spin-isospin-dependent 3N scattering formalism in a 3D Faddeev scheme

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