[Paper Review] Relativistic Nucleon-Nucleon potentials using Dirac's constraint instant form dynamics

H. V. von Geramb, Bayansan Davaadorj+1 more|ArXiv.org|Aug 1, 2003

Algebraic and Geometric Analysis4 references3 citations

TL;DR

This paper proposes a relativistic nucleon-nucleon (NN) potential derived from two coupled Dirac equations within Dirac's constraint instant form dynamics, incorporating meson exchange (π, ρ, ω, σ) and a universal repulsive core. It achieves high-precision fits to np and pp phase shifts up to 3 GeV by combining the relativistic Dirac potential with a phenomenological complex optical model potential (OMP), revealing a universal core radius of 0.5 ± 0.025 fm and identifying a transition from fusion/scission to fusion/fission mechanisms above 1 GeV lab energy.

ABSTRACT

The formalism of two coupled Dirac equations within constraint instant form dynamics is used to study the nucleon-nucleon interaction. The salient features and the final Schroedinger type equation is given. Explicitly energy dependent coupled channel potentials, for use in partial wave Schroedinger like equations, with nonlinear and complicated derivative terms, result. We developed the necessary numerics and study np and pp scattering phase shifts for energies 0-3 GeV and the deuteron bound state. The interactions are inspired by meson exchange of pi, eta, rho,omega and sigma mesons for which we adjust coupling constants. This yields, in the first instant, high quality fits to the Arndt phase shifts 0-300 MeV. Second, the potentials show a universal, independent from angular momentum, core potential which is generated from the relativistic meson exchange dynamics. Extrapolations towards higher energies, up to 3 GeV, allow to separate a QCD dominated short range zone as well as inelastic nucleon excitation mechanism contributing to meson production. A local and/or nonlocal optical model, in addition to the meson exchange Dirac potential, produces agreement between theoretical and data phase shifts. Third, the 1S0, 3P0 and 3P1 partial waves elicit a fusion/scission, for T-Lab<1GeV, and a fusion/fission, for T-Lab>1 GeV, mechanism for intermediate dibaryon formation.

Motivation & Objective

• To develop a Poincaré-invariant relativistic NN potential using two coupled Dirac equations within constraint instant form dynamics.
• To model nucleon-nucleon interactions via meson exchange (π, η, ρ, ω, σ) and determine coupling constants from low-energy phase shift data.
• To address inelasticity and absorption at higher energies (T_Lab > 280 MeV) by introducing a complex optical model potential (OMP).
• To identify universal features such as a momentum-independent core radius and dibaryon formation mechanisms in partial waves.
• To distinguish between fusion/scission and fusion/fission mechanisms in intermediate-energy NN scattering.

Proposed method

• Formulate the NN interaction using two coupled Dirac equations with relativistic kinematics and Poincaré invariance.
• Derive explicitly energy-dependent, coupled-channel potentials from meson exchange interactions (scalar, pseudoscalar, vector) using constraint instant form dynamics.
• Implement numerical solutions for partial wave Schrödinger-type equations with the relativistic Dirac potential for S, P, and D waves.
• Introduce a complex optical model potential (OMP) with real (U) and imaginary (W) components, modeled as a Gaussian or delta-function at r₀ = 0.5 fm.
• Adjust OMP parameters U_G(T) and W_G(T) to reproduce experimental phase shifts and absorption data from GWU/VPI SP03 and SM00.
• Use boundary conditions f_r(0) = 0, f_r(h) = h^(ℓ+1), f_i(r) = 0 for 0 ≤ r ≤ r₀ to solve the coupled OMP equations.

Experimental results

Research questions

• RQ1 Does a relativistic NN potential derived from coupled Dirac equations with meson exchange reproduce low-energy np and pp phase shifts accurately?
• RQ2 What is the nature and origin of the universal repulsive core radius observed in the Dirac potential, independent of partial wave?
• RQ3 How do inelasticities and absorption in NN scattering at T_Lab > 280 MeV arise, and can they be modeled effectively by a phenomenological OMP?
• RQ4 Does the transition from fusion/scission to fusion/fission mechanisms occur at T_Lab ≈ 1 GeV, and what does it imply for dibaryon formation?
• RQ5 Can the total energy and width of intermediate dibaryon states be estimated from phase shift behavior in 1S₀, 3P₀, and 3P₁ channels?

Key findings

• The Dirac potential alone reproduces experimental phase shifts δ(T) for 1S₀, 3P₀, and 3P₁ partial waves with high accuracy up to 1100 MeV lab energy.
• A universal repulsive core radius of r_c = 0.5 ± 0.025 fm emerges from the relativistic meson exchange dynamics, independent of angular momentum or nucleon substructure.
• The optical model potential (OMP) with U(r) = 0 and W(r) = W_G(r)δ(r - r₀) successfully reproduces absorption ρ(T) > 0 for T_Lab > 280 MeV, while preserving real phase shifts.
• The OMP strength parameters W_G(T) and U_G(T) are found to be energy-dependent, with W_G(T) peaking around 1 GeV, indicating enhanced inelasticity.
• The estimated mass of intermediate dibaryon states is m_BB = 2400 ± 150 MeV with a width Γ > 150 MeV, suggesting short-lived resonant formation above 1 GeV.
• A transition from a fusion/scission mechanism (T_Lab < 1 GeV) to a fusion/fission mechanism (T_Lab > 1 GeV) is indicated by the phase shift and absorption behavior in the 1S₀, 3P₀, and 3P₁ channels.