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

We present an overview of our framework used to treat two-and three-nucleon (2N, 3N) systems employing three dimensional momentum eigenstates. Using a three dimensional formalism instead of the classical partial wave approach is an attractive alternative for a number of reasons, the most prominent being the very direct way of performing calculations. With the use of our tools it is possible to produce a working numerical realization of calculations in only a couple of steps from the fundamental (Schrödinger or Lippmann-Schwinger) equations. The FORTRAN implementations of the most complicated parts of the calculations are generated automatically by Mathematica ® software that was written in our group. Additionally, at higher energies, three dimensional calculations avoid problems arising from slow convergence of partial wave decomposition based techniques. Our approach utilizes a very general form of the 2N and 3N forces and has been successfully used to obtain results for the 2N transition operator as well as for the 2N and 3N bound states (Golak et al. in Phys Rev C 81:034006, 2010; Few-Body Syst 53:237, 2012a; Few-Body Syst, 2012b).

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“…An example of the three dimensional treatment of proton-proton scattering, taken from [8], is shown in Fig. 1.…”

Section: Results and Summarymentioning

confidence: 99%

“…For the case presented in the plots exponential screening was used. The additional contribution to the two nucleon potential is proportional to [8]:…”

Section: Results and Summarymentioning

confidence: 99%

2N and 3N Systems in a Three Dimensional Formalism

et al. 2014

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“…For the results presented in the next section we chose the form factors g V 1 , g A 1 , g V 2 , g A 2 in (4) to agree with [5]. The scattering part in (3) includes the transition operator t which can be calculated using 3D methods described for example in [1]. The calculation scheme presented there allows for the incorporation of a very general form of the 2N potential.…”

Section: Formal Ingredientsmentioning

confidence: 99%

“…This formalism was successfully applied to transition operator calculations in [1] and to the description of electron induced deuteron disintegration in [2]. This short paper aims at show the advantages of this method by underlining the direct approach that it makes possible.…”

Section: Introductionmentioning

confidence: 99%

Muon induced deuteron disintegration in three-dimensions

Topolnicki

Golak

Skibiński

et al. 2014

EPJ Web of Conferences

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Abstract. We present a three-dimensional (3D) description of muon induced deuteron disintegration. This reaction is treated as the decay of the muonic atom with the muon initially on the lowest K shell. Our aim is to calculate the total and differential decay rates. We work in momentum space and use 3D momentum eigenstates directly. This approach allowed us to calculate the appropriate nuclear matrix elements, necessary building blocks for the differential decay rate, in a single step. For contrast -in classical calculations many partial-waves have to be taken into account. We achieved a very good agreement between the 3D and partial-wave methods for calculations that involve single-nucleon currents. Our result for the total decay rate is also in agreement with experimental values, though these are not very precise. This success motivates us to also include two-nucleon current contributions that include the meson exchange currents. Additionally, our formalism can also be applied to other, so far poorly described, processes like: μ + 3 He → ν + n + d or μ + 3 He → ν + n + n + p.

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“…The 2N transition operatorť appearing in (1-3) is a crucial element of the calculation. In our "three dimensional" treatment of 3N scattering this operator is calculated using methods from [4,5]. First, the 2N potential and transition operator are written in their general forms that explicitly obey the usual symmetries of parity, time reversal, particle exchange and spatial rotations [6]:…”

Section: Introductionmentioning

confidence: 99%

Three Nucleon Scattering in a 3D Approach at the First Order

et al. 2016

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The "three dimensional" (3D) approach to few-nucleon calculations, instead of working with partialwave states, uses the momentum degrees of freedom of the nucleons directly. As a result, 3D calculations are equivalent to incorporating all partial waves into the calculation. This equivalence is limited by the available computational resources, nonetheless, the new approach provides an opportunity to construct numerical descriptions of physical systems that were previously unavailable with more traditional methods. We present selected observables for the neutron-deuteron inelastic scattering process calculated using the 3D approach and the traditional partial wave approach. This comparison was carried out using the first order terms of the series expansion of the Faddeev equations and is a strong motivator for a development of a complete 3D calculation that utilizes all orders.

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

Cited by 15 publications

References 25 publications

2N and 3N Systems in a Three Dimensional Formalism

2N and 3N Systems in a Three Dimensional Formalism

Muon induced deuteron disintegration in three-dimensions

Three Nucleon Scattering in a 3D Approach at the First Order

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