Hi, This is a problem for the Docs APIs group:
http://groups.google.com/group/Google-Docs-Data-APIs Cheers, -Jeff On Oct 2, 6:01 pm, Bobby <[EMAIL PROTECTED]> wrote: > 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} > > Error: We have encountered an error, which we will investigate > immediately. 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