Relativistic nucleon-nucleon potentials in a spin-dependent three-dimensional approach

Area of Science:

• Nuclear Physics
• Quantum Mechanics
• Theoretical Physics

Background:

• Understanding nucleon-nucleon (NN) interactions is fundamental in nuclear physics.
• Relativistic effects are crucial for accurately describing NN potentials, especially at higher energies.
• Existing methods often involve complex partial wave decompositions.

Purpose of the Study:

• To develop a direct method for calculating relativistic NN potentials from nonrelativistic potentials.
• To formulate the relationship between relativistic and nonrelativistic NN potentials in a momentum-helicity basis.
• To solve the resulting integral equations for spin-singlet and spin-triplet states.

Main Methods:

• Formulation of a quadratic operator relation between relativistic and nonrelativistic NN potentials.
• Utilizing a momentum-helicity basis for the formulation.
• Solving a single integral equation for the spin-singlet state and four coupled integral equations for spin-triplet states via an iterative method.

Main Results:

• The developed method allows direct calculation of relativistic NN potential matrix elements.
• Numerical analysis using the CD-Bonn potential demonstrates high accuracy.
• The calculated potential accurately reproduces the deuteron binding energy.
• Accurate reproduction of neutron-proton elastic scattering differential and total cross-sections.

Conclusions:

• The direct calculation method is effective and accurate for relativistic NN potentials.
• The approach provides a robust framework for nuclear structure and reactions.
• This work offers a computationally efficient alternative to traditional methods.