# Nuclear effects in deep inelastic scattering Page: 2 of 14

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1 Introduction

The term "EMC-effect" refers to the observation that the cross sections for

deep inelastic lepton-nucleus scattering (DIS) differ significantly from the

sum of the nucleonic DIS cross sections. At 0.3 < z < 0.8, where z is the

Bjorken scaling variable, the nuclear cross section is reduced by up to 20%,

for 0.1 < z < 0.3 a small enhancement is observed, and for x < 0.05 a

reduction by up to 30% is found.

A very large number of publications have presented calculations to explain

these observations. For recent reviews we refer the reader to [1, 2]. Here we

cannot do justice to this large body of work, and can only very summarily list

the main results. For 0.3 < z < 0.8 the main effect could be due to nucleon

binding and Fermi motion; however, most calculations still have difficulties

to explain the size of the "dip" at x - 0.7, and the inclusion of binding at the

parton level is not without ambiguities. While early calculations occasionally

got close to reproducing the "dip", later calculations which included the

so called flux-factor (see below) and realistic spectral functions could not

reproduce the data. For 0.1 < z < 0.3 the contribution of excess pions

in nuclei, related to the pion-exchange nature of the long-range nucleon-

nucleon force, is considered to be mainly responsible. Several calculations

gave contributions of the size as required by the data. Difficulties originated

from the fact that this pion excess could not yet be identified in Drell-Yan

processes (p + A -+ p+ + p-) and appeared not to show up in the expected

enhancement of the spin-longitudinal response measured in (p,n) reactions

on nuclei. However, more recent analysis of the (p, n) reaction data [3] does

not contradict the pion excess hypothesis and the assumptions needed to

interpret the Drell-Yan data are less clear. For z < 0.05, the shadowing in

terms of the vector dominance model largely explains the data.

In the z > 0.3 region many new ideas have been employed to reproduce

the EMC-ratios: Q-rescaling, z-rescaling, multi-quark clusters, and others.

With the present paper we want to study the degree to which the most

conventional nuclear physics - the fact that nucleons in nuclei are bound

- can account for the data. Only once this aspect is treated in the most

quantitative way can one hope to learn physics beyond it from the comparison

with the data.

In previous works, we have systematically studied inclusive electron-

nucleus cross sections in the region of the quasielastic peak, at values of Bjor-

ken z = Q2/2mv ~ 1, with Q2 - q12 - 2, Iq] being the three-momentum

transfer, v the electron energy loss and m the nucleon mass. These studies

[4]-[7] were performed for infinite nuclear matter, using cross sections obtai-

ned by extrapolating finite-nucleus data to mass number A= oo, and for light

nuclei [8]. For both infinite nuclear matter and light nuclei having A< 4 it is

possible to perform a quantitative calculation of the nucleon spectral functionP(kl, E) starting from a realistic nucleon-nucleon interaction. The spectral

function describes the distribution of the nucleons in momentum and energy,

and contains the information on nucleons in both single-particle and corre-

lated states. The inclusive cross sections were calculated using Plane Wave

Impulse Approximation (PWIA) [9] for the description of scattering from

an initially bound nucleon. The effects of the nucleon-nucleus final state in-

teraction, important at very large z where the impulse-approximation cross

section becomes very small, were treated using a generalization of Glauber

theory.

We have found that for both the nuclear matter cross sections and the

nuclear matter to deuteron cross section ratios most of the features of the

data can be quantitatively understood.

We recently extended [10] this approach to the study of nuclear matter

cross sections in the region 0.1 < z < 1. A quantitative description of the

dip in observed EMC ratios at z ~ 0.7 was obtained for nuclear matter when

using a realistic spectral function and the generalization of PWIA to the

scattering of electrons by bound nucleons. In the present paper we present

a derivation of the relation between the cross sections for free and bound

nucleons in the context of deep inelastic scattering, give additional details on

the calculations presented in [10], and provide new results for EMC ratios

for 4He and 'He.

2 Formalism

Inclusive electron-nucleus scattering data at moderate Q2 (1.5 < Q2 <

3 (GeV/c)2) and z ~ 1 has been quantitatively accounted for [4]-[7]. At

z ~ 1 the PWIA is sufficient to account for the data, while at large z Final

State Interactions (FSI) are important. In this paper we extend the PWIA

treatment to the deep inelastic scattering region. The basic assumption un-

derlying this scheme is that, at large momentum transfer, scattering off a

nuclear target reduces to the incoherent sum of elementary scattering pro-

cesses off individual nucleons distributed according to the spectral function

P(Jk, E), and that the FSI of the debris from the struck nucleon with the

(A-1) nucleus can be neglected. The spectral function P(lk, E) yields the

probability of finding a nucleon of momentum k in the target with the residual

system having an excitation energy E '. We use the four vectors k = (E, k)

to denote the energy/momentum of an off-shell nucleon in the nucleus, and

k = (Ek, k) with E = ,m2 + k2 to denote the energy/momentum for the

free nucleon.

'more precisely, E is the removal energy given by the sum of the excitation energy

of the (A-1)-nucleon spectator system and the one-nucleon separation energy, plus (in a

finite system) the recoil energy2

3

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Benhar, O.; Pandharipande, V.R. & Sick, I. Nuclear effects in deep inelastic scattering, article, March 1, 1998; Newport News, Virginia. (https://digital.library.unt.edu/ark:/67531/metadc709218/m1/2/: accessed April 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.