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\voffset 1cm
\preprint{JLAB-THY-11-...}

\usepackage{amsmath}
\usepackage{bm}
\usepackage{graphicx}
\usepackage{color}

\newcommand{\ee}{\ifmmode (e,e^{\prime}) \else $(e,e^{\prime})$\fi}
\newcommand{\eep}{\ifmmode (e,e^{\prime}p) \else $(e,e^{\prime}p)$\fi}
\newcommand{\eepp}{\ifmmode (e,e^{\prime}pp) \else $(e,e^{\prime}pp)$\fi}
\newcommand{\eepn}{\ifmmode (e,e^{\prime}pn) \else $(e,e^{\prime}pn)$\fi}
\newcommand{\eepN}{\ifmmode (e,e^{\prime}pN) \else $(e,e^{\prime}pN)$\fi}
\newcommand{\pppn}{\ifmmode (p,2pn) \else $(p,2pn)$\fi}
\newcommand{\ppp}{\ifmmode (p,2p) \else $(p,2p)$\fi}
\newcommand{\heeepN}{\ifmmode {{}^4\textrm{He}(e,e^{\prime}pN)}
    \else ${}^4\textrm{He}(e,e^{\prime}pN)$\fi}
\newcommand{\gevcsq}{\ifmmode {(\textrm{GeV}/c)^2} \else $(\textrm{GeV}/c)^2$\fi}
\newcommand{\gevc}{\ifmmode {\textrm{GeV}/c} \else $\textrm{GeV}/c$\fi}
\newcommand{\mevc}{\ifmmode {\textrm{MeV}/c} \else $\textrm{MeV}/c$\fi}
\newcommand{\hefour}{\ifmmode {{}^4\textrm{He}} \else ${}^4\textrm{He}$\fi}
\newcommand{\ctwelve}{\ifmmode {{}^{12}\textrm{C}} \else ${}^{12}\textrm{C}$\fi}
\begin{document}




\title{Approaching the Nucleon-Nucleon short-range repulsive core \\ via the {\heeepN} triple-coincidence reaction.}


\newcommand*{\JLAB}{Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606}
\newcommand*{\TLV}{Tel Aviv University, Tel Aviv 69978, Israel}
\newcommand*{\MIT}{Massachusetts Institute of Technology, Cambridge, MA 02139}
\newcommand*{\KENT}{Kent State University, Kent, OH 44242}
\newcommand*{\DOMINION}{Old Dominion University, Norfolk, VA 23529}
\newcommand*{\CALIF}{California State University, Los Angeles, Los Angeles, CA 90032}
\newcommand*{\HAMPTON}{Hampton University, Hampton, VA 23668}
\newcommand*{\PENNSYLVANIA}{Pennsylvania State University, State College, PA 16801}
%\newcommand*{\Paris}{University Paris-Sud, Orsay, France}
\newcommand*{\Paris}{Institut de Physique Nucl\'{e}aire (UMR 8608), CNRS/IN2P3 - Universit\'e Paris-Sud, F-91406 Orsay Cedex, France}
\newcommand*{\Syracuse}{Syracuse University, Syracuse, NY 13244}
\newcommand*{\Kentucky}{University of Kentucky, Lexington, KY 40506}
\newcommand*{\William}{College of William and Mary, Williamsburg, VA 23187}
\newcommand*{\Virginia}{University of Virginia, Charlottesville, VA 22904}
\newcommand*{\Halifax}{Saint Mary's University, Halifax, Nova Scotia, Canada}
\newcommand*{\Glasgow}{University of Glasgow, Glasgow G12 8QQ, Scotland, United Kingdom}
\newcommand*{\Temple}{Temple University, Philadelphia, PA 19122}
\newcommand*{\Argonne}{Physics Division, Argonne National Laboratory, Argonne, IL 60439}
\newcommand*{\China}{China Institute of Atomic Energy,Beijing, China}
\newcommand*{\NRCN}{Nuclear Research Center Negev, Beer-Sheva, Israel}
\newcommand*{\Catania}{Universita di Catania, Catania, Italy}
\newcommand*{\Pittsburgh}{Carnegie Mellon University, Pittsburgh, PA 15213}
%\newcommand*{\Longwood}{Longwood College, Farmville, VA}
\newcommand*{\LongwoodUniv}{Longwood University, Farmville, VA 23909}
\newcommand*{\Florida}{Florida International University, Miami, FL 33199}
\newcommand*{\Tallahassee}{Florida State University, Tallahassee, FL 32306}
%\newcommand*{\INFN}{INFN, Sezione di Roma, I-00161 Rome, Italy}
\newcommand*{\INFN}{INFN, Sezione Sanit\`{a} and Istituto Superiore di Sanit\`{a}, 00161 Rome, Italy}
\newcommand*{\INFNBari}{INFN, Sezione di Bari and University of Bari, I-70126 Bari, Italy}
\newcommand*{\Ohio}{Ohio University, Athens, OH 45701}
\newcommand*{\Tennessee}{University of Tennessee, Knoxville, TN}
\newcommand*{\Kharkov}{Kharkov Institute of Physics and Technology, Kharkov 61108, Ukraine}
\newcommand*{\LOSALAMOS}{Los Alamos National Laboratory, Los Alamos, NM 87545}
\newcommand*{\Duke}{Duke University, Durham, NC 27708}
\newcommand*{\Texas}{Unversity of Texas, Houston, TX 77030}
\newcommand*{\Seoul}{Seoul National University, Seoul, Korea}
\newcommand*{\Indiana}{Indiana University, Bloomington, IN 47405}
\newcommand*{\Hampshire}{University of New Hampshire, Durham, NH 03824}
\newcommand*{\Blacksburg}{Virginia Polytechnic Inst. and State Univ., Blacksburg, VA}
\newcommand*{\France}{Universit\'e Blaise Pascal/IN2P3, F-63177 Aubi\`ere, France}
\newcommand*{\Mississippi}{Mississippi State University, Miss. State, MS}
\newcommand*{\Austin}{The University of Texas at Austin, Austin, Texas 78712}
\newcommand*{\Norfolk}{Norfolk State University, VA 23504}
\newcommand*{\Lanzhou}{Lanzhou University, Lanzhou, China}
\newcommand*{\Hebrew}{Racah Institute of Physics Hebrew University of Jerusalem, Israel}
\newcommand*{\Rutgers}{Rutgers, The State University of New Jersey, Piscataway, NJ 08855}
\newcommand*{\Yerevan}{Yerevan Physics Institute, Yerevan 375036, Armenia}
\newcommand*{\Ljubljana}{Univ. of Ljubljana, Ljubljana, Slovenia}
\newcommand*{\Michigan}{Northern Michigan University}
\newcommand*{\Hefei}{University of Science and Technology, Hefei, China}	
\newcommand*{\Jozef}{Jozef Stefan Institute, Ljubljana, Slovenia}
\newcommand*{\Ecole}{CEA Saclay, F-91191 Gif-sur-Yvette, France}
\newcommand*{\Massachusetts}{University of Massachusetts, Amherst, MA, 01006, USA}

\title{Approaching the Nucleon-Nucleon short-range repulsive core \\ via the {\heeepN} triple-coincidence reaction.}

\author{I. Korover}
\affiliation{\TLV}
\author{N. Muangma}
\affiliation{\MIT}
\author{O. Hen}
\affiliation{\TLV}
\author{R. Shneor}
\affiliation{\TLV}
\author{V. Sulkosky}
\affiliation{\MIT}
\affiliation{\LongwoodUniv}
\author{A. Kelleher}
\affiliation{\MIT}
\author{S. Gilad}
\affiliation{\MIT}
\author{D. Higinbotham}
\affiliation{\JLAB}
\author{E. Piasetzky}
\affiliation{\TLV}
\author{J. Watson}
\affiliation{\KENT}
\author{S. Wood}
\affiliation{\JLAB}


\author{Abdurahim Rakhman}
\affiliation{\Syracuse}
\author{P. Aguilera}
\affiliation{\Paris}
\author{Z. Ahmed}
\affiliation{\Syracuse}
\author{H. Albataineh}
\affiliation{\DOMINION}
\author{K. Allada}
\affiliation{\Kentucky}
\author{B. Anderson}
\affiliation{\KENT}
\author{D. Anez}
\affiliation{\Halifax}	
\author{K. Aniol}
\affiliation{\CALIF}
\author{J. Annand}
\affiliation{\Glasgow}
\author{W. Armstrong}
\affiliation{\Temple}	
\author{J. Arrington}
\affiliation{\Argonne}
\author{T. Averett}
\affiliation{\William}
\author{T. Badman}
\affiliation{\William}
\author{H. Baghdasaryan}
\affiliation{\Virginia}
\author{X. Bai}
\affiliation{\China}
\author{A. Beck}
\affiliation{\NRCN}	
\author{S. Beck}
\affiliation{\NRCN}	
\author{V. Bellini}
\affiliation{\Catania}
\author{F. Benmokhtar}
\affiliation{\Pittsburgh}
\author{W. Bertozzi}
\affiliation{\MIT}
\author{J. Bittner}
\affiliation{\LongwoodUniv}	
\author{W. Boeglin}
\affiliation{\Florida}
\author{A. Camsonne}
\affiliation{\JLAB}
\author{C. Chen}
\affiliation{\HAMPTON}
\author{J. Chen}
\affiliation{\JLAB}
\author{K. Chirapatpimol}
\affiliation{\Virginia}
\author{E. Cisbani}
\affiliation{\INFN}
\author{M. Dalton}
\affiliation{\Virginia}
\author{A. Daniel}
\affiliation{\Ohio}
\author{D. Day}
\affiliation{\Virginia}
\author{C.W. de Jager}
\affiliation{\JLAB}
\affiliation{\Virginia}
\author{R. De Leo}
\affiliation{\INFNBari}
\author{W. Deconinck}
\affiliation{\MIT}
\author{M. Defurne}
\affiliation{\Ecole}	
\author{D. Flay}
\affiliation{\Temple}
\author{N. Fomin}
\affiliation{\Tennessee}
\author{M. Friend}
\affiliation{\Pittsburgh}
\author{S. Frullani}
\affiliation{\INFN}
\author{E. Fuchey}
\affiliation{\Temple}
\author{F. Garibaldi}
\affiliation{\INFN}
\author{D. Gaskell}
\affiliation{\JLAB}
\author{R. Gilman}
\affiliation{\Rutgers}
\affiliation{\JLAB}
\author{O. Glamazdin}
\affiliation{\Kharkov}
\author{C. Gu}
\affiliation{\LOSALAMOS}
\author{P. Gueye}
\affiliation{\HAMPTON}
\author{D. Hamilton}
\affiliation{\Glasgow}
\author{C. Hanretty}
\affiliation{\Tallahassee}
\author{O. Hansen}
\affiliation{\JLAB}
\author{M. Hashemi Shabestari}
\affiliation{\Virginia}
\author{T. Holmstrom}
\affiliation{\LongwoodUniv}
\author{M. Huang}
\affiliation{\Duke}
\author{S. Iqbal}
\affiliation{\CALIF}
\author{G. Jin}
\affiliation{\Virginia}
\author{N. Kalantarians}
\affiliation{\Texas}
\author{H. Kang}
\affiliation{\Seoul}
\author{M. Khandaker}
\author{J. LeRose}
\affiliation{\JLAB}
\author{J. Leckey}
\affiliation{\Indiana}	
\author{R. Lindgren}
\affiliation{\Virginia}
\author{E. Long}
\affiliation{\Hampshire}
\author{J. Mammei}
\affiliation{\Blacksburg}
\author{D. J. Margaziotis}
\affiliation{\CALIF}
\author{P. Markowitz}
\affiliation{\Florida}
\author{A. Marti Jimenez-Arguello}
\affiliation{\France}
\author{D. Meekins}
\affiliation{\JLAB}
\author{Z. Meziani}
\affiliation{\Temple}
\author{R. Michaels}
\affiliation{\JLAB}
\author{M. Mihovilovic}
\affiliation{\Jozef}
\author{P. Monaghan}
\affiliation{\MIT}
\affiliation{\HAMPTON}
\author{C. Munoz Camacho}
\affiliation{\France}
\author{B. Norum}
\affiliation{\Virginia}
\author{Nuruzzaman}
\affiliation{\Mississippi}
\author{K. Pan}
\affiliation{\MIT}
\author{S. Phillips}
\affiliation{\Hampshire}
\author{I. Pomerantz}
\affiliation{\TLV}
\affiliation{\Austin}
\author{M. Posik}
\affiliation{\Temple}
\author{V. Punjabi}
\affiliation{\Norfolk}	
\author{X. Qian}
\affiliation{\Duke}	
\author{Y. Qiang}
\affiliation{\Duke}
\author{X. Qiu}
\affiliation{\Lanzhou}
\author{P.E. Reimer}
\affiliation{\Argonne}
\author{S. Riordan}
\affiliation{\Virginia}
\affiliation{\Massachusetts}
\author{G. Ron}
\affiliation{\Hebrew}
\author{O. Rondon-Aramayo}
\author{A. Saha}
\altaffiliation{deceased}
\affiliation{\JLAB}
\author{E. Schulte}
\affiliation{\Rutgers}
\author{L. Selvy}
\affiliation{\KENT}
\author{A. Shahinyan}
\affiliation{\Yerevan}
\author{S. Sirca}
\affiliation{\Ljubljana}
\author{J. Sjoegren}
\affiliation{\Glasgow}
\author{K. Slifer}
\affiliation{\Hampshire}
\author{P. Solvignon}
\affiliation{\JLAB}
\author{N. Sparveris}
\affiliation{\Temple}	
\author{R. Subedi}
\affiliation{\Virginia}
\author{W. Tireman}
\affiliation{\Michigan}	
\author{D. Wang}
\affiliation{\Virginia}
\author{L. B. Weinstein}
\affiliation{\DOMINION}
\author{B. Wojtsekhowski}
\affiliation{\JLAB}
\author{W. Yan}
\affiliation{\Hefei}	
\author{I. Yaron}
\affiliation{\TLV}
\author{Z. Ye}
\affiliation{\Virginia}
\author{X. Zhan}
\affiliation{\MIT}
\author{J. Zhang}
\affiliation{\JLAB}
\author{Y. Zhang}
\affiliation{\Rutgers}
\author{B. Zhao}
\affiliation{\William}
\author{Z. Zhao}
\affiliation{\Virginia}
\author{X. Zheng}
\affiliation{\Virginia}
\author{P. Zhu}
\affiliation{\Hefei}
\author{R. Zielinski}
\affiliation{\Hampshire}	


%\affiliation{Tel Aviv University\\ Israel}\\
\collaboration{JLab Hall A E07006 Collaboration}


\date{\today}
\label{dead}

\begin{abstract}

We measured simultaneously the ${}^4\textrm{He}\eep$, ${}^4\textrm{He}\eepp$, and
${}^4\textrm{He}\eepn$ reactions at\\ $Q^2=2~\gevcsq$ and $x_B>1$, for a
\eep\ missing-momentum range of 400 to 830 {\mevc}. The knocked-out proton
was detected in coincidence with a proton or neutron recoiling almost
back to back to the missing momentum, leaving the residual $A=2$ system at low excitation
energy. These data were used to
identify two-nucleon short-range correlated pairs and to deduce their
isospin structure as a function of missing momentum in a region where
the nucleon-nucleon force is expected to change from predominantly
tensor to repulsive. Neutron-proton pairs dominate the
high-momentum tail of the nucleon momentum distributions, but 
their abundance is reduced as the nucleon momentum increases beyond
$\sim500$ ${\mevc}$. The extracted fraction of proton-proton pairs is
small and almost independent of the missing momentum in the range we
studied. Our data are compared with {\em ab-initio} calculations of
two-nucleon momentum distributions in {\hefour}.
\end{abstract}

\pacs{}

\maketitle

%\section{\label{sec:level1}First-level heading}
% sections are not used for PRL papers
The existence of stable nuclei is due to a delicate interplay between
the long-range attraction that binds nucleons, and the short-range
repulsion that prevents the collapse of the system. In between, the
dominant scalar part of the nucleon-nucleon force almost vanishes and
the interaction is dominated by the tensor force, which depends on the
spin orientations and the relative orbital angular momentum of the
nucleons.

Recent high-momentum-transfer triple-coincidence \ctwelve\eepN\ and
\ctwelve\pppn\ measurements \cite{paper1,paper2,paper3,paper4} have
shown that nucleons in the nuclear ground state form pairs with large
relative momentum and small center-of-mass (CM) momentum, where large
and small is relative to the Fermi momentum of the nucleus. We refer to these pairs 
as short-range correlated (SRC)
pairs~\cite{paper5,paper6,paper20}. In the missing momentum range of $300-600~\mevc$,
these pairs were found to dominate the high-momentum tails of
the nuclear wave functions, with neutron-proton ($np$) pairs
nearly $20$ times more prevalent than proton-proton ($pp$) pairs, and by
inference neutron-neutron ($nn$) pairs. This is due to the strong
dominance of the $NN$-tensor interaction, at the probed sub-fermi
distances~\cite{paper7,paper8,paper9}.


The association of the small \ctwelve\eepp\ / \ctwelve\eepn\ ratio, at
\eep\ missing-momenta of $300-600~\mevc$, with dominance of the
$NN$-tensor force, leads naturally to the quest to increase
missing momenta. This allows looking for pairs that are even closer to each other,
at distances in which the nuclear force changes from being
predominantly tensor to the essentially unexplored repulsive
interaction. We report here on a simultaneous measurement of the
{\hefour}\eep, {\hefour}\eepp\ and {\hefour}\eepn\ reactions at
\eep\ missing-momenta from 400 to 830 {\mevc}. The observed changes in
the isospin composition of the SRC pairs as a function of the missing
momentum are presented, discussed, and compared to calculations.

The experiment was performed in Hall A of Jefferson Laboratory (JLab)
using a 4 $\mu$A electron beam with energy of 4.454 GeV incident on a
high pressure (13 atm) {\hefour} gas target at 20 K. The
20 cm long gas target had a density of 0.033 $\textrm{g}/\textrm{cm}^3$, and was
contained in an aluminum cylinder with a 4 cm radius.

The two Hall A high resolution spectrometers (HRS)~\cite{paper10}
were used to identify \hefour\eep\ events. Scattered electrons were
detected in the left HRS (L-HRS) at a central scattering angle of
$20.3^{\circ}$ and momentum of $3.602~\gevc$. This kinematic
corresponds to the quasi-free knockout of a single proton with
transferred three-momentum $\left| \vec{q} \right| \approx 1.64~\gevc$,
transferred energy $\omega \approx 0.86$ GeV, the negative four-momentum transfer squared $Q^{2}$ = 2
{\gevcsq}, and $x_B = \frac{Q^2}{2m_p\omega}=1.2$, where $m_p$ is
the proton mass. Knocked-out protons were detected using the
right HRS (R-HRS) which was set at $3$ different central angles and
momenta: (33.5$^{\circ}$, $1.38~\gevc$), ($29^{\circ}$, $1.3~\gevc$),
and ($24.5^{\circ}$, $1.19~\gevc$).  These kinematical settings
correspond to \eep\ central missing-momentum ($ \vec{p}_{\textrm{\textrm{miss}}} =
\vec{p}_{p} - \vec{q}$) values of $500~\mevc$, $625~\mevc$, and $750~\mevc$,
respectively, and covering a missing
momentum range of $400-830~\mevc$, with overlap between the three different
settings. The angle between $\vec{q}$ and the recoil nucleon was $40 - 50 ^{\circ}$.

For highly correlated pairs, the missing momentum of the
$A\eep$ reaction is expected to be balanced almost entirely by a single
recoiling nucleon.  A large acceptance spectrometer (BigBite) followed
by a neutron detector (HAND) with matching solid angles were used to
detect such correlated recoiling protons or neutrons.  The layout of
the experimental setup is schematically presented in~Fig.~\ref{fig1}.


\begin{figure}
\includegraphics[width=0.5\textwidth,height=2.2in]{/home/igorko/PhD/Paper/figure1/kin.jpeg}
\caption{A vector diagram of the layout of the experiment. The
  electron kinematics was fixed and three combinations of $\theta_p$/
  $P_p$ were used to cover the full missing momentum range. See text
  for details. The spectrometers are shown with
  their magnets (D-dipole, Q-quadropole) and their main detection
  systems, more details in Ref.\cite{paper10}.}
\label{fig1} 
\end{figure}


The BigBite spectrometer~\cite{paper11} consists of a large
acceptance, non-focusing dipole magnet followed by a detector
package consisting of two planes of plastic
scintillators ($\Delta$E - E),
referred to collectively as the trigger counters, and two wire
chambers. The magnet was centered at an angle of $97^{\circ}$, for the $500$ and
$625~\mevc$ measurements, and $92^{\circ}$ for the $750~\mevc$
measurement. The angular acceptance was about $96$ msr and the
detected momenta acceptance ranged from $0.25~\gevc$ to $0.90~\gevc$.

The Hall A neutron detector (HAND) consists of several elements. A 2.4 cm thick lead shield (to block low-energy photons and most of the charged particles coming from the target), followed by 64 2-cm thick scintillators (to identify and veto charged particles), and 112 plastic scintillator bars arranged in six 10-cm thick layers covering an area of 1x3 m$^2$ (to detect the neutrons). The neutron detector array was placed six meters from the
target, just behind BigBite, covering a similar solid angle as
BigBite.

The experiment triggered on e-p coincidences between the HRS spectrometers, 
with BigBite and HAND detectors read out for every trigger. Thus, we could determine simultaneously the
triple/double coincidence ratios: \hefour\eepp/{\hefour\eep},
\hefour\eepn/{\hefour}\eep\ as well as the triple/triple coincidence
ratio, \hefour\eepp/{\hefour\eepn}.



The {\hefour}\eep\ events were selected by placing a $\pm3\sigma$ cut around
the coincidence timing peak which had a resolution of $\sigma = 0.6$
ns. The resulting event sample contained $1-9 \%$ random events. The
other cuts on the \eep\ data were the nominal HRS phase-space cuts on
momentum ($|\Delta p/p| \le 0.045$), and angles ($\pm 60$ mrad vertical,
$\pm 30$ mrad horizontal). To reduce the random-coincidence background, a
cut on the target-reconstructed vertex from the two HRSs ensured that,
for every event, both the electron and the proton emerged from the
same place in the \hefour\ target. A cut on the two-dimensional
distribution of the $y$-scaling variable \cite{paper12} versus
$\omega$ and a missing mass cut were applied to remove the contribution from $\Delta(1232)$
excitation~\cite{paper13} (see appendix). With all these cuts applied, 
a data set of {\hefour}\eep\ events was generated, each with a measured missing momentum.


The recoiling protons were identified in BigBite using the measured
energy loss in the $\Delta$E - E scintillator detectors, the measured time-of-flight (TOF), and the momentum
reconstructed using the trajectory in the magnetic field. The momentum
resolution of BigBite, determined from elastic electron-proton
scattering, was $\Delta p/p = 1.5\%$. The overall proton
detection efficiency, as measured with e-p elastic scattering, was
$73 \pm 1\%$, primarily due to the gaps between scintillators and the tracking
inefficiency of the wire chambers.

The pattern of hits in sequential layers of HAND was used to identify
neutrons~\cite{paper14}. The momentum of the neutrons was determined
using the measured TOF between the target and HAND. A time resolution of
$1.5$~ns allowed determination of the neutron momentum with an
accuracy that varied from $2.5\%$ (at $400~\mevc$) to $5\%$ (at $830~\mevc$).
The neutron detection efficiency was $40 \pm 1.4\%$ for
$400-830~\mevc$ neutrons. This determination is based on the efficiency
measured up to $450~\mevc$ using the $d\eepn$ reaction, and extrapolation
using a simulation that reproduces well the measured efficiency at
lower momenta~\cite{paper15}.


Figure~\ref{fig2} shows the distribution of the cosine of the
angle between the missing momentum and the recoiling neutrons ($\gamma$).  We
also show the angular correlation for the random background as defined
by a time window off the coincidence peak.  The back-to-back peak of
the real triple coincidence events is demonstrated clearly.  The curve
is a result of a simulation of the scattering of a moving pair having
a center-of-mass (CM) momentum width of $100~\mevc$ as discussed
below. Similar back-to-back correlations were observed for the
recoiling protons detected in BigBite. The timing peak shown in the
insert of Fig.~\ref{fig2} is due to real triple coincidences and the
flat background is due to random coincidences between the
\hefour\eep\ reaction and neutrons in HAND. The signal to background
ratio at the three kinematics setups were $1:2-2.5$.



\begin{figure}
\includegraphics[width=0.5\textwidth,height=2.2in]{/home/igorko/PhD/Paper/opening.png}
\caption{The distribution of the cosine of the opening angle $\gamma$
  between the $\vec{p}_{\textrm{miss}}$ and $\vec{p}_{\textrm{recoil}}$ for the
  $p_{\textrm{miss}}=625$ and 750~{\mevc} kinematics combined. The histogram
  (dashed dotted, red online) shows the distribution of random
  events. The solid curve is a simulation of scattering off a moving
  pair with a CM momentum having a width of 100 {\mevc}. The insert is
  the TOF spectrum for neutrons detected in HAND in coincidence with
  the {\hefour}\eep\ reaction in the highest missing-momentum
  kinematics. The random background is shown as a dashed line.}
\label{fig2} 
\end{figure}


Figure~\ref{fig3} shows the missing mass and energy for the
\hefour\eepp\ reaction corresponding to a two-neutron residual
system. Taking into account the binding energy of the two protons, the
excitation energy and the CM kinetic energy of the residual
two-neutron system is relatively low supporting the picture that they
are essentially spectators in a reaction that breaks a $pp$-SRC
pair. Similar missing-energy and -mass distributions were obtained for
the \hefour\eepn\ reaction but with inferior resolution due to the lower momentum resolution for neutrons.


\begin{figure}
\includegraphics[width=0.5\textwidth,height=2.2in]{/home/igorko/PhD/Paper/Mmass.png}
\caption{The background subtracted missing-mass distribution for
  \hefour\eepp\ events. The insert represents the background
  subtracted missing energy for the \hefour\eepp\ events. Note that
  subtracting the binding energy of the two protons leaves the two
  neutrons residual system with a low excitation energy.}
\label{fig3} 
\end{figure}

Software cuts were applied to both BigBite and HAND that limited their
acceptances to be $\pm14^\circ$ in the vertical direction,
$\pm4^\circ$ in the horizontal direction, and $300-900~\mevc$ in momentum.
 We used a simulation based on the measurements to
correct the yield of the \hefour\eepN\ events for
the finite acceptances of the recoiling protons and neutrons in
Bigbite and HAND.  Following Ref.~\cite{paper1}, the simulations
assume that an electron scatters off a moving SRC pair with a
CM momentum relative to the $A-2$ spectator system described by a
Gaussian distribution as in~\cite{paper16}.  We assumed an isotropic
$3$-dimensional motion of the pair and varied the width of the
Gaussian motion equally in each direction until the best agreement
with the data was obtained. The
nine measured distributions (three components in each of the three
kinematic settings for $np$ pairs) yield, within the uncertainties,
the same width with a weighted average of $100 \pm 20~\mevc$. This is in good agreement with the CM momentum distribution calculated in Ref.~\cite{paper9}.
Figure~\ref{fig2} compares the simulated and the measured
distributions of the opening angle between the knocked-out and
recoiling nucleons.  The fraction of events detected within the finite
acceptance was used to correct the measured yield. The uncertainty in
this correction was typically $15\%$, which dominates the systematic
uncertainties of the \hefour\eepN\ yield.

The measured $\frac{\hefour\eepN}{\hefour\eep}$ ratios are given by the number of events in the
background-subtracted triple-coincidence TOF peak (as shown in the
insert in Fig.~\ref{fig2}) corrected for the finite acceptance and detection
efficiency of the recoiling nucleons, divided by the number of random-subracted double coincidence 
\hefour\eep\ events. These ratios, as a function of $p_{\textrm{miss}}$ in the
\hefour\eep\ reaction, are displayed as full symbols in the two
upper panels of Fig.~\ref{fig:wide}. Because the electron can scatter from either proton of a pp pair (but only from the single proton of an np pair), we divided the \hefour\eepp\ yield by two. Also displayed in Fig.~\ref{fig:wide},
 as empty symbols with dashed bars, similar ratios for \ctwelve~obtained from previous electron scattering
~\cite{paper1,paper2} and proton scattering~\cite{paper4} measurements. In comparing
 the \ctwelve\ and \hefour\ data notice that there is a difference in the naive 
counting ratio of $\frac{NZ}{Z(Z-1)}$ between the two cases.
The horizontal bars show the overlapping momentum acceptance ranges of the various kinematic settings. 
The vertical bars are the uncertainties,
which are predominantly statistical.


Because we obtained the \hefour\eepp\ and {\hefour}\eepn\ data
simultaneously and with the same solid angles and momentum
acceptances, we could also directly determine the ratio of
\hefour\eepp\ to {\hefour\eepn}. In this ratio, many of the
systematic factors needed to compare the triple-coincidence yields
cancel out, and we need to correct only for the detector
efficiencies. This ratio as a function of the missing momentum is
displayed in the lower panel of Fig.~\ref{fig:wide} together with the previously
measured ratio for \ctwelve~\cite{paper2}.

 \begin{widetext*}
\begin{figure*}[ht!]

\includegraphics[width=5.8in,height=3.4in]{/home/igorko/PhD/Paper/Figure4.png}
\caption{ Lower panel: The measured ratios \hefour\eepp/
  \hefour\eepn\ are shown as solid symbols as a
  function of the $\hefour\eep$ missing momentum. Each point is the result of a different spectrometers setting. The
  bands represent the data corrected for FSI to obtain the pair
  ratios, see text for details. Also shown are calculations using the
  momentum distribution of \cite{paper9} for pairs with no CM momentum
  (dashed blue line) and with weighted-average CM momentum assuming
  arbitrary angles between it and the relative momentum in the pair
  (solid black line). The middle panel shows the measured {\hefour}\eepp /
  {\hefour}\eep\ and extracted $\#pp/\#p$ ratios. The upper panel shows the measured {\hefour}\eepn
  /{\hefour}\eep\ and extracted $\#pn/\#p$ ratios The unphysical region above $100\%$ obtained due to statistical fluctuations is marked by white strips. Ratios for {\ctwelve} are shown as empty symbols
  with dashed bars. The empty star is the BNL result \cite{paper4} for \ctwelve\pppn/\ctwelve\ppp. See text for a comment on the \ctwelve / \hefour\ naive counting ratios.}
\label{fig:wide}

\end{figure*}
\end{widetext*}






To correct for final-state interactions (FSI), we calculated the attenuations
of the leading and recoiling nucleons as well as the probability for
single-charge-exchange (SCX) using the Glauber
approximation~\cite{paper17}. To a good approximation the correction to the ratios
due to the leading-proton attenuation is small. The attenuation of the
recoiling nucleon decreases the measured triple/double coincidence
ratios. Because the measured \hefour\eepn\ rate is about an order of
magnitude larger than the \hefour\eepp\ rate,
\hefour\eepn\ reactions followed by a single-charge exchange (and
hence detected as {\hefour\eepp}) increase the
\hefour\eepp/\hefour\eepn\ and the
\hefour\eepp/\hefour\eep\ measured ratios.





The Glauber corrections ($T_{\textrm{L}}=0.75$ and
$T_{\textrm{R}}=0.66-0.73$), where $T_{\textrm{L}}$ and $T_{\textrm{R}}$ the leading and recoil transparencies, 
were calculated by the Ghent group ~\cite{paper17}. We assumed
the uncertainties to be $\pm20\%$ of these values. The probability for SCX ($P_{\textrm{SCX}}$) was
assumed to be $1.5\pm1.5\%$ based on the SCX total cross section of
$1.1\pm0.2$ mb ~\cite{paper18}. The pair fraction extracted from the measured ratios with the FSI calculated corrections are
shown in Fig.~\ref{fig:wide} as bands (see appendix for details). The statistical and systematic uncertainties
of the measurements and the calculated corrections were treated as independent and combined by simulation to create the width of the
one standard deviation bands shown in Fig.~\ref{fig:wide}.



The two-nucleon momentum distributions were calculated for the ground
states of {\hefour} using variational Monte-Carlo wave functions derived
from a realistic Hamiltonian with two- and three-nucleon
potentials~\cite{paper9}. The number of $pp$-SRC pairs is much smaller
than $np$-SRC pairs for values of the relative nucleon momentum $K_{rel} \approx400~\mevc$.
This is because the correlations induced by the
tensor force are strongly suppressed in the case of the $pp$ pairs,
which are mostly in a ${}^1S_0$ state \cite{paper7,paper8,paper9, paper19}. As the relative momenta increase,
the tensor force is less dominant, the role played by the short-range
repulsive force increases and with it the ratio of $pp/np$ pairs. The
solid (black) curve in Fig.~\ref{fig:wide} was obtained using the weighted
average of the calculations with arbitrary angles between $\vec K_{rel}$ and $\vec K_{CM}$,
the CM momentum or the pair. The dashed curve (blue) is the
calculations with $K_{CM}=0$ which is very little different from the average and agrees quantitatively with the Perugia group calculations~\cite{paper19}.
To compare the calculations to the data in Fig.~\ref{fig:wide} we assumed that the virtual photon hits the leading proton and $p_{\textrm{miss}}=K_{rel}$ (PWIA).

To summarize, measurements reported here facilitate
the isospin decomposition of the $2N$-SRC in the high-momentum tail of
the nucleon momentum distribution. The small, relatively constant
measured \hefour\eepp/\hefour\eep\ ratio reflects a small
contribution from $pp$-SRC pairs, most probably dominated by the
repulsive short-range force. The large \hefour\eepn/\hefour\eep\ ratio clearly shows $np$-SRC\\ dominance. The observed 
reduction in the fraction of measured 2N-SRC contribution to the total \eep\ removal strength as a function of the 
missing momentum can be due to increasing FSI and/or the onset of 3N-SRC~\cite{paper5}. A definitive conclusion on the relative contribution of these effects requires a more detailed theoretical study.


 The missing-momentum dependence of the \hefour\eepn/\hefour\eep\ ratio, and the
\hefour\eepp/\hefour\eepn\ ratio, which agree well with the
calculated ratio of $pp$-SRC / $np$-SRC pairs in the ground state,
reflect the transition from tensor force dominance to the repulsive
force domain as the nucleons momenta increase. Comprehensive
calculations, which take into account the full reaction mechanism in a relativistic treatment, as well as
additional data with better statistics will allow a more detailed
determination of the role played by the elusive repulsive short-range
nucleon-nucleon interaction.

We would like to acknowledge the contribution of the Hall A
collaboration and technical staff. We thanks C. Colle, W. Cosyn and J. Ryckebusch
for the Glauber Calculations. We want to also thank R.B. Wiringa, R. Schiavilla, S. Steven,
and J. Carlson for some of the calculations presented in Ref \cite{paper9} that
were provided specifically for this paper. Useful discussions with J. Alster,
C. Ciofi degli Atti, W. Cosyn, A. Gal, L. Frankfurt, J. Ryckebusch,
M. Strikman, and M. Sargsian, are gratefully acknowledged. This work
was supported by the Israel Science Foundation, the U.S. National Science
Foundation, the U.S. Department of Energy grants DE-AC02-06CH11357,
DE-FG02-94ER40818, and U.S. DOE Contract No. DE-AC05 84150,
Modification No. M175, under which the Southeastern Universities
Research Association, Inc. operates the Thomas Jefferson National
Accelerator Facility.


\appendix*
\section{Appendix}

To extract the SRC pair ratios {$\#pp/\#np$, $\#pp/\#p$, and
  $\#np/\#p$) from the measured cross sections ratios
  ($R=\frac{\hefour\eepp}{\hefour\eepn}$, $R1 = \frac{\hefour\eepn}{\hefour\eep}$,
  $R2=\frac{\hefour\eepp}{\hefour\eep}$) we assumed factorization and used
  the equations A.1-A.3 listed below:

\begin{equation}
\frac{\#pp}{\#np} = \frac{ T_L \cdot R - P_{\textrm{SCX}} \cdot
  \frac{\sigma_{en}}{\sigma_{ep}} }{2 \cdot T_L - 2\cdot P_{\textrm{SCX}} \cdot
  \frac{\sigma_{en}}{\sigma_{ep}} \cdot R }
\end{equation}



\begin{equation}
\frac{\#pp}{\#p} = \frac{R_1 \cdot \frac{\sigma_{en} }{\sigma_{ep} }
  \cdot \frac{P_{\textrm{SCX}}}{T_L} \cdot T_R - R_2 \cdot T_R }{2\cdot
  (\frac{\sigma_{en}}{\sigma_{ep}} \cdot \frac{P_{\textrm{SCX}}}{T_L} \cdot T_R )^2 -2
  \cdot T^2_R}
\end{equation}


\begin{equation}
\frac{\#np}{\#p} = \frac{R_2 - 2 \cdot \frac{\#pp}{\#p} \cdot T_R }{ \frac{\sigma_{en}}{\sigma_{ep}}\cdot \frac{P_{\textrm{SCX}}}{T_L}\cdot T_R }
\end{equation}


where $\sigma_{ep}$ $(\sigma_{en})$ is the cross section for
electron scattering off the proton (neutron) \cite{paper21}.

The expression for missing mass is:

\begin{equation}
M_{miss}=\sqrt{ (\omega + M_A - E_f - E_{\textrm{rec}})^2 - (\vec{q} - \vec{p}_f -
  \vec{p}_{\textrm{rec}})^2 }
\end{equation}


$M_A$ is the mass of \hefour\ and the mass of the deuteron when applying the $\Delta(1232)$ cut.
$E_f$ and $p_f$ $(E_{\textrm{rec}}$ and $p_{\textrm{rec}})$ are the energy and momentum of the knocked-out proton (recoil nucleon).
The missing energy is given by:
\begin{equation}
E_{miss} = \omega - T_p - T_{rec} - T_B
\end{equation}
\\
where $T_p$, $T_{rec}$, and $T_B$ are the kinetic energy of the knocked-out proton, recoil partner and remaining $A-2$ system, respectively.



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