Multinucleon excitations in neutrino-nucleus scattering: connecting different microscopic models for the correlations

TL;DR

This paper explores the connection between independent particle models and ab initio correlated models in neutrino-nucleus scattering, providing a formal framework to compare different microscopic approaches to nucleon correlations.

Contribution

It introduces a unitary transformation technique to relate independent particle and correlated wave function approaches, deriving general formulas applicable to various effective interactions.

Findings

Established a formal correspondence between different correlation models.

Derived formulas for spectral and response functions applicable to various interactions.

Evaluated the compatibility of effective interaction approaches with ab initio correlation estimates.

Abstract

The problem of nucleon-nucleon correlations and meson exchange currents has been vividly debated in connection with the neutrino-nucleus cross sections. In this work we focus on nucleon-nucleon correlations by discussing a formal correspondence between the approaches based on independent particles and the ab initio approaches involving correlated wave functions. We use a general technique based on unitary transformation mapping the Fermion operators relative to bare nucleons into quasi-particle operators relative to dressed nucleons. We derive formulas for spectral functions, response functions, momentum distribution, separation energy, general enough to be applied with any kind of effective nucleon-nucleon interaction. We establish the relation between the non-energy-weighted sum rule and the Fermi sea depopulation. With our tools we evaluate whether approaches based on effective interactions are compatible with the expected amount of correlations coming from ab initio calculations. For this purpose we use as a test the Fermi sea depopulation and the value of the kinetic energy per nucleon.