Nuclear effects in deep inelastic scattering Page: 4 of 14
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Equation (9) has also been written in the form:
WA,(q) =J d'k P(k) ( ) .(k,q),
where k is a 4-vector with ko = E and W, is the tensor for bound (off-
shell) nucleons for which k2 # m2. This is our basic equation, used in
refs.[4, 5, 7, 10] to calculate inclusive cross sections within PWIA.
In PWIA we have proved that:
W,,(k, q) = W,(N 4) = -WN (f, i. - ) (gp, +
+2 k , - 4 v k - , q , ( 1 1 )
+ W 2 (2,44) /
W1 and W2 being the nucleon structure functions that can be extracted
from the proton and deuteron data. The appearance of 4, k (rather than q, k)
in the factors multiplying WN in eq.(11) is a direct consequence of PWIA and
Lorents invariance for the case of scattering from an off-shell nucleon. The
total four momentum of the hadronic final state IX, px) is k + 4 where k is
the on-shell four momentum of the struck nucleon. These factors are of great
importance for the understanding of inclusive electron-nucleus scattering.
q X q
Figure 3: Example of two-nucleon coherent contribution.
in nuclear matter is mainly absorptive, its effect can be accounted for by a
d2-Fsv, q) , q) F(v - v' (12)
where the folding function F(v - v') is related to the decay rate of the state
(X, px) in matter. This folding has significant consequences at large x where
the cross section varies rapidly with energy transfer P. However, in the z-
region of interest here, the cross section varies slowly with v and the effect
of FSI is expected to be negligible.
At large values of momentum transfer q most of the coherent processes
with participation of more than one nucleon are expected to be negligible as
well. However, the process shown in fig.3 can contribute. It involves deep
inelastic scattering with a slow nucleon in the final state. Pion current con-
tributions, called "excess pion contributions" in the deep inelastic scattering
regime, are examples of such coherent contributions. They are expected to
become important at small x due to the small mass of the pions, and they
are responsible for a good part of the meson exchange contributions present
in observables such as the form factors of light nuclei at large momentum
transfer . We will return to these pion contributions below.
Contraction of W,,, constructed according to the above procedure, with
the leptonic tensor L"" leads to the standard expression for the inclusive
Figure 2: FSI of the knocked out system with the residual
The above relations are not exact due to the use of PWIA. The two
leading corrections to PWIA, shown in figures 2 and 3, are due to FSI and
coherent contributions. At high energies and x > 1 the effect of FSI on
inclusive scattering cross sections has been estimated using the Correlated
Glauber Approximation (CGA) . Since the FSI of high energy hadrons
dit = [ 2W (Q2Y)tan2 + Wi(Q2,v) ,
where oM is the Mott cross section
oM = 4a2 coa2
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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/m1/4/: accessed April 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.