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Chapter 7
Off-Shell Ambiguities
A major point of concern in any A(e, e ′ p)B calculation are the ambiguities regarding
the off-shell electron-proton coupling. Most multi-body calculations do not obey
current conservation and as outlined in Sec. 4, a variety of prescriptions have been
proposed to partially cure this deficiency. Any attempt to address off-shell effects
from the microscopic point of view seems to fail at some point.
In this section we will attempt to quantify the ambiguities caused by the use
of different current operators and the methods employed to restore current conservation.
Hereby, we will concentrate, not only on differential cross sections and
structure functions, but also on polarization observables and left-right asymmetries.
A key issue in these considerations will be the Q 2 dependence of the off-shell ambiguities.
We adopt a heuristic view and estimate the sensitivity of the calculated
observables by comparing the results obtained with different viable prescriptions
for the electron-proton coupling. These investigations will allow us to put forward
favorable choices for the current operators that produce reaction observables which
are reasonably stable against minor changes.
We start our investigations into the role of off-shell ambiguities by considering
the 16 O(e, e ′ p) differential cross section at Q 2 = 0.8 (GeV/c) 2 and ω = 0.439 GeV, in
quasi-perpendicular kinematics. Fig. 7.1 compares the predictions for the differential
cross section for various choices of the current operator. This is done by comparing
the predictions relative to the CC2 results. In line with other investigations [41,
42, 101], we find that the ambiguities grow with increasing missing momenta. This
is not so surprising and can be understood in the following sense. Short-range and
tensor forces give rise to strong nucleon correlations among the nucleons in the mean
field, with the result that the Fermi surface is smeared out significantly. This means
that relatively high excited states are present and contribute to the high missing
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