# 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),N

q -

N(10)

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

N NR

A

A-2

A

Figure 3: Example of two-nucleon coherent contribution.

in nuclear matter is mainly absorptive, its effect can be accounted for by a

folding expression:

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 [12]. 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

cross section:A

Figure 2: FSI of the knocked out system with the residual

nucleus.

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) [4]. Since the FSI of high energy hadrons6

dit = [ 2W (Q2Y)tan2 + Wi(Q2,v) ,

where oM is the Mott cross section

oM = 4a2 coa2

7(13)

(14)

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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.