The cross section for quasielastic ^(12)C(e,e’p) scattering has been measured at momentum transfer Q^2=1, 3, 5, and 6.8 (GeV/c)^2. The results are consistent with scattering from a single nucleon as the dominant process. The nuclear transparency is obtained and compared with theoretical calculations that incorporate color transparency effects. No significant rise of the transparency with Q^2 is observed

Arrington, J.

Beise, E. J.

Belz, E.

Filippone, B. W.

Gao, H.

Lorenzon, W.

Makins, N. C. R.

McKeown, R. D.

Mueller, B.

O'Neill, T. G.

English

Caltech Authors - Main

VOLUME 72, NUMBER 13 PHYSICAL REVIEW LETTERS 28 MARCH 1994 
Momentum Transfer Dependence of Nuclear Transparency from the Quasielastic 
12C(e, e'p) Reaction 
N. C. R. Makins, R. Ent,• M. S. Chapman, J.-0. Hansen, K. Lee, R. G. Milner, and J. Nelsont 
Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02199 
R. G. Arnold, P. E. Bosted, C. E. Keppel, A. Lung,t S. E. Rock, M. Spengos, Z. M. Szalata, L. H. Tao, 
and J. L. White 
The American University, Washington, D.C. 20016 
K. P. Coulter,§ D. F. Geesaman, R. J. Holt, H. E. Jackson, V. Papavassiliou, D. H. Potterveld, and B. Zeidman 
Aryonne National Laboratory, Aryonne, fllinois 60499 
J. Arrington, E. J. Beise,ll E. Belz, B. W. Filippone, H. Gao, W. Lorenzon," B. Mueller, R. D. McKeown, 
and T. G. O'Neill 
W. K. Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California 91125 
M. Epstein and D. J. Margaziotis 
California State University, Los Angeles, California 90092 
J. Napolitano 
Rensselaer Polytechnic Institute, Troy, New York 12180 
E. Kinney 
University of Colorado, Boulder, Colorado 80909 
P. L. Anthony, K. van Bibber, and F. S. Dietrich 
Lawrence Livermore National Laboratory, Livermore, California 94550 
R. A. Gearhart and G. G. Petratos 
Stanford Linear Accelerator Center, Stanford, California 94909 
S. E. Kuhn** 
Stanford University, Stanford, California 94905 
J. F. J. van den Brand, H.-J. Bulten, and C. E. Jonestt 
University of Wisconsin, Madison, Wisconsin 59706 
(Received 15 December 1993) 
The cross section for quasielastic 12C(e,e'p) scattering has been measured at momentum transfer 
Q2 = 1, 3, 5, and 6.8 {GeV /c) 2 • The results are consistent with scattering from a single nucleon 
as the dominant process. The nuclear transparency is obtained and compared with theoretical 
calculations that incorporate color transparency effects. No significant rise of the transparency with 
Q2 is observed. 
PACS numbers: 25.30.Fj, 24.85.+p 
Mueller and Brodsky [1) have suggested that, at suf-
ficiently high momentum transfer, the final (and initial) 
state interactions of hadrons with the nuclear medium 
should be reduced, leading to the phenomenon termed 
"color transparency." Although the arguments were orig-
inally formulated within the context of perturbative QCD 
(high momentum transfer approximation of the strong 
interaction), recent work [2) indicates that this phe-
nomenon occurs in a wide variety of model calculations 
with nonperturbative reaction mechanisms. 
The requirements for the existence of color trans-
parency have been discussed recently [2) and are briefly 
summarized here. First, high momentum transfer scat-
tering should take place via selection of amplitudes in the 
initial and final state hadrons characterized by a small 
transverse size (much smaller than the hadron radius). 
Secondly, this small object should be "color neutral" out-
side of this small radius in order not to radiate gluons 
(which would lead to inelasticity). The object, being 
small and color neutral, would then have reduced inter-
1986 0031-9007/94/72(13)/1986(4)$06.00 
© 1994 The American Physical Society 
VOLUME 72, NUMBER 13 PHYSICAL REVIEW LETTERS 28 MARCH 1994 
actions with hadrons in the surrounding nuclear medium 
("color screening"). Finally, it is necessary that this com-
pact size be maintained for some distance in traversing 
the nuclear medium in order that the reduction in the 
interaction probability be observable. 
Various models have been used to estimate the mag-
nitude of this effect at experimentally accessible ener-
gies, and the predictions differ considerably. Therefore it 
is important to establish experimentally the momentum 
scale required to observe this novel prediction. 
An observed energy dependence in large angle 
quasielastic A(p, 2p) scattering at high energies [3] has 
been interpreted as evidence for color transparency [4]. 
However, this dependence is strongly correlated with the 
known oscillation of the free nucleon-nucleon scattering 
cross section [5], complicating the interpretation. Data 
from A(e, e'p) can provide additional strong constraints 
on the momentum transfer ( Q2) dependence of color 
transparency. In particular, the electromagnetic probe 
samples the complete nuclear volume; the fundamental 
electron-proton scattering cross section is smoothly vary-
ing and accurately known in this kinematic range; de-
tailed knowledge of the nucleon energy and momentum 
distribution in a nucleus A has been provided by low 
energy A(e, e'p) experiments; and the relatively high en-
ergy resolution of the experiment allows clean detection 
of quasielastically scattered protons over a large kine-
matic range. Here we report on a measurement of the 
Q2 dependence of the nuclear transparency of recoiling 
protons from 12C(e, e'p) quasielastic scattering in the mo-
mentum transfer region from 1.0 to 6.8 (GeV /c)2. Anal-
ysis of data from additional nuclear targets is in progress 
and will be published in a future paper [6]. 
Quasielastic (e, e'p) scattering from nuclei involves 
scattering from the moving, off-shell protons of a finite 
nucleus [7]. In the plane wave impulse approximation 
(PWIA) the proton is ejected without final state interac-
tions with 4-momentum (T' + M, p') from a target nu-
cleus A by exchange of a virtual photon [4-momentum 
(v, q)] with the incident electron, leaving an A- 1 nu-
cleon system B with kinetic energy TB. In PWIA the co-
incidence differential cross section for quasielastic (e, e'p) 
scattering from nuclei is written as [7] 
dE'd::;T'dflp = Kuc:;s(Em,Pm), (1) 
where K is a kinematic factor, u~ is the off-shell electron-
nucleon scattering cross section, and S(Em,Pm) is the 
spectral function, i.e., the probability to find a proton 
with 4-momentum (M- Em - TB, Pm), where the miss-
ing energy Em = v - T' - TB and missing momentum 
Pm = p'-q. The spectral function is normalized so that 
/000 J!;: S(Em,Pm)d3pmdEm = Z. Extensive measure-
ments of quasielastic (e, e'p) scattering from nuclei have 
been made in the low momentum transfer region Q2 :5 
0.3 (GeV /c)2 and the spectral function in the single par-
tide region (Em < 80 MeV and IPml < 250 MeV /c) 
has been determined [8]. The presence of final state in-
teractions, where the proton can scatter both elastically 
and inelastically from the surrounding nucleons as it ex-
its the nucleus, reduces the measured A(e, e'p) cross sec-
tion. The nuclear transparency, the ratio of the measured 
cross section to the PWIA prediction, is a direct measure 
of this reduction. In the limit of complete color trans-
parency, final state interactions vanish and the nuclear 
transparency approaches unity. 
The experiment was performed at the Stanford Linear 
Accelerator Center and used the Nuclear Physics Injec-
tor. Data were taken with the pulsed beam duty factor 
of 2 x 10-4, and the beam energy resolution ranged from 
±0.1% to ±0.2%. The targets consisted of 2% and 6% 
radiation lengths of 12C. The scattered electrons were 
detected using the 1.6 GeV jc spectrometer [9] and iden-
tified in a detector stack of three drift chambers (each 
with two wire planes), two plastic scintillator hodoscopes, 
a lead glass shower counter, and a C02 gas Cherenkov 
detector. The electron momentum resolution was 0.15% 
over the momentum acceptance of ±5%. The recoiling 
protons were detected using the 8 Ge V / c spectrometer 
[10] with a detector stack of ten multiwire proportional 
chambers and a 3-plane hodoscope system. The proton 
momentum resolution was 0.15% over the momentum 
acceptance of ±5%. Cuts of ±15 and ±40 mrad were 
placed on the in-plane and out-of-plane angles in both 
spectrometers. The coincidence performance of the dou-
ble arm system was checked at each momentum transfer 
setting by measuring 1H(e,e'p) scattering from a liquid 
hydrogen target. The double arm coincidence timing res-
olution (FWHM) was !:::! 600 ps. The FWHM resolution 
in missing energy (momentum) ranged from 8 MeV (28 
MeV/c) at Q2 = 1 (GeVjc)2 to 20 MeV (44 MeVjc) at 
Q2 = 6.8 (GeV/c)2. 
The experiment used perpendicular kinematics, where, 
at each Q2, the recoil proton momentum is fixed and a 
distribution in proton scattering angle ()P is measured 
(see Table I). The kinematics were chosen to cover the 
region -25 <Em< 140 MeV and 0 < Pm < 250 MeV/c 
[11] at each momentum transfer. 
The PWIA prediction needed for the calculation of the 
transparency was obtained using Eq. (1). The single 
particle spectral function, normalized to Z, was gener-
ated with energies and widths of 16.2 and 5 MeV for the 
1p shell, and 38.1 and 20 MeV for the 1s shell [7]. The 
missing momentum distributions were generated using a 
TABLE I. Kinematics for the 12C(e,e'p) measurements. 
1.04 
3.06 
5.00 
6.77 
.02 
3.19 
4.21 
5.12 
E' 
(GeV) 
1.39 
1.47 
1.47 
1.47 
p' 
(GeV/c) 
1.20 
2.45 
3.54 
4.49 
9. 
~deg) 5.5 
47.7 
53.4 
56.6 
Bp 
~deg) 3.4,46.2,49.0,51.8,54.6 
27. 7,30.5,33.3 
20.9,22.6 
15.9,17.3 
1987 
VOLUME 72, NUMBER 13 PHYSICAL REVIEW LETTERS 28 MARCH 1994 
120 
Q2 ~ 1.0 (GeV /c)2 
100 
'"' 
80 
~ 
~ 60 
E { 
"' 
40 
<..., 
20 
0 
-25 0 25 50 75 100 125 150 
E. (MeV) 
80 
Q' ~ 68 (GeV/c) 2 
60 
' ~ 
~ 40 
E 
"-
~ 
"' <..., 20 
0 25 50 75 100 125 150 
E. (MeV) 
FIG. 1. The missing energy distributions at Q2 = 1 and 
6.8 (GeV/c)2 • The solid line is the PWIA model normalized 
to the data. The error bars on the data are statistical only. 
Radiative effects are taken into account by the model. A 5 
MeV energy shift has been applied to the model at Q2 = 
1 ( Ge V /c) 2 to account for uncertainties in the spectrometer 
optics. 
Woods-Saxon potential, while the missing energy distri-
butions were described by a Lorentzian with a cutoff at 
the proton separation energy. For both distributions pa-
rameters were obtained from low energy (e, e'p) data [7]. 
Model sensitivity was tested by varying the parameters, 
and also by using asymmetric forms for the missing en-
ergy distributions via a parametrization of Brown and 
Rho [12]. The resulting uncertainty on the transparency 
is 2%. In addition, the model spectral function was cor-
rected for correlation strength not contained in the single 
particle description by dividing it by the Q2 independent 
factor 1.11 ± 0.03, which has been estimated from calcu-
lations of 160 [13] and 12C [14]. Calculations [13,15] indi-
cate that correlation strength is only significant well past 
the Fermi momentum, and so should not modify the form 
of the single particle spectral function within our accep-
tance. The off-shell prescription used was u eel of de For-
est [16], but O'ee2 and an on-shell prescription were also 
used to check model dependences (a variation of 2% in 
the transparency was found). We used the dipole form for 
the proton electric form factor, and the parametrization 
of Gari and Kriimpelmann (17] for the proton magnetic 
form factor. The PWIA Monte Carlo model included the 
experimental resolution, the spectrometer acceptances, 
and radiative effects. Radiative effects were calculated 
1988 
~r 
;o' J 
:) 2 = 5.0 (GeV/c) 2 f 
; 
+-,~~~~,-,-,-,,._,,_,T"~, ---,~-' T' 
o so 100 1 :10 :=-:oo 
P m (MeV/c:: 
FIG. 2. The missing momentum distributions at Q2 = 5 
(GeV/c?. The solid line is the PWIA model normalized to 
the data. The error bars on the data are statistical only. 
Radiative effects are taken into account by the model. 
in a coincidence framework [18] from the prescription of 
Mo and Tsai [19], and included the contribution from the 
recoil proton. 
The measured spectral function [determined from Eq. 
(1) [7]] integrated over the missing momentum vector 
is compared with the PWIA model at Q2 = 1 and 6.8 
( Ge V J c) 2 in Fig. 1. The spectral function is integrated 
over missing energy and compared with the model at Q2 
= 5 (GeV /c)2 in Fig. 2. In both figures, the PWIA model 
is multiplied by the measured nuclear transparency at 
each Q2 • The good agreement between the shapes of 
the data and model validates our assumptions about the 
12C(e,e'p) reaction mechanism at high Q2 • There is no 
evidence for sizable contributions from other processes. 
The transparency is defined as the ratio of the number 
of events measured in the region !R: [-25 < Em < 100 
MeV; 0 < Pm < 250 MeV Jc] to the PWIA model predic-
tion (determined for each Bp and then averaged) for the 
same region: 
(2) 
By restricting Em< 100 MeV< m ... we ensure that no 
inelastic processes have occurred. 
The results are compared in Fig. 3 with a series 
of calculations. The extracted transparency for elas-
tic scattering from hydrogen is also shown and is found 
to be consistent with unity, as expected. The error 
bars include systematic errors of 6% for hydrogen and 
7% for carbon, as well as a model dependence of 4% 
for carbon. The measured transparencies of Fig. 3 
are found to be independent within errors of the Em 
upper limit of !R for values of this limit between 50 
and 130 MeV for hydrogen and between 80 and 130 
MeV for carbon. The carbon results are compared with 
two calculations which include color transparency: the 
naive parton model (dotted) of [20] and the correla.ted-
Glauberjquantum-diffusion model (dashed) of [21]. Cal-
VOLUME 72, NUMBER 13 PHYSICAL REVIEW LETTERS 28 MARCH 1994 
1.0 -----~--- --------+-- _______ j_ _________ J _____ _ 
0.8 
2:, 0.6 
0.4 
0.2 
. . . . . . . . . . -. . . . . . . . . . . . . . . . . - . . . . . 
. t ~_:_:_:_: _ _,_~·~---r----1---
2 3 4 5 
0 2 :ceV/c) 2 
6 7 8 
FIG. 3. The measured transparency as a function of Q2 
(hydrogen: open circles; carbon: solid circles), compared with 
several calculations described in the text. The inner error bars 
are statistical while the outer are the statistical and system-
atic errors added in quadrature. 
culations [22-24] in the hadronic basis evolution model 
yield similar results to those of [21]. Conventional cal-
culations which do not include color transparency effects 
[21,23] typically predict Q2 independent transparencies 
and vary in magnitude between 0.55 and 0.65; one such 
calculation [21] is shown (solid line) in Fig. 3. Clearly, 
the color transparency predictions with the largest Q2 
dependence are ruled out, although a gradual rise in Q2 
is allowed within experimental error. 
In summary, the 12C(e, e'p) cross section has been mea-
sured over the range -25 < Em < 140 MeV and 0 
< Pm < 250 MeV/ c in the momentum transfer range 
Q2 = 1 to 6.8 (GeV fc)2 • This extends the Q2 range of 
these measurements by over an order of magnitude. The 
distribution of strength is consistent with the impulse 
approximation for scattering from a single nucleon. The 
measured transparency ratios are essentially independent 
of Q2, indicating the absence of large color transparency 
effects in this energy range. 
This work was supported in part by the Department 
of Energy under Contracts No. W-31-109-ENG-38 (Ar-
gonne), DE-FG02-86ER40269 (Colorado), W-2705-Eng-
48 (LLNL), DE-AC02-76ER03069 (MIT), DE-AC03-
76SF00515 (SLAC), DE-FG03-88ER40439 (Stanford), 
and by the National Science Foundation under Grants 
No. PHY-9014406 and PHY-9114958 (American), PHY-
9115574 (Caltech), PHY-9101404 (CSLA), PHY-9208119 
(RPI), and PHY-9019983 {Wisconsin). R.G.M. acknowl-
edges the support of a Presidential Young Investigator 
Award from NSF. B.W.F. acknowledges the support of a 
Sloan Foundation Fellowship. 
• Present address: CEBAF, Newport News, VA 23606. 
t Present address: SLAC, Stanford, CA 94305. 
* Present address: Caltech, Pasadena, CA 91125. 
§ Present address: University of Michigan, Ann Arbor, MI 
48109. 
II Present address: University of Maryland, College Park, 
MD 20742. 
• Present address: TRIUMF, Vancouver, BC, Canada 
V6T 2A3. 
** Present address: Old Dominion University, Norfolk, VA 
23529. 
tt Present address: Argonne National Laboratory, Ar-
gonne, IL 60439. 
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1989 


Momentum Transfer Dependence of Nuclear Transparency from the Quasielastic ^(12)C(e, e'p) Reaction

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Momentum Transfer Dependence of Nuclear Transparency from the Quasielastic ^(12)C(e, e'p) Reaction

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