\documentstyle[12pt,psfig,epsfig]{article}
%\input{cebaf.tex}
\textwidth 6.5in
\textheight 8.75in
\topmargin -0.42truein
\oddsidemargin -0.02cm
\evensidemargin -0.02cm
\raggedbottom
\parindent=20pt
\baselineskip=14pt
\pagestyle{empty}
\begin{document}
\noindent{\LARGE\bf C \ \ Project Description}
\bigskip
\medskip
\medskip
\medskip
\noindent{\Large\bf C.0 \ \ Project Summary}
\medskip
The proposed research project focuses on the physics of high-energy
and high momentum transffer(hard) electro-nuclear processes
which can resolve the structure of the nuclei at short space-time
distances. The main {\em objectives} of the research are\\
- the development of theoretical methods of calculation of
hard electro-nuclear reactions\\
- use of hard $eA$ processes for the study of microscopic structure of
short-range correlations in nuclei\\
- use of hard processes to study the role of the coherent color interactions
of hadrons in nonperturbative domain of Quantum Chromodynamics (QCD) \\
- the study of the quark-gluon degrees of freedom in high-momentum
transfer electro/photo-nuclear reactions\\
\vspace{0.12cm}
\noindent
The core of the research will be the study of
high energy electron nucleus scattering phenomena where
high energy and high momentum are transfered to the nucleus.
This includes inclusive $x\ge 1$ reactions, the semiinclusive
reactions with single- and multi-hadron emission; and high
energy exclusive photo/electro-disintegration of lightest nuclei.
The {\em methodology} of the research is based on the application of
high-energy approach in building of comprehensive theoretical
framework for calculation of high-energy high-momentum transfer
electronuclear processes. The ultimate goal of the research is,
based on the theoretical framework of hard interactions, to
advance the understanding of short-range nuclear dynamics
within microscopic theory of strong interactions - QCD.
The {\em actuality} of the research steams from the several factors which
makes the situation rather unprecedented for the nuclear physics community.
For the first time huge sets of previously nonexistent experimental data are
becoming available for various high-energy electro-nuclear reactions from
Thomas Jefferson National Accelerator Facility (Jefferson Lab)
and DESY (Germany). Next few years could lead to major breakthroughs in
understanding of the role of quarks and gluons in the short-distance
nuclear structure as well as in the dynamics of high energy electro-nuclear
interaction. The proposed project will significantly contribute to these
advancements. In addition, the analysis of ongoing and newly planned
experiments would benefit directly from our research. This includes several
experimental proposals already approved by Physics Advisory Committee at
Jefferson Lab\footnote {P.I. is one of the principal theory collaborators in
the seven of these projects}.
Presently the nuclear physics community actively discussing the upgrade
of the Jefferson Lab for higher energies and possibilities for construction
of e-A collider in USA. The proposed project will also substantially
contribute toward the preparation of the physics program of these facilities.
If successful, the proposed project will establish a new theoretical
research program at Florida International University. This will
be very beneficial for the newly established and highly motivated
%High Energy
Nuclear Physics experimental group at FIU, whose research is
mainly focused on the physics of the Jefferson Lab. The ``logistic'' goal
of the project is to create a small interactive theory group focused on the
physics of ``High-Energy Electro-Nuclear Processes''
\footnote{The proposed project asks for funding for one graduate student}.
The group will try to use all advantages of the ``bridged'' (between JLab
and FIU) position which the principal investigator currently holds. It will
continue the previously established collaboration with the physicists from
several scientific centers in United States and Europe and will strive to
establish itself as a very active unit in the international high energy
nuclear physics community.
%It is also our hope that the
%successful operation of the group will attract
%more students into theoretical Nuclear Physics.
%hayr-mer
\medskip
\medskip
\medskip
\noindent {\Large\bf C.1 \ \ Introduction}
\medskip
The electro-nuclear processes in which a large momentum and
energy are transferred to the nuclei have significant importance
in understanding the microscopic structure of the nuclei.
It is worth to note that the spectacular development of the field theory
of strong interactions - QCD to large extent was stimulated by the studies
of electromagnetic interactions of strongly interacting objects - hadrons
(\cite{Feynman}). This is natural, since in electromagnetic interactions
with hadrons, the probe that represents electron, or photon is rather well
understood in terms of Quantum Electrodynamics - (QED)\cite{Feynman}.
This success particularly attributed to the investigation of high momentum
transfer (hard) electromagnetic reactions, which allowed to determine the
short-range constituent structure of the hadrons in terms of the quarks
and gluons.
Currently, the analogous field of high-momentum transfer electro-nuclear
reactions is emerging. The main hope, based on the experience of QCD studies
of hadrons, is that these processes would allow to look beyond the potential
model description of internucleon forces and attempt to reveal the dynamics
that are hidden in the parameters that are deduced from the experimental data
on NN interactions.
Overall one can expect that the use of high-momentum
transfer probes would allow to resolve the microscopic structure of
short-range nuclear interaction, to investigate the onset of
quark-gluon degrees of freedom in nuclei, to reveal the role of
the color and coherence in nonperturbative domain of QCD and its
relation to the nuclear physics.
The {\em main aim} of the project will be the development of the theoretical
framework for high-energy electro-nuclear processes,
the development of quantitative description of properties of nuclear
interaction at short distances and studies aiming at the understanding
the role of the quark-gluon degrees of freedom in high energy interaction
involving nuclear targets.
Such a research assumes development of the theoretical ``apparatus'' of
high energy electro-nuclear scattering based on the principles of
high-energy physics such as the light-cone dynamics of the interaction,
the specifics of the space-time evolution at high energies and careful
account for the microscopic properties of nuclei based on a realistic
description of the nuclear wave functions.
The part of the proposed project (section C.2) is a natural extension of
the ongoing investigation which started several years ago.
It concentrates on the developent of theoretical framework to
describe high energy and momentum transfer electro-nuclear reactions.
The apparatus of high energy transfer electronuclear reactions
allows selfconsistently study the short-range correlations in nuclei
The second part of the project (section C.3) will extend our
ongoing research in the physics of color coherence interaction
of hadrons in nuclear medium - phenomenon is known as color transparency.
The recent observation of color transparency in the perturbative
region of QCD\cite{Ashery} made this issue very challenging for
the nonperturbative region of QCD in which the present porject
is concerntrated.
The third part of the project (section C.4) addresses specifically
the problem of the investigation of quark-gluon degrees of
freedom in nuclei. It consists of two main directions of research.
One is based on the recent progress in understanding the role of
the QCD hard rescatterings in high energy disintegration of the
deuteron\cite{34}. The project will continue the investigation of the
mechanisms of quark-gluon rescattering in electro-nuclear
reactions involving two and more hadronic final states with very large
($\gg m_N$) center of mass energies.
And the other direction includes the studies of the nuclear
mechanisms of generation of superfast quarks (with $x>1$) in
deep inelastic scattering (DIS) from nuclei.
In many cases the research will be carried out in constant
contact with interested experimental groups involved in experimental
high-energy nuclear physics studies at Jefferson Lab and HERMES experiment
at DESY. Since the research will proceed in the time when many of these
experiments will produce first data the project assumes an
intensive computing practically for each of the components
of our research. We hope to increase our abilities of
numerical calculations by continuously increasing the number of
the students involved in the project.
The proposed project will contribute also into the future scientific program
of high energy nuclear physics.
We were an active participants in the working groups involved
in the development of future physics program at
Jefferson Lab\cite{cbhen,26,nstarc,vmc,ct12,gdpn12},
DESY\cite{27,27b,27c} and EPIC/ERHIC\cite{27e}, as well as in organizing
workshops on the topics of high energy electronuclear processes.
In 1998, the principal investigator was a co-organizer of the workshop at
European Centre of Theoretical Studies in Nuclear Physics and
Related Areas (ECT*), Trento, Italy on the subject of ``Coherent QCD
Processes with Nucleons and Nuclei''. In March, 2000 we have organized the
workshop at FIU on the physics of Hadrons in the Nuclear Medium,
which was concentrated on the physics issues important for 12 GeV upgrade
of JLab. In March, 2001 at the Institute of Nuclear Theory
(University of Washington), together with W.~Bertozzi (MIT),
G.~Miller (UW) and M.~Strikman (PSU) we are organizing
three-months INT workshop on Correlations in Nuclei and Nucleons,
which is largely related to the physics of the current project.
The successful execution of the project will allow to intensify the
above activities, establishing at FIU new research program and
hopefully an active working group.
\bigskip
\medskip
\medskip
\medskip
\medskip
\medskip
\noindent{\Large\bf C.2 \ High Energy Quasielastic Reactions off Nuclei
and the Studies of Short-Range Nucleon Correlations}
\medskip
\medskip
One of the major tasks is to develop a theoretical framework for
description of high energy electron-nucleus interactions which
would incorporate both the main features of high energy strong
interaction dynamics and the microscopic (short-range)
structure of nuclei.
This cannot be done by simply extending the traditional methods
of intermediate energy nuclear physics based on the potential
models of nucleon-nucleon interactions. One faces here the problems
of large inelasticities in the nucleon-nucleon scattering, extremely
relativistic dynamics and the linear increase with energy of the
relevant angular momenta of scattering states.
Therefore one needs a new theoretical framework for description
of electro-nuclear processes with nuclei when
the (minus) square of four-momentum transfer:
%hayr-mer
$Q^2\ge 1~GeV^2$ and the methods of nonrelativistic physics become
increasingly inapplicable.
Such theoretical framework was developed first for the
case of electrodisintegration of the deuteron in
$d(e,e'p)n$ reaction~\cite{1} and then for more general case of
hard semi-exclusive A(e,e'N)(A-1) reactions \cite{2} for
fixed missing energy and missing momentum.
In collaboration with L.~Frankfurt(Tel Aviv University(TAU)), G.A.~Miller(UW)
and M.~Strikman(PSU) we were able to build a formalism
of Generalized Eikonal approximation (GEA) based on the effective
Feynman diagram rules which unambiguously account for the relativistic
dynamics of high energy processes. The final formulae that account for the
finite values of missing momenta and missing energy are markedly
different from the formulae of the conventional eikonal approximation
(e.g. the Glauber approximation) and coincide with the later only
in the limiting case of negligible missing energy and momenta.
The obtained formalism allows to calculate cross sections for a broad
range of hard nuclear reactions:
\medskip
\medskip
\noindent{\bf C.2.1 \ \ Exclusive Reactions off the Deuteron}
\medskip
We first applied GEA to calculate the electrodisintegration of the
deuteron~\cite{1}. The investigations of exclusive electro-nuclear
reactions off the deuteron have a fundamental significance in
understanding the short range structure of strong interaction.
The resent Jefferson Lab experiments on elastic $d(e,e')d$ scattering
demonstrated that study of the elastic channel is not sufficient
to discriminate~\cite{3} between the multitude of different approaches
in describing the dynamics of electron scattering off deeply bound
two-nucleon system.
The theoretical reason for such situation is that many distinctive
features are smearing-out due to the integration in the elastic amplitude.
This underscores the necessity of carrying out exclusive
$d(e,e'p)n$ reactions and indeed the Jefferson Lab's
experimental program already contains several dedicated
projects which will be underway within the next two years.
However because of strong soft hadronic interaction, the final
state interaction~(FSI) will contribute significantly to the exclusive
cross section.
Thus the understanding of the dynamics of deeply bound nucleon will
be tied strongly with the understanding of the hadronic final
state interaction at the case of the reactions with large
missing energy (or missing momenta).
We addressed this problem in our early project\cite{1,2}, where we
studied the electrodisintegration of the deuteron~\cite{1} in the kinematics
where the reaction is dominated by final state rescatterings.
In these calculations we were restricted by recoil momenta of spectator
nucleon $\le 400MeV/c$ in order to be separated from the problem of
the $Z$-diagrams and the nonnucleonic degrees of freedom.
The obtained result considerably differs from the result of the conventional
Glauber approximation at large spectator recoil momenta
$200~MeV/c \le p_s \le 400~Mev/c$ (Figure 1).
\begin{figure}[ht]
\centerline{\psfig{file=figure1.ps,width=14cm,height=10cm}}
\caption{
Dependence of $\kappa$, the ratio of the $d(e,e'p)n$ cross section
calculated including the Impulse Approximation(IA) and FSI to the
cross section which includes IA term only, on the angle
$\Theta_{\vec p_s \vec q}\equiv \hat{\vec p_s \vec q}$ for different
spectator(neutron) momenta $p_s$ (or missing energy of reaction-$E_m$).
$\vec q$ is transferred momentum vector. Solid line corresponds to FSI,
calculated according GEA dashed line corresponds to FSI calculated
according to conventional Glauber approximation.
}
\end{figure}
The important result of our calculations is that at the smallest values of
$Q^2\approx 1~GeV^2$ when Generalized Eikonal approximation still valid
it agrees with the result of the calculation based on the
approach of intermediate energy nuclear physics\cite{Arenhovel}, in which
the final hadronic state is described through the sum of the partial wave
functions with the given angular momentum and the hadronic interactions are
calculated through the realistic nucleon-nucleon potential.
Note that $Q^2\approx 1~GeV^2$ rather represents the upper limit for
these calculations. Thus such an agreement indicates that there
is continuity between two different theoretical approaches and
that there is a smooth transition from intermediate to high energy regime
of the interaction.
Our predictions for $d(ee'n)p$ reactions were the part of the theoretical
objectives of the proposal~\cite{4} approved by Physics Advisory Committee
(PAC) at Jefferson Lab and we expect soon to have a wealth of the experimental
data which will allow to check our calculations.
Most recently in collaboration with M.~Johnson(LANL) and W.~Weise(Muenchen)
we extended the Generalized Eikonal approximation to the processes
which involve exclusive production of resonances $R$ in $d(e,e'R)n$
reactions\cite{nstar}.
\medskip
As it was mentioned above in Ref.\cite{1} we were restricted by the
relatively small missing momenta ($\le 400 MeV/c)$ in order to be separated
from the uncertainties related to the problem of high Fermi momenta.
Thus the problem of deeply bound states was not addressed.
In the proposed project in collaboration with G.~Miller (UW),
L.~Frankfurt (TAU) and M.~Strikman (PSU) we are planning to investigate
the dynamics of hadronic reinteraction at the case of deeply bound two-nucleon
system. In particular we are planning to apply the approach of
light-cone dynamics, which allows to address the problem of the
negative states consistently. Note that calculation of
the exclusive $d(e,e'p)n$ reaction within light-cone approach has been
carried out only within the plane wave impulse approximation\cite{5}.
Our project for the first time will aim to calculate the rescattering
amplitudes within the approach of light cone dynamics. In this case
one will be able to extend our calculations to the larger range of
Fermi momenta $400-700~MeV/c$, up to the limit when the nonnucleonic
components of the deuteron will become important.
The preparation of a new dedicated experiments on exclusive
electrodisintegration of the deuteron is presently underway\cite{6,7}
in Jefferson Lab, in which FIU group has an active participation.
Thus we expect these studies to become the distinctive part of the
research of the newly established high-energy nuclear physics group at FIU.
\medskip
\medskip
\noindent{\bf C.2.2 \ \ Multi-nucleon electro-production off lightest nuclei
at $Q^2=1-4~GeV^2$}
\medskip
The high energy approach developed in Ref.\cite{1,2} was demonstrated to
work down to $Q^2\sim 1~GeV^2$.
Thus we will be able to use this technique to build a detailed model
for the break up of $^3He$ and $^4He$ targets (e.g. processes like
$e +^3He \rightarrow e+p+p+n,\ e + p + ^2H$) in the range of $Q^2= 1-4~GeV^2$
where hadronic picture is the relevant degree of freedom in soft
reinteractions (no color transparency effects are expected).
These reactions can be used to investigate the short-range
nucleon correlation effects in multi-nucleon production.
The preliminary calculation of $^4He(e,e'p)^3H$ reaction within GEA
demonstrated that there exist a high-energy kinematics where
the dip in the two-body break up momentum distribution, which is the result
of short-range NN correlation in $^4He$ is not masked by rescatterings.
The experiment E-97-111 based on this observation will allow to check
the validity of GEA predictions and study directly the short-range
correlations\cite{8}.
Hence it is absolutely crucial to perform detailed calculations of this
process as well as scattering off $^3He$.
In the latter case we plan together with H.~Lee(ANL) and V.~Guzey(Adelaide)
to calculate the reaction involving two- and three- body
break-up channels and investigate the sensitivity of these reactions
to the structure of short range NN correlations.
We also plan to investigate the potential of using polarized $^3He$ target
for probing the spin structure of short-range nucleon correlations.
Overall this would allow to build a detailed theoretical framework for
extraction of the properties of short-range nucleon-nucleon
correlations for the lightest nuclei from the high $Q^2$ break-up reactions.
We will also investigate manifestations of short-range correlations
in the processes where fast backward nucleons are produced i.e. the case
when one of the produced nucleons flies backward, to the direction of
transferred momentum, with a momentum $\ge 300 MeV/c$. Parallel study of
these and break-up processes may help to get a decisive answer to the long
standing puzzle - what is the origin of the large cross section of the
fast backward nucleon production in high-energy hadronic processes.
Second part of this project is related to the extension of our calculations
to the reactions with multi-nucleon production from heavier nuclei like
$^{12}C$, $^{56}Fe$.
The multihadron collaboration of CLAS detector in Hall B at Jefferson Lab
just completed the dedicated run which specifically studied the multi-nucleon
production from $^4He$, $^3He$ ${12}C$ and $^{56}Fe$ targets collecting
{\it billions of events}.
One of the basic ideas to be checked in these measurements is whether
short-range correlations will reveal universal structure in multihadron
production from different nuclei if the effects of hadronic reinteractions are
properly accounted for.
\medskip
\medskip
\noindent{\bf C.2.3 \ \ Short-range nucleon correlations in
$x>1$ $(e,e')$ and $(e,e'p)$ reactions}
\medskip
In Ref.\cite{22} we studied the large $Q^2$ inclusive $(e,e')$
reaction at $x>1$, where $x$ is the Bjorken scaling variable
defined as $x = {Q^2\over 2 m_N q_0}$, $m_N$-is the nucleon mass and
$q_0$ is the transferred energy. It has been predicted
in Ref.\cite{22} that existence of
short range nucleon correlations in nuclei will produce unique
scaling (called $\alpha$-scaling) behavior for the ratio of cross
sections of scattering off nuclei and deuteron at $x > 1$. The
predictions agree well with experimental data for the ratios which were
extracted from the SLAC measurements taken at slightly different $Q^2$.
New direct measurements \cite{23,xm1} recently finished at Jefferson Lab
will provide much more stringent test of these predictions.
Additional degree of understanding of the structure of short-range
correlations will be gained by considering $x>1$ kinematics for semiinclusive
$(e,e'p)$ reactions off nuclei. However in this case one shall account for
the final state interaction of knocked-out nucleon which may substantially
mask the genuine feature of short-range correlations. Moreover if one naively
applies the Glauber theory for $x>1$ kinematics one may conclude
that the correlations can not be detected at these kinematics because of
FSI. However as we discussed above the Glauber theory is derived
for kinematics, in which momenta of target nucleons can be neglected.
Since Generalized Eikonal Approximation\cite{2} was derived for
given finite values of missing momentum and energy it is legitimate
to apply it for $x>1$ kinematics as well.
This application\cite{2} revealed a new kinematic restriction on the
region where the contribution of short-range correlations is enhanced
in semiinclusive $(e,e'N)$ reactions. Namely the additional requirement on
the kinematics of semiinclusive $(e,e'N)$ reactions is
\begin{equation}
|p_{mz}|-{q_0\over |\vec q|}E_m \ge k_F\approx 250~MeV/c,
\label{kinem}
\end{equation}
where $q_0, \vec q$ are the transferred energy and momentum of the reaction
(energy and momentum of virtual photon), $p_{mz}$ is the projection of the
missing momentum of the reaction to the direction of $\vec q$ and
$E_m$ is the missing energy of the reaction. $k_F$ characterizes the
momentum of the Fermi surface of particular nucleus. This result was used
to choose the kinematics for three new Jefferson Lab experiments
E97-011\cite{24}, E97-106 \cite{8} and E97-123 \cite{25} which aim to
study the short-range correlations in semi-exclusive $(e,e'p)$ reactions.
Proposed research will include the calculation of the final state interaction
in $(e,e')$ reactions at $x\ge 1$ by taking into account the relativistic
effects which follows from the QCD dynamics. The result will be used for the
analysis of existing and forthcoming data from the
upgrade of the experiment of E-89-008\cite{23}, which will allow to
extract nucleon light-cone density matrix of nuclei\cite{26,C28}.
The further development of this subject would be the
calculation of semiexclusive $(e,e'p)$ reaction at $x>1$
with account for the final state interaction using the method
developed in \cite{2}.
The aim is to implement in the calculation of final state interactions
the relativistic kinematics of high-energy processes which leads
to the dominance of the light-cone dynamics in the scattering processes.
The calculation will be applicable both for unpolarized and polarized
targets. Experiments of this kind are underway at Jefferson Lab.
Recent calculations we performed within the framework of the
``Future physics at HERA'' demonstrated the feasibility of investigation
of these reactions at DESY using the HERMES detector\cite{27}.
\bigskip
\medskip
\medskip
\noindent{\Large\bf C.3 \ Color Coherence Phenomena and Nuclear Transparency}
\medskip
\medskip
\noindent{\bf C.3.1 \ \ Nucleon Propagation in the Nuclear Medium and Nuclear
Transparency}
\medskip
The investigation of the propagation in a nuclear medium of a nucleon
knocked-out by a highly virtual photon ($Q^2\ge 1~GeV^2$) is of
great importance for the understanding of the dynamics of high energy
hard elastic lepton-nucleon scattering.
The main goal of these studies is the understanding of the
transparency of nuclear matter for the hadronic products of
hard scattering in which final state hadronic wave functions are
dominated by small size quark-gluon configurations. The idea originally
suggested by Brodsky\cite{9} and Mueller\cite{10} is that at asymptotically
large $Q^2$ the hadronic state is produced in a point-like configuration
and therefore will not experience final state interaction or otherwise the
nuclear matter will be transparent for such an ejectile.
However the practical question is at which values of finite
$Q^2$ one should observe the onset of the increased transparency.
The main problem is that at finite energies even if produced
hadronic state is in the point-like configuration it will
expand being not an eigenstate (it is rather a wave packet) of QCD
Hamiltonian\cite{11,12}.
Thus at presently accessible energies the expected effect is rather
small, which was confirmed by the first experiment at SLAC
which measured the nuclear transparency in $(e,e'p)$
reaction\cite{13} at $Q^2= 1-7~GeV^2$.
Moreover this experiment shows that the expected color transparency effect
is on the level of theoretical uncertainties related to the composite
structure of the nucleus (nucleon correlations, shell structure, etc).
Thus one of the pressing problems is the understanding of the effects of
nuclear dynamics on the measure of the nuclear transparencies in
$A(e,e'N)(A-1)$ reactions.
In collaboration with L.~Frankfurt(TAU), E.~Moniz(MIT) and M.~Strikman(PSU) we
developed the framework\cite{14}, in which the short-range correlation
properties of the ground state wave function of nucleon
incorporated with the Glauber theory of reinteractions at small values
of missing momenta and missing energy of $A(e,e'N)(A-1)$ reactions.
We also demonstrated that the study of nuclear transparency in $(e,e'p)$
reactions for shell-level excitations which is feasible at Jefferson Lab
considerably reduces the nuclear effects, thereby making it more sensitive
to the onset of the Color Transparency\cite{14,cbhen}.
In collaboration with M.~Zhalov (St. Petersburg), M.~Strikman(PSU) and
L.~Frankfurt(TAU), we propose to extend our calculation of exclusive cross
sections of $A(e,e'p)A-1$ reactions to the larger missing momentum range
at shell-level excitations.
In these calculations we will consistently include different
nuclear effects such as central and tensor correlations,
calculate the effects of nondiagonal transitions
using up-to-date realistic wave functions of nuclei.
Our calculation will allow to understand how much short-range
correlations and how much FSI are responsible for the transparency
of nuclear medium and for high momentum tail of the shell wave functions.
Based on these calculations we will perform a detailed analysis
of available/forthcoming data on nuclear transparency and
nuclear shell structure from three high precision JLab
experiments Ref.\cite{15,Gees,16}.
\medskip
\medskip
\noindent{\bf C.3.2 \ \ Double Scattering Reactions off Lightest Nuclei}
\medskip
The main idea of the studies in Section C.3.1 is to investigate the
probability that knocked-out object will escape the nucleus without
additional final state interaction - nuclear transparency.
The increase of nuclear transparency with the increase of the transferred
momentum or $Q^2$ of the reaction will indicate the onset of color
coherence phenomena, when QCD degrees of freedom become relevant
and the effect of the color screening will diminish the
cross section of reinteraction.
In Refs.\cite{1,17,18} we suggested a new method to study physics of color
coherence, which is complementary to the study of $(e,e'p)$ processes.
The idea is to investigate the rescatterings of high momentum (few GeV/c)
knocked-out nucleon with slow nucleon-spectator leading to production
of recoil nucleon with momentum $\sim 300-400$ MeV/c.
Such processes can be reliably singled out in $(e,e'NN)$ reactions off
lightest nuclei.
Our detailed study of $d(e,e'pn)$ reaction off the polarized and
unpolarized deuteron target\cite{1,18} has demonstrated that for
a special recoil kinematics, even such a loosely bound nucleus as a
deuteron can provide significant rescattering of knocked-out nucleon
with spectator nucleon.
Recently our calculations have been confirmed by the new calculations
of the group of J-M.~Laget \cite{19}. It is important to note that
both our \cite{1,18} and Laget's \cite{19} calculations demonstrate
the feasibility of such an investigation at presently accessible
energies at Jefferson Lab and HERMES. The approved proposal at
Jefferson Lab\cite{20} could provide the first data on these processes.
We propose to extend the calculation of the multi-nucleon production
from $^3He$ and $^4He$ described in Section C.2.2 to the region of the
high $Q^2> 4~GeV^2$. We are specifically interested in the kinematics
where the production is dominated by the double scattering and the momentum
of the recoil nucleon is the result of this rescattering.
The calculation in the region of high $Q^2> 4~GeV^2$ is qualitatively
different from the calculations described in Section C.2.2.
In this case one can not describe the rescattering as
an elastic scattering of conventional hadrons \cite{11,12}.
The intermediate hadronic state in this case is hadronic
wave packet which will expand during the rescattering process.
Thus the major task of this project is to model the
hadronic packet through coherent superposition of different
hadronic states\cite{1,12,21} or expressing it in the quark-gluon
framework describing properly the diffusion properties of
this configuration\cite{11}.
This project is part of our commitment for theoretical
support of the approved experiment, E-019-94 at Jefferson Lab\cite{20},
which is dedicated to the studies of double scattering
processes on $^2H$, $^3He$ and $^4He$ targets.
\medskip
\medskip
\noindent{\bf C.3.3 \ \ Color Coherence in Electroproduction of Vector Mesons}
\medskip
The intriguing result of E665~\cite{28} provides a strong hint for
existence of color transparency in the electroproduction of vector mesons
already at relatively low $Q^2\sim 5~GeV^2$. However the very same experiment
highlights the necessity of understanding the finite
longitudinal interaction length effects, which are present
in any high-energy process as soon as this length is comparable or
exceeds the average internucleon distance.
These effects in most cases may mimic the signature of color coherence.
Moreover in the most interesting case of the diffractive electroproduction of
vector mesons at large $t$, one can not directly apply
the procedure of well understood diffraction at $t\approx 0$~\cite{29}
to estimate the effects of the interaction length.
The naive application will yield the conclusion that at finite $t$
interaction length ceases to grow with the increase of energy. Thus the
detailed investigation of the diffractive scattering at finite t was
necessary. Such a project was initiated in collaboration with
L.~Frankfurt(TAU), G.~Piller(Munich), J.~Mutzbauer(Munich) and
M.~Strikman(PSU). We derived the formulae for coherent diffractive
photo/electroproduction of vector mesons from the deuterium at
finite $-t\le 1~GeV^2$~\cite{30,31}. We obtained the formulae for
longitudinal interaction length at finite $t$ which continually grows
with the increase of scattering energy. Our formulae also predicts
the specific $t$ dependence for the interaction length which can be
verified in the proposed experiment~\cite{32}, which will be presented
to the Jefferson Lab's Physics Advisory Committee at the summer session
of 2000.
This project is based on our ongoing collaboration with Munich group
W.~Weise and G.~Piller. We are in the process of calculating the coherent
and noncoherent production of $\rho$ mesons from $^3He$ target.
The main goal in these calculations is to provide the theoretical
description of the ongoing experiment in HERMES, DESY.
%Followup project with G.~Piller will be the calculation of the
%electroproduction of $\rho$ mesons from $^{12}C$. The idea here is
%that the careful account of finite interaction length effect
%and inelastic recoil channels
%will allow us to obtain the answer on unresolved question
%about whether the transparency
%observed in the experiment of E665\cite{28} unambiguously
%is related to the Color Transparency phenomena.
\bigskip
\medskip
\medskip
\noindent{\Large\bf C.4 \ Quark-Gluon Degrees of Freedom in Nuclei}
\medskip
\medskip
\noindent{\bf C.4.1 \ \ Studying Quark-Gluon Degrees of Freedom in the
Electro-Nuclear Reactions with Hard Rescattering}
\medskip
The high-energy photodisintegration of the deuteron is a unique
process to investigate manifestations of quark-gluon degrees of
freedom in quasielastic processes. It is interesting to note that
calculations using the conventional mesonic picture of nuclear
interactions qualitatively disagree with the data\cite{33}.
On the other hand all QCD based theoretical approaches were unable
to make quantitative descriptions.
Our calculation is based on the hypothesis\cite{34} that the
high-energy photodisintegration reaction is determined by the
physics of high-momentum transfer, contained in the nucleon-nucleon
hard scattering amplitude.
Our starting point is the observation that the process in which
the photon absorption by a quark in one nucleon followed by its
high momentum transfer interaction with a quark in the other nucleon
may produce two final-state nucleons with high relative momentum.
Summing all relevant quark rescattering diagrams corresponding to the
above scenario we derived the scattering amplitude which depends
on convolution of the hard photon-quark interaction vertex, the
large angle pn scattering amplitude and the low momentum deuteron
wave function~\cite{34}. Within this approach for the first time
we calculated the absolute values of the photodisintegration cross
section which are in reasonable agreement with the data at
$\theta_{c.m.}=90^0$ center of mass scattering angle~(Figure 2).
Our approach predicts also the existence of universal
scaling function C(t/s) for the case of the different
scattering angles. The comparison with the data suggests
$C(t/s)\approx {-t/s\over 1 + t/s}$\cite{C12}. More detailed
measurements of angular dependence will allow a verification of
such a scaling pattern.
\begin{figure}[ht]
\begin{center}
%\psfig{angle=0,width=3.4in,height=2.4in,file=figure2.ps}
\centerline{\psfig{file=figure2.ps,width=14cm,height=10cm}}
\caption{The scaled differential cross sections as a function of the photon
energy, for different values of c.m. angle. Data are from
\cite{33} (triangles) and \cite{Slac}(squares). The theoretical
calculation (shaded area) has a finite width because it uses
the experimental data of high momentum transfer $pn$ elastic scattering.}
\end{center}
\end{figure}
Above hypothesis if confirmed by additional studies suggests an entirely
new QCD based approach for calculating high momentum transfer
quasielastic nuclear reaction. It suggests also that there should be a new
class of the nuclear reactions where one shall see unambiguously an
implication of quark-gluon degrees of freedom.
The observation that the hard structure of high momentum
transfer nuclear reactions may be defined by the hard structure of
final rescattering suggests that for these class of the reactions one
should expect several regularities. Moreover these reactions are unique
in a sense that we will be able to do quantitative calculations
within QCD.
The investigation of following processes will be the subject of
our research in collaboration with
G.A.~Miller(UW), L.L.~Frankfurt(TAU) and M.I.~Strikman(PSU):
- Photodisintegration of the deuteron with polarized photons and/or with
recoil polarization of final proton. These reactions
will allow to investigate the long-standing problem of the
asymmetries observed in hard $pp$ scattering. The result of our
new calculation\cite{FMSS} of the tranverse polarization
$P_y$ in deuteron photodisintegration reaction at photon
energies $E_{\gamma}> 2~GeV$ agrees reasonably
with the very recent data from Jefferson Lab. The new proposal\cite{GHM}
recently approved by Physics Advisory Committee at JLab will be
able to check our predictions at higher photon energies.
- Photodisintegration of both polarized and
unpolarized $^3He$ target in kinematics:
$\gamma + ^3He \rightarrow p(high p_t)+ p(high \ -p_t) + n(p_t\approx 0)$.
In these reactions we expect to observe regularities characteristic
to hard $pp$ scattering. One of the striking features will be
the observation of energy oscillations which are suggested by the
data on $pp$ scattering.
- Extension of the above analysis to the case of the virtual
photons. The comparison of the cross sections of interactions of
transverse and longitudinal photons will allow to separate the
contribution from contact terms of interaction appearing
in the description within light-cone dynamics.
- The calculation of the photo(electro)- production of two high
$p_t$ protons off heavier nuclei such as $^{12}C$ with main
emphasize on the absorption of two protons in the
nuclear medium. These measurements according to our approach could
be related to the data on hard $^{12}C(p,2p)$ scattering measured
at BNL~\cite{35}.
%In future we also plan to extend our calculations including the reactions
%which involve the production of high $p_t$ protons with different
%flavor composition e.g. $\gamma d \rightarrow \Lambda K N$ or
%$\gamma d \rightarrow \Lambda_c D N$.
\medskip
\medskip
\noindent{\bf C.4.2 \ \ Deep Inelastic Scattering from Nuclei
at $x>1$ (``Superfast Quarks'')}
\medskip
The discovery of Bjorken scaling in late 60's\cite{Panofsky} was one of
the key steps in the establishing the microscopic theory of strong
interaction---QCD.
These experiments unambiguously demonstrated that hadrons contain
point-like constituents--partons (subsequently identified
with ---quarks and gluons) (see e.g. \cite{Bjor_Pasch,Feynman}).
In the language of quark-partons, the explanation
of the observed approximate scaling was remarkably simple:
a virtual photon knocks out a point-like quark and as a result the
structure function of the target nucleon measured experimentally
depends only on the fraction $x$ of the nucleon momentum that quark
carries (up to $\log Q^2$ corrections calculable in QCD).
It is crucial that the QCD factorization theorem can be proven, namely,
that all final state interactions are canceled in this process so that the
light-cone wave function of the nucleon is unambiguously measured.
Naturally $x\le 1$ for a single nucleon since the quark can not
carry a larger momentum than the whole nucleon.
The fraction $x$ (Bjorken scaling variable) can be expressed
through the square of the virtual photon four momentum $-Q^2$ and
its energy $\nu$: $x= {Q^2 / 2 m_N \nu}$.
Experimentally such a scaling for hydrogen
target was observed for the range of $Q^2 \ge 4$~GeV$^2$ and $W > 2.5$ GeV.
Here $W^2 = -Q^2 + 2m_N\nu + m_N^2$ is the invariant mass squared of
the hadronic system produced in the $\gamma^*$ $N$ interaction.
Since the nucleus is a loosely bound system it is natural to define
Bjorken $x$ in this case as $x_A={AQ^2 / 2m_A\nu}$ so that for
the case of scattering in the kinematics allowed for scattering off a free
nucleon $x_A \approx x$. In the case of electron scattering from quarks
in nuclei it is possible that Bjorken $x > 1$ ($A\ge x_A \ge 0$).
This corresponds to the situation that knocked-out quark carries
larger light-cone momentum fraction than a nucleon which is at rest in
the nucleus rest frame. Such situation could occur for example if
quark would belong to a fast nucleon in the nucleus. In this
approximation
\begin{equation}
F_{2A}(x,Q^2)=\int_x^A
\rho^N_A(\alpha,p_t)F_{2N}(\frac{x}{\alpha},Q^2)\frac{d\alpha d^2p_t}{\alpha}.
\label{conv}
\end{equation}
%
Choosing $x\ge 1 + k_F/m_N \ge 1.2$ completely eliminates contribution
of the scattering off the quarks belonging to nucleons with momenta
smaller than the Fermi momentum-$k_F$. (Actually, the contribution of the
component of the wave function with $k\ge k_F$ dominates already for $x
\ge 1$ practically for any realistic nuclear wave function. ) In
this kinematics a quark has to get its momentum from several nucleons
with large relative momenta which are significantly closer to each other
than the average internucleon distance in nuclei\cite{FS81}.
Thus such superfast quarks in nuclei could
arise from some kind of superdense configurations either consisting of
few nearby nucleons with large momenta or more complicated multiquark
configurations. In particular, a comparison with eq.\ref{conv} would
provide a quantitative test of applicability of the approximation
that a fast nucleon in the nucleus has the same wave function as a free
nucleon.
The kinematic requirement for detecting the signature of superfast quarks at
$x>1$ is to provide large enough $Q^2$ that the tail of
deep-inelastic scattering will overwhelm the contribution from
quasielastic electron scattering from nuclei.
If such a requirement is provided, then the
the first signal of the existence of superfast quarks will be the
experimental observation of scaling in the region $x\ge 1$.
(In the case of the scaling structure functions $F_{2A}$
becomes independent of $Q^2$ (up to $\log Q^2$ terms).)
Previous experimental attempts to observe such superfast quarks were
inconclusive: the BCDMS collaboration \cite{BCDMS} has observed a
very small $x\ge 1$ tail, while the CCFR collaboration \cite{CCFR} has
observed a tail consistent with presence of very significant SRCs.
A possible reason of the inconsistencies is that the resolution in
$x$ at $x \ge 1$ of the high energy muon and neutrino experiments
is relatively poor.
Our recent studies of the deep inelastic scattering at $x>1$ in
the working group of ``Hadrons in the Nuclear Medium''\cite{HNM},
demonstrated that the Jefferson Lab upgraded for 12~GeV
will be an ideal place for such investigations.
The energy resolution, intensity and energy of JLAB12 may
allow it to become the first laboratory to observe the onset of
scaling in the $x>1$ region and thereby confirm the existence of
superfast quarks.
The very important feature of the scaling is that its onset depends strongly
on the underlying structure of nuclear matter at short distances. In the
Figure 3 we present our calculation\cite{FSS} within different models
describing the nuclear state at $A>3$ that contains the superfast quark.
For illustrative purposes we are restricted only by two models to
demonstrate the sensitivity of the reaction on underlying dynamics
of nuclear matter at short distances.
In the first model the high momentum component of the nuclear wave function
is calculated within a two-nucleon short range correlation model
(solid lines). (Within this approximation the shapes of the structure
functions for deuteron and $A>2$ targets at very large $Q^2$ will be the
same.) In the second model we used the multi-nucleon correlation model (dashed
lines) of Ref.~\cite{FS81}. Its prediction agrees reasonably with
recent measurements of the nuclear structure functions by the
CCFR collaboration~\cite{CCFR}.
\begin{figure}[ht]
\begin{center}
\epsfig{width=4.8in,height=3.6in,file=figure3.eps}
\caption{Prediction of the onset of the scaling for $^{56}Fe(e,e')X$
scattering. The data from Ref.\cite{Arrin}.}
\end{center}
\label{Fig.3}
\end{figure}
The figure emphasizes the significant potential of the considered reactions
in a detailed study of dense configurations in nuclei.
Encouraged by the positive response of Eighteenth Physics Advisory Committee of
Jefferson Lab to the experimental proposal of studying DIS at $x>1$\cite{BB},
we are planning to carry out intensive theoretical studies related to
the physics of superfast quarks. Main purpose of the research will
be the identification of the role of the quark-gluon degrees of freedom
in the correlations and their implication in the scaling properties
of DIS at large x. Special attention will be paid to
the region of $x>1.5$ and $Q^2\ge 10~GeV^2$ where the naive kinematic
estimations show that if they where the nucleons in the correlations they
should substantially overlap. Thus one of the challenging problem of
the study will be the description of these overlapped states based on
the present level of understanding the quark-gluon structure of
nucleons.
\begin{thebibliography}{00}
\bibitem{Feynman}R.~P.~Feynman, {\em Photon-Hadron Interactions},
W.A. Benjamin Inc., Reading, Massachusetts, 1972.
\bibitem{Ashery}D.~Ashery and R.~Weiss-Babai, ``Pion production of
minijets''
\bibitem{cbhen}L.L.~Frankfurt, M.~M.~Sargsian and M.~M.~Strikman,
{\em Color Coherent Effects in $(e,e'N)$ and $(e,e'N,N(h))$
processes}, in Proceedings of the Workshop {\em CEBAF at High
Energies}, Eds. N.~Isgur and P.~Stoler, April~14-16, 1994, CEBAF,
Newport News, VA, p.499-508.
\bibitem{26}{D.~B.~Day, L.L.~Frankfurt M.~M.~Sargsyan and M.~Strikman,
{\em Evidence for Short-Range Correlations from High
$Q^2 ~ (e,e')$ Reactions},
in Proceedings of the Workshop {\em CEBAF at High Energies},
Eds. N.~Isgur and P.~Stoler, April~14-16, 1994, CEBAF,
Newport News, VA, p.529-533.
\bibitem{nstarc}L.~Frankfurt, M.~Johnson, M.~Sargsian, M.~Strikman and
W.~Weise, {\em Study of the Hadronic Properties of N$^*$s
in Electroproduction Reactions off the Deuteron}, in Proceedings
of the Workshop on Physics and Instrumentation with 6-12~GeV
Beams, Eds. S.~Dytman, H.~Fenker, P.~Roos, June-1998, JLAB,
Newport News, p.307.
\bibitem{vmc}L.L.~Frankfurt, G.~Piller, M.~Sargsian, M.~Strikman,
{\em Coherent Vector Meson Production from Deuterons},
in Proceedings of the Workshop on Physics
and Instrumentation with 6-12~GeV Beams,
Eds. S.~Dytman, H.~Fenker, P.~Roos, June-1998, JLAB,
Newport News.
\bibitem{ct12}M.M.~Sargsian, {\em Where to Look for Color Transparency at
12 GeV}, Invited talk at the Workshop on Physics Opportunities
with 12-GeV Electrons, Jefferson Lab, Newport News, Virginia,
January 13-15, 2000.
\bibitem{gdpn12}M.M.~Sargsian, {\em Hard Rescattering in QCD in Exclusive
Reactions on Light Nuclei}, Invited talk at the Workshop
on Physics Opportunities with 12-GeV Electrons,
Jefferson Lab, Newport News, Virginia, January 13-15, 2000.
\bibitem{27}L.~Frankfurt, M.~Sargsian and M.~Strikman,
{\em Near Threshold Large $Q^2$ Electroproduction off
Polarized Deuteron}, in Proceedings of the Workshop on
{\em Future Physics at HERA},
Hamburg, Germany, Sept.1995 -- May 1996, nucl-th/9609003.
\bibitem{27b}W.~Melnitchouk, M.~Sargsian and M.~Strikman,
{\em Tagged Structure Functions of the Deuteron and the
Origin of EMC Effect}, in Proceedings of the Workshop on
{\em Future Physics at HERA},
Hamburg, Germany, Sept.1995 -- May 1996.
\bibitem{27c}L.~Frankfurt, W.~Koepf, M.~Sargsian and M.~Strikman,
{\em Color Transparency and Color Opacity in Coherent Production of
Vector Mesons off Light Nuclei at Small x}, {\em Future Physics at
HERA}, Hamburg, Germany, Sept.1995 -- May 1996, hep-ph/9608492.
\bibitem{27e}M.~Sargsian, {\em Electroproduction of Vector Mesons from
Light Nuclei}, invited talk at ``Second Workshop on Physics
with an Electron-Polarized Light-Ion Collider'',
14-16 September, 2000, MIT, Cambridge, Massachusetts, USA.
\bibitem{1}L.L.~Frankfurt, W.~R.~Greenberg, G.~A.~Miller M.~M.~Sargsian
and M.~Strikman, {\em Color Transparency Effects in Electron Deuteron
Interactions at Intermediate $Q^2$,} Z.Phys. {\bf A352}, 97-113 (1995).
\bibitem{2}L.L.~Frankfurt, M.~Sargsian and M.~Strikman, {\em Feynman Graphs
and Generalized Eikonal Approach to High-Energy Knock-out Processes},
Phys. Rev. {\bf C56}, 1124-1137 (1997).
\bibitem{3}W. Van Orden, {\em The Deuteron in the Light of the New Data from
JLab}, Plenary talk at Jefferson Lab User Meeting 24-25 June 1999.
\bibitem{Arenhovel}H.~Arenh\"ovel, W.~Leidemann, E.L.~Tomisiak,
{\em Exclusive deuteron electrodisintegration with polarized
electrons and a polarized target},
Phys. Rev. {\bf C46}, 455-470 (1992).
\bibitem{nstar}L.~Frankfurt, M.~Johnson, M.~Sargsian, M.~Strikman and W.~Weise,
{\em Hadronic Properties of the $S_{11}(1535)$ Resonance
Studied by Electroproduction off the Deuteron}
Phys. Rev. {\bf C60}, 055202 (1999).
\bibitem{4}S.E.~Kuhn and K.A.~Griffioen (spokespersons),
{\em Electron Scattering From A High-Momentum Nucleon in Deuterium},
CEBAF-PR-102-94, 39pp, 1994.
\bibitem{5} L.L.~Frankfurt and M.I.~Strikman, {\em Hard Nuclear
Processes and Microscopic Nuclear Structure}.
Phys. Rep. {\bf 160}, 235-427 (1988).
\bibitem{6}W.~Boeglin and H.~Anklin (spokespersons) {\em Measurement of
the (e,e'p) Cross Section on Tensor Polarized Deuterium},
JLAB proposal E-97-102 (1997).
\bibitem{7}J.~Templon and W.~Boeglin,
{\em Measurement of High Momentum Transfer $d(e,e'p)$
Reactions}, in progress.
\bibitem{8}J.~Templon (spokesperson), {\em Systematic Probe of Short-Range
Correlations via the Reaction $^4He(e, e', p)^3H$}, JLAB
proposal, E-97-111 (1997).
\bibitem{22}D.~B.~Day, L.L.~Frankfurt, M.~M.~Sargsian and M.~I~Strikman,
{\em Evidence for Short Range Correlations from High $Q^2$
$(e,e')$ Reactions}, Phys.~Rev. {\bf C48}, 2451-2461 (1993).
\bibitem{23}B.~Filippone and D.~Day, {\em Inclusive Scattering for Nuclei
at x>1 and High $Q^2$}, Jefferson Lab proposal,
E-89-008 (extended for 6~GeV electron beam, 1999).
\bibitem{xm1}J.~Arrington, et al., {\em Inclusive Electron - Nucleus
Scattering at Large Momentum Transfer}, Phys. Rev. Lett.
{\bf 82}, 2056-2059 (1999).
\bibitem{24}J.~Zhao, W.~Bertozzi and S.~Gilad (spokespersons)
{\em Initial Exploration of Semi-exclusive Scattering
in x > 1 Region with $^3He(e,e'p)$ Redactions}, Jefferson
Lab proposal, E-97-011 (1997).
\bibitem{25}E.~Piasetzky, W.~Bertozzi, John.~Watson S.~Wood (spokespersons),
{\em Studying the Internal Small-Distance Structure of Nuclei
via the triple Coincidence $(e,ep+N)$ Measurement}, Jefferson
Lab proposal E-97-106 (1997).
\bibitem{C28}D.~B.~Day, L.L.~Frankfurt M.~M.~Sargsyan and M.~Strikman,
{\em Evidence for Short-Range Correlations from High $Q^2$
$(e,e')$ Reactions}, in the Proceedings of PANIC XIII,
-Particle and Nuclei, June 28-July-2, 1993 Italy,
Editor A.~Pascolini, World Scientific.
\bibitem{9}S.J.~Brodsky, {\em in Proceedings of the Thirteenth
International Symposium on Multiparticle Dynamics}, Volendaum,
The Netherlands, 6-11 June 1982, edited by E.W.~Kittel,
W.~Metzger, and A.~Stergion (Word Scientific, Singapore).
\bibitem{10}A.F.~Mueller, {\em in Proceedings of the Seventeenth Recontree
de Moriond}, Les Arcs, France, Edited by J.~Tran Thanh Van
(Editions Frontieres, Gif/sur-Yvette, 1982).
\bibitem{11}G.R.~Farrar, L.L.~Frankfurt, M.I.Strikman and H.~Liu,
{\em Transparency in Nuclear Quasiexclusive Processes with
Large Momentum Transfer}, Phys. Rev. Lett. {\bf 61},
686-689 (1988).
\bibitem{12}B.K.~Jennings and G.A.~Miller {\em Realistic Hadronic
Matrix Element Approach to Color Transparency},
Phys. Rev. Lett. {\bf 69} 3619-3622, (1992).
\bibitem{13}N.C.R.~Makins et al., {\em Momentum Transfer Dependence of Nuclear
Transparency from the Quasielastic $^{12}C(e,e'p)$ Reaction},
Phys. Rev. Lett. {\bf 72}, 1986-1989 (1994).
\bibitem{14}L.L.~Frankfurt, E.~J.~Moniz, M.~M.~Sargsian and M.~M.~Strikman,
{\em Correlation Effects in Nuclear Transparency},
Phys.~Rev. {\bf C51}, 3435-3444 (1995).
\bibitem{15}R.~Ent and R.~Milner(spokespersons), {\em Measurement of the
Nuclear Dependence and Momentum Transfer Dependence of
Quasielastic $(e,e'p)$ Scattering at Large Momentum Transfer},
PR-91-007/013(extended for 6~GeV electron beam), 1991.
\bibitem{Gees}D. Geesaman {spokesperson}, {\em The Energy Dependence of Nucleon
Propagation in Nuclei as Measured in the (e,e'p) Reaction},
JLab proposal E-91-013, (1991).
\bibitem{16} A.~Saha, B.~Bertozzi, L.~Weinstein and R.~Lourie(spokespersons)
{Study of the Quasielastic (e,e'p) reaction in $^{16}O$ at
High Recoil Momentum}, JLab proposal, E-89-003 (1989).
\bibitem{17}K.~Sh.~Egiyan, L.~L.~Frankfurt, W.~R.~Greenberg, G.~A.~Miller,
M.~M.~Sargsyan and M.~I.~Strikman,
{\em Searching for Color Coherent Effects at Intermediate $Q^2$
via Double Scattering Processes},
Nucl.~Phys. {\bf A580} 365-382 (1994).
\bibitem{18}L.~Frankfurt, W.~Greenberg, G.~Miller M.~Sargsyan and
M.~Strikman, {\em Color Transparency and the Vanishing Deuterium
Shadow}, Phys.~Lett. {\bf B369} 201-206 (1996).
\bibitem{19}J.M.~Laget, {\em What we can Learn from Experiments with 10 GeV
Photons}, Plenary Talk, in Proceedings of the Workshop on Physics
and Instrumentation with 6-12~GeV Beams, Eds. S.~Dytman, H.~Fenker,
P.~Roos, June-1998, JLAB, Newport News, p.57.
\bibitem{20}K.Sh.~Egiyan, K.A.~Griffioen and M.I.~Strikman (spokespersons),
{\em Nuclear Transparency in Double Scattering Processes}
Jefferson Lab proposal E-019-94 (1995).
\bibitem{21}L.L.~Frankfurt, W.R.~Greenberg, G.A.~Miller and M.I.~Strikman,
{\em Sum Rule Description of Color Transparency},
Phys. Rev. {\bf C46}, 2547-2553 (1992).
\bibitem{28}M.R.~Adams et al., {\em Measurement of Nuclear Transparencies
from Exclusive $\rho^0$ Meson Production in Muon - Nucleus
Scattering at 470-GeV}, Phys.~Rev.~Lett. {\bf 74},
1525-1529, (1995).
\bibitem{29}V.N.~Gribov, {\em Interaction of Gamma Quanta and Electrons
with Nuclei at High Energies}, JETP {\bf 30}, 709-717 (1970).
\bibitem{30}L.~Frankfurt, W.~Koepf, J.~Mutzbauer G.~Piller,
M.~Sargsian and M.~Strikman, {\em Coherent Photo- and
Leptoproduction of Vector Mesons from Deuterium},
Nucl.~Phys. {\bf A622}, 511-537 (1997).
\bibitem{31}L.L.~Frankfurt, G.~Piller, M.~Sargsian, M.~Strikman,
{\em Coherent Vector Meson Production from Deuterons},
Eur. Phys. J. {\bf A2}, 301-309, (1998).
\bibitem{32}W.K.~Brooks, L.L~Frankfurt, K.~Griffioen, K.~Sh.~Egiyan,\\
S.G.~Stepanyan, M.M.~Sargsyan and M.I.~Strikman,
{\em Investigation of the Onset of Coherence Phenomena in
production of Vector Mesons of (Polarized) Deuteron},
LOI-004-95, 18pp, 1995.
\bibitem{Slac}J.E.~Belz et al.,{\em Two Body Photodisintegration of the
Deuteron up to 2.8-GeV} Phys.Rev. Lett. {\bf 74}, 646-649 (1995).
\bibitem{33}C. Bochna et al.(E89-012 Collaboration),
{\em Measurement of Deuteron Photodisintegration up to 4.0-GeV},
Phys. Rev. Lett. {\bf 81}, 4576-4579 (1998).
\bibitem{34}L.L.~Frankfurt, J.A.~Miller, M.M.~Sargsian, M.I.~Strikman,
{\em QCD Rescattering and High Energy Two-Body
Photodisintegration of the Deuteron},
Phys. Rev. Lett.\ {\bf 84}, 3045 (2000).
\bibitem{C12}L.L.~Frankfurt, J.A.~Miller, M.M.~Sargsian, M.I.~Strikman,
{\em Hard Rescattering in QCD and High-Energy Two Body
Photodisintegration of the Deuteron},
Presented at 15th International Conference on Particle and
Nuclei (PANIC 99), Uppsala, Sweden, 10-16 June 1999,
hep-ph/9908392.
\bibitem{jmt}M.M.~Sargsian, {\em Deuteron Photodisintegration and QCD
Dynamics}, Plenary talk at Jefferson Lab User Meeting
24-25 June 1999.
\bibitem{FMSS}L.L.~Frankfurt, J.A.~Miller, M.M.~Sargsian, M.I.~Strikman,
{\em in preparation}.
\bibitem{GHM}R.~Gilman, R.J.~Holt and Z.E.~Meziani (spokespersons),
``Proton Polarization in Deuteron Photodisintegration
to $E_{gamma}>3~GeV$ at $\Theta_{cm}=90^0$'', JLab
Proposal E-00-107, 2000.
\bibitem{Panofsky}W.~Panofsky, {\em In} Proceedings of International
Symposium on High Energy Physics, Vienna, 1968.
\bibitem{Bjor_Pasch}J.D.~Bjorken and F.A.~Paschos, Phys. Rev. {\bf 185},
1975, (1969).
\bibitem{FS81}L.~L.~Frankfurt and M.~I.~Strikman, Phys. Rep. {\bf 76},
215 (1981).
\bibitem{BCDMS}A.~C.~Benvenuti {\it et al.} [BCDMS Collaboration],
Z.\ Phys.\ {\bf C63}, 29 (1994).
\bibitem{CCFR}M.~Vakili {\it et al.} [CCFR Collaboration],
Phys.\ Rev.\ {\bf D61}, 052003 (2000)
\bibitem{HNM}Working Group of {\em Hadrons in the Nuclear Medium},
January-August, 2000,\\
$http://www.fiu.edu/^\sim sargsian/hnm/hnm.html$,
\bibitem{FSS}L.L.~Frankfurt, M.M.~Sargsian and M.I.~Strikman, {\em in
progress}.
\bibitem{Arrin}J.~Arrington et all, E89-008.Phys.Rev.Lett.82:2056-2059,1999
\bibitem{BB}W.~Bertozzi and W.~Boeglin (spokespersons),
``Short Range Correlations with DIS'', presentation at PAC-18,
14-15 July, 2000, Jefferson Lab, Newport News.
%\bibitem{28}M.R.~Adams et al., {\em Measurement of Nuclear Transparencies
% from Exclusive $\rho^0$ Meson Production in Muon - Nucleus
% Scattering at 470-GeV}, Phys.~Rev.~Lett. {\bf 74},
% 1525-1529, (1995).
%\bibitem{29}V.N.~Gribov, {\em Interaction of Gamma Quanta and Electrons
% with Nuclei at High Energies}, JETP {\bf 30}, 709-717 (1970).
%\bibitem{30}L.~Frankfurt, W.~Koepf, J.~Mutzbauer G.~Piller,
% M.~Sargsian and M.~Strikman, {\em Coherent Photo- and
% Leptoproduction of Vector Mesons from Deuterium},
% Nucl.~Phys. {\bf A622}, 511-537 (1997).
%\bibitem{31}L.L.~Frankfurt, G.~Piller, M.~Sargsian, M.~Strikman,
% {\em Coherent Vector Meson Production from Deuterons},
% Eur. Phys. J. {\bf A2}, 301-309, (1998).
%\bibitem{32}W.K.~Brooks, L.L~Frankfurt, K.~Griffioen, K.~Sh.~Egiyan,\\
% S.G.~Stepanyan, M.M.~Sargsyan and M.I.~Strikman,
% {\em Investigation of the Onset of Coherence Phenomena in
% production of Vector Mesons of (Polarized) Deuteron},
% LOI-004-95, 18pp, 1995.
\bibitem{35}I.~Mardor, et al. (EVA collaborations}, {\em Nuclear Transparency
in Large Momentum Transfer Quasielastic Scattering},
Phys. Rev. Lett. {\bf 81}, 5085-5088 (1998).
%\bibitem{36}G.R.~Farrar, L.L. Frankfurt, H.~Liu, M.I.~Strikman,
% {\em Study of Bound Nucleons by Quasielastic Scattering with
% Large Momentum Transfer}, Phys. Rev. Lett. {\bf 62},
% 1095-1098 (1989)
%\bibitem{37}L.~Frankfurt, E.~Piasetzky, M.~Sargsian and M.~Strikman,
% {\em Probing Short Range Nucleon Correlations in High-Energy Hard
% Quasielastic $pd$ Reactions}, Phys.~Rev. {\bf C51},
% 890-900 (1995).
%\bibitem{38}L.L. Frankfurt, E. Piasetzky, M.M. Sargsian and M.I.Strikman,
% {\em On The Possibility to Study Color Transparency in the Large
% Momentum Transfer Exclusive $D(p,2p)n$ Reaction},
% Phys. Rev. {\bf C56} 2752-2766 (1997).
%\bibitem{39}J.~Aclander et al (EVA collaboration), {\em The Large Momentum
% Transfer Reaction $^{12}C(P,2P+N)$ as a New Method for Measuring
% Short Range NN Correlations in Nuclei}, Phys. Lett. {\bf B.453},
% 211-216 (1999).
%\bibitem{PRKim}K.Sh.~Egiyan (spokesperson), {\em Study of Short Range
% Properties of Nuclear Matter in CLAS}, Jefferson Lab proposal,
% E-89036, 25pp (1989).
%\bibitem{40}M.M.~Sargsian, {\em Radiative Corrections for Coincidence
% Experiments}, Yerevan Physics Institute Preprint,
% YERPHI-1331-26-91, 1991, 22pp.
%\bibitem{41}M.M.~Sargsian, {\em Computer Code for $(e.e')$ Electroproduction
% and Radiative Corrections}, CEBAF, CLAS-NOTE-90-007, 1990, 18pp.
%\bibitem{42}M.M.~Sargsian, {\em Monte Carlo Event Generator for
% Electro-nuclear Reactions}, CEBAF, CLAS-NOTE-92-018, 1992, 14pp.
\end{thebibliography}
\end{document}