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\bigskip
\title {\bf Measurement of $F_2$ and $R = \sigma_L / \sigma_T$ \\
on Nuclear-Targets in the Nucleon Resonance Region - E03-110\\
  \ \\
(First Stage of a Program to Investigate  Quark Hadron Duality in 
Electron and
Neutrino Scattering on Nucleons and Nuclei)}

\author{A. Bodek (spokesperson), S. Manly, K. McFarland, (J. Chovjka,
G.B. Yu),\footnote[1]{PhD thesis students, pending funding}
(D. Koltun, L. Orr, S. Rajeev) \footnote[2]{Collaborating theorists}
}
\address {Department of Physics and Astronomy,
University of Rochester, Rochester, NY 14627}

\author{M.E. Christy, W. Hinton,  C. Keppel (spokesperson), E. 
Segbefia}
\address { Hampton University, Hampton, VA}
\author{P. Bosted, S. E.  Rock}
\address { University of Massachusetts, Amherst, MA}

\author{I. Niculescu}
\address{ James Madison University, Harrisonburg, VA}

\author{R. Ent, D. Gaskell, M. Jones, D. Mack, S. Wood}
\address{Thomas Jefferson National Accelerator Facility, Newport
News, VA}

\author{J. Arrington}
\address{Argonne National Laboratory,  
Argonne, IL}

\author{ H. Gallagher}
\address{Tufts University, Medford, MA}

\author{J. Dunne}
\address{Mississippi State University, Mississippi State, MS}

\author{P. Markowitz, J. Reinhold}
\address{ Florida International University, University Park, FL}

\author{E. Kinney}
\address { University of Colorado, Boulder, Colorado}


\author{H.P. Blok}
\address{Vrije Universiteit, Amsterdam, Netherlands\\
\ \\}



\date{ April 28, 2003, JLab Experiment  E03-110 (updated Jun 13, 
03) $http://www.pas.rochester.edu/~bodek/jlab/Rnuclear-E03-110.pdf$}
%\begin{verbatim} http://www.pas.rochester.edu/~bodek/jlab/Rnuclear-E03-110.pdf \end{verbatim}}


\maketitle

\newpage

%\section*{Abstract}
\section*{Summary}

We propose to measure the longitudinal-transverse (L-T) separated 
structure
functions from nuclear targets in the resonance region.
This is the first stage
of an overall program to investigate quark-hadron duality in
electromagnetic and weak structure of nucleons and nuclei.
The targets proposed include Carbon, Quartz, Aluminum, Calcium, Steel
and Copper 
%(also Hydrogen and Deuterium from previous JLab
%experiments).
to compliment existing baseline data on Hydrogen and Deuterium.  
The targets
proposed are (or closely resemble) nuclear
targets commonly used in neutrino  experiments
such as the low statistics experiments on
Hydrogen, Deuterium, Neon, and  Argon and high statistics
neutrino experiments on Scintillator, Water and Steel. In addition
to 
performing studies of quark-hadron duality in electron scattering
on 
nuclear targets for the separated structure functions, these
data 
will used as input vector form factors in a future analysis
of 
neutrino data in order to investigate quark hadron-duality
in the 
axial structure function of nucleons and nuclei.

Measurements will be made in the nucleon resonance region ($1<W^2<4$ 
GeV$^2$)
spanning the four-momentum transfer range $0.5<Q^2<4.0$ (GeV/c)$^2$ at
identical kinematic points to those to be run during JLab Deuterium 
experiment 02-109.
(Therefore, it is most efficient for both experiments to be run at
the same time).
The 
%separation 
decomposition
of the inclusive electroproduction cross sections into 
longitudinal
and transverse strengths will accomplished by performing Rosenbluth 
separations
to extract the transverse structure function $F_1(x,Q^2)$, the 
longitudinal structure function
$F_L(x,Q^2)$, and the ratio $R={{\sigma_L} / {\sigma_T}}$.  
%
%This 
%proposal represents the first
%global survey of these fundamental separated quantities in the 
%resonance
%region for nucleons bound in nuclei.

The analysis of the separated resonance region proton data from 
experiment
E94-110~\cite{e94110}, which was performed in Hall~C, has recently 
been completed and the excellent precision
obtained from that measurement has been presented in JLab hydrogen 
proposal E94-110~\cite{e94110}.
The extension of the proton measurements to deuterium is approved and
will be run by E02-109~\cite{e02109}.
This 
proposal represents the first
global survey of these fundamental separated quantities in the 
resonance
region for nucleons bound in nuclei.
%UPDATE
Data from all of the previous
experiments will be incorporated into the analysis.

Given the experience of these previous experiments, the data taking
is straightforward and allows the precision
of the proposed measurements to be predicted with great confidence. 
In addition, the analysis
machinery which was developed for E94-110 can be used with only very 
little modification.
The great care and time invested in developing the experimental 
requirements, systematic uncertainty
measurements, and analysis machinery will be of immediate benefit to 
the proposed experiment.
%
We will also build upon the experience
from 
previous lower statistics studies with (electrons)  of the 
nuclear-dependence of the separated
structure functions in the DIS region that  were done by SLAC 
experiment E140~\cite{dasu}, as well as
the very low $Q^2$ high $W^2$ 
studies (to test the
HERMES effect) that were done by JLab experiment 
E99-118~\cite{e99118}.



\section*{Physics Overview, Motivation and Goals}

Due to the small value of the electromagnetic coupling constant, the
scattering of electrons
from nucleons can be well approximated by the exchange of a single
virtual photon, which carries
the exchanged 4-momentum squared, $q^2$.  In terms of the incident
electron energy, $E$, the scattered electron
energy, $E^{'}$, and the scattering angle, $\theta$, the absolute
value of the exchanged 4-momentum squared is
given by
\begin{equation}
(-q)^2 = Q^2 = 4EE^{'}{\sin}^2 \frac{\theta}{2}.
\end{equation}
In the one photon exchange approximation, the spin-independent cross
section for inclusive
electron-nucleon scattering can be expressed in terms of the photon
helicity coupling as
\begin{equation}
\frac{d\sigma}{d\Omega dE^{'}} = \Gamma\left[\sigma_T(x,Q^2) +
\epsilon \sigma_L(x,Q^2)\right],
\label{eq:cs1}
\end{equation}
where $\sigma_T$ ($\sigma_L$) is the cross section for
photo-absorption of purely
transverse (longitudinal) polarized photons,
\begin{equation}
\Gamma = \frac{\alpha E^{'}(W^2 - M_p^2)}{2 \pi Q^2 M_p E (1 - 
\epsilon)}
\end{equation}
is the flux of transverse virtual photons, and
\begin{equation}
\epsilon = \left[1 + 2(1+\frac{\nu^2}{Q^2}) {\tan}^2
\frac{\theta}{2}\right]^{-1}
\end{equation}
is the relative flux of longitudinally polarized virtual photons.

In terms of the structure functions $F_1(x,Q^2)$ and $F_L(x,Q^2)$, 
the double
differential cross section can be written as
\begin{equation}
\frac{d\sigma}{d\Omega dE^{'}} = \Gamma \frac{4{\pi}^2 
\alpha}{x(W^2-M_p^2)}
\left[ 2xF_1(x,Q^2) + \epsilon F_L(x,Q^2) \right].
\label{eq:cs2}
\end{equation}
Comparison of equations \ref{eq:cs1} and \ref{eq:cs2} shows that 
$F_1(x,Q^2)$
is purely transverse, while the combination
\begin{equation}
F_L(x,Q^2)= \frac{1+4M_p^2 x^2}{Q^2} F_2(x,Q^2)-2xF_1(x,Q^2)
\label{eq:fl}
\end{equation}
is purely longitudinal.  The separation of the unpolarized structure
functions into longitudinal
and transverse parts from cross section measurements can be
accomplished via the Rosenbluth
technique~\cite{rosen}, by making measurements at two or more values
of $\epsilon$ for
fixed  $x$ and $Q^2$.  Fitting the reduced cross section,
$d\sigma/\Gamma$, linearly in $\epsilon$,
yields $\sigma_T$ (and therefore $F_1(x,Q^2)$) as the intercept, and
the structure function ratio
$R(x,Q^2) = \sigma_L/\sigma_T = F_L(x,Q^2)/2xF_1(x,Q^2)$ as the 
slope.

In neutrino scattering, the separated vector structure 
functions are related to the separated vector structure functions in 
electron scattering on  protons and neutrons via CVC and 
Clebsch-Gordan coefficients which depend on the contributions of 
different isospin amplitudes to the scattering. The relations 
between the vector structure functions are well determined for 
elastic (quasi-elastic) scattering on free nucleons for which the 
isospin of the initial and final states are well determined.  
Similarly, the relationships between the vector form factors are also 
well determined for the scattering on free quarks (i.e.the  high 
$Q^2$ DIS scattering) for which the isospin states of the initial and
final state quarks are also well determined. 
%UPDATE
In general, even in these well 
understood cases, in order to extract the axial structure function
in neutrino scattering experiments, the separated vector structure functions 
from electron scattering,  $F_{2p}$, $F_{2n}$, $R_{p}$, $R_{n}$
for bound nucleons are needed.

In contrast, in the 
resonance region which includes contributions from final states with 
different isospins, the relationships between the vector form factors 
in neutrino and electron scattering is more complicated. Therefore, a 
unified investigation of quark-hadron duality for the same nuclear 
targets with electrons and neutrinos is interesting. 

High  
%statistical 
statistics
samples in neutrino experiments  
%(for nuclear targets 
%such such as iron and scintillator/carbon)  
on nuclear targets such as iron and hydrocarbons
will 
%become available
%over the next two years from
be measured beginning in 2005 in
experiments at the near detector hall at 
the 
%Fermilab-NUMI/MINOS beams.
Fermilab-NUMI beam 
%
At present, as described in the next section,  the physics emphasis of 
these experiments is the investigation of neutrino cross sections at 
low energies as a tool to study neutrino oscillations. Members of 
this collaboration are proposing to investigate quark-hadron duality 
in high statistics electron scattering with the same nuclear targets 
first. This will be followed by 
%performing 
a comparison with all 
existing neutrino data, with the aim of continuing these studies with 
the higher statistics  neutrino experiments in the future. Note that 
investigation of quark-hadron duality in the axial structure 
functions
of nucleons and nuclei with neutrinos also  add 
a
new 
dimension to these studies. 

\begin{figure}
\begin{center}
\epsfig{figure=ra.ps,width=14cm,height=8cm,angle=0}
\caption{The SLAC E140 data set of $R_{A}-R_{D}$ on deuterium in the
Deep Inelastic Region .}
\label{fig1}
\end{center}
\end{figure}

The existing world's data measurements of the nuclear dependence of 
$R$  in the DIS region from SLAC Experiment E140~\cite{dasu} are
shown in Figure~\ref{fig1}.  As seen in the figure, the errors in the 
DIS region
are very large, and no data exists in the resonance 
region.  Preliminary JLab data on tests of duality in the resonance 
region at higher $Q^2$ is shown in Figure~\ref{emc.eps}.

\begin{figure}
\begin{center}
\epsfig{figure=emc.eps,width=14cm,height=8cm,angle=0}
\caption{A comparison of the ratio of cross sections of iron to 
deuterium in the resonance region versus the ratio measured in
the DIS region. These preliminary data from JLab
indicate that the nuclear
effects in the DIS and resonance region are the same if plotted
versus the Nachtman variable as expected from duality.}
\label{emc.eps}
\end{center}
\end{figure}



\section*{Broad Impact of These Measurements on  Neutrino Physics}

A detailed study of $\sigma_L/\sigma_T$ on nuclear targets in the
resonance region is an important ingredient in forming an integrated
description of charged lepton and neutrino scattering cross-sections.
High rate neutrino beams now under construction or planned at Fermilab and
J-PARC will allow the first precision experimental comparisons of
electron and neutrino cross-sections and present and future neutrino
oscillation experiments will use these results to predict event rates.

The recent discoveries of neutrino oscillations in atmospheric
neutrinos~\cite{SK} and in neutrinos from the sun~\cite{SNO,KAMLAND}
motivate the detailed studies of neutrino oscillations at future high
intensity neutrino beams from accelerators.  The two disparate mass
scales observed in oscillations from these astrophysical sources,
$\dmsq_{\rms atm}\approx \evsq{2\times10^{-3}}$ and $\dmsq_{\rms solar}\sim
\evsq{10^{-4}}$, along with the stringent limits on $\nuebar$
disappearance at the atmospheric $L/E$ in the CHOOZ and Palo Verde
reactor experiments experiments\cite{CHOOZ,PaloVerde}, have raised the
possibility that there may be an observable CP-asymmetry in
$\numu\to\nue$ transitions.  This rare, sub-leading transition in the
neutrino flavor sector is analogous to to searching for first and
third generation mixing in the quark sector, which has led to a rich
phenomenology of CP-violation, meson mixing and rare decays in the
quark sector.

These neutrino oscillation experiments are very challenging, because
of the required $L/E$ of $400$~km/GeV, and require megawatt proton
sources, $1$~GeV neutrino beams and multi-kiloton detectors to make
the observations.  The measurements are further complicated by the low
transition probability of $\numu\to\nue$ and the need to compare to
$\numubar\to\nuebar$ at high precision.  This requires a detailed
knowledge of the neutrino interaction cross-sections both for the
dominant signal processes and for background processes, such as
$\nu N\to\nu N \pi^0$ where the $\pi^0$ is misidentified as an
electron in a many kiloton sampling detector.  

The phenomenology of neutrino cross-sections in relatively simple when
$E\nu\ll 1$~GeV or when $E\nu\gg$~few GeV since these regimes are
dominated by (quasi)-elastic and deep inelastic processes,
respectively.  However in the $1$ to few GeV region, there are
contributions to the cross-section from both of these processes as
well as resonance-dominated hadroproduction.  A successful
phenomenological approach to modeling the resonance region in electron
scattering is the use of quark-hadron duality to relate quark-model
cross-sections to the cross-section over the discrete
resonances~\cite{bodek-yang3} as shown in Fig.~\ref{fig:f1fit},
Fig.~\ref{fig:predict} and Fig.~\ref{fig:predictD}.
 Figure~\ref{fig:f1fit} shows a fit by Bodek and Yang to inelastic
 electron and muon scattering data with a modified scaling variable
 and GRV98 PDFs with additional corrections (based on consideration
of the Adler and Gilman sum rules~\cite{Adler}. 
Figure~\ref{fig:predict} and Figure~\ref{fig:predictD} compare
the predictions of the fit to data in the resonance region
(which is not included in the fit, as well as other data
%UPDATE
such a photoproduction and high energy neutrino data).  All 
predictions assume quark-model relations, and an empirical
fit to R ($R_{1998}$).
This approach requires the separation
of the $F_{2}$, which has a simple representation in the quark
model, and $R$ whose description requires a different
prescription.  We hope to build successful models of neutrino
scattering using this same prescription with the addition of a
quark-model representation of the axial vector component of the
cross-section.
As mentioned earlier, since neutrino data are
measured in nuclear targets, even in 
the quark model case,  the separated vector structure functions 
from electron scattering,  $F_{2p}$, $F_{2n}$, $R_{p}$, $R_{n}$
for bound nucleons are needed in order 
to understand the axial structure function
in neutrino scattering experiments.
%

The new precise data will also allow us to redo a combined analysis
of electron-nucleon and neutrino nucleon data in the resonance region
within the Feynman quark-oscillator model as done
years ago (with poor precision)  by Rein and Seghal~\cite{rs}.
The results
of the updated Rein-Seghal type of analysis will be compared to an analysis
which is based on duality.

The full program of studies requires first additional precise electron
scattering data, in particular $\sigma_L$ and $\sigma_T$ 
%UPDATE
(or equivalenty $F_{2}$ and $R$)
%
on nuclear
targets (materials suited for future neutrino oscillation detectors --
water \cite{jhf}, hydrocarbons \cite{numi}, liquid argon -- and steel,
where the most precise high energy neutrino cross-sections have been
measured \cite{CCFR}) in the relevant kinematic regime.  Later, as the
new generation of high rate neutrino beams at Fermilab and J-PARC become
available, the approach can be directly validated with
comparisons to data from high rate neutrino cross-section experiments
on the same targets \cite{eois}.


\begin{figure}
    %[t]
    \begin{center}
\epsfig{figure=Fig1Mex.eps,width=6.0in,height=8.0in}
\caption{Electron and muon $F_2$ data (SLAC, BCDMS, NMC, H1 94)
used to obtain the parameters of the Bodek-Yang
modified GRV98 $\xi_w$ fit compared to the predictions of the unmodified GRV98
PDFs (LO, dashed line) and the modified GRV98 PDFs 
fits (LO+HT, solid line); [a] for $F_2$ proton, [b] for $F_2$ deuteron,
and [c] for the H1 and NMC proton data at low $x$.}
\label{fig:f1fit}
\end{center}
\end{figure}



\begin{figure}
    %[t]
    \begin{center}
\epsfig{figure=Fig2Mex.eps,width=6.0in,height=7.0in}
\caption{ Comparisons to proton and
iron data not included in the Bodek-Yang GRV98 $\xi_w$  fit. 
(a) Comparison of SLAC and JLab 
(electron) $F_{2p}$ data
in the resonance region (or fits to these data)
and the predictions of the GRV98 PDFs with (LO+HT, solid)
and without (LO, dashed) the  Bodek-Yang modifications.
(b)  Comparison of photoproduction
       data on protons  to predictions using
 Bodek-Yang modified GRV98 PDFs. 
(c)  Comparison of representative CCFR $\nu_\mu$ and $\overline\nu_\mu$
charged-current differential cross sections 
on iron at 55 GeV and the predictions of the GRV98 PDFs with (LO+HT,
solid) and without (LO, dashed)
       Bodek-Yang modifications.  }
\label{fig:predict}
\end{center}
\end{figure}

\begin{figure}
    %[t]
    \begin{center}
\epsfig{figure=
Fig3Mex.ps,width=5.5in,height=3.2in}
\caption{ Comparisons to data on deuterium
which were not included in the  Bodek-Yang GRV98 $\xi_w$ fit. 
(a) Comparison of SLAC and JLab 
(electron) $F_{2d}$ data
in the resonance region 
and the predictions of the GRV98 PDFs with (LO+HT, solid)
and without (LO, dashed) our modifications.
(b)  Comparison of photoproduction
       data on deuterium  to predictions using
Bodek-Yang modified GRV98 PDFs (including shadowing corrections). 
(c) The  shadowing corrections that were applied to the PDFs for
predicting the photoproduction cross section on deuterium.}
\label{fig:predictD}
\end{center}
\end{figure}





\begin{table}
    %[th]
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
    $Target$ & $(Z, A), Z/A$     & $r.l. (g/cm^2)$   &  $r.l. (cm)$ \\
\hline
    &        &        &            \\
H &   (1,~1.00794),~ 0.99212  & 61.28& 866 \\
D &   (1,~2.01404),~  0.49652  & 122.4& 724 \\
C (approx CH2) &   (6,~12.011),~ 0.49954  &   42.7& 18.8 \\
Ne &   (10,~20.1797),~ 0.49555  & 28.94& 14.0 \\
Poly-CH2 & 0.53768 &43.72& 43.4 \\
Water-H2O & 0.55509 &36.08& 36.1 \\
Quartz-SiO2& 0.49926 & 27.05 &12.3 \\
O2(in Water, Quartz) &    (8,~15.999),~ 0.50002  &  &  \\
Si(in Quartz) &   (14,~28.0855),~  0.49848  &21.82  &9.36  \\
Al(Approx Si) &   (13,~26.9815),~ 0.48181  &24.01  &8.90  \\
Ar &   (18,~39.948),~ 0.45059  &19.55  &14.0  \\
Ca (approx Ar) &   (20,~40.078),~ 0.49903  &16.14  &10.42  \\
Fe &    (26,~55.805),~ 0.46556  &13.84  &1.76  \\
Cu (approx Fe) &    (29,~63.506),~ 0.45636  &12.86  &1.43   \\
\hline
\end{tabular}
\caption{Targets used in low energy low statistics neutrino 
experiments (H, D, Ne, Ar, Polystyrene Scintillator, Water,  Iron), 
and  additional targets
that may be used to approximate them (Carbon, 
Quartz, Silicon, Calcium, Copper). Note that future high statistics 
experiments are planned with 
%Polystyrene Scintillator
Hydrocarbon, Water and Iron targets.}
\label{table1}
\end{center}
\end{table}

%\section*{The Nuclear Targets and Kinematics of E02-109 and this Proposal}
\section*{Nuclear Targets and Kinematics}

Table~\ref{table1} shows the kinds of nuclear targets that are
of interest to neutrino experiments. 
%
Table~\ref{table2} shows nuclear
targets that we propose to add to the target ladder of experiment
% \section*{Kinematics of E02-109 and this proposal}
% Table~\ref{kin} lists the kinematics and cross sections proposed for
E02-109 
%that alread 
%includes a Deuterium target and
%an Aluminum empty target replica. 
which already is approved to take data with a Deuterium target and with
an Aluminum empty target replica.
%

The differential cross sections for inclusive electron scattering
on Deuterium
will be measured in E02-109 according to the following definition:
\begin{equation}
{ {d^2 \sigma \over d\Omega dW^2 } = {{\Delta N}\over{\Delta \Omega
\Delta W^2}}{1\over{Qnd}}},
\end{equation}
where $\Delta N$ is the counts per $W^2$ bin, $n$ is the density of
deuterium, $d$ the target thickness, and Q is the integrated
number of incident electrons on target.
Table~\ref{kin} gives a breakdown of beam time requirements for 
E02-109 for the $\Delta$ running only. 
%We have added the
The
 last column  
%which 
shows 
%the 
additional time that is needed to measure
nuclear targets 
with the same number of events at each point as for Deuterium 
if this experiment (E03-110) were to run at the same time
%.
as E02-109.
%(if the number of events with each nuclear target is the
%same as that for Deuterium)

\begin{table}
   %[th]
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
    $Target-Thickness~r.l.$& Running Ratio & $ Data $   &  $comment$ \\
\hline
    &        &        &            \\
$H-0.005$ &  2.0    & $All$~$Q^2$ & $E94-110$ \\
$D-0.005$ &  1.0  & $All$~$Q^2$  & $E02-109$ \\
$Al-0.005$ &  $(5.1*)$   & $All$~$Q^2$ & $E02-109$ \\
\hline
$C-0.06$ &  0.2    & $All$~$Q^2$ & $nominal$ \\
$Quartz-0.06$& 0.4   & $Q^2$~$<4$ & $nominal$ \\
$Si -  0.06$& 0.5  & $Q^2$~$<4$ & $nominal$ \\
$Ca- 0.06$& 0.6  &  $Q^2$~$<4$ & $nominal$ \\
$Fe-  0.06$& 0.7  & $Q^2$~$<4$ & $nominal$ \\
$Cu- 0.06$ &  0.8  & $All$~$Q^2$ & $nominal$ \\
\hline
$C -  0.02$&0.7   &  $All$~$Q^2$ & $Rad-Cor$ \\
$C  - 0.12$& 0.1  & $All$~$Q^2$ & $Rad-Cor$ \\
$Cu - 0.02$&  2.4 & $All$~$Q^2$ & $Rad-Cor$ \\
$Cu - 0.12$& 0.4  &  $All$~$Q^2$ & $Rad-Cor$ \\
$Fe - 0.02$&2.2  & $Q^2$~$<4$ & $Rad-Cor$ \\
$Fe - 0.12$&0.4   & $Q^2$~$<4$ & $Rad-Cor$ \\ 
$Water  -  0.02$& 0.8  &  $ Q^2$~$<4$ & $TBI$ \\
\hline
\end{tabular}
\caption{ Targets to be used  in this proposal (E03-110). Running Ratio is the ratio 
of the running time  
relative to running with a $4$~cm~($0.005$~r.l.) Deuterium target
to get the same number of events (at constant  current of  80 $\mu$A,
which is planned for E02-109).  Note that data 
with Hydrogen is already available from JLab experiment E94-110, and 
Deuterium and Aluminum data 
need need NOT be taken if this experiment (E03-110) 
runs at the same time as E02-109 (thus minimizing the error on the 
ratio of structure functions on nuclear targets to deuterium). All 
$Q^2$ identifies targets for which data will be taken at all values 
of $Q^2$, and $Q^2$~$<4$ identifies targets for which no high $Q^2$ 
data will be taken.  The nominal targets are identified. Rad-Cor 
indicates targets to be used for Radiative Corrections Studies,
and 
TBI indicates Option To Be Investigated. $*$ Note that the Al target is
only used for empty target, and therefore statistics
equal to D2 are not needed.}
\label{table2}
\end{center}
\end{table}

\subsection*{Details of Event Rate Calculations}

A minimum time of one half hour per kinematic setting, a maximum rate
of 1000 Hz, and a beam current of $80$ $\mu$A were used in the 
calculation of the running time for Deuterium for E02-109. 
The calculated rates listed are for bins of width $\Delta W^2 = (25
\rm MeV)^2$ averaged over a momentum acceptance of $\pm 8 \%$
and assuming an effective solid angle of the HMS of 6.5 msr at the
$\Delta$ resonance.  The data for the higher resonances comes
in at higher rates and requires $\approx 50\%$ additional beam time.
The data acquisition time listed in Table~\ref{kin} reflects
the total time required for the $\Delta$ resonance only.  The SOS
will be used to collect positron yields (from neutral pion
production) for charge symmetric background studies and will be run
in a simultaneous single arm mode with the HMS data and, so,
this adds little time to the beam time
request.  The extraction of neutron structure functions
from D$_2$ data for E02-109 requires the
subtraction of the proton data taken in E94-110.  As a cross
check on relative normalizations, E02-109 plans to do measurements of
the hydrogen resonance region cross sections for
$Q^2$ $<$ 3.0~$\rm (GeV/c^2)^2$ to compare to E94-110.  This takes
 an additional 8 hrs.
A minimum central
spectrometer momentum setting of 400 MeV/c was assumed. All proposed
measurements with deuterium in 
E02-109 use the Hall C 4 cm deuterium target.  In
addition, E02-109 plans to take
elastic proton data  at all angles and
energies for kinematic uncertainty checks.



\begin{table}
    %[tbhc]
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
$Q^{2}_{\Delta}$  &  $E$  &  $E^{'}_{\Delta}$ & $\theta_{\Delta}$ &
${\epsilon}_{\Delta}$ & $Rate_{\Delta}$ & D$_2$-Time &Nucl. Tgts \\
$(GeV/c)^2$ & ($GeV$) & ($GeV$) & (deg) & & (Hz) & (Hours)&(hours) \\
	        &      &      &         &     &    & E02-109 &  E03-110\\
\hline
0.5  & 1.16 & 0.55 & 52*      & 0.54   & 1 K  &   0.5&      \\
        & 1.64 & 1.0  & 33      & 0.78   & 1 K  &   0.5 &     \\
        & 4.04 & 3.4  & 11      & 0.97   & 1 K  &   0.5&      \\
1.0  & 1.64 & 0.77 & 52*      & 0.53   & 1 K  &   0.5&      \\
        & 2.28 & 1.4  & 33      & 0.77   & 1 K  &   0.5&      \\
        & 4.52 & 3.6  & 14      & 0.95   & 1 K  &   0.5&      \\
2.0  & 2.28 & 0.87 & 60*      & 0.43   & 65   &   0.5 &     \\
        & 3.24 & 1.8  & 35      & 0.73   & 285  &   0.5&      \\
        & 5.64 & 4.2  & 17      & 0.92   & 1 K  &   0.5 &     \\
3.0  & 3.24 & 1.3  & 52*      & 0.51   & 16   &   2 &       \\
        & 4.04 & 2.1  & 35*      & 0.70   & 40   &   1&        \\
        & 5.64 & 3.7  & 22      & 0.86   & 172  &   0.5&      \\
\hline
&      &      &         &        &  sub-total   &  8 & 24   \\
\hline
	4.0  & 3.24 & 0.77 & 79*      & 0.23   & 1    &   22&       \\
        & 4.04 & 1.6  & 47*      & 0.51   & 3    &   8  &      \\
        & 5.64 & 3.2  & 27      & 0.77   & 53   &   1   &     \\
5.0  & 4.04 & 1.0  & 66*      & 0.29   & 1    &   22  &     \\
        & 4.52 & 1.4  & 52*      & 0.42   & 3    &   8 &       \\
        & 5.64 & 2.5  & 35      & 0.66   & 6    &   4 &       \\
\hline
&      &      &         &        &  sub-total   &  65 & 40  \\
\hline       
&      &      &         &        &      &  Total D  &  Total-Nucl\\
        &      &      &         &        &      &   \bf{73} &  \bf{64}\\
	        &      &      &         &     &    & E02-109 &  E03-110\\
\hline
\hline
\end{tabular}
\caption{D$_2$ Running for E02-109 Beam 
time requirements for all proposed measurements, as in the
E02-109 proposal.  All kinematics
and rates shown are for
a single bin in $W^2$ of 25 $(\rm MeV)^2$ width at the $\Delta$
resonance.  Positron data will be taken
in the SOS for the angles indicated by an asterisk. The last column is
the additional time needed for heavy targets for this proposal: 6 targets at
(C, Quartz, Si, Ca, Fe and Cu) $Q^2<4$ and
2 targets (C and Cu) at all $Q^2$. The beam energies in this table
differ slightly and inconsequentially from those in this proposal
text, as the original E02-109 energies were slightly disparate
from the actual common JLab energies. The text energies are the
correct ones for both experiments.}
\label{kin}
\end{center}
\end{table}


Note that the assumption made in the calculation of the rates
for E02-109  are conservative. The 80 $\mu$A current is assumed to
minimize density difference in the deuterium target.  For some of the
solid targets in the proposed experiment (E03-110) a higher current 
of 100 $\mu$A 
can be used (especially at high $Q^{2}$).
Similarly, a data taking rate of 1000 Hz is also 
conservative and data can be taken with 2000 Hz (and possibly
at 3000 Hz with some upgrades).  

The chosen beam energies in the table assume a linac energy of 1.12
GeV (1.18, 2.30, 3,42, 4.54, 5.66), with the exception of
two 
%bean 
beam energies which assume a linac energy of 0.80 GeV (1.64,
4.04).  Both base energies are standard CEBAF accelerator tunes.
The required beam time was determined such that the statistical
accuracy per $W^2$ bin was $\approx$ 3 times greater than
the systematic point-to-point accuracy expected.  The rates were
estimated based upon a fit of previous deuterium resonance region
cross section data from JLab~\cite{ioana}.
%
Using the parameters in Table~\ref{table2} we can scale the 
running time for Deuterium and obtain the corresponding
additional running time for the nuclear targets (shown in
the last columns of Table~\ref{kin} and  Table~\ref{time}.
%
The total  beam time requested for both  E02-109 (D$_2$) and for this experiment 
E03-110 (last
column Nucl. Tgts) are listed in Table~\ref{time}). 

For 
%D2 
D$_2$
running for E02-109
the total
data acquisition time listed
%, 
reflects the total time from
Table~\ref{kin}, as well as
an additional 40 hours to complete the higher resonances, an 
%addition
additional
60 hours for dummy runs which are
needed to subtract the yield contributions from the aluminum end caps
of the target, 
an additional 24 hours needed to complete the hydrogen elastic
scattering measurements, and an additional 16 hours
to obtain hydrogen resonance region data which is needed for
cross checks with E94-110.  Also,
since the positron data comes in at a slower rate, E02-109 requested an
additional 22 hours to complete these
measurements.  The E02-109 proposal assumes
one-quarter hour for each angle change
required at a given beam energy, and
one-quarter hour for each spectrometer central momentum change not
possible to be done concurrently
with angle changes.  Combined with one day for checkout, the 
total beam time approved for E02-109 is 13 days~\cite{hallc}.

This experiment (E03-110) requests an additional 5 days of running to do the
measurements with the nuclear targets.  With 2.5 days of additional 
running, data with all six targets can be measured for all of
the E02-109 data points with 
%$Q2<4$. 
$Q^2<4$. 
The additional 2.5 days are
requested for the measurements at the higher $Q^2$.  
%Therefore,
%a significant amount of physics can be done even with a
%a 2.5 day extension.

\begin{table}
    %[tbhc]
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
    & D- Time Required &Nucl. Tgts. \\
    &  (Hours) &  (Hours)\\
     & E02-109& E03-110 \\
\hline
Data acquisition (Deuterium $\Delta$)/+Nucl. Tgts. & 73 & 64 \\
Data acquisition (Deuterium $W^2$ $>$ $\Delta$)/+Nucl. Tgts. & 40& 38 \\
Data acquisition (Dummy)          &  60 & \\
Data acquisition (hydrogen elastics) & 24 & \\
Data acquisition (hydrogen resonance region) & 16 & \\
Data acquisition (additional positrons) & 22 & \\
D Angle changes (12)/+Nucl. Tgt Changes   & 3 & 10 \\
Spectrometer momentum changes (60) & 15 & \\
Major beam energy changes (1) & 8 & \\
Minor beam energy changes (5) & 20 & \\
D Checkout /+ Nucl. Rad correction Tests& 24 &10 \\
\hline
\bf{Total} & \bf{305}& \bf{120} \\
 & E02-109& E03-110 \\
\hline
\end{tabular}
\caption{D$_2$ Running for E02-109: Breakdown and tabulation of the total time requested.  Based
on previous experience, we assume
one-half hour for angle changes, 15 minutes for momentum changes,
eight hours for linac energy changes (major), and four
hours for each energy change accomplished by changing the number of
cycles (minor). The last column is the additional time required for 
heavy targets in this proposal (E03-110)}
\label{time}
\end{center}
\end{table}

%\clearpage



\section*{The Collaboration}

%The collaboration consists of E02-109 experimenters. 
The collaboration consists primarily of members of the current
E02-109 collaboration.
These 
scientists have participated in a substantial amount of Hall C running.
The collaboration has implemented and proven successful techniques to
reduce systematical uncertainties in Hall C experiments, including
detailed studies of spectrometer optics, spectrometer survey studies,
raster phase analysis, and additional beam line
instrumentation. This collaboration has the on-site experience, knowledge and
expertise requisite to perform a precision measurement of the type proposed.
These experimenters include  spokespersons of the previous JLab
%UPDATE
experiments on which this proposal is founded (E94-110, E02-109 and 
E99-118). 

In addition, this proposal brings a significant number of 
%the 
new collaborators from 
%Rochester and American University
the University of Rochester and University of Massachusetts,
%include 
including
the two spokespersons of SLAC experiment E140 and E140X, and
the Rochester NuTeV neutrino group.  Two potential Rochester 
%PhD
Ph.D.\ 
students are shown as well as Rochester theorists who have expressed
interest in the results.


\section*{Conclusion}

Using the existing Hall C apparatus, JLab experiment
E02-109 has been approved to perform a global
survey of L-T separated unpolarized
structure functions on deuterium throughout the nucleon resonance
region with an order
of magnitude better precision than has been achieved before.  The
recent analysis of the proton data from E94-110
clearly show that these goals are both realistic and attainable.
Furthermore, the analysis machinery previously
developed can be used nearly without modification and should allow
the analysis of the data to proceed in an
accelerated fashion.

Here we propose  another experiment 
%(E02-xxx) 
(E03-110)
that in 
only five days of
additional running
yields a substantial amount of new data with nuclear targets.
These data 
%will launch 
are a key ingredient in a new program 
linking the nuclear and high-energy physics communities
%to  investigate 
in investigating
quark-hadron duality in nuclear
targets using both electron and neutrino beams.

\section*{Appendix A - Radiative Corrections Studies}


%SLAC Experiment
SLAC-E140~\cite{dasu} and SLAC-E139~\cite{E139} have performed tests with 0.02, 0.06 
and 0.12 radiation length targets.  Figure~\ref{radcor.eps}
illustrates that the radiative corrections can be well understood
even for these relatively thick targets using the analysis techniques
of E140.
%below shows that with
%the improved SLAC-E140 radiative corrections, 0.06 radiation length
%targets can be used.   
In this experiment, we add a variety of
target thicknesses to repeat these radiative corrections tests in
the JLab kinematic region.

In addition, in order to obtain more statistics
with Aluminum in E01-109
(using the the Aluminum Empty Target runs), we plan to go back to using
 thick empty targets, 
%as originally
% invented 
a technique pioneered
at SLAC~\cite{radcorbodek}. 
The Aluminum Empty Target
replica is made thicker to match the radiation length of the  0.005
r.l. Deuterium target.   This greatly increases the counting
rate for the empty target replica, as well as making sure that
the radiative corrections for the empty target are indeed the
same as the correction for the full Deuterium target. Therefore,
if this target is used instead, then the 
60 hours allocated for empty target replica by E02-109 can yield 
Aluminum data with about 1/6 of the statistics of the running with
deiterium,

\section*{Appendix B - Practical Issues in Choices of Targets}


A consideration in the choice of targets is the maximum amount
of current that can be delivered without damaging or changing the
density of the target. This experiment as proposed can be done in 5 days
  using standard targets, but we have made some compromises and
  may wish to consider future alternatives, as outlined below.

  At present 0.02, 0.06 and 0.12 r.l. C, Fe and Cu targets already
  exist in Hall C.  The current that the Fe target can withstand depends on the thermal
  contact with the water cooled frame. 
%With a proper job one can
%  allow up to 60 $\mu$A on the Fe targets. In practice, if one does
%  not want to bank on how proper the job of thermal contact is
%  done, a safer limit may be 30-40 $\mu$A.  
  Safe current limits will likely be in a range $30$--$60\mu$A, 
  depending on the our confidence in this thermal contact.
  In contrast, C and Cu can easily withstand 80 $\mu$A,
%, probably 100 $\mu$A is also
%  reasonable
%  (if one uses the proper type of Carbon). 
%   This is why 
and therefore those targets
    were chosen for the high $Q^2$ running.
  
%Since a scintillator target can only withstand 0.5 to 2  $\mu$A, we
%do not propose to use such a target in this experiment. 
The best measurement of cross-sections on water would come from use
 of the Hall A ``waterfall'' target, which consists of
three "free-falling" water
  curtains, each of $250$~mg/cm$^2$
and can probably withstand 
$100$~$\mu$A.  Issues to be investigated with this target include
density variation with current and whether it is practical to add
this target to the Hall C scattering chamber.
% (but one needs
%  to check its density variation vs. current).
%The current Hall A waterfall target consists of  The Hall A version is
%  standalone, i.e. no possibility to combine with other targets.
%  It may be possible to add waterfall target to the Hall C scattering
%  chamber, but it would require some thinking. 
Therefore, this
  kind of target is not part of the proposed run plan, but is
  a subject of investigation.
  
   The  existing Hall C Calcium target may have a current limitation
  of 30 $\mu$A.  We plan to investigate if a new Calcium sandwich target may be
  able to handle higher current.
  



 
\begin{figure}
\begin{center}
\epsfig{figure=radcor.eps,width=20cm,height=14cm,angle=0}
\caption{Radiative Corrections tests from SLAC E140 and E139.}
\label{radcor.eps}
\end{center}
\end{figure}

\section*{Appendix C -Other Data that will be used in our analysis} 

We plan to  use previous low $Q^2$
data in the inelastic region (e.g. Jlab  experiment~\cite{e99118} E99-118), and 
previous data from experiment  E02-109 taken in the quasielatic region~\cite{quasi}
(for radiative corrections).  Other lower precision very  high $Q^2$ data such as SLAC experiment E140 
and E140x will also be included in the overall analysis.


%\vfill
%\pagebreak

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\pagebreak
\end{document}
\bye


