Comprehensive Comparison of State-of-the-Art Nucleon-Nucleon Potentials: From Phase Shifts to Nuclear Matter

Concetti Chiave

The study systematically compares 17 high-precision nucleon-nucleon (NN) interaction potentials, including AV18, CD-Bonn, pvCD-Bonn, and chiral effective field theory models, in terms of scattering phase shifts, differential cross sections, entanglement properties, and nuclear matter equations of state.

Sintesi

This study provides a comprehensive comparison of 17 state-of-the-art nucleon-nucleon (NN) interaction potentials. The key highlights are:

1. Phase Shift Analysis:

   • The phase shifts for np (T=1), nn (T=1), and pp channels are calculated and compared across the 17 potentials.
   • For channels with angular momentum l<3, the potentials yield consistent results at low incident energies, but deviations emerge at higher energies, especially for the chiral potentials with smaller cutoff values.
   • Significant discrepancies are observed in the F-wave channels between the chiral potentials and partial wave analysis results, particularly at energies above 200 MeV.

2. Differential Cross Sections:

   • The differential cross sections for pp scattering are computed and compared to experimental data at various incident energies.
   • At lower energies (e.g., 50 MeV), the potentials produce nearly identical results that agree well with experiments.
   • At higher energies (e.g., 212 MeV and 284 MeV), the chiral potentials that do not accurately describe the F-channels exhibit significant deviations from experimental data, especially at forward and backward scattering angles.

3. Entanglement Analysis:

   • The entanglement power of the scattering matrix, which quantifies the averaged entanglement ability, is calculated for the np (T=0) channel.
   • The entanglement powers from the 17 potentials show small differences, as the phase shifts for the 1S0 and 3S1 states are well-determined.
   • The pvCD-Bonn A potential exhibits the minimum entanglement power and is most consistent with the partial wave analysis results.

4. Nuclear Matter Equations of State:

   • The study also explores the equations of state for symmetric nuclear matter and pure neutron matter using the 17 NN potentials.
   • Significant differences are observed among the potentials, especially in the high-density regions.

Overall, this work provides a detailed and systematic comparison of state-of-the-art NN interaction potentials, highlighting their strengths, weaknesses, and differences across various observables. The findings have important implications for nuclear structure and nuclear astrophysics studies.

Statistiche

The phase shifts of various interaction potentials in the np 1S0 channel at different incident energies are provided in Table I.
The phase shifts of various interaction potentials in the np 3S1 channel at different incident energies are provided in Table II.
The phase shifts of various interaction potentials in the pp 1S0 channel at different incident energies are provided in Table IV.

Citazioni

"The nucleon-nucleon (NN) interaction is a fundamental aspect of nuclear physics, governing the intricate quantum behavior of protons and neutrons within atomic nuclei."
"Recent contributions from the Granada group have explored phase shifts with delta potentials, addressing associated uncertainties."
"Over the past 20 years, significant advances have been achieved in understanding baryon-baryon interactions, particularly NN potentials, through lattice QCD simulations."

Approfondimenti chiave tratti da

The comparison of the state-of-the-art nucleon-nucleon potentials from phase shift to nuclear matter

by Ke Nan, Jinn... alle arxiv.org 10-02-2024

https://arxiv.org/pdf/2410.00679.pdf

Domande più approfondite

How do the differences in the NN potentials affect the predictions of nuclear structure properties, such as binding energies and radii of finite nuclei?

The differences in nucleon-nucleon (NN) potentials significantly influence the predictions of nuclear structure properties, including binding energies and radii of finite nuclei. Each NN potential encapsulates distinct characteristics of the nuclear force, such as short-range repulsion and intermediate-range attraction, which are critical for accurately modeling the interactions between nucleons within a nucleus.
For instance, high-precision NN potentials like AV18 and CD-Bonn have been developed to reproduce experimental scattering data with high fidelity, achieving a χ²/N of approximately 1. However, variations in the treatment of charge dependence, tensor forces, and the inclusion of higher-order corrections in chiral effective field theories can lead to discrepancies in the calculated binding energies and radii.
In particular, the binding energy of a nucleus is sensitive to the strength and range of the NN interaction. Potentials that predict stronger attraction at intermediate ranges tend to yield larger binding energies, while those with weaker interactions may result in underbound nuclei. Similarly, the predicted radii of nuclei are affected by the balance between the short-range repulsion and long-range attraction; different NN potentials can lead to variations in the calculated root-mean-square radii of nuclei, impacting our understanding of nuclear size and structure.
Moreover, the observed differences in phase shifts, especially in higher angular momentum channels (F-wave channels), can lead to significant variations in the saturation properties of nuclear matter, which in turn affect the predictions for finite nuclei. As such, the choice of NN potential is crucial for accurate nuclear structure calculations, and discrepancies among different models highlight the need for further refinement and validation against experimental data.

What are the implications of the observed discrepancies in the F-wave channels for the chiral potentials on the description of nuclear many-body systems?

The observed discrepancies in the F-wave channels for chiral potentials have profound implications for the description of nuclear many-body systems. Chiral effective field theory (EFT) aims to provide a systematic and consistent framework for understanding nuclear interactions based on the symmetries of quantum chromodynamics (QCD). However, the significant deviations in phase shifts and scattering observables in the F-wave channels indicate that the current chiral potentials may not adequately capture the complexities of the nuclear force at higher energies and angular momentum states.
These discrepancies can lead to inaccuracies in the predictions of many-body nuclear phenomena, such as the properties of nuclear matter, the formation of nuclei, and the dynamics of nuclear reactions. For example, if the F-wave interactions are not well-represented, it could result in incorrect predictions for the binding energies and excitation spectra of nuclei, as well as the behavior of neutron stars and other astrophysical objects where nuclear forces play a critical role.
Furthermore, the inability of certain chiral potentials to reproduce experimental data in the F-wave channels suggests that the current power counting schemes and regularization methods may need to be revisited. This could involve refining the treatment of higher-order corrections or exploring alternative formulations of chiral EFT that better account for the tensor forces and charge dependence observed in NN interactions. Ultimately, addressing these discrepancies is essential for improving the predictive power of nuclear models and enhancing our understanding of nuclear structure and dynamics.

Can the insights gained from this comparative study of NN potentials be leveraged to develop more accurate and comprehensive models of nuclear interactions that can bridge the gap between phenomenological and first-principles approaches?

Yes, the insights gained from the comparative study of NN potentials can indeed be leveraged to develop more accurate and comprehensive models of nuclear interactions that bridge the gap between phenomenological and first-principles approaches. By systematically analyzing the strengths and weaknesses of various NN potentials, researchers can identify key features that contribute to their success in reproducing experimental data.
One potential avenue for improvement is the integration of successful aspects of phenomenological models, such as the AV18 and CD-Bonn potentials, with the systematic framework of chiral effective field theory. This could involve refining the chiral potentials to better account for the empirical data, particularly in the higher angular momentum channels where discrepancies have been noted. By incorporating empirical phase shifts and scattering observables into the chiral framework, it may be possible to enhance the accuracy of predictions for nuclear structure properties.
Additionally, insights from lattice QCD simulations, which provide first-principles calculations of NN interactions, can inform the development of new NN potentials. By comparing lattice results with phenomenological models, researchers can identify areas where the models diverge and adjust the parameters or functional forms of the potentials accordingly. This iterative process of refinement can lead to a more unified understanding of nuclear interactions that is both theoretically sound and empirically validated.
Ultimately, the goal is to create a comprehensive model of nuclear interactions that can accurately describe a wide range of nuclear phenomena, from the structure of finite nuclei to the behavior of nuclear matter under extreme conditions. By bridging the gap between phenomenological and first-principles approaches, researchers can enhance the predictive power of nuclear physics and contribute to advancements in related fields, such as astrophysics and nuclear engineering.