The theoretical description of matter in the interior of neutron stars, needed for the interpretation of of astrophysical observations, requires a quantitative understanding of both equilibrium and non equilibrium properties at densities (ρ) as high as five times nuclear density and temperatures (T) up to few tens of MeV. The availability of a theoretical framework reliably applicable in such a broad region of the ρ-T plane, will be essential to describe the unprecedented data provided by multimessenger observations; see, e.g. "Nuclear Theory in the Age of Multimessenger Astronomy". Edited by O. Benhar, A. Lovato, A. Maselli, and F. Pannarale (CRC Press, 2024). Equilibrium properties—such as the equation of state (EOS) at T=0— are generally obtained from realistic dynamical models, strongly constrained by nuclear systematics and nucleon-nucleon scattering data. On th other hand, theoretical studies of the dynamical properties often resort to oversimplified treatment of nuclear dynamics and thermal effects.

Over the past two decades, my group has been developing a consistent description of the nuclear matter EOS and low-energy weak response. This work is based on a density-dependent effective nuclear Hamiltonian, derived using realistic two- and three-nucleon interaction potentials, the formalism of correlated basis functions (CBF) and the cluster expansion technique [Phys. Rev. Lett. 99 (2007) 232501; Phys. Rev. C 96 (2017) 054301]. By construction, the CBF effective Hamiltonian provides the EOS obtained from state-of-the-art ab initio approaches, such as Fermi Hyper-Netted Chain (FHNC) summation scheme and the Auxiliary Field Diffusion Monte Carlo (AFDMC) technique. However, unlike the bare nuclear Hamiltonian, it is suitable to carry out perturbative calculations of a variety of nuclear matter properties, including the transport coefficients and the linear responses.

The CBF efective Hamiltonian has been employed to carry out systematic calculations of the equation of state of dense nuclear matter with proton fraction in the range 0 ≤ x ≤ 0.3 and temperature up to 50 MeV. [Astrophys. J 939 (2022) 52], as well as to study the response of isospin-symmetric matter and pure neutron matter to charged- and neutral current weak interactions [Nucl. Phys. A 901 (2013) 22; Phys. Rev. C 87 (2013) 014601; Phys. Rev. C 89 (2014) 025804].

The work of recent years has been primarily focused on: (i) a systematic study of the interplay between dynamical and thermal effects on nuclear matter properties [Phys. Rev. D 106 (2022) 103020; Universe 9 (2023) 9, 345]; (ii) a Bayesian analysis aimed at inferring information on three-nucleon forces from multimessenger astronomical data [Phys. Rev.C 103 (2021) 065804; Phys. Rev. D 106 (2022) 083010]; (iii) the development of an advanced model of the CBF efective Hamiltonian including relativistic boost corrections [Phys. Rev. C 110 (2024) 055801]; and (iv) a detailed study of the neutrino emission and propagation in charge-neutral β-stable matter. Preliminary results of these calculations—thoroughly described in the PhD Thesis of Lucas Tonetto—are reported in arXiv:2505.24485 [nucl-th].