Effective Field Theory for Neutron-Deuteron Scattering: Higher Partial Waves
chir.tex
\documentstyle[sprocl,graphicx]{article}
%\documentclass{ws-p8-50x6-00}%{graphicx}
\bibliographystyle{unsrt} %for BibTeX - sorted numerical labels by
                          %order of first citation.
\begin{document}

\title{Effective Field Theory for Neutron-Deuteron Scattering:
Higher Partial Waves}

\author{F.~Gabbiani\footnote{New permanent address: Department of
Physics and Astronomy, Iowa State University, Ames, IA 50011-3160}}

\address{Department of Physics, Duke University\\Box 90305, Durham, NC
27708-0305, USA\\Email: fg@phy.duke.edu}

\maketitle

We present several theoretical results \cite{fabrizio1} for the phase
shifts of higher partial waves for neutron-deuteron elastic
scatterings in the quartet (J = 3/2) and doublet (J = 1/2)
channels. This is the first case in which EFT has been successfully
applied to these channels in a systematic way. Only the pionless case
is investigated here, reserving the inclusion of pion
exchanges for a later investigation.

Results for the quartet case are shown in Fig. \ref{fig:quartet}.  The
phase shifts in degrees are plotted vs. the CM energy of the
system. The only experimental results available in the literature are
phase-shift analyses for processes with protons
\cite{fabrizio2}. Yet, their agreement with our theoretical
predictions is excellent, indicating that electro-magnetic effects are
not significant at the energies we study in this work. Potential
models like the ones based on the Bonn and the av$_{14}$ potentials
\cite{fabrizio3} give also similar results, but it is important to
notice that we are able in principle not only to reproduce their
results, but our effective theory framework with its well-defined
power counting will in addition allow us to include higher order
corrections and external currents in a consistent and systematic way.

The doublet case involves the solution of two coupled integral
equations (see for example \cite{fabrizio4}). The S-wave component
relates to the triton bound state, and will be studied in a future
work. We show our results in Fig. \ref{fig:doublet}.

\begin{figure}[!t]
  \begin{center}
    \vspace{1ex}\noindent \centerline{\includegraphics*[height=0.40\linewidth,
      angle=90]{quartetsre.eps} \hfill
      \includegraphics*[height=0.40\linewidth,angle=90]{quartetpre.eps} }

    \vspace{1ex}\noindent \centerline{\includegraphics*[height=0.40\linewidth,
      angle=90]{quartetdre.eps} \hfill
      \includegraphics*[height=0.40\linewidth,angle=90]{quartetfre.eps} }

     \caption{\sl Real parts of the first four partial waves in
       the quartet channel of \protect$nd$ scattering versus
       the center-of-mass energy.}
    \label{fig:quartet}

    \vspace{1ex}\noindent \centerline{\includegraphics*[height=0.40\linewidth,
      angle=90]{doubletpre.eps} \hfill
      \includegraphics*[height=0.40\linewidth,angle=90]{doubletdre.eps} }

    \vspace{1ex}\noindent \centerline{\includegraphics*[height=0.40\linewidth,
      angle=90]{doubletfre.eps} \hfill
      \includegraphics*[height=0.40\linewidth,angle=90]{doubletgre.eps} }

    \caption{\sl Real parts of the first four higher partial
      waves in the doublet channel of \protect$nd$ scattering versus the
      center-of-mass energy.}
    \label{fig:doublet}
  \end{center}
\end{figure}

\begin{thebibliography}{6}

\bibitem {fabrizio1}
F.~Gabbiani, P.~F.~Bedaque and H.~W.~Grie{\ss}hammer,
Nucl. Phys. {\bf A~675} (2000) 601.

\bibitem{fabrizio2}
E.~Huttel {\sl et al.}, Nucl. Phys. {\bf A~406} (1983) 443;
P.~A.~Schmelzbach {\sl et al.}, Nucl. Phys. {\bf A~197}
(1972) 273.

\bibitem{fabrizio3}
A.~Kievsky {\sl et al.},
Nucl. Phys. {\bf A~607} (1996) 402; A.~Kievsky, private communication.

\bibitem{fabrizio4}
G.~V.~Skorniakov and K.~A.~Ter-Martirosian,
Sov. Phys. {\bf JETP 4} (1957) 648.

\end{thebibliography}

\end{document}

nucl-th0009072.extracted_bib
\begin{thebibliography}{6}

\bibitem {fabrizio1}
F.~Gabbiani, P.~F.~Bedaque and H.~W.~Grie{\ss}hammer,
Nucl. Phys. {\bf A~675} (2000) 601.

\bibitem{fabrizio2}
E.~Huttel {\sl et al.}, Nucl. Phys. {\bf A~406} (1983) 443;
P.~A.~Schmelzbach {\sl et al.}, Nucl. Phys. {\bf A~197}
(1972) 273.

\bibitem{fabrizio3}
A.~Kievsky {\sl et al.},
Nucl. Phys. {\bf A~607} (1996) 402; A.~Kievsky, private communication.

\bibitem{fabrizio4}
G.~V.~Skorniakov and K.~A.~Ter-Martirosian,
Sov. Phys. {\bf JETP 4} (1957) 648.

\end{thebibliography}