[Paper Review] Weak Response of Nuclear Matter

Nicola Farina|ArXiv.org|Jan 16, 2009

Pulsars and Gravitational Waves Research10 references3 citations

TL;DR

This thesis develops a many-body approach based on correlated wave functions to calculate the weak response of nuclear matter, using effective interactions derived from realistic nuclear Hamiltonians. It demonstrates that many-body correlations significantly suppress the response at low momentum transfer, providing a more accurate description of neutrino-nucleus interactions relevant to supernova physics and neutrino oscillation experiments.

ABSTRACT

The quantitative understanding of neutrino interactions with nuclei and nuclear matter is needed to the study of many different problems. In the astrophysics environment, neutrino-nucleon and neutrino-nucleus reaction rates are used as inputs in the simulations of phenomena like supernov$æ$ explosions and neutron star cooling. In the field of neutrino physics, the quantitative knowledge of neutrino-nucleus cross-section is critical to reduce the systematic uncertainty of the long baseline oscillation experiments. It is important to realize that, while neutrinos interacting in stellar matter typically have energies of the order of few MeV, the energies involved in long baseline oscillations experiments are much larger. For example, K2K experiment takes data in the region $E_ν =0.5-3$ GeV. In this thesis, we describe how nuclear many-body theory provide a scheme allowing for a consistent treatment of neutrino-nucleus interactions at both high and low energies. We will show our predictions of the neutrino-nucleus cross section in the high energy regime and the results of our calculations for the nuclear matter weak response in the low energy regime.

Motivation & Objective

• To improve the theoretical description of neutrino-nucleus interactions by incorporating realistic many-body correlations.
• To address the limitations of the independent particle model in predicting nuclear response functions.
• To compute the weak response of nuclear matter using a consistent framework based on correlated wave functions.
• To assess the impact of dynamical correlations on neutrino mean free paths and transport properties.
• To bridge the gap between low-energy (MeV) and high-energy (GeV) neutrino interactions in nuclear matter.

Proposed method

• Employing correlated wave functions derived from the Fermi Hypernetted Chain (FHNC) formalism to describe nuclear many-body correlations.
• Using the cluster expansion method to construct an effective interaction from realistic two- and three-nucleon forces.
• Applying the effective interaction within standard perturbation theory to compute the weak response function.
• Relating the weak response to the spectral function through the random phase approximation (RPA) and sum rules.
• Validating the approach against known results for nuclear matter binding energy and saturation properties.
• Extending the formalism to include both weak neutral and charged current interactions in uniform nuclear matter.

Experimental results

Research questions

• RQ1 How do many-body correlations affect the weak response function of nuclear matter at low momentum transfer?
• RQ2 To what extent do dynamical correlations suppress the strength of the weak response compared to the independent particle model?
• RQ3 Can the effective interaction derived from correlated wave functions accurately reproduce known nuclear matter properties?
• RQ4 How does the weak response evolve across the transition from low-energy (MeV) to high-energy (GeV) neutrino regimes?
• RQ5 What is the role of the spectral function in connecting the weak response to observable neutrino cross sections?

Key findings

• Many-body correlations lead to a significant suppression of the weak response at low momentum transfer, particularly in the region of the quasielastic peak.
• The calculated response function shows a reduced strength near the quasielastic peak compared to the independent particle model, consistent with experimental data on electron scattering.
• The effective interaction derived from correlated wave functions reproduces the saturation properties of nuclear matter, including binding energy and incompressibility.
• The weak response is strongly sensitive to the choice of correlation functions, with the FHNC approach providing a good description of short-range correlations.
• The model predicts a reduced neutrino mean free path in dense nuclear matter due to enhanced correlations, with implications for supernova core dynamics.
• The framework successfully interpolates between low-energy and high-energy regimes, showing a smooth transition from collective to independent-nucleon-like behavior.