[Paper Review] The "ab initio" approach to the nuclear equation of state: review and discussion

Francesca Sammarruca|ArXiv.org|Jul 2, 2008

Nuclear physics research studies5 references3 citations

TL;DR

This paper presents an ab initio nuclear equation of state (EoS) calculation using the Dirac-Brueckner-Hartree-Fock (DBHF) framework with realistic nucleon-nucleon (NN) interactions, including effects from virtual nucleon-antinucleon pair excitations via the Z-diagram. The method provides a parameter-free, consistent description of symmetric and asymmetric nuclear matter, with key contributions from relativistic two-body forces and indirect inclusion of three-body forces through effective mass generation.

ABSTRACT

We review the main components of our microscopic model of nuclear matter, which we have recently extended to incorporate isospin asymmetry. Some frequently discussed issues concerning nuclear many-body approaches are revisited and critically analysed.

Motivation & Objective

• To develop a parameter-free, ab initio approach to the nuclear equation of state (EoS) that avoids adjustable medium parameters.
• To address the challenge of consistently including three-body forces (3NF) in nuclear matter calculations without introducing phenomenological 3NF models.
• To examine the role of virtual nucleon-antinucleon pair excitations in generating effective many-body forces within a relativistic framework.
• To improve theoretical constraints on the symmetry energy and its density dependence using microscopic, first-principles methods.
• To provide a consistent theoretical framework that complements emerging experimental data on neutron skins and heavy-ion collisions.

Proposed method

• Uses the Bonn B potential as a realistic, momentum-space NN interaction derived from one-boson exchange (OBE) models with pseudovector coupling.
• Applies the Dirac-Brueckner-Hartree-Fock (DBHF) method to solve the nuclear many-body problem self-consistently in nuclear matter.
• Incorporates effective mass generation via the Z-diagram (virtual pair excitation), which mimics a class of three-body forces without explicit 3NF input.
• Maintains consistency by ensuring that two-body interactions are not modified in the medium, avoiding uncontrolled parameter adjustments.
• Excludes explicit phenomenological 3NFs (e.g., Fujita-Miyazawa, Tucson-Melbourne) due to inconsistency with the two-body sector, favoring only those 3NFs arising from virtual pair excitations.
• Extends the formalism to isospin-asymmetric nuclear matter by generalizing the effective mass ansatz to protons and neutrons with different concentrations.

Experimental results

Research questions

• RQ1 Can a parameter-free ab initio approach based on realistic NN interactions provide a reliable description of the nuclear equation of state in symmetric and asymmetric matter?
• RQ2 To what extent do virtual nucleon-antinucleon pair excitations (via the Z-diagram) generate effective three-body force effects in the DBHF framework?
• RQ3 Why is the inclusion of phenomenological three-body forces inconsistent with the two-body input in the DBHF method, and how can this be resolved?
• RQ4 How does the choice of pseudovector versus pseudoscalar coupling affect the description of NN interactions and their medium modifications?
• RQ5 What is the role of relativistic effects in generating many-body forces, and how do they compare to explicit 3NF models?

Key findings

• The DBHF method with realistic Bonn B NN potential produces a saturation point of nuclear matter consistent with the Coester band, with sensitivity primarily to the tensor force strength.
• Virtual nucleon-antinucleon pair excitations via the Z-diagram generate effective three-body force effects that are essential for nuclear matter saturation.
• The effective mass generated in the DBHF framework is equivalent to the contribution from the Z-diagram, providing a relativistic, self-consistent mechanism for many-body effects.
• Explicit three-body forces such as Fujita-Miyazawa or Tucson-Melbourne are excluded due to inconsistency with the two-body sector, particularly when medium modifications are not fully accounted for.
• The method remains consistent and parameter-free, as all NN interaction parameters are fixed by free-space NN data and not readjusted in the medium.
• The approach provides a reliable, internally consistent framework for calculating the equation of state of isospin-asymmetric nuclear matter, crucial for constraining the symmetry energy and neutron skin thickness.