%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%    INSTITUTE OF PHYSICS PUBLISHING                                   %
%                                                                      %
%   `Preparing an article for publication in an Institute of Physics   %
%    Publishing journal using LaTeX'                                   %
%                                                                      %
%    LaTeX source code `ioplau2e.tex' used to generate `author         %
%    guidelines', the documentation explaining and demonstrating use   %
%    of the Institute of Physics Publishing LaTeX preprint files       %
%    `iopart.cls, iopart12.clo and iopart10.clo'.                      %
%                                                                      %
%    `ioplau2e.tex' itself uses LaTeX with `iopart.cls'                %
%                                                                      %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% First we have a character check
%
% ! exclamation mark    " double quote
% # hash                ` opening quote (grave)
% & ampersand           ' closing quote (acute)
% $ dollar              % percent
% ( open parenthesis    ) close paren.
% - hyphen              = equals sign
% | vertical bar        ~ tilde
% @ at sign             _ underscore
% { open curly brace    } close curly
% [ open square         ] close square bracket
% + plus sign           ; semi-colon
% * asterisk            : colon
% < open angle bracket  > close angle
% , comma               . full stop
% ? question mark       / forward slash
% \ backslash           ^ circumflex
%
% ABCDEFGHIJKLMNOPQRSTUVWXYZ
% abcdefghijklmnopqrstuvwxyz
% 1234567890
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\documentclass{iopart}

%
%change this to the following line for use with LaTeX2.09
%
%\documentstyle[twoside,fleqn,espcrc2]{article}

% if you want to include PostScript figures
\usepackage{graphicx}
% if you have landscape tables
\usepackage[figuresright]{rotating}

% put your own definitions here:
%   \newcommand{\cZ}{\cal{Z}}
%
%KL \newtheorem{def}{Definition}[section]
%
%KL \newcommand{\ttbs}{\char'134}
\newcommand{\AmS}{{\protect\the\textfont2 
A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}}

% add words to TeX's hyphenation exception list
\hyphenation{author another created financial paper re-commend-ed Post-Script}

%\pagestyle{empty}
%\setlength {\textwidth}{1.24\textwidth}
%\setlength {\oddsidemargin}{.6\oddsidemargin}
%\setlength {\textheight}{1.2\textheight}
%\begin{document}

%% A useful Journal macro
\def\Journal#1#2#3#4{{#1} {\bf #2}, #3 (#4)}
% Some useful journal names
\def\NCA{\rm Nuovo Cimento}
\def\NIM{\rm Nucl. Instrum. Methods}
\def\NIMA{{\rm Nucl. Instrum. Methods} A}
\def\NPA{{\rm Nucl. Phys.} A}
\def\NPB{{\rm Nucl. Phys.} B}
\def\PLB{{\rm Phys. Lett.}  B}
\def\PRL{\rm Phys. Rev. Lett.}
\def\PR{{\rm Phys. Rev.}}
\def\PRD{{\rm Phys. Rev.} D}
\def\PRC{{\rm Phys. Rev.} C}
\def\ZPA{{\rm Z. Phys.} A}
\def\ZPC{{\rm Z. Phys.} C}
\def\EJP{\rm Eur. Phys. J.}
\def\RMP{\rm Rev. Mod. Phys.}
% Some other macros used in the sample text
\def\st{\scriptstyle}
\def\sst{\scriptscriptstyle}
\def\mco{\multicolumn}
\def\epp{\epsilon^{\prime}}
\def\vep{\varepsilon}
\def\ra{\rightarrow}
\def\ppg{\pi^+\pi^-\gamma}
\def\vp{{\bf p}}
\def\ko{K^0}
\def\kb{\bar{K^0}}
\def\al{\alpha}
\def\ab{\bar{\alpha}}
\def\be{\begin{equation}}
\def\ee{\end{equation}}
\def\bea{\begin{eqnarray}}
\def\eea{\end{eqnarray}}

%..overall commands
\newcommand{\bd}{\begin{displaymath} }
\newcommand{\ed}{\end{displaymath} }
\newcommand{\ttbs}{\char'134}
\newcommand{\nubar}[0]{\overline{\nu}}
\newcommand{\qbar}[0]{\overline{q}}
\newcommand{\numu}[0]{\nu_{\mu}}
\newcommand{\nuebar}[0]{\overline{\nu}_{e}}
\newcommand{\nue}[0]{\nu_{e}}
\newcommand{\numubar}[0]{\overline{\nu}_{\mu}}
\newcommand{\muebar}{(\numu \nuebar)}
\newcommand{\mubare}{(\numubar \nue)}
\newcommand{\Rnu}{R^{\nu}}
\newcommand{\Rnub}{R^{\overline{\nu}}}
\newcommand{\Rmup}{R^{\mu^{+}}}
\newcommand{\Rmum}{R^{\mu^{-}}}
%KL \newcommand{\pt}{{\rm p}_t}

\newcommand{\stw}{\mbox{$\sin^2\theta_W$}}
\newcommand{\nub}{\overline{\nu}}
%\newcommand{\nue}{\nu_{e}}
%\newcommand{\numu}{\nu_{\mu}}
\newcommand{\nubmu}{\overline{\nu_{\mu}}}
\newcommand{\nube}{\overline{\nu_{e}}}
\newcommand{\ubar}{\overline{u}}
\newcommand{\dbar}{\overline{d}}
\newcommand{\cbar}{\overline{c}}
\newcommand{\sbar}{\overline{s}}
\newcommand{\alps}{\mbox{$\alpha_s$}}
\newcommand{\asop}{\mbox{$\frac{\alpha_s}{\pi}$}}
\newcommand{\qsq}{\mbox{$Q^2$}}
\newcommand{\qnsq}{\mbox{$Q_0^2$}}
\newcommand{\mztwo}{\mbox{$M_Z^2$}}
\newcommand{\lmsb}{\mbox{$\Lambda_{\overline{MS}}$}}
\newcommand{\rmt}{\rm\textstyle}
\newcommand{\rms}{\rm\scriptstyle}

\begin{document}

% declarations for front matter
\title{A Fine-grained Detector to Study Nuclear Effects in a NuMI Neutrino 
Scattering Experiment}

\author{Jorge G. Morf\'{\i}n}

\address{Fermi National Accelerator Laboratory,\\P.O. Box 500, Batavia,
IL,\\60510}

%KL \begin{document}

\begin{abstract}
The NuMI Facility at Fermilab will provide an extremely intense beam of
neutrinos making it the ideal location for high statistics
(anti)neutrino-nucleon/nucleus experiments.  With such intensities, a
fine-grained, solid scintillator detector becomes practical.  The ability
of such a detector to examine so-far unstudied nuclear effects in neutrino
scattering will be addressed.  Recent theoretical work suggests that such
effects will be considerably different than those measured with electron
and muon beams.
\vspace{1pc}
\end{abstract}

% typeset front matter (including abstract)
% \maketitle



%\end{center}
%\newpage

\section{Introduction}

The upcoming neutrino oscillation experiments around the world are driving
the construction of new, very-intense neutrino beamlines. These new
beamlines will allow us to continue a very active research program at a
detector, located close to the production target, where event rates are
much higher than at the previous generation of neutrino beam facilities.

At Fermilab, the new neutrino facility NuMI, designed for the MINOS neutrino
oscillation experiment, will be based on the Main Injector (MI) accelerator.
The neutrino beams from the MI yield several
orders of magnitude more events per kg-year of detector than earlier
neutrino beams.  

\section{The Fermilab NuMI Facility}

The Fermilab NuMI facility is made up of the technical beamline components
including target, two magnetic focusing horns, evacuated decay pipe,
monitoring devices, shielding...., the underground facilities to contain
the beamline components and a large, on-site experimental detector hall
$\sim$ 100 meters underground.  

\subsection{The NuMI Near Experimental Hall}
The upstream end of the near detector hall is just over 1 km
downstream of the target. This experimental hall is being constructed and
completely outfitted for the MINOS near detector.  The hall is 45 m long,
9.5 m wide and  9.6m high.  There is a space upstream of the MINOS near
detector amounting to, roughly, a cylinder 26 m long and 3m in radius for
additional detector(s) which, were it desired, could use the MINOS near
detector as an external muon identifier and spectrometer.

\subsection{The NuMI Neutrino Beam}

The neutrino energy distribution of the NuMI beam can be chosen by changing
the distance of the target and second horn with respect to the first horn,
as in a zoom lens. There are three standard configurations foreseen for the
target and second horn called simply low-energy (le), medium-energy (me) and
high-energy (he). The neutrino energy distributions are shown in
Figure 1. It is now expected that the Main Injector will deliver
2.5x$10^{20}$ POT/year at the start of MINOS running, and build up to
3.8x$10^{20}$ POT/year after the first several years of running if the
necessary funds can be obtained.  The CC event rates per ton (of detector)
- year at startup of MINOS in 2005 will be le - 200 K, me - 675 K and he -
1575 K.  The reader should be aware that there is a potential increase of
{\bf 50\%} when the MI reaches the goal of 3.8x$10^{20}$ POT/year.

\begin{figure}
\label{fig:lemehe}
  \begin{center}

%    \includegraphics[angle=-90,width=3.0in]{v14_all_lemehe.epsi}
    \includegraphics[width=3.0in]{v14_all_lemehe.epsi}

    \caption{The neutrino event energy distribution for the three 
     configurations of the NuMI beam corresponding to low-energy (le),
     medium-energy (me) and high-energy (he)}

  \end{center}
\end{figure}

For the MINOS experiment the beamline will be operating mainly in its
lowest possible neutrino energy configuration to be able to reach desired
low values of $\delta m^2$.  However, to minimize systematics, there will
also be running in the pseudo-me and pseudo-he modes (obtaind by simply
varying the distance of target from the first horn and leaving the second
horn fixed in the le position). For the approved MINOS run the total CC
event rate would be 860 K/ton. Of this rate, 140 K/ton would be
quasi-elastic, 360 K/ton would be resonance/transition events and 360 K/ton
would be deep-inelastic (DIS) with W $\geq$ 2 GeV and Q$^2$ $\geq$ 1.0
GeV$^2$.

For a NuMI neutrino scattering experiment as prime user of the NuMI beam,
the beamline would be run in the high-energy configuration  A NuMI Neutrino
Scattering Experiment, for example, running with the he-beam for a 1 year
$\nu$ and a 2 years $\nubar$ period would accumulate 1575 K CC $\nu$
events/ton and 0.9 M CC $\nubar$ events/ton. Of these 0.9 M CC $\nu$
events/ton and 0.35 M CC $\nubar$ events/ton would be DIS.

The event rates for various scenarios are summarized in the following table 
giving events/ton-year where a "year" is defined as 2.5x$10^{20}$ POT.

\vspace{0.5 cm}
\begin{center}
\begin{tabular}{@{}llll} 
\hline
\multicolumn{4}{c}{Event Rates per ton of detector} \\ \hline \\
Run Period & Total CC  & Elastic & DIS \\ \cline{1-4}
MINOS: 3yr & 860 K & 140 K & 360 K \\
he-$\nu$: 1yr & 1575 K & 200 K & 900 K \\ 
he-$\nubar$: 2yr & 900 K & 60 K  & 350 K \\ \cline{1-4}
\end{tabular}
\end{center}

\section{Neutrino Scattering Physics}

A neutrino scattering experiment in the NuMI Near Experimental Hall will 
offer a unique opportunity to study a diverse array of physics topics.  
Most of these topics have either never been studied or the few results that
do exist are plagued by large statistical and systematic errors. In
addition to being significant fields of study in their own right, many of
these topics are essential to help minimize the systematics of neutrino
oscillation experiments.

\begin{itemize}
\item quasi-elastic neutrino scattering and associated form-factors
\item the poorly studied resonance production region
\item the intriguing region where resonance production joins deeply
inelastic scattering
\item parton distribution functions (pdf), particularly in the high-$x_{Bj}$ 
region
\item leading exponential contributions of pQCD
\item $\stw$ via the ratio of NC / CC as well as d$\sigma$/dy from $\nu$ -
electron scattering to check the recent surprising NuTeV result 
\cite{Zeller:2001hh}
\item charm physics including the mass of the charm quark ($m_c$) to an 
order of magnitude better accuracy than current values, $V_{cd}$, s(x) and, 
independently, $\sbar$(x)
\item {\bf nuclear effects involving neutrinos. In particular are nuclear
effects the same for valence and sea quarks? Are they different for $u_v$ 
as compared to $d_v$?}
\item strange particle production for $V_{us}$, flavor-changing neutral 
currents and measurements of hyperon polarization
\item contribution of the spin of the strange quark through $\nu$ elastic
scattering. This measurement is far more accurate and needs many fewer
assumptions than charged lepton results for $\Delta$s.
\item nuclear physics studies with neutrinos (complementary to JLab studies 
in the same kinematic range)
\end{itemize}

For this paper, the subject of nuclear effects will be addressed in more 
detail.

\subsection{Studying Nuclear Effects with Neutrinos}

  Nuclear effects in DIS have been studied extensively using muon and
electron beams but have only been glanced at for neutrinos in
low-statistics bubble chamber experiments. A neutrino scattering program at
NuMI would provide experimental conditions where a systematic, precision
study of this field would be possible by using a variety of heavy nuclear
targets as well as $H_{2}$ and $D_{2}$ targets.  Briefly reviewing these
nuclear effects as a function of $x_{Bj}$ we find:

\subsubsection{Low x: Nuclear Shadowing}

  In the shadowing region, $x<0.1$, there are several effects where a
neutrino probe could provide different insights compared  to charged lepton
probes. "Shadowing" is a phenomena which occurs with nuclear targets and 
is characterized by the cross section per nucleon being less for larger A 
nuclei, such as Fe, than for smaller A nuclei such as D$_2$. See 
\cite{Frankfurt:2002kd} for a recent summary of theoretical ideas on 
this topic.

Vector meson dominance (VMD) is the accepted explanation for shadowing in
the scattering of charged leptons off nuclei (i.e. $\mu/e - A$) for $Q^{2}$
roughly $\leq$ 5 $GeV^{2}$. In essence, the incoming boson dissociates into
a q-$\qbar$ pair which interacts with the nucleus as a meson.  Due to the
V-A nature of the weak interaction, it is predicted that neutrino
scattering should involve not only a VMD effect but also additional
contributions from axial-vector mesons such as the $A_{1}$. Other sources
of nuclear shadowing (mainly in larger nuclei) involve gluon recombination
from nucleons neighboring the struck nucleon that shift the parton
distributions towards higher values of $x$.  At higher $\qsq$, shadowing is 
dominated by Pomeron exchange in diffractive scattering.  

A quantitative analysis by Kulagin~\cite{Kulagin} of shadowing effects in
neutrino interactions predicts shadowing effects in $\nu$ - A scattering. 
As seen in Figure 2, which gives predictions of the ratio of scattering off
Fe to scattering off D$_2$, shadowing effects with neutrinos are expected
to be dramatically large at low $\qsq$ (the kinematic region of the NuMI
neutrino beam) and still significant at large $\qsq$.  Kulagin also
attempts to determine the quark flavor dependence of shadowing effects by
separately predicting the shadowing observed in $F_{2}(x,Q^{2})$ (sum of
all quarks) and $xF_{3}(x,Q^{2})$ (valance quarks only). These predictions
of Kulagin would be testable with the NuMI beam.

\begin{figure}
\label{fig:Kulagin}
  \begin{center}

%    \includegraphics[angle=-90,width=3.0in]{v14_all_sum2cycl.epsi}
    \includegraphics[width=3.0in]{fe2n_small_x.eps}

    \caption{Expected shadowing effects off an Fe target at $Q^{2}$ = 0.7
        GeV$^2$ with Kulagin's non-perturbative parton model.  The arrows
	in the vicinity of R = 	0.8 indicate the expected shadowing strength 
	at $Q^{2}$ = 15.0 GeV$^2$}

  \end{center}
\end{figure}

\subsubsection{Mid x: Anti-shadowing and the EMC Effect}

 Drell-Yan experiments have also measured nuclear effects and their results
are quite similar to DIS experiments in the shadowing region.  However, in
the anti-shadowing region where $R_{A}$, the ratio of scattering off a
nucleus A to scattering off of deuterium,  makes a statistically
significant excursion above 1.0 in DIS, Drell-Yan experiments see no
effect.  This could be an indication of differences in nuclear effects
between valence and sea quarks as also predicted by Kulagin.

  Eskola et al.~\cite{Eskola} has quantified this difference using a model
which predicts that the differences between nuclear effects in
$xF_{3}(x,Q^{2})$ and $F_{2}(x,Q^{2})$, quantified by Kulagin in the
shadowing region, should persist through the anti-shadowing region as well.
More recent work by Kumano~\cite{Kumano} supports these findings using 
different fitting techniques.

  Based on the various theoretical explanations for the anti-shadowing and 
EMC effects existing today, the measured effects could be considerably 
different for neutrinos.  Neutrino scattering results would help the 
theoretical understanding of these phenomena.

\subsubsection{High x: Multi-quark Cluster Effects}

  Analyses from DIS experiments of $F_{2}(x,Q^{2})$ in the "Fermi-motion"
region, $x \geq 0.7$, have used few-nucleon-correlation models and
multi-quark cluster models in order to fit the data. These models boost the
momentum of some quarks, which translates into a high-$x$ tail in
$F_{2}(x,Q^{2})$ that is predicted to behave as $e^{-ax}$. However, fits to
$\mu - C$~\cite{Benvenuti:1994bb} and $\nu - Fe$~\cite{Vakili:1999qt} have
obtained two different values for the fitted constant $a$: $a = 16.5 \pm
0.5$ and $a = 8.3 \pm 0.7 \pm 0.7$ (systematic), respectively. This is
considered surprising because of the expectation that any
few-nucleon-correlation or multi-quark effects would have already saturated
by carbon.   A high statistics data sample, off several nuclear targets,
with precise kinematic reconstruction of the Bjorken $x$ values for each
event, could go a long way towards resolving the dependence of the value of
$a$ on the nucleus and on the lepton probe.

\section{A Staged Detector Concept}

        The detector studies for a dedicated NuMI $\nu$ scattering experiment
are at a very early stage. In order to perform the full spectrum of physics
outlined in this paper, the target and detector must eventually be able to:

\begin{itemize}
\item  identify muons and measure their momentum with high precision
\item  identify and measure the energy of protons
\item  achieve a high level of rejection against tracks which fake
        neutral current scattering, such as neutron scattering events
\item  measure the energy of both the hadronic and electromagnetic shower 
	with reasonable precision
\item  accommodate other nuclear targets.
\item  incorporate particle identification for complete reconstruction of 
	final states
\end{itemize}

These goals can be readily met in a staged approach to detector development 
and installation.  Both for running in a parasitic mode with the MINOS 
experiment and for an initial he-configuration $\nu$ exposure, the physics
goals can be met by a comparatively simple active
target/detector~\cite{roypaul} consisting essentially of solid scintillator
interspersed with occasional planes of variable A target.  The detector
would have the approximate overall dimensions of a cube 2.0 m on a side. 
Significant granularity could be achieved by the use of 2.0 m long by 2 cm
x 2 cm strips of plastic scintillator(CH) with a fiber down the center of
the strip for readout. Recent work at the Fermilab Scintillator R\&D
Facility has shown that using light division across triangularly shaped
scintillator strips of this size can yield measuring precisions of a few
mm.  The orientation of the scintillator strips are alternated so that
tracking can be performed.  The detector overall mass would be around 8 metric
tons with somewhat over 3 tons of scintillator in a fiducial volume defined
as r $\leq$ 0.8m and 150 cm long.  Readout would be performed with VLPC 
technology most recently developed at Fermilab for the D0 experiment.

The downstream end of this detector would be placed as close as possible to
the upstream face of the MINOS near detector in order to use the magnetic
field and steel of the MINOS near detector as a muon identifyer and
spectrometer for the energetic forward going muons.  Side muon
ID/spectrometers (EMI) consisting of several planes of scintillator
interspersed with permanent magnet steel planes would be installed
surrounding the four sides of the detector to increase acceptance of the
low energy muons and measure the hadronic energy leaving the sides of the
central detector.

With such a detector, for the initial energy-dependent MINOS run given
earlier, two such cycles (32 months running) would result in {\bf 2.6 M
events} in the fiducial volume of the scintillator while for a 1 year
he-configuration $\nu$ run, the corresponding statistics would be {\bf 4.9 M
events}.

\subsection{Measuring Nuclear Effects}
For the study of nuclear effects a selection of nuclear targets would be
installed within the scintillator based detector.  As an example, 1 ton of
C, Fe and Pb were included in the simulation as eleven planes of pure C,
three planes of Fe and 2 planes of Pb.  The following table summarizes the
event rates during the initial MINOS run and a subsequent he $\nu$ run for
the scintillator plus nuclear target detector concept described here:

\vspace{0.5 cm}
\begin{center}
\begin{tabular}{@{}lll}
\hline
\multicolumn{3}{c}{CC Event Rates} \\ \hline \\
Target & MINOS 2-cycle & 1 year he $\nu$ \\ \cline{1-3}
CH & 2.6 M & 4.9 M \\
C & 860 K & 1575 K \\
Fe & 860 K & 1575 K \\
Pb & 860 K & 1575 K\\ \cline{1-3}
\end{tabular}
\end{center}
\vspace{0.5 cm}

Somewhat over 20\% of the above event rates have $x_{Bj}$ $\leq$ 0.10 for 
studies of shadowing.  The (approximate) statistical accuracy for
measurements of the nuclear effects in the ratios of Fe to C events at
small x (shadowing region) are summarized in the following table. The
columns designated DIS implies that a cut has been made to keep only events
with W $\geq$ 2.0 and Q$^2$ $\geq$ 1.0.  For the MINOS DIS analysis, the
first three bins could be combined into two bins to reduce the statistical
errors.

\vspace{0.5 cm}
\begin{center}
\begin{tabular}{@{}lllll}
\hline
\multicolumn{5}{c}{Ratio Fe/C: $\sim$ Statistical Errors} \\ \hline \\
x$_{Bj}$ & MINOS   & MINOS  & he $\nu$ & he $\nu$ \\
         & 2-cycle &  DIS   & 1 year  & DIS \\ \cline{1-5}
0.0 - .01 & 1.8 \%& xxx   & 1.3 \%    & xxx \\
.01 - .02 & 1.4   & 10 \% & 1.0       & 9 \% \\
.02 - .03 & 1.3   & 6     & 1.0       & 5   \\
.03 - .04 & 1.2   & 4     & $\leq$ 1  & 3.2   \\
.04 - .05 & 1.1   & 3     & $\leq$ 1  & 2.1   \\
.05 - .06 & 1.1   & 2.6   & $\leq$ 1  & 1.7   \\
.06 - .07 & 1.0   & 2.3   & $\leq$ 1  & 1.4   \\ \cline{1-5}
\end{tabular}
\end{center}
\vspace{0.5 cm}

Assuming the magnitude of shadowing as predicted by Kulagin, the measured
ratio of Fe/C, with statistical errors corresponding to the data
accumulated during the MINOS run, would be as in Figure 3.  The ratios
plotted are for all events.  The statistical errors would increase as
indicated in the above table when making a DIS cut.

\begin{figure}
\label{fig:Kulagin-MINOS}
  \begin{center}

%    \includegraphics[angle=-90,width=3.0in]{v14_all_sum2cycl.epsi}
    \includegraphics[width=3.0in]{Kulagin-MINOSpar.eps}

    \caption{Kulagin's predicted ratio of shadowing effects off Fe and C
     targets with the expected errors from all events from the MINOS run}

  \end{center}
\end{figure}

The statistics from the first 3-year MINOS run would be adequate to perform
many of the physics topics listed in this paper although some would be limited
by the kinematic reach of the neutrino beam energies used for MINOS
running.  In addition, all studies involving $\nubar$ statistics would be 
impossible with only the approved MINOS ($\nu$) exposure.  To realize the
{\bf full potential} of the NuMI facility for a $\nu$ scattering
experiment, the impressive statistics and kinematic reach of a he-beam
$\nu$ and $\nubar$ runs would be required.

In a subsequent stage it would also be most beneficial, for all physics
topics of interest, to have a low-A target, preferably $H_2$ or $D_2$. An
investigation of the technical and safety challenges of such a target is
currently underway at Fermilab and a recent report indicates that there are
no real technical challenges in fabricating or efficiently operating a
large L$H_2$ or L$D_2$ target.  The main effort (and expense) for such a
facility would be in satisfying safety requirements. For a fiducial volume
with r = 80 cm. and l = 150 cm. we would expect 350 K CC events in L$H_2$
and 800 K CC events in L$D_2$ per year of he-$\nu$ running.  With such
samples of L$H_2$ and/or L$D_2$, the statistical errors in shadowing
studies would be:

\vspace{0.5 cm}
\begin{center}
\begin{tabular}{@{}lll}
\hline
\multicolumn{3}{c}{Ratios(he, 1 year, DIS): $\sim$ Stat. Errors} \\ \hline \\
x$_{Bj}$ & Fe/C & Fe/L$D_2$    \\ \cline{1-3}
.01 - .02 & 9 \%   & 11 \%  \\
.02 - .03 & 5      &  6     \\
.03 - .04 & 3      &  4    \\
.04 - .05 & 2      &  3    \\
.05 - .06 & 1.7    &  2    \\
.06 - .07 & 1.4    &  1.7  \\ \cline{1-3}
\end{tabular}
\end{center}
\vspace{0.5 cm}

This large sample of events would allow extraction of the nuclear effects
on the individual structure functions $F_2$ and $xF_3$ via the ratios of Pb
and Fe to $D_2$.  

\vspace{0.5 cm}
\large {\bf REFERENCES}

\begin{thebibliography}{99}

%\cite{Zeller:2001hh}
\bibitem{Zeller:2001hh}
G.~P.~Zeller {\it et al.}  [NuTeV Collaboration],
%``A precise determination of electroweak parameters in neutrino nucleon  
%scattering,''
Phys.\ Rev.\ Lett.\  {\bf 88}, 091802 (2002)
[arXiv:hep-ex/0110059].


%\cite{Frankfurt:2002kd}
\bibitem{Frankfurt:2002kd}
L.~Frankfurt, V.~Guzey, M.~McDermott and M.~Strikman,
%``Nuclear shadowing in deep inelastic scattering on nuclei: Leading twist  
%versus eikonal approaches,''
JHEP {\bf 0202}, 027 (2002)
[arXiv:hep-ph/0201230].
%%CITATION = HEP-PH 0201230;%%

\bibitem{Adler}
S.~L.~Adler,
``Sum Rules Giving Tests Of Local Current Commutation Relations In
High-Energy
Neutrino Reactions,''
Phys.\ Rev.\ 143, 1144 (1966).
%%CITATION = PHRVA,143,1144;%%

\bibitem{Kulagin}
S.~A.~Kulagin,
``Nuclear shadowing in neutrino deep inelastic scattering,''
hep-ph/9812532.
%%CITATION = HEP-PH 9812532;%%

%\bibitem{hermes}
%K.~Ackerstaff et al. [HERMES Collaboration],
%``Nuclear effects on R = sigma(L)/sigma(T) in deep inelastic scattering,''
%Phys.\ Lett.\ B {\bf 475}, 386 (2000). e-print Archive: hep-ex/9910071.

\bibitem{Eskola}
K.~J.~Eskola, V.~J.~Kolhinen, P.~V.~Ruuskanen and C.~A.~Salgado,
``Nuclear parton distributions: A DGLAP analysis,''
Nucl.\ Phys.\ {\bf A661}, 645 (1999)
e-Print Archive: hep-ph/9906484.
%%CITATION = HEP-PH 9906484;%%

%\cite{Kumano:2001dk}
\bibitem{Kumano}
S.~Kumano,
``Determination of parton distribution functions in nuclei,''
arXiv:hep-ph/0109152.
%%CITATION = HEP-PH 0109152;%%

\bibitem{Benvenuti:1994bb}
A.~C.~Benvenuti {\it et al.}  [BCDMS Collaboration],
%``Nuclear structure function in carbon near x = 1,''
Z.\ Phys.\ C {\bf 63}, 29 (1994).

\bibitem{Vakili:1999qt}
M.~Vakili {\it et al.}  [CCFR Collaboration],
%``Nuclear structure functions in the large x large Q**2 kinematic region  
%in neutrino deep inelastic scattering,''
Phys.\ Rev.\ D {\bf 61}, 052003 (2000)
[arXiv:hep-ex/9905052].

\bibitem{roypaul}
The original design of this "pure scintillator" detector resulted from a 
study for physics at Fermilab with a new high-intensity booster.  J. 
Arrington, R. Holt, D. Potterveld and P. Reimer from Argonne National 
laboratory, along with the author, were involved in the original concept of 
this detector. 

\end{thebibliography}

\end{document}

