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.
Highlights
The problem of nucleon-nucleon correlations and meson exchange currents has been vividly debated in connection with the neutrino-nucleus cross sections
The explanation of this disagreement came from the Lyon group [5]: nucleons are correlated, via short-range correlations (SRC) and meson exchange currents (MEC), which implies the possible ejection of a pair of nucleons
The technique is based on unitary transformation mapping the Fermion operators relative to the bare nucleon into quasi-particle operators relative to dressed nucleon. With this technique we derive explicit formulas for spectral functions, response functions, for the momentum distribution, the separation energy, general enough to be applied with any kind of effective nucleon-nucleon interaction
Summary
Before presenting a more detailed treatment of the main quantities discussed in this paper, we would like to remind that similar problem on the role and of the treatment of correlations, discussed here in connection with neutrino scattering, already happened thirty. Concluded that conventional nuclear models are unable to reproduce the EMC effect, the major part coming from other sources possibly related to an intrinsic modification of the nucleon structure in the nuclear medium This conclusion as well was premature, as shown below. One can conclude that the independent particle picture is a very approximate view of the nucleus or that the Hartree Fock scheme with bare nucleons is a poor approximation of the nuclear ground state This conclusion looks surprising at first since we know that independent particle models based on the HF scheme reproduce accurately many basic properties of nuclei. We will come with more details to this question, a central aspect of the present article,
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