I'm using the C# GData libraries to retrieve documents from Google
Docs and i'm commonly getting an html error page appended to the
document contents. The documents where i'm seeing this are in LaTeX
which use plenty of backslashes and other characters, so that may be
contributing to the error.
For example, the following contents are returned (at the top there is
the actual full document, followed by the html error page):
\documentclass[12pt]{article} \textwidth=160mm \textheight=237mm
\setlength{\voffset}{-20mm} \oddsidemargin -5mm \evensidemargin -5mm
\usepackage{epsf} \usepackage[dvips]{graphicx} \begin{document}
\begin{center} {\bfseries DEUTERON-PROTON CHARGE EXCHANGE REACTION AT
SMALL TRANSFER MOMENTUM} \vskip 5mm N.B. Ladygina$^{1 \dag}$,
A.V.Shebeko$^{2}$ \vskip 5mm {\small (1) {\it Laboratory of High
Energies, Joint Institute for Nuclear Research, 141980 Dubna,
Russia, } \\ (2) {\it NSC Kharkov Institute of Physics \&
Technology, 61108 Kharkov, Ukraine } \\ %\vskip 5mm $\dag$ {\it E-
mail: [EMAIL PROTECTED] }} \end{center} \vskip 5mm \begin{center}
\begin{minipage}{150mm} \centerline{\bf Abstract} The charge-exchange
reaction $pd\to npp$ at 1 GeV projectile proton energy is studied.
This reaction is considered in a special kinematics, when the transfer
momentum from the beam proton to fast outgoing neutron is close to
zero. Our approach is based on the Alt-Grassberger-Sandhas formulation
of the multiple-scattering theory for the three-nucleon system. The
matrix inversion method has been applied to take account of the final
state interaction (FSI) contributions. The differential cross section,
tensor analyzing power $C_{0,yy}$, vector-vector $C_{y,y}$ and vector-
tensor $C_{y,xz}$ spin correlation parameters of the initial particles
are presented. It is shown, that the FSI effects play a very important
role under such kinematical conditions. The high sensitivity of the
considered observables to the elementary nucleon-nucleon amplitudes
has been obtained. \end{minipage} \end{center} \vskip 10mm
\section{Introduction} During the last decades the deuteron- proton
charge exchange reaction has been studied both from the experimental
and theoretical point of view. A considerable interest in this
reaction is connected, first of all, to the opportunity to extract
some information about the spin-dependent part of the elementary
nucleon-nucleon charge exchange amplitudes. This idea was suggested by
Pomeranchuk \cite {Pom} already in 1951, but until now it continues to
be of interest. Later, this supposition has been developed in \cite
{Dean, Wil, Car}. It was shown, that in the plane-wave impulse
approximation (PWIA) the differential cross section and tensor
analyzing power $T_{20}$ in the dp-charge exchange reaction are
actually fully determined by the spin-dependent part of the elementary
$np\to pn$ amplitudes. Nowadays the experiment on the study of the dp-
charge exchange reaction at the small transfer momentum in the GeV-
region is planned at ANKE setup at COSY \cite {cosy}. The aim of this
experiment is to provide information about spin-dependent np-elastic
scattering amplitudes in the energy region where phase-shift analysis
data are absent. From our point of view, under kinematical conditions
proposed in this experiment, when momentum of the emitted neutron has
the same direction and magnitude as the beam proton (in the deuteron
rest frame), and relative momentum of two protons is very small, the
final state interaction (FSI) effects play very important role. The
contribution of the D-wave in the DWF into differential cross section
in this kinematics must be negligible \cite {vvg}. However, for the
polarization observables the influence of the D-component can be
significant. The goal of our paper is to study the importance of the D-
wave and FSI effects under kinematical conditions of the planned
experiment. We consider $pd\to npp$ reaction in the approach, which
has been used by us to describe the pd breakup process at 1 GeV
projectile proton energy \cite {LSh}. This approach is based on the
Alt-Grassberger-Sandhas formulation of the multiple-scattering theory
for the three-nucleon system. The matrix inversion method has been
applied to take account of the FSI contributions. Since unpolarized
and polarized mode of the deuteron beam are supposed to be employed in
the experiment, we also calculate both the differential cross section
and a set of the polarization observables. It should be noted, in this
paper we have not considered the Coulomb interaction in the (pp)-pair.
This problem is nontrivial and requires a special investigation.
\section{Theoretial formalism} In accordance to the three-body
collision theory, the amplitude of the deuteron proton charge exchange
reaction, \begin{eqnarray} p(\vec p)+d(\vec 0)\to n(\vec p_1)+p(\vec
p_2)+p(\vec p_3) \end{eqnarray} is defined by the matrix element of
the transition operator $U_{01}$ \begin{eqnarray} \label{ampl} {U}_{pd
\to ppn} \equiv \sqrt {2} <123|[1-(1,2)-(1,3)] U_{01}|1(23)>=
\delta (\vec p -\vec p_1-\vec p_2 -\vec p_3){\cal J}. %\nonumber
\end{eqnarray} As consequence of the particle identity in initial and
final states the permutation operators for two nucleons $(i,j)$ appear
in this expression. As was shown in ref.\cite {LSh} the matrix element
$U_{pd \to npp}$ can be presented as \begin{eqnarray} \label{am} U_{pd
\to npp}&=&\sqrt {2} <123|[1-(2,3)][1+t_{23}(E-E_1) g_{23}
(E-E_1)]t_{12}^{sym}|1(23)>, \end{eqnarray} where the operator
$g_{23} (E-E_1)$ is a free propagator for the (23)-subsystem and the
scattering operator $t_{23}(E-E_1)$ satisfies the Lippmann-Schwinger
(LS) equation with two-body force operator $V_{23}$ as driving term
\begin{eqnarray} \label{LS} t_{23}(E-E_1) = V_{23} + V_{23} g_{23}(E-
E_1) t_{23}(E-E_1) . \end{eqnarray} Here $E$ is the total energy of
the three-nucleon system $E=E_1+E_2+E_3$. Let us rewrite the matrix
element (\ref{am}) indicating explicitly the particle quantum numbers,
\begin{eqnarray} U_{pd\to npp}=\sqrt {2} <\vec {p_1} m_1
\tau_1,\vec {p_2} m_2 \tau_2,\vec {p_3} m_3 \tau_3| [1-(2,3)]
\omega_{23} t^{sym}_{12} |\vec {p} m \tau ,\psi _{1 M_d 0 0} (23)>,
\nonumber \end{eqnarray} where $\omega_{23}=[1+t_{23}(E-E_1) g_{23} (E-
E_1)]$ and the the spin and isospin projections denoted as $m$ and $
\tau$, respectively. The operator $t_{12}^{sym}$ is symmetrized NN-
operator, $t_{12}^{sym}=[1-(1,2)]t_{12}$. In this paper we consider
the special kinematics, when transfer momentum $\vec q=\vec p -\vec
p_1 $ is close to zero. In other words, the neutron momentum has the
same value and direction as the beam proton. In fact, since the
difference between proton and neutron masses and deuteron binding
energy take place, the transfer momentum is not exactly zero, $q
\approx 1.8$ MeV/c. But because of this value is very small and has no
significant influence on the results, we shall suppose $q=0$ in the
subsequent calculations. Under such kinematical conditions one can
anticipate that the FSI in the $^1S_0$ state is prevalent at
comparatively small $p_0$-values. In such a way we get the following
expression for amplitude of the dp charge exchange process \cite {EPJ}
\begin{eqnarray} \label{ampl} {\cal J}&=&{\cal J}_{PWIA}+{\cal
J }_{^1S_0} \nonumber\\ \nonumber\\ {\cal J}_{PWIA}&=& u_L
( p_0 ) Y_L^{M_L}(\widehat { p_0}) \nonumber\\ &&\Bigl\{ <
{1\over 2} m_2^\prime {1\over 2} m_3|1 {\cal M_S}> < m_1 m_2|
t^0 (\vec p,\vec p_0) -t^1(\vec p,\vec p_0) | m m_2 ^ \prime >-
\nonumber\\ &&<{1\over 2} m_2^\prime {1\over 2} m_2|1 {\cal
M_S}> < m_1 m_3| t^0(\vec p,\vec p_0) -t^1(\vec p,\vec p_0) | m
m_2 ^ \prime > \} %\nonumber \\ \nonumber\\ {\cal
J}_{^1S_0}&=&\frac {(-1)^{1-m_2 -m_2^\prime}}{\sqrt {4\pi }}
\delta _{m_2 ~ -m_3} <{1\over 2} m^{\prime\prime } {1\over 2} -m_2^
\prime|1 M_D> \nonumber\\ &&< m_1 m _2^\prime | t^0(\vec
p\vec p_0^\prime) -t^1(\vec p,\vec p_0^\prime) | m m ^ {\prime\prime }
> \int dp _0 {^\prime } p _0 {^\prime } ^2 \psi _{00} ^{001} (p_0^
\prime ) u_0(p_0^\prime). %\nonumber \end{eqnarray} The wave function
of the final $pp$-pair $\psi _{00} ^{001} (p_0^\prime )$ can be
expressed by a series of $\delta$-functions, what enables us to
perform the integration over $p_0^\prime$ in this expression. We use
the phenomenological model suggested by Love and Franey \cite {LF} for
description the high energy nucleon-nucleon matrix $t(\vec p,\vec p_0^
\prime)$. \section{Results and discussions} We define general spin
observable related with polarization of initial particles in terms of
the Pauli $2 \times 2$ spin matrices $\sigma$ for the proton and a set
of spin operators $S$ for deuteron as following \begin{eqnarray}
C_{\alpha\beta}=\frac {Tr ({\cal J}\sigma _\alpha S_\beta {\cal J})}
{Tr ({\cal J} {\cal J}^+) }, \end{eqnarray} where indices $\alpha$ and
$\beta$ refer to the proton and deuteron polarization, respectively; $
\sigma _0$ and $S_0$ corresponding to the unpolarized particles are
the unit matrices of two and three dimensions. In such a way, Eqs.
(\ref {ampl}) for dp- charge exchange amplitude enables us to get the
relation for any variable of this process taking into account two slow
protons final state interaction in $^1S_0$ -state. So, we have
following expression for the spin- averaged squared amplitude in
kinematics, when one of the slow protons is emitted along the beam
direction as well as neutron $(\theta_2=0^0)$ \begin{eqnarray}
\label{c0} C_0&=&{1\over {2 \pi}}\left( \frac{m_N+E_p}{2E_p}
\right) ^2\{ (2B^2+F^2)({\cal U}^2(p_2)+w^2(p_2))+ \\ &&(F^2-
B^2)w(p_2)(w(p_2)-2\sqrt 2 Re{\cal U}(p_2))\}, \nonumber
\end{eqnarray} where ${\cal U}(p_2)=u(p_2)+\int dp_0^\prime {p_0^
\prime }^2 \psi _{00}^{001}(p_0^\prime ) u(p_0^\prime )$ is the S-
component of the DWF $u(p_2)$ corrected on the FSI of the (pp)-pair
and $w(p_2)$ is the D-component of the DWF; $B$ and $F$ are the spin
dependent nucleon-nucleon amplitudes \cite {LF}. We use a right-hand
coordinate system defined in accordance to the Madison convention
\cite {mad}. The quantization $z$-axis is along the beam proton
momentum $\vec p$. Since the direction of $\vec p \times \vec p_1$ is
undefined in the collinear geometry, we choose the $y$-axis normal to
the beam momentum. Then third axis is $\vec x =\vec y\times \vec z$.
The tensor analyzing power can be presented in the following form
\begin{eqnarray} C_{0,yy}\cdot C_0&=&{1\over {4 \pi}}
\left( \frac{m_N+E_p}{2E_p} \right) ^2 \{2(F^2-B^2)({\cal
U}^2(p_2)+w^2(p_2))+ \\ &&(2F^2+B^2)w(p_2)(w(p_2)-2\sqrt 2 Re
{\cal U}(p_2))\} \nonumber \end{eqnarray} Note, that only squared
nucleon- nucleon spin- flip amplitudes $B^2$ and $F^2$ are in
expression for the tensor analyzing power $C_{0,yy}$ and differential
cross section. However, the spin correlation due to vector
polarization of deuteron and beam proton contains the interference
terms of this amplitudes \begin{eqnarray} C_{y,y}\cdot C_0&=&-
{2 \over {4 \pi}}\left( \frac{m_N+E_p}{2E_p} \right) ^2 \{Re(FB^*)
[2{\cal U}^2(p_2)-2w^2(p_2)- \sqrt 2 Re{\cal U}(p_2)w(p_2)]- \nonumber\
\ &&3\sqrt 2 Im(FB^*)Im{\cal U}(p_2)w(p_2)\} \end{eqnarray} It
is interesting, that there is the term proportional to the imaginary
part of ${\cal U}(p_2)$. It has a non-zero value only in case when FSI
is taken into account. The analogous result we have obtained for the
vector-tensor spin correlation \begin{eqnarray} \label{cyxz} C_{y,xz}
\cdot C_0&=&-{3 \over {4 \pi}}\left( \frac{m_N+E_p}{2E_p}
\right) ^2 \{Im(FB^*)[2{\cal U}^2(p_2)-2w^2(p_2)- \sqrt 2 Re{\cal U}
(p_2)w(p_2)]+ \nonumber\\ &&3\sqrt 2 Re(FB^*)Im{\cal U}
(p_2)w(p_2)\} \end{eqnarray} The differential cross section and three
polarization observables are presented in figs.(1-4). The Love and
Franey parametrization with a set of parameters obtained by fitting of
the modern phase shift data SP00 \cite {ar, said} has been employed
for NN-amplitude. All calculations were carried out with Paris NN-
potential \cite {NN} and Paris DWF \cite {Par}. One can see, the FSI
contribution to the differential cross section (fig.1) is significant
even at the very small proton momentum, while for the polarization
observables the difference between PWIA and PWIA+FSI is visible only
for $p_2 \ge 10-15 $ MeV/c. However, with increase of the proton
momentum up to 50 MeV/c the importance of the FSI corrections to the
PWIA also increases. Note, the absolute value of the tensor analyzing
power $C_{0,yy}$ (fig.2) in the momentum interval of interest is near
zero. In order to understand the source of that, we disregard the D-
wave in the DWF. Then the polarization observables are defined by the
ratio of the nucleon-nucleon charge exchange amplitudes only
\begin{eqnarray} \label{w0} C_{0,yy}&=&{1\over 2}\cdot \frac
{F^2-B^2}{2B^2+F^2} \nonumber\\ C_{y,y}&=&-2\cdot \frac
{Re(FB^*)}{2B^2+F^2} \\ C_{y,xz}&=&-3\cdot\frac {Im(FB^*)}
{2B^2+F^2} \nonumber \end{eqnarray} Thus, the nearness of the tensor
analyzing power to zero indicates that the absolute values of the spin-
flip NN-amplitudes approximately equal each other, $|B|\approx |F|$.
The vector-tensor spin correlation $C_{y,xz}$ (fig.4) has also very
small value, $|C_{y,xz}|\approx 0.06$. The magnitude of this
observable decreases up to zero for $p_2\approx 50$ MeV/c, if the FSI
corrections and D-wave in the deuteron are taken into account, while
it is almost constant in the PWIA and PWIA+FSI without D-wave. One can
see from Eqs.(\ref {cyxz}, \ref {w0}) for $C_{y,xz}$, the reason of
this behaviour is connected with the small value of the imaginary part
of the nucleon-nucleon amplitudes product, $Im (FB^*)$. In such a way,
the great contribution into $C_{y,xz}$ gives the term proportional to
$Re (FB^*)$, which defined by D-wave and imaginary part of the
generalized function ${\cal U}(p_2)$. Note, that $Im {\cal U}(p_2)\ne
0$, if FSI taken into account. The other situation is for the vector-
vector spin correlation $C_{y,y}$ (fig.3). The term proportional to
$Re(FB^*)$ gives also a considerable contribution in this observable ,
but it is multiplied on the ${\cal U}^2(p_2)$. The magnitude of
$C_{y,y}$ is close to the theoretical limit -2/3, that confirms to the
conclusion about approximate equality of the nucleon-nucleon
amplitudes, $|B|$ and $|F|$. Besides, this allows to conclude, that
the relative phase between these amplitudes is close to zero. It is
seen from Eq.(\ref {w0}), where D-wave was neglected. %% To insert
figure (with the help of epsf.sty) \begin{figure}[t] \begin{minipage}
{7.5cm} \epsfysize=90mm % \centerline{ \epsfbox{fig1.eps} %}
\vspace*{-3cm} \caption{ The differential cross section at $\vec q=0$
as a function of one of the slow proton momentum. The dashed and full
line correspond to the PWIA and PWIA+FSI, respectively. }
\end{minipage} \end{figure} \begin{figure}[t] \vspace*{-9.9cm} \hfill
{ \begin{minipage}{7.5cm} \epsfysize=90mm %
\centerline{ \epsfbox{fig2.eps} %} \vspace*{-3cm} \caption{ The tensor
analyzing power $C_{yy}$ vs. $p_2$. The dashed line corresponds to
PWIA; dash-dotted and full lines are PWIA+FSI without D-component in
the DWF and with it, respectively. } \end{minipage} } \end{figure}
\begin{figure}[t] \begin{minipage}{7.5cm} \epsfysize=90mm %
\centerline{ \epsfbox{fig3.eps} %} \vskip -3cm \caption{ The spin-
correlation $C_{y,y}$ due to the vector polarization of the deuteron.
The curves are the same as in fig.2. } \end{minipage} \end{figure}
\begin{figure}[t] \vspace*{-8.4cm} \hfill { \begin{minipage}{7.5cm}
\epsfysize=90mm % \centerline{ \epsfbox{fig4.eps} %} \vskip -3cm
\caption{ The spin-correlation $C_{y,xz}$ due to the tensor
polarization of the deuteron. The curves are the same as in fig.2. }
\end{minipage}} \end{figure} \section{Conclusion} We have studied the
deuteron -proton charge exchange reaction at 1 GeV energy in special
kinematics, $\vec q \approx 0$. The influence of the D-wave in the
deuteron and FSI between two slow protons has been considered. It was
shown, that D-wave and FSI effects are negligible for the polarization
observables at proton momentum up to 10-15 MeV/c. As a result, in this
region the polarization observables are defined by the ratio of the
nucleon- nucleon charge exchange amplitudes only. However, it should
not be ignored that the importance of the D-wave and , especially, FSI
into polarization observables increases at $p_2 \ge 15$ MeV/c. In such
a way, we conclude, that the ratio of the nucleon- nucleon charge
exchange amplitudes and phase shift between them can be extracted from
experimental data rather simple, if the experimental conditions and
technical setup possibilities allow to work in this small momentum
interval. In the opposite case, this procedure is more complicated and
model dependent. It should be remembered that the FSI contribution to
the differential cross section is very significant in comparison with
PWIA predictions even at very small proton momentum. This fact does
not enable us to get the absolute value of the nucleon-nucleon spin
flip amplitudes without considering the FSI corrections. \vspace{2cm} %
\begin{acknowledge} We are grateful to V.V.Glagolev, M.S.Nioradze and
A.Kacharava for inspiration of interest to this problem. The authors
are thankful to V.P. Ladygin for fruitful discussions. %
\end{acknowledge} \begin{thebibliography}{99} \bibitem {Pom}
I.Pomeranchuk, Doklady Academii Nauk USSR {\bf 78}, 249 (1951)
\bibitem {Dean} N.W.Dean, Phys.Rev. D{\bf 5}, 1661 (1972); Phys.Rev.
D{\bf 5}, 2832 (1972) \bibitem {Wil} D.V.Bugg, C.Wilkin, Nucl.Phys.
A{\bf 467}, 575 (1987) \bibitem {Car} J.Carbonell, M.B.Barbaro,
C.Wilkin, Nucl.Phys. A{\bf 529}, 653 (1991) \bibitem {cosy}
A.Kacharava, F.Rathmann (spokespersons) {\it et al.}, COSY proposal \#
125, 2003 \bibitem {vvg} V.V.Glagolev {\it et al.} Eur.Phys.J. A{\bf
15}, 471 (2002) \bibitem {LSh} N.B.Ladygina, A.V.Shebeko, Few Body
Syst.{\bf 33}, 49 (2003) \bibitem {EPJ} N.B.Ladygina, A.V.Shebeko,
Eur.Phys.J. A{\bf 22}, 29 (2004) \bibitem {LF} W.G.Love, M.A.Franey,
Phys.Rev. C{\bf 24}, 1073 (1981); W.G.Love, M.A.Franey, Phys.Rev.
C{\bf 31}, 488 (1985) \bibitem {mad} {\it Proceedings of the 3-d
Int.Symp., Madison,1970} edited by H.H. Barshall, W.Haeberli (Madison,
WI: University of Wisconsin Press) \bibitem {ar} R.A.Arndt,
I.I.Strakovsky, R.L.Workman, Phys.Rev. C{\bf 62}, 034005 (2000)
\bibitem {said} http://gwdac.phys.gwu.edu \bibitem {NN} M.Lacombe {\it
et al.}, Phys.Rev. C{\bf 21}, 861 (1980) \bibitem {Par} M. Lacombe
{\it et al.}, Phys.Lett.B {\bf 101}, 139 (1981) \end{thebibliography}
\end{document}
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