Calculation of relativistic nucleon-nucleon potentials in three dimensions

Abstract

In this paper, we have applied a three-dimensional approach for calculation of the relativistic nucleon-nucleon potential. The quadratic operator relation between the non-relativistic and the relativistic nucleon-nucleon interactions is formulated as a function of relative two-nucleon momentum vectors, which leads to a three-dimensional integral equation. The integral equation is solved by the iteration method, and the matrix elements of the relativistic potential are calculated from non-relativistic ones. Spin-independent Malfliet-Tjon potential is employed in the numerical calculations, and the numerical tests indicate that the two-nucleon observables calculated by the relativistic potential are preserved with high accuracy.PACS. 21.45-v Few-body systems -21.45.Bc Two-nucleon system -24.10.Jv Relativistic models arXiv:1701.05279v1 [nucl-th]

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

“…Moreover, in a prior study for calculating relativistic potentials from spin-independent MT potential 10 , which has no spin and isospin complexity of CD-Bonn, we obtained a relative percentage difference of between nonrelativistic and relativistic deuteron binding energies and a maximum relative percentage difference of in two-body total elastic scattering cross-sections, which can be compared with and relative percentage differences obtained in this study for CD-Bonn potential. This comparison indicates calculating relativistic NN interactions from realistic interactions in a 3D scheme provides almost the same accuracy as a spin-independent calculation.…”

“…We have recently implemented this iterative technique in a 3D scheme to calculate the matrix elements of relativistic two-body (2B) potentials for spin-independent Malfliet-Tjon (MT) potential as a function of the magnitude of 2B relative momenta and the angle between them. To do so, we formulated the quadratic operator relation between the nonrelativistic and relativistic NN potentials in momentum space leading to a 3D integral equation 10 . We successfully implemented this iterative approach to calculate the matrix elements of boosted 2B potential from the MT potential to study the relativistic effects in a 3B bound state 11 .…”

General operator form of the non-local three-nucleon force

“…[11,12]. More detailed information about the 3D formalism, with emphasis on few-nucleon bound and scattering states, can be found in works by the Kraków, Bohum, Tehran, Ohio, and University of Iowa groups [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28].…”

Three-boson stability for boosted interactions towards the zero-range limit

“…The inputs for the solution of relativistic Lippmann-Schwinger equation ( 2) are the matrix elements of boosted potentials V k (p, p ) which can be obtained directly from p (fm nonrelativistic interaction V nr (p, p ) by solving the integral Eq. (3) using an iterative scheme proposed by Kamada and Glöckle [18] and successfully implemented in a threedimensional scheme [26,27]. The iteration starts with the initial guess…”

“…[28]), we obtain relativistic 3B binding energies E t and Faddeev components ψ(p, k) for ground and excited states. We use the Gauss-Legendre quadratures with hyperbolic plus linear mapping for Jacobi momenta and linear mapping for angle variables to discretize continuous momentum and angle variables [26]. The cutoffs of Jacobi momenta and the distribution of their mesh points strongly depend on the potential form factor parameters β and Λ.…”