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110 Chapter 9. Nuclear Transparency
In A(e, e ′ p) processes the nuclear transparency is determined as the ratio of the
measured to the plane wave impulse approximation cross section. Hereby both the
data and the PWIA results are integrated over that region of phase space where the
IA approximation is established to be a valid approximation. One has
∫
∆
T exp =
3 k d⃗ k ∫ ∆E dE S exp( ⃗ k, E)
∫
∆ 3 k
∫∆E dE S P W IA( ⃗ k, E) , (9.5)
where S exp(P W IA) is the measured (plane wave) cross section divided by a kinematic
factor and the off-shell elastic electron-proton scattering cross section σ ep
cc1 of
Ref. [39]. For the SLAC experiment, the boundaries in the above integrals were
fixed at -30 < E m < 100 MeV for the missing energy and 0 < p m < 250 MeV/c for
the missing momentum.
Studying the A-dependence of the experimental nuclear transparency is a very
efficient tool to search for CT effects. Indeed, CT implies that the ejectile experiences
a reduced attenuation through the presence of the other nucleons over a
distance comparable to the nuclear radius. Evidently, this means that the onset of
CT effects in heavier nuclei should be slower, and, hence, a change in the shape of
the A-dependence with increasing Q 2 could indicate the onset of CT. If one simply
parametrizes this A-dependence as T (Q 2 ) = c(Q 2 )A α(Q2) , then complete CT would
correspond to α = 0, or, a vanishing dependence on the radius of the nucleus.
The results of such A-dependence measurements of the nuclear transparency are
displayed in Figs. 9.3 and 9.4. Fig. 9.3 shows the measured transparency as a
function of Q 2 . The hypothesis of color transparency predicts an increase of T with
increasing Q 2 . The data in Fig. 9.3 show no evidence for this. Inspecting Fig. 9.4
which shows T as a function of A, a similar conclusion has to drawn. Indeed, within
experimental errors the α values from the fit of the data to T = cA α are independent
of Q 2 , pointing towards the absence of CT effects. A calculation based on a classical
attenuation model for protons propagating in the nucleus basically reproduces the
A-dependence of the results.
It would be too simplistic to claim that CT has been ruled out by experiment.
On the other hand, there are strong indications that color transparency is a small
effect in the few-GeV regime. Another possibility is that CT effects are suppressed
in this energy regime by a yet unknown QCD effect. One could also argue that
the underlying model to determine the “normal” hadronic attenuation of the struck
proton through the medium is too crude. For example, to our knowledge all Glauber
calculations that have been done up to now adopt a factorized approach separating
the photon-nucleus physics from the nuclear dynamics and ignore relativistic effects.
In the preceding sections we have shown that the unfactorized Glauber model is
fairly accurate in describing all major A(⃗e, e ′ ⃗p) observables. In what follows we
will put our unfactorized and relativistic Glauber approach to test by comparing its
calculated transparencies to the 12 C data.