Introduction

Exclusive and semi-exclusive quasielastic proton knockout reactions, 
(e,e'p) have been very successful in the study of both nuclear 
structure and reaction mechanism.  In general, but not without 
exceptions, the single-particle aspect of nuclear structure was 
studied using the proton removal from valance states, while other 
aspects of the structure as well as reaction mechanism were studied 
at higher missing energies.  Unfortunately, no coherent theoretical 
picture exists that describe data in these two excitation regions 
and the theoretical tools used to describe these two regions are 
different.  Hence, in our present understanding [muther] these two 
regions are related mainly by the transfer of strength from the 
valance states to higher missing energies.  Experimentally, it it 
cenvenient to perform measurements simultaneously in these two 
excitation regions.

The response functions which make up the cross section provide 
independent observables which are sensitive selectively to various 
aspects of the nuclear current.  Hence, in addition to measuring 
cross sections, the extraction of these additional observables is 
important in forming a complete picture of the structure and the reactions.

^16O has been a favorite nucleus for theorists, being a doubly 
closed-shell nucleus whose structure is easier to model than other 
nuclei.  Experimentally, oxygen has been studied extensively.  
However, it is not as convenient a target as carbon for example, 
hence less experimental data are available from ^16O(e,e'p) reactions.

The knockout of 1p-shell protons in ^16O(e,e'p) was studied  at 
Saclay [chinitz,bernheim], NIKHEF [spaltro,leuschner], and Mainz 
[blomquist] at momentum transfers Q^2<0.4 (GeV/c)^2.  In these 
experiments, the cross sections were measured as a function of missing 
momentu and spectroscopic factors were extracted.  The published 
spectroscopic factors range between 0.5 and 0.7, but Kelly showed 
[kellysf] that the Mainz data [blomquist] suggest a significantly 
smaller normalization factor.  Chinitz et al. [chinitz] and Spaltro 
et al. [spaltro] extracted the longitudinal-transverse interference 
response, R_lt, as well at Q^2=0.3 (GeV/c)^2 and 0.2 (GeV/c)^2 
respsctively.  Their extracted R_lt for the 1p1/2-state agree, but 
those for the 1p3/2-state disagree dramatically (see figure 1).  DWIA 
calculations by Kelly [kelly] are consistent with the data of Chinitz 
et al. [chinitz].  The same calculations well describe more recent 
data at Q^2=0.8 (GeV/c)^2 [gao] which are described below.

Not many data are available for ^16O(e,e'p) to higher missing energies, 
and much of what we know about this excitation region is from studies 
of other nuclei, mainly from Carbon.  Above the two-nucleon emission 
threshold, access strength is observed for many nuclei, which is more 
transverse than longitudinal [ulmer,steenhoven,dutta].  This phenomenon 
persists over a large range of momentum transfers, though the access 
transverse strength seems to decrease with increasing momentum transfers 
[dutta].  Several theoretical attempts to explain the data at high missing 
energies by two-body knockout models [ryckebusch1,gil,takaki] and by tensor 
and short-range correlations [muther] fail to adequately describe those 
data.  It is generally understood thought, that even for quasielastic 
kinematics, high missing energy data are associated with significant 
contributions to the cross section from other than single-particle processes.

More recently, this group has used the ^16O(e,e'p) reaction to study 
nucleon removal from the valance 1p-shells [gao] and from the s-shell 
and also at higher residual excitations [liyanage].  This was the 
first part of CEBAF experiment 89-003 (89-003a) [89003] which was the first 
commissioning experiment in Hall A.  All measurements 
were performed at a fixed momentum transfer, Q^2=0.8 (GeV/c)^2, and in 
quasielastic kinematics.  Cross sections as a function of missing 
momentum (``distorted momentum distributions'') up to p_miss=340 MeV/c 
were measured, as well as several response functions for the various 
residual excitation energies.  One of the most striking results, 
is the contrast between the success of theoretical calculations to 
describe the measured observables in the 1p-shell removal and the 
failure of the same calculations to describe the observables related 
to the 1s-shell removal and higher residual excitations.  It is clear, 
that even up to missing momentum of about 340 MeV/c, the single-
particle aspect of the 1p-shell structure is dominant, whereas 
for the 1s-shell and for higher missing energies, other aspects of 
the wave function (such as correlations) and/or of the reaction 
mask the single-particle picture.  These other aspects become more 
prominent with increasing missing momenta.

The 5-fold differential cross section was measured for the proton removal 
from the p1/2 and p3/2 shells at 8 p_miss values in the range  
-340<p_miss<+340 MeV/c (see figure 2).  The cross-section is well discribed by fully 
relativistic DWIA calculations [udias] which solve the Dirac equation 
and include Dirac spinor distortions of both the bound and scattered 
states.  It is also well described by relativistic DWIA calculations 
which solve a relativized schrodinger equation and use the effective 
momentum approximation (EMA) to include the lower components of the 
Dirac spinors [kelly].  However, the EMA breaks down at p_miss>275 
MeV/c, and hence the latter calculations are less successful in 
reproducing the data in this p_miss range.  Both calculations use the 
NLSH [nlsh] bound-state wave function (bswf) which yields values of 
binding and single-particles energies, as well as the charge radius 
for ^16O which are in good agreement with data.  The spectroscopic 
factors extracted for the p1/2 (p3/2) states were 0.73 (0.71) and 
0.72 (0.67) for the udias' and kelly's calculations respectively.  
The extraction of spectroscopic factor is not independent from the 
choice of bswf, as there are other good bswf's with slightly different 
parameters.  Unfortunately, the 8 p_miss points from this experiment 
were not sufficient to uniquely fix the bswf, and the spectroscopic 
factors independently.  Hence, additional precise measurements over a 
wide p_miss range (but especially at p_miss<200 MeV/c) are needed for 
the independent determination of the bswf and spectroscopic factors.  
The spectroscopic factors extracted by Udias are consistent with those 
he extracted from the data of Chinitz [chinitz], Spaltro [spaltro], 
and Leuschner [leuschner] at lower momentum transfers, but only when
taking into account the large uncertainties that some of 
these values (most notably [leuschner]) extracted at lower momentum 
transfer have.  We note this point in light of recent suggestions by 
Lapikas et al. [lapikas] that spectroscopic factoes for the 1p-shell 
of ^12C may be momentum-transfer dependent.  

The R_l+(v_tt/v_l)R_tt, R_t and R_lt response functions as well as the 
left-right asymmtery, A_lt, were also extracted for the p-shell proton 
knockout and compared to the relativistic DWIA calculations.  The calculations 
are in good agreement with the measured quantities.  The most stiking 
result is a structure in the asymmetry A_lt which is predicted and well 
reproduced by the calculations only when spinor distortions are included (see figure 3).  
While A_lt is very sensitive to this dynamic enhancement of the lower 
components of the Dirac spinors, especially at p_miss>275 MeV/c, the 
inclusion of these spinor distortions is also needed to reproduce R_lt 
at p_miss<275 MeV/c.  Udias predicts [udiaspc] that A_lt is increasingly 
sensitive to the above dynamical relativistic effects with increasing 
p_miss (see figure 4).  Hence, measurements at higher p_miss can thest the importance of 
these effects.  It should be emphasized that neither DWIA calculations 
include contributions from 2-body effects such as meson exchage currents 
(MEC), isobar contributions (IC) or from initial-state correlations.  Hence, 
it was concluded that up to p_miss of 340 MeV/c, these effects are not 
important.  It is important, then, to push measurements to higher p_miss, 
also in the hope of observing where these effects become important.  In 
this respect it is noteworthy that Udias et al. may be able to include the 
effects of initial state correlations and of MEC in the foreseeable 
future [udiaspc].

The results for the 1p-shell removal and their comparison to theory 
are described in more details in the published manuscript [gao], which 
is attached below as addendum 1.

The ^16O(e,e'p) was also studied at higher missing energies [liyanage].  
Missing energy spectra up to E_miss=120 MeV were measured for four missing 
momenta in the range 50-340 MeV/c.  Also measured were the R_l and R_t 
responses for p_miss~60MeV/c, and the R_l+(v_tt/v_l)R_tt, R_t and R_lt 
responses for p_miss=145 and 280 MeV/c.  he neasured observables were 
compared to similar DWIA calculations [udiaspc,kelly] used successfully 
for the comparison with the p-shell removal data.  As mentioned above, 
these calculations are based on a single particle picture and hence a 
comparison to data is relevant only for the s-shell (20<E_miss<60 MeV).  
The data were also compared to calculations by Ryckebusch et al. 
[ryckebusch] which include single-particle non-relativistic Hartree-Fock 
(HF) component which uses the same potential for the bond state and 
the ejectile nucleon.  They also include contributions from (e,e'pp 
and (e,e'pn) due to MEC, IC as well as central and tensor short-range 
correlations (figure 5).

The main feature of this measurement is the clear manifestation of 
the s-shell at p_miss~50-60 MeV/c, and its decreasing manifestation 
with increasing p_miss.  The s-shell is clearly visible in the E_miss 
spectrum at p_miss=50 MeV/c, and in the response functions at p_miss=60 
MeV (figure 6).  These observables are also well described by all calculations 
(kelly, udiaspc,ryckebusch] with reasonable occupancy in Kelly's 
calculations of 0.67.  However, the s-shell peak in the missing 
energy spectra is increasingly masked by strength at higher and lower 
missing energies, and for p_miss>=280 MeV, the missing energy spectrum 
is flat with a constant cross-section of a few picobarns/MeV^2/sr^2 up 
to the highest measured E_miss, 120 MeV.  The s-shell peak is decreasingly 
noticeable in the measured response functions as well with increasing 
p_miss (figures 7,8).  Similarly, the calculations increasingly fail to reproduce the 
measured 1s-shell observables with increasing p_miss.  It should be noted 
that the HF calculations by Ryckebusch are able to qualitatively reproduce 
the strength of the 1s-shell for the entire p_miss range.  However, this 
is due to the non-absortive potential used, that yields strength at 
p_miss>250 MeV/c which is an order of magnitude larger than that of the 
DWIA calculations.  As a result, the HF calculations overpredict the 
cross-section of the 1p-shell by the same mount for p_miss>250 MeV, and 
should be considered unreliable at that p_miss range.  Hence, neither 
DWIA nor the HF calculations are able to reproduce reliably the 1s-shell 
behavior, because the single-particle aspect of the 1s-shell removal is 
increasingly masked by other components of the wave function or processes 
with increasing p_miss.

For missing energies higher than the 1s-shell, the measured strength, 
including the flat strength at p_miss>250 MeV/c,  
is described to a factor of 2 in the calculations by Ryckebusch et al.
by contributions from (e,e'pn) and (e,e'pp) arising from 2-body currents 
and from central and tensor short-range correlations. 
Measurements of additional observables are needed to verify these contributions.

The results for the 1s-shell and higher missing energies as well as comparison 
to theory are described in details in  the manuscript of addendum 2 [liyanage] 
which is to be submitted to Phys. Rev. Lett..








		Proposed Measurement


We propose to measure the ^16O(e,e'p) reaction at a single momentum transfer, 
Q^2=0.8(GeV/c)^2, similar to that of 89-003a.  This will enable to greatly
enhance the data base available for this momentum transfer.  
All measurement will be done in perpendicular kinematics, 
and at a fixed quasielastic electron kinematics (electron-arm setting).  This will 
facilitate the use of the electron arm as a continuous luminosity monitor.  
The target will be similar to the 3-foil waterfall target used in 89-003a, 
but the flow rate will be increased to provide a thickness of about 180 mg/cm^2 
per foil.  As we did in 89-003a, the hydrogen in the waterfall target will 
be used for the experimental determination of the q vector's magnitude 
and direction, and for absolute normalization.

Very good data exist in this Q^2 from the first part of this 
experiment [gao, liyanage].  Very good calculations 
for the 1p-shell [udias, kelly] and for higher excitations [ryckebusch] 
reproduce and predict many features of these data.  It is possible now 
to test these calculations and constrain the respective models further by 
extending the data to higher p_miss with better precision.  We  plan to 
measure cross-sections with statistical
accuracy of 1-2 percent (3 percent in very few cases) and with systematic 
uncertainties of 3 percent or better.  The count-rate estimates are descibed 
in the next section.  Based on the cummulative experience of Hall A, attaining
systematic uncertaities of 3 percent is very realistic.  

It is convinient to divide the proposed measurement into the two excitation 
regions of the residual nucleus.  In the removal of protons from the 1p1/2 
and 1p3/2 shells, we propose to measure in detail the cross-section as a 
function of missing momentum (``distorted momentum distributions'') in order 
to constrain the bound-state wave function and to accurately determine the 
spectroscopic factors.  We also propose to measure the R_lt response and A_lt 
asymmetry in order to further test the relativistic DWIA calculations 
which predict great sensitivity to  relativistic dynamical effects 
in these observables.  In processes where the 
residual nucleus is left at higher excitation (``high E_miss''), we propose to 
emphasize the correlation ridge, E_miss = (recoil factor)*[(p_miss)^]/2m_p, 
where p_miss is large enough to suggest short-range correlations.  We further 
propose to measure the R_lt response in order to characterize this ridge.  
We note that combining the measurement in these two regions in the same 
experiment, results in substential saving in set-up, calibrations and 
overhead time (see section on beam-time request).


1p-shell removal

Very good calculations [Udias, Kelly] exist now for the removal of protons 
from the 1p-shell doublet.  The success of these calculations (as well as 
others) depend on the use of good bound-state wave functions (bswf).  
Although the bswf used are very good, it is within the scope of this 
experiment to further constrain them.  For this purpose, it is important to 
measure the cross-section as a function of p_miss accurately over as large a 
range of p_miss as experimentally feasible.  It is noteworthy that for the
purpose of constraining the bswf, sufficient number of data points at low 
p_miss are needed.  Coupled to the choice of bswf 
are the extracted normalization factors (related to the spectroscopic factors)
between the calculated cross-sections and the measured ones.  The accurate 
determination of these normalization factors is important for understanding 
the ``missing strength'' which is believed to be related mainly to two-body 
effects.  These normalization factors gained greater importance recently with 
the publication of a paper [lapikas] suggesting that these factors may be 
momentum-transfer dependent.  Since this suggestion challenges our 
understanding of the normalization factors, it should be put to further test. 
 Accurate data sets of normalization factors is therefore necessary for 
different momentum transfers.  Although our proposed measurement is at a 
single momentum transfer, analysis of our and other (past and future) data 
may help to test the q-dependence suggestion.

Obviously, the bswf is not sufficient to produce the measured (distorted) 
momentum distributions.  Other ingredients enter into the calculations with 
various affects.  We asked Udias to investigate the sensitivity of the 
calculations to the choice of bswf and other various ingredients.  Details of 
this investigation can be found in addendum 3.  A summary is presented below.

Relativistic effects - Here we do not refer to relativistic kinematics which 
is used in all calculations.  Rather, to the inclusion of negative-energy 
components and spinor distortions in the Dirac formalism [udias] or the 
introduction of spinor distortions by the effective momentum approximation 
(EMA) in the relativized Schroedinger formalism [kelly] (the EMA breaks down 
at p_miss ~ 300 MeV/c).  The 1p-shells on oxygen are very suitable for this 
study, because the effect of negative energy components is different for the 2 
p-shells as it is known to be more noticeable for the j+1/2 shell than for 
the j-1/2 shell.  Our previous results strongly indicate that the R_lt and 
(even more so) A_lt observables are very sensitive to the inclusion of these 
relativistic dynamical effects.  The calculations suggest that this 
sensitivity is even larger at higher p_miss (see figure 4).

Current operator - The sensiticvity was tested to two of the most widely 
used current operators [deforest].  It is known that cc2 tends to minimize 
the role of the negative energy components, while cc1 over-emphasizes their 
role.  Although our published data preferes the 
use of cc2 over cc1 , this determination should withstand the test of a larger 
range of p_miss.  Our studies indicate that the sensitivity to the choice of
current operator is larger than to that of the bswf, if the latter are 
restricted to the more modern bswf (such as NLSH and NL3).

Optical potential - The sensitivity was tested to several widely used optical 
potentials of 2 classes:  a purely phenomenological S-V potentials based on 
Dirac equation and fitted to elastic scattering data which is energy 
dependent and with or without A dependence, and a potentials based on 
parametrization of N-N data.  In general, the sensitivity to the optical 
potential is very small, especially in R_lt and A_lt.  Our previous data 
(and other data) are very well described by using  the EDAI-O of the first 
type.  Note that the calculations indicate that the the amount of 
negative-energy components in the wave function is the largest for the 
calculations using the EDAI-O optical potential.

Gauge prescription - Fully relativistic calculations are less sensitive to 
gauge prescriptions than non-relativistic ones.  Low p_miss data exclude the 
use of the Weyl gauge.  The differences between the Landau and Coulomb gauges 
are small, especially for the l=j-1/2.

Two-body currents - The calculations by Udias do not include two-body 
currents, yet their success in predicting our recent data is impressive and 
suggest that these contributions are small for the published momentum transfer range.  It is 
hard to predict reliably the effects of two-body currents, especially at high 
p_miss.  However, over the range of our previously measured p_miss, the 
contribution of two-body currents to R_lt is estimated to be only 2 and 8 
percent for the 1p3/2 and 1p1/2 states respectively [amaro].  
Additional work on the sensitivity of the calculations to two-body 
currents is under way.

Channel coupling - Work on the effect of channel coupling is under way.

Contamination of the 1p3/2 state - Contributions to the 1p3/2 state from the
un-separated positive parity (2s1/2,1d5/2) doublet at 17.4 MeV were taken 
into account in all calculations by including an incoherent contribution of 
these states as parametrized by Leuschner [leuschner].


We propose to measure the ^16O(e,e'p) cross section for the removal of 
protons from the 
two 1p-shells at 20 p_miss values ranging from -515 MeV/c to +755 MeV/c.  
All measurements will be done at Q^2=0.8 (GeV/c)^2 and a fixed range of 
energy-transfer (quasielastic kinematics), so our data from 89-003a 
could be added to form a more comprehensive data-set.  For 
the range -515<= p_miss<=+515 MeV/c, the R_lt response and A_lt asymmetry will 
be measured.  For a summary of the proposed kinematics, see table XXX below.


1s-shell and higher missing energies

The same calculations [udias, kelly] which well reproduce the 
characteristic of the  
1p-shell removal, fail to describe the experimentally observed features of 
the s-shell removal, and of the high missing energies [liyanage].  
This failure increases with increasing 
missing momentum.  This is not surprizing, as even the 1s-shell is a 
deep-lying state for which the single-particle characteristics are masked 
by more complicated structures and processes.

Calculations by Ryckebusch [ryckebusch], though not reliable in their 
treatment of the mean field characteristics of the 1p- and 1s-shell 
removal at p_miss>275 MeV/c, are able to reproduce the deep missing 
energies spectra [liyanage] by including two-body currents, and N-N 
short-range (Jastrow) and tensor correlations.  To further understand the 
nature of the 1s-shell and deeper missing energies spectra, we propose to 
measure the R_lt response and A_lt asymmetry for several missing momenta, 
centered at +/-70, +/-140, +/-210 and +/-345 MeV/c (the lattes up to 
E_miss=160 MeV).  This will help us to determine whether these strengths 
are due to two-body currents which are mainly transverse in nature, or to initial 
state correlations (i.e. Jastrow) which are predominantly longitudinal.  
We expect the nature of the observed strength to change as a function of 
missing momentum.  In particular, the ridge defined by 
E_miss = (recoil factor)*[(p_miss)^]/2m_p, should be different for low 
p_miss than for p_miss above the Fermi momentum, where it is expected to 
be due to short-range N-N correlations.

The details of the proposed kinematics are given in the table below.  
Note that these measurement at the higher E_miss entail only lowering the magnitic-field 
settings of the hadron spectrometer, hence there is essentially no 
additional overhead.  Moreover, the monitoring of the luminosity does 
not change, as the electron-arm setting stays fixed.  Hence, there are 
no additional or separate systematic uncertainties to this part of the 
measurement.











References

[muther]     H. Muther et al., Phys. Rev. C49, R17 (1994)
[chinitz]    L. Chinitz et al., Phys. Rev. Lett. 67, 568 (1991)
[bernheim]   M. Bernheim et al., Nucl. Phys. A375, 381 (1982) 
[spaltro]    C. M. Spaltro et al., Phys. Rev. C48, 2385 (1993)
[leuschner]  M. Leuschner et al, Phys. Rev C49, 955 (1994)
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[kellysf]    J. J. Kelly, Adv. Nucl. Phys. 23, 75 (1996); Phys. Rev. C56, 2672 (1997)
[kelly]      J. J. Kelly, Phys. Rev. C60, 044609 (1999)
[gao]        J. Gao et al., Phys. Rev. Lett. 84, No. 15, 3265 (2000)
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[gil]        A. Gil et al., Nucl. Phys. A627, 599 (1997)
[takaki]     T. Takaki, Phys. Rev. C39, 359 (1989)
[liyanage]   N. Liyanage et al., to be submitted to Phys. Rev. Lett.
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[udias]      J. M. Udias et al., Phys. Rev. Lett. 83, 5451 (1999)
[nlsh]       M. M. Sharma, M. A. Nagarajan, and P. Ring, Phys. Lett. B312, 377 (1993)
[lapikas]    L. Lapikas et at., LANL preprint nucl-ex/9905009 v2 (2000)
[udiaspc]    J. M. Udias, private communications
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[deforest]   T. de Forest Jr., Nucl. Phys. A392, 232 (1983)
[amaro]      J. E. Amaro, private communications



Addendum 1
Juncai's manuscript

Addendum 2
Nilanga's manuscript (to be updated after comments)

Addendum 3
Udias' latest writeup (to be updated)





Figures 

figure 1: chinitz_spaltro.ps
figure 2: Juncai's figure 1
figure 3: Juncai's figure 2
figure 4, A_tl by Udias for 1p1/2 and 1p3/2 (upper right hand 
figures of cartl.p1.nlsh.ps and cartl.p3.nlsh.ps of
the ones you mailed to me 3/20/00)
figure 5: Nilanga's figure 1
figure 6: Nilanga's figure 2
figure 7: Nilanga's figure 3
figure 8: Nilanga's figure 4