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70 Chapter 6. Final State Interactions and the Eikonal Approximation
factors as [94, 95]
I 0 P l ′ = ɛ + ɛ′ √
τ(1 + τ)G 2 M tan 2 (θ e /2) , (6.7)
M p
√
I 0 P t ′ = −2 τ(1 + τ)G M G E tan(θ e /2) , (6.8)
I 0 = G 2 E + τG 2 M[1 + 2(1 + τ) tan 2 (θ e /2)] , (6.9)
τ = Q 2 /4M 2 p (6.10)
The ratio of the transferred polarizations is then
P ′ t
P ′
l
=
G E
−2M p
(ɛ + ɛ ′ (6.11)
) tan(θ/2) G M
For a free proton target, the ratio of the polarizations can be used to determine the
ratio of the form factors. This ratio is independent of beam polarization provided
it is not zero of course. Pioneering work on this terrain was done in the early 90’s
at SLAC [96, 97]. For nuclear targets the polarization transfer also depends on the
nuclear wave functions. In addition they are affected by the final state interactions
of the outgoing proton, off-shell effects and relativity. In Fig. 6.7 the ratios of the
polarization observables of Fig. 6.6 are compared to the data.
We have already mentioned the pronounced sensitivity of the R T L response function
to the different ingredients that enter into the model calculations. A quantity
that reflects this sensitivity is the left-right asymmetry A LT
A LT = σ(φ = 0◦ ) − σ(φ = 180 ◦ )
σ(φ = 0 ◦ ) + σ(φ = 180 ◦ ) =
v T L R T L
v L R L + v T R T + v T T R T T
. (6.12)
Also this ratio is independent of the spectroscopic factors. In Fig. 6.8 we have
plotted the left-right asymmetry for both 1p 1/2 and 1p 3/2 knockout from 16 O in the
kinematics of Ref. [15]. When discussing the shape of the differential cross sections it
was already stressed that the predicted asymmetry between the positive and negative
p m side was too large. This reflects itself in the calculations predicting too large a
A LT value. Note that above p m ≈ 250 MeV/c the A LT exhibits a strong sensitivity
to FSI effects. Both the Glauber and optical-model approach, albeit showing very
different p m dependences, reproduce the trend set by the data at high p m . Note
that the inclusion of FSI effects is essential for an accurate description of the data
points at p m = 275 and 350 MeV/c.
6.2 12 C(e, e ′ p) 11 B
We also compare our predictions with data from a recent 12 C(e, e ′ p) SLAC experiment
(NE18 experiment) at Q 2 = 1.1 (GeV/c) 2 [98, 99]. The differential cross