Pauli Blocking for a Relativistic Fermi Gas in Quasielastic Lepton Nucleus Scattering

TL;DR

This paper corrects previous inaccuracies in the expressions for Pauli blocking in relativistic Fermi gas models of quasielastic lepton-nucleus scattering, providing accurate geometrical derivations and highlighting the larger effects compared to other models.

Contribution

It provides the correct geometrical derivation of Pauli blocking effects in the RFG model, correcting errors in prior publications and comparing the magnitude of these effects with other models.

Findings

Corrected expressions for Pauli blocking in RFG model.

Identified errors in previous literature.

Pauli blocking effects are larger in RFG than in other models.

Abstract

The expressions for the overall effect of Pauli blocking in quasielastic (QE) lepton scattering from nuclear targets within the framework of the Relativistic Fermi Gas (RFG) given in several publications are incorrect. For example, the expressions published by Bell and Llewelyn Smith in 1972 are incorrect (probably a typographical error). The expressions for Pauli blocking presented in several subsequent publications including the paper of C.H. Llewelyn Smith in 1972 and the paper of Paschos and Yu in 2002 have the same error. Another example is a 1992 paper by Singh and Oset which has a different (probably also a typographical) error. Other papers such as the papers of Tsai in 1974 and Bosted and Mamyan in 2012 use the correct expressions. In this short preprint we review the geometrical derivation of the overall reduction of the QE cross sections due to Pauli blocking for electron and neutrino scattering for targets with equal numbers of neutrons and protons and for targets with unequal numbers of neutrons and protons and derive the correct expressions. However, we note that the effects of Pauli blocking within the framework of the RFG model are much larger than in other more realistic models of QE scattering such as $\psi^\prime$ superscaling or a spectral function approach.