Nuclear effects in deep inelastic scattering Page: 2 of 14
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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  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
- 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 . For both infinite nuclear matter and light nuclei having A< 4 it is
possible to perform a quantitative calculation of the nucleon spectral function
P(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)  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
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  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 , and provide new results for EMC ratios
for 4He and 'He.
Inclusive electron-nucleus scattering data at moderate Q2 (1.5 < Q2 <
3 (GeV/c)2) and z ~ 1 has been quantitatively accounted for -. 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
'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 energy
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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.