A New Treatment of 2N and 3N Bound States in Three Dimensions

Glöckle, W.; Elster, Ch.; Golak, J.; Skibiński, R.; Witała, H.; Kamada, H.

doi:10.1007/s00601-009-0064-1

Cited by 18 publications

(49 citation statements)

References 18 publications

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“…(Note this set is different from the one used in [7].) Also for the transition operator t tmt , generated by the Lippmann-Schwinger equation,…”

Section: An Alternative Form Of the Faddeev Equation Using The Operatmentioning

confidence: 99%

“…As pointed out in Ref. [7], it is crucial for the present formulation to write the Faddeev amplitude ψ tT (p, q) ≡ pq | ψ tT in the operator form [10]. It reads 5 where |χ m = |(0 1 2 ) 1 2 m is a specific state in which the three spin-1/2 states are coupled to the total angular momentum quantum numbers of the 3N bound state.…”

Section: An Alternative Form Of the Faddeev Equation Using The Operatmentioning

confidence: 99%

“…Note that we actually use the second set of operators from Ref. [7]. Note also that several misprints in Eq.…”

Section: An Alternative Form Of the Faddeev Equation Using The Operatmentioning

confidence: 99%

“…Using exactly the same algebra as in Ref. [7], we arrive at the final form of the Faddeev equation (2), which corresponds to Eq. (50) in Ref.…”

Section: An Alternative Form Of the Faddeev Equation Using The Operatmentioning

confidence: 99%

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A Three-Dimensional Treatment of the Three-Nucleon Bound State

et al. 2012

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Recently a formalism for a direct treatment of the Faddeev equation for the three-nucleon (3N) bound state in three dimensions has been proposed. It relies on an operator representation of the Faddeev component in the momentum space and leads to a finite set of coupled equations for scalar functions which depend only on three variables. In this paper we provide further elements of this formalism and show the first numerical results for chiral NNLO nuclear forces.

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“…(Note this set is different from the one used in [7].) Also for the transition operator t tmt , generated by the Lippmann-Schwinger equation,…”

Section: An Alternative Form Of the Faddeev Equation Using The Operatmentioning

confidence: 99%

Section: An Alternative Form Of the Faddeev Equation Using The Operatmentioning

confidence: 99%

“…Note that we actually use the second set of operators from Ref. [7]. Note also that several misprints in Eq.…”

Section: An Alternative Form Of the Faddeev Equation Using The Operatmentioning

confidence: 99%

“…Using exactly the same algebra as in Ref. [7], we arrive at the final form of the Faddeev equation (2), which corresponds to Eq. (50) in Ref.…”

Section: An Alternative Form Of the Faddeev Equation Using The Operatmentioning

confidence: 99%

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A Three-Dimensional Treatment of the Three-Nucleon Bound State

et al. 2012

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“…[3]. When considering the deuteron which carries isospin t = 0 and total spin s = 1, we start from an operator equation [1] and again use the expansion of Eq. (1).…”

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confidence: 99%

Recent Developments of a Three-dimensional Description of the NN System

et al. 2011

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A recently developed three-dimensional formulation of nucleon-nucleon (NN) scattering is briefly presented. Here the NN t-matrix is represented by six spin-momentum operators accompanied by six scalar functions of momentum vectors. A numerical example for the NN scattering cross section is given.Traditionally numerical calculations for two-or three-nucleon systems are based on the partial wave decomposition (PWD) of states taking advantage of the rotational invariance of the interactions involved. This is an established and successful procedure for describing processes at moderate projectile energies. However, if one wishes to move to a higher energy regime, the number of partial waves needed to obtain a converged result proliferates and a scheme that avoids a PWD becomes more appealing.Recently we proposed a three-dimensional (3D) formulation of the momentum space Faddeev equations for 3N bound states [1] and 3N scattering [2] taking advantage of the fact that traces over spin-momentum operators can be analytically evaluated, leaving the Faddeev equations as a finite set of coupled equations for

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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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A New Treatment of 2N and 3N Bound States in Three Dimensions

Cited by 18 publications

References 18 publications

A Three-Dimensional Treatment of the Three-Nucleon Bound State

A Three-Dimensional Treatment of the Three-Nucleon Bound State

Recent Developments of a Three-dimensional Description of the NN System

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

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