Deuteron Disintegration in Three Dimensions

Topolnicki, K.; Golak, J.; Skibiński, R.; Elmeshneb, A. E.; Glöckle, W.; Nogga, A.; Kamada, H.

doi:10.1007/s00601-012-0479-y

Cited by 9 publications

(11 citation statements)

References 19 publications

(31 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1, 2 and 3 are obtained in the three-dimensional formalism of Ref. [22], without any resort to partial wave decomposition (PWD). These results for the Bonn B potential [23] can be used to additionally prove the convergence of other results based on partial waves.…”

Section: Results For Thementioning

confidence: 99%

See 1 more Smart Citation

Break-up channels in muon capture onHe3

et al. 2014

Self Cite

View full text Add to dashboard Cite

The µ − + 2 H → ν µ +n+n, µ − + 3 He → ν µ + 3 H, µ − + 3 He → ν µ +n+d and µ − + 3 He → ν µ +n+n+p capture reactions are studied with various realistic potentials under full inclusion of final state interactions. Our results for the two-and three-body break-up of 3 He are calculated with a variety of nucleon-nucleon potentials, among which is the AV18 potential, augmented by the Urbana IX three-nucleon potential. Most of our results are based on the single nucleon weak current operator. As a first step, we have tested our calculation in the case of the µ − + 2 H → ν µ + n + n and µ − + 3 He → ν µ + 3 H reactions, for which theoretical predictions obtained in a comparable framework are available. Additionally, we have been able to obtain for the first time a realistic estimate for the total rates of the muon capture reactions on 3 He in the break-up channels: 544 s −1 and 154 s −1 for the n + d and n + n + p channels, respectively. Our results have also been compared with the most recent experimental data, finding a rough agreement for the total capture rates, but failing to reproduce the differential capture rates.

show abstract

Section: Results For Thementioning

confidence: 99%

“…Differential capture rate dΓ F d /dE ν for the µ − + 2 H → ν µ +n+n process, calculated with the Bonn B potential [23] in the three-dimensional formalism of Ref. [22] and using the single nucleon current operator from Eqs. (2.7) and (2.8) for F = FIG.…”

Section: Results For Thementioning

confidence: 99%

Break-up channels in muon capture onHe3

et al. 2014

Self Cite

View full text Add to dashboard Cite

show abstract

“…On the right panel the convergence to the full 3D result (solid) is shown for dierent numbers of partial waves (j ≤ 4 dashed-dotted, j ≤ 7 dotted, j ≤ 9 dashed). Results reprinted from our paper [6] for kinematics K6.…”

Section: Resultsmentioning

confidence: 99%

The Two-Nucleon and Three-Nucleon System in Three Dimensions

et al. 2015

Self Cite

View full text Add to dashboard Cite

We present a brief overview of the three-dimensional formalism that is under development in our group. Using the 3D momentum eigenstates of the nucleon directly, instead of relying on the partial wave decomposition of operators involved in the calculations, allows us to use a very direct approach. This in turn enabled us to successfully tackle a large variety of few-body problems. Our calculation of the two nucleon transition operator and bound state can incorporate a very general form of the two-nucleon potential. Calculations of the three-nucleon bound state can include in addition to the two-nucleon potential also a very general operator form of the threenucleon force. Recently the 3D formalism is also applied to processes that involve electro-weak probes. Carrying out these calculations for a wide spectrum of two-nucleon and three-nucleon potentials using the classical partial wave approach is unpractical due to the complicated spin structure of the operators. Using the 3D formalism, the calculations can be quickly adapted to test new models. The starting point for our calculations are operator forms of two-nucleon (2N) and three-nucleon (3N) operators and states, developed to take into account symmetry considerations. In these forms the operators and states are typically written as linear combinations of scalar functions and spin, isospin operators. Our rst goal is to rewrite the fundamental equations that govern a particular few-body problem into a linear problem acting in a space spanned by the scalar functions.The 2N potential has the general form [1]:Here p |V tmt |p is the matrix element of the 2N force between 2N relative momentum eigenstates |p , |p and states |tm t where the isospins of the two nucleons are coupled to t with projection m t . Finallyw i (p , p) are a spin operator and the potential can be reconstructed from a set of scalar functions v tmt i (|p |, |p|, p · p). The form (1) takes into account the partity and time reversal symmetries and assumes no isospin mixing. The same symmetry considerations that led to (1) can be applied to the transition operator satisfying the LippmannSchwinger equatioň * corresponding author; e-mail: kacper.topolnicki@uj.edu.pl where |p is the 3D eigenstate of the relative 2N momentum,σ(1) (σ (2)) is a vector of spin operators acting in the space of particle 1 (2), |1m d is a spin state with the spins of the particles coupled to the total spin 1 with the projection m d . Note that the isospin of the system is 0. The main challenge is to calculate the scalar functions {φ 1 , φ 2 } that can be used to reconstruct the 2N wave function. The general form of the 3N bound state is more complicated [3]. The wave function projected onto a 3N isospin state (t 1 2 )T | (where the isospins of two particles are coupled to t and then coupled with the isospin of the third particle to a total isospin T ) has the form(4) and a more detailed description of operators involved in (4) can be found in [3]. Also in this case the 3N wave function can be reconstructed from the set of ...

show abstract

“…(2) are a sum of the plane wave and scattering parts. Both contributions can be calculated using the same formalism as was developed in [2] for deuteron electro-disintegration. Calculation of both the plane wave and scattering parts in (3) require the knowledge of the weak current j λ .…”

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

View full text Add to dashboard Cite

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.

show abstract

Deuteron Disintegration in Three Dimensions

Cited by 9 publications

References 19 publications

Break-up channels in muon capture onHe3

Break-up channels in muon capture onHe3

The Two-Nucleon and Three-Nucleon System in Three Dimensions

Muon induced deuteron disintegration in three-dimensions

Contact Info

Product

Resources

About