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\begin{document}
\begin{center}
{\large \bf $pn \rightarrow p\Lambda$ reaction and its feasibility }

\medskip

A. Sakaguchi

\medskip

Department of Physics, Osaka University

\end{center}

The non-mesonic decay of hypernuclei is believed to be the two body weak 
decay process $\Lambda N \rightarrow NN$, then it is a different category 
of weak decay, which happens only in finite baryon density, from the free 
decay of the $\Lambda$ particle \cite{non-mesonic}.  
Based on the meson exchange model with the $\Lambda N \pi$ coupling 
studied through the mesonic decay of hypernuclei, one can explore 
the direct weak process by the $\Lambda NNN$ coupling as deviations 
from the simple meson exchange model.  
On the other hand, explanations of the observables of the non-mesonic 
decay of hypernuclei is not unique or measured physical quantity has 
large ambiguity due to the inter-nuclear cascade process after the weak 
decay of hypernuclei.  

To exclude the ambiguity and to make a complementary measurement 
to the non-mesonic weak decay of hypernuclei, a measurement of 
the inverse reaction $pn \rightarrow p\Lambda$ at a threshold energy 
region is proposed.  
The measurement is relatively free from the inter-nuclear cascade 
because p+N collisions in the initial state lower the energy of 
the proton and the proton with the lower energy does not contribute 
to the $\Lambda$ creation.  
The $\Lambda$ particle in the final state enables a polarization 
measurement by its weak decay asymmetry, and polarized proton 
may be combined with the polarization measurement to investigate 
the spin dependent property of the weak interaction.  
{\em A challenge in the $pn \rightarrow p\Lambda$ reaction measurement 
is the small cross section of the reaction, $10^{-39} cm^2$.}

The $pn \rightarrow p\Lambda$ reaction measurement is proposed at 
the Ring Cyclotron of the Research Center for Nuclear Physics (RCNP), 
Osaka University.  
The highest energy of proton beam available at the Ring Cyclotron 
is 416 MeV and is in the threshold energy region of the 
$pn \rightarrow p\Lambda$ reaction (threshold energy is 
$E_p$=$368 MeV$).
The measurement of the reaction is based on a simultaneous detection 
of a proton and $\pi^-$ pair from a $\Lambda$ decay:
\[ p + n \rightarrow p + \Lambda \]
\[ \Lambda \rightarrow p + \pi^- \]
An estimation of yield tells one can get about 45 events/30 days 
with 300 nA proton beam, 1 cm Be target and overall detection efficiency 
of 5 \%.  
So, the main issue of the measurement is the discrimination of 
background events from strong processes.  
The main background of proton is coming from the quasi-elastic 
scattering of proton by the target and a typical cross section of 
the process is 25 mb.  
The main $\pi^-$ background comes from the quasi-free pion production 
process, $pn \rightarrow pp\pi^-$.  
A typical cross section of the process is 30 $\mu$b.  
Both processes are highly stronger than the $pn \rightarrow p\Lambda$ 
process, $10^{13}$ and $10^{10}$ for proton and $\pi^-$.

A collimator made of heavy metal which fully stops protons with 
the beam energy and other charged particles is proposed to discriminate 
events which have reaction vertexes in the target and to accept 
only the proton and $\pi^-$ pair from $\Lambda$ particle which has 
decay vertex out of the target.  
To achieve reasonable single counting rate at the outside of 
the collimator, about $10^4$ reduction of charged particles from 
the target, which corresponds to about 1 $\mu$b in cross section, 
is needed.  
Monte Carlo (MC) studies of the collimator based on GEANT is in progress.  
Importance of hardness of the detectors against neutral particles (mainly 
neutrons and gamma rays) is realized from the studies since energetic 
protons create low energy neutral particles in the collimator.  
A test experiment was carried out at the Ring Cyclotron of RCNP with 
a collimator prototype made of W-alloy, and about $10^2$ reduction of 
charged particles was obtained.  
Some optimization are needed to increase the reduction rate up to $10^4$ 
with the help of the MC studies.  

For the determination of the vertex point of the proton and $\pi^-$ pair 
and further discrimination of the background processes, a Silicon 
Strip Detector (SSD) system at the most inner layer of the experimental 
setup is in designing \cite{ssd}.  
A Central Drift Chamber (CDC) system is in preparation for a large angular 
coverage (about $2\pi$ rad) and a measurement of proton and pion momenta 
to reconstruct $\Lambda$ invariant mass.  
A conceptual design of the experimental setup is shown in 
Fig.\ref{fig:setup}.  
\begin{figure}
    \begin{center}
    \epsfile{file=setup.eps,width=11cm}
    \caption{Conceptual design of the experimental setup.
             The collimator covers the target to stop all charged particles 
             from the target for the laboratory angle down to 15 degrees.
             The SSD system (shown with wire frames) is installed in 
             the most inner part of the setup to reconstruct the $\Lambda$ 
             decay vertex.  
             The CDC covers about 2$\pi$ radian acceptance.  
             To avoid CDC hits by charged particles from the target, 
             an absorber made of heavy metal is installed at forward angle.  
             Counters are surrounding the CDC for trigger purpose.}
    \label{fig:setup}
    \end{center}
\end{figure}

\begin{thebibliography}{99}
\setlength{\itemsep}{-5pt}  % Adjust Item Separation
\bibitem{non-mesonic}
        {For more detail on the non-mesonic decay process, please refer 
         theoretical talks in this workshop.}
\bibitem{ssd}
        {See also the report by Y. Shimizu on the SSD design in this 
         workshop.}
\end{thebibliography}

\end{document}









