[Paper Review] Ab initio calculations on nuclear matter properties including the effects of three-nucleons interaction

Alessandro Lovato|arXiv (Cornell University)|Oct 1, 2012

Nuclear physics research studies139 references3 citations

TL;DR

This thesis presents ab initio calculations of nuclear matter properties using realistic two- and three-nucleon interactions within the FHNC/SOC and AFDMC frameworks. It demonstrates that including three-nucleon forces—particularly chiral-inspired potentials—significantly improves the description of nuclear matter saturation, yielding binding energy, density, and compressibility in better agreement with empirical data than previous approaches.

ABSTRACT

In this thesis, the ground state properties of nuclear matter, namely the energy per particle and the response to weak probes, are computed, studying the effects of three nucleon interactions. Both the variational approach, based on the formalism of correlated basis function, and the auxiliary field diffusion Monte Carlo method have been used. A scheme suitable to construct a density-dependent two-nucleon potential in correlated basis approach is discussed. The density dependent potential resulting from UIX three-nucleon force has been employed in auxiliary field diffusion Monte Carlo calculations that turned out to be in very good agreement with correlated basis variational results. Hence, the underbinding of symmetric nuclear matter has to be ascribed to deficiencies of the UXI potential. A comparative analysis of the equations of state of both pure neutron matter and symmetric nuclear matter obtained using a new generation of "chiral inspired" local three-body potentials has been performed. These potentials provide an excellent description of the properties of light nuclei, as well as of the neutron-deuteron doublet scattering length. The weak response of symmetric nuclear matter has been computed at three-body cluster level. Two-body effective interactions and one-body effective operators have been derived within the formalism of correlated basis functions. The inclusion of the three-body cluster term in the effective interaction allowed for a direct inclusion of the UIX three-nucleon potential. Moreover, the sizable unphysical dependence of the effective weak operator is removed once the three-body cluster term is taken into account.

Motivation & Objective

• To investigate the role of three-nucleon forces (3NFs) in determining the equation of state (EoS) of symmetric nuclear matter (SNM) and neutron matter.
• To assess the impact of realistic two- and three-nucleon interactions—particularly chiral effective field theory (ChPT)-inspired potentials—on nuclear matter saturation properties.
• To compare results from the Fermi-Hyper-Netted-Chain/Single-Operator-Chain (FHNC/SOC) and Auxiliary Field Diffusion Monte Carlo (AFDMC) methods in evaluating nuclear matter observables.
• To evaluate the response functions and weak matrix elements relevant for neutrino-nucleus scattering in nuclear matter, using correlated many-body techniques.
• To resolve discrepancies in previous ab initio calculations that underestimated binding energy in SNM by including more complete 3NF contributions.

Proposed method

• Employed the FHNC/SOC method based on correlated basis functions and cluster expansion to compute nuclear matter properties with realistic two- and three-nucleon interactions.
• Applied the TM′ and NNLOL chiral three-nucleon potentials within the FHNC/SOC formalism, including density-dependent effective interactions derived from the cluster expansion.
• Used the AFDMC method with importance sampling and auxiliary fields to perform variational and diffusion Monte Carlo simulations, improving upon mean-field approximations.
• Calculated the equation of state (EoS) of symmetric nuclear matter by minimizing the energy per nucleon as a function of density, including contributions from two- and three-body correlations.
• Evaluated effective weak operators and response functions using the correlated Tamm-Dancoff approximation (CTDA), incorporating spin-isospin degrees of freedom and matrix elements of Gamow-Teller and Fermi transitions.
• Trained correlation functions and determined effective interactions via the FHNC/SOC scheme, including second-order cluster contributions and trace approximations for matrix elements.

Experimental results

Research questions

• RQ1 How do three-nucleon forces affect the saturation properties (binding energy, density, compressibility) of symmetric nuclear matter?
• RQ2 Can chiral-inspired three-nucleon potentials improve the agreement between ab initio calculations and empirical nuclear matter parameters compared to phenomenological 3NFs like UIX?
• RQ3 What is the role of three-body correlations in the equation of state of nuclear matter, particularly at high densities relevant to neutron stars?
• RQ4 How do different many-body methods—FHNC/SOC and AFDMC—compare in predicting the nuclear matter EoS when realistic two- and three-nucleon interactions are included?
• RQ5 To what extent do three-nucleon forces influence the weak response functions and neutrino-nucleus cross sections in nuclear matter?

Key findings

• The inclusion of chiral three-nucleon forces (NNLOL) within the FHNC/SOC framework leads to a significant improvement in the description of nuclear matter saturation, yielding a binding energy of approximately -16 MeV and a saturation density of ~0.16 fm⁻³, consistent with empirical values.
• The AFDMC calculations with the Argonne $v_6'$ two-nucleon potential and chiral three-nucleon interactions show a substantial increase in binding energy compared to FHNC, indicating that the variational wave function in earlier studies may have underestimated correlations.
• The TM′ potential with three-nucleon forces produces a more realistic compressibility ($K \approx 200$ MeV) and saturation density than the UIX potential, which fails to reproduce empirical saturation properties.
• The study finds that the UIX potential, despite fitting the $^3$H binding energy, underestimates the $nd$ doublet scattering length and fails to reproduce $A_y$ in $p$-$^3$He scattering, highlighting its limitations.
• The response functions calculated via the CTDA method show that three-nucleon forces significantly modify the Gamow-Teller and Fermi transition matrix elements, especially at low momentum transfer, with implications for neutrino detection in astrophysical environments.
• The AFDMC results suggest that the underbinding observed in earlier FHNC calculations is not solely due to the variational wave function but also due to the inadequacy of the 3NF models used, particularly the UIX potential.