[Paper Review] Kinetic symmetry energy of nucleonic matter with tensor correlations

O. Hen, Bao-An Li+2 more|arXiv (Cornell University)|Aug 4, 2014

Pulsars and Gravitational Waves Research3 references1 citations

TL;DR

This paper proposes an analytical model for the kinetic symmetry energy, E^kin_sym(0), in correlated nucleonic matter by accounting for short-range tensor correlations, particularly in neutron-proton pairs. It derives E^kin_sym(0) = 3.8 ± 0.7 MeV using experimental free neutron/proton ratios from intermediate-energy collisions, showing a significant reduction from the 12.5 MeV predicted by the free Fermi gas model, and provides a density-dependent analytical expression for E^kin_sym(ρ).

ABSTRACT

sym( 0), equals the dierence in the per-nucleon kinetic energy between pure neutron matter (PNM) and symmetric nuclear matter (SNM), which is often calculated in a simple Fermi gas model. However, experiments show that about 20% of nucleons in nuclei belong to high-momentum correlated pairs. Short-range correlations (SRC) due to the tensor force acting predominantly on neutron-proton pairs shift nucleons to high momentum in SNM where there are equal numbers of neutrons and protons, but have almost no eect in PNM. We present an approximate analytical expression for E kin( 0) of correlated nucleonic matter. We further constrain our model with data on free neutron/proton ratios measured recently in intermediate energy nucleus-nucleus collisions to obtain E kin sym( 0) = 3:8 0:7 MeV. This result agrees qualitatively with microscopic many-body calculations and diers signicantly from the 12.5 MeV obtained for a free Fermi gas with no correlations. We also present an approximate analytical expression for the kinetic symmetry energy of correlated nucleonic matter as a function of nuclear density, E kin sym( ).

Motivation & Objective

• To develop a model that accounts for short-range correlations (SRC) due to the tensor force in nucleonic matter, particularly in symmetric nuclear matter (SNM) and pure neutron matter (PNM).
• To quantify the kinetic symmetry energy E^kin_sym(0) beyond the free Fermi gas approximation, which neglects correlations.
• To constrain the model using recent experimental data on free neutron/proton ratios from intermediate-energy nucleus-nucleus collisions.
• To derive an analytical expression for the density-dependent kinetic symmetry energy E^kin_sym(ρ) in correlated nucleonic matter.

Proposed method

• Incorporates tensor-force-induced short-range correlations (SRC) that predominantly affect neutron-proton pairs, shifting nucleons to high momentum in SNM but not in PNM.
• Uses a perturbative approach to calculate the per-nucleon kinetic energy difference between SNM and PNM, accounting for SRC effects.
• Applies experimental free neutron/proton ratios from intermediate-energy nucleus-nucleus collisions as a constraint to fix the model parameters.
• Derives an analytical expression for E^kin_sym(ρ) as a function of nuclear density ρ, based on the correlation-induced modification of kinetic energy.
• Compares the resulting E^kin_sym(0) with the free Fermi gas prediction (12.5 MeV) and with microscopic many-body calculations.

Experimental results

Research questions

• RQ1 How do tensor-force-induced short-range correlations modify the kinetic symmetry energy in symmetric nuclear matter compared to the free Fermi gas model?
• RQ2 What is the value of the kinetic symmetry energy E^kin_sym(0) when correlations are included, and how does it compare to the standard Fermi gas prediction?
• RQ3 To what extent do experimental free neutron/proton ratios from intermediate-energy collisions constrain the kinetic symmetry energy in correlated nucleonic matter?
• RQ4 Can an analytical, density-dependent expression for E^kin_sym(ρ) be derived that includes the effects of short-range correlations?

Key findings

• The kinetic symmetry energy E^kin_sym(0) is found to be 3.8 ± 0.7 MeV when short-range correlations are included, significantly lower than the 12.5 MeV predicted by the free Fermi gas model.
• The reduction in E^kin_sym(0) arises primarily from the asymmetric effect of tensor-force correlations: they shift nucleons to high momentum in SNM (due to np pairs) but have negligible effect in PNM.
• The model's prediction is in qualitative agreement with microscopic many-body calculations, validating the role of SRC in modifying kinetic energy contributions.
• An analytical expression for the density-dependent kinetic symmetry energy E^kin_sym(ρ) is derived, enabling further study of its behavior across nuclear densities.
• The experimental neutron/proton ratios from intermediate-energy collisions provide a crucial constraint that anchors the model’s quantitative predictions.