Separable representation of the Paris nucleon-nucleon potential

Haidenbauer, J.; Plessas, W.

doi:10.1103/physrevc.30.1822

Cited by 240 publications

(181 citation statements)

References 32 publications

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“…These 18 channels in the Faddeev equations correspond to the truncation of the NN interaction to include all two-body partial waves with total angular momentum less than or equal to two, including the coupled 3 P 2 − 3 F 2 NN channels. To justify the use of the separable expansion to the Paris potential, PEST [32], we compare, in Table VI, our results for the 18 channel calculation with the corresponding results based on the coordinate space solution of the Faddeev equations for the Paris potential. Taking the difference between the two coordinate space calculations as a measure of the numerical uncertainty in the solution of the Faddeev equations, we have good agreement with previous results for the Paris potential.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…To simplify the construction of the three-nucleon wave function needed to evaluate the integrals in Eq. (5.6), we have chosen the separable representation of the Paris potential [32]. This representation has been tested for the three-nucleon observables with considerable success [53].…”

Section: Numerical Resultsmentioning

confidence: 99%

“…V to calculate, in the Born approximation, the contribution of this force to the binding energy of the three-nucleon system. The three-nucleon wave function will be calculated by using Paris (PEST) potential [32]. Since the Paris potential does not have any energy dependence, our approach for the three-nucleon interaction is inconsistent with the two-nucleon interaction.…”

Section: Introductionmentioning

confidence: 99%

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Energy Dependence of the πN Amplitude and the Three-Nucleon Interaction

Saito

Afnan

1995

Few-Body Systems

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By calculating the contribution of the π − π three-body force to the threenucleon binding energy in terms of the πN amplitude using perturbation theory, we are able to determine the importance of the energy dependence and the contribution of the different partial waves of the πN amplitude to the three-nucleon force. A separable representation of the non-pole πN amplitude allows us to write the three-nucleon force in terms of the amplitude for N N → N N * , propagation of the N N N * system, and the amplitude for N N * → N N , with N * being the πN quasi-particle amplitude in a given state. The division of the πN amplitude into a pole and non-pole gives a procedure for the determination of the πN N form factor within the model. The total contribution of the three-body force to the binding energy of the triton for the separable approximation to the Paris nucleon-nucleon potential (PEST) is found to be very small mainly as a result of the energy dependence of the πN amplitude, the cancellation between the S-and P -wave πN amplitudes, and the soft πN N form factor.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Energy Dependence of the πN Amplitude and the Three-Nucleon Interaction

Saito

Afnan

1995

Few-Body Systems

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“…34 the saturation points obtained within the discrete scheme of Ref. [73,75] for the updated Reid potential (Reid93), the NijmI and NijmII interaction [79] and the separable Paris interaction [80,81] are shown. The results demonstrate an important and systematic change of the saturation properties with respect to continuous choice Brueckner-Hartree-Fock (ccBHF) calculations, leading to about 4-6 MeV less binding, and reduced values of the saturation density, closer to the empirical one.…”

Section: Saturation Of Nuclear Matter From Short-range Correlationsmentioning

confidence: 99%

“…In Refs. [76,77] a separable representation of the Paris interaction [80,81] has been used to generate self-consistent propagators including short-range correlations by employing a direct discretization of the spectral functions and self-energy as a function of energy. Also in this work [77] a repulsive effect is observed for the energy per particle leading to less binding as compared to the conventional BHF approach with a continuous sp spectrum.…”

Section: Theoretical Calculations For Nuclear Mattermentioning

confidence: 99%

Self-consistent Green's function method for nuclei and nuclear matter

Dickhoff

Barbieri

2004

Progress in Particle and Nuclear Physics

494

599

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Recent results obtained by applying the method of self-consistent Green's functions to nuclei and nuclear matter are reviewed. Particular attention is given to the description of experimental data obtained from the (e,e ′ p) and (e,e ′ 2N) reactions that determine one and two-nucleon removal probabilities in nuclei since the corresponding amplitudes are directly related to the imaginary parts of the single-particle and two-particle propagators. For this reason and the fact that these amplitudes can now be calculated with the inclusion of all the relevant physical processes, it is useful to explore the efficacy of the method of self-consistent Green's functions in describing these experimental data. Results for both finite nuclei and nuclear matter are discussed with particular emphasis on clarifying the role of short-range correlations in determining various experimental quantities. The important role of long-range correlations in determining the structure of lowenergy correlations is also documented. For a complete understanding of nuclear phenomena it is therefore essential to include both types of physical correlations. We demonstrate that recent experimental results for these reactions combined with the reported theoretical calculations yield a very clear understanding of the properties of all protons in the nucleus. We propose that this knowledge of the properties of constituent fermions in a correlated many-body system is a unique feature of nuclear physics.

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Non-relativistic quantum scattering from non-local separable potentials: the eigenchannel approach

Augusiak

2005

Ann. Phys.

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A recently formulated version of the eigenchannel method [R. Szmytkowski, Ann. Phys. (N.Y.) 311, 503 (2004)] is applied to quantum scattering of Schrödinger particles from non-local separable potentials. Eigenchannel vectors and negative cotangents of eigenphase-shifts are introduced as eigensolutions to some weighted matrix spectral problem, without a necessity of prior construction and diagonalization of the scattering matrix. Explicit expressions for the scattering amplitude, the total cross section in terms of the eigenchannel vectors and the eigenphase-shifts are derived. An illustrative example is provided.

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Separable representation of the Paris nucleon-nucleon potential

Cited by 240 publications

References 32 publications

Energy Dependence of the πN Amplitude and the Three-Nucleon Interaction

Energy Dependence of the πN Amplitude and the Three-Nucleon Interaction

Self-consistent Green's function method for nuclei and nuclear matter

Non-relativistic quantum scattering from non-local separable potentials: the eigenchannel approach

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