# LaTeX2HTML 2002-2-1 (1.71)
# Associate images original text with physical files.


$key = q/%latex2htmlidmarker7605textstyleparbox{11cm}{Î Î¯Î½Î±ÎºÎ±Ï‚ref{tableClO3}Î£Ï„Î±Î±Ï‡ÏÏ„Î·Ï„Î±Ï‚Ï„Î·Ï‚Î±Î½Ï„Î¯Î´ÏÎ±ÏƒÎ·Ï‚{Cl+O_3rightarrowClO+O_2{.};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="502" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img184.png"
 ALT="% latex2html id marker 7605
$\textstyle \parbox{11cm}{Î Î¯Î½Î±ÎºÎ±Ï‚ \ref{table...
...±Ï‡ÏÏ„Î·Ï„Î±Ï‚ Ï„Î·Ï‚
Î±Î½Ï„Î¯Î´ÏÎ±ÏƒÎ·Ï‚ $Cl + O_3 \rightarrow ClO + O_2$.}$">|; 

$key = q/displaystyle{frac{{N_T-N_r}}{{N_TN_r}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img182.png"
 ALT="$\displaystyle {\frac{{N_T-N_r}}{{N_TN_r}}}$">|; 

$key = q/displaystyleleft.vphantom{{frac{2}{kT}}}right)^{{3slash2}}_{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$\displaystyle \left.\vphantom{ {\frac{2}{kT}}}\right)^{{3/2}}_{}$">|; 

$key = q/displaystyle{frac{{dp_i}}{{dt}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$\displaystyle {\frac{{dp_i}}{{dt}}}$">|; 

$key = q/displaystyleleft(vphantom{-mux-frac{pi}{4}overline{mu}^2x^2}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img288.png"
 ALT="$\displaystyle \left(\vphantom{ -\mu x-\frac{\pi}{4}\overline{\mu}^2 x^2}\right.$">|; 

$key = q/displaystyleleft(vphantom{-frac{E_r}{kT}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="$\displaystyle \left(\vphantom{-\frac{E_r}{kT}}\right.$">|; 

$key = q/displaystylesum_{nu}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$\displaystyle \sum_{\nu}^{}$">|; 

$key = q/displaystylebf{pdq;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img188.png"
 ALT="$\displaystyle \bf pdq$">|; 

$key = q/displaystyleleft.vphantom{-frac{E_{J,m}}{kT}}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img128.png"
 ALT="$\displaystyle \left.\vphantom{-\frac{E_{J,m}}{kT}}\right)$">|; 

$key = q/displaystylexi_{1}^{i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img149.png"
 ALT="$\displaystyle \xi_{1}^{i}$">|; 

$key = q/displaystylechi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="$\displaystyle \chi$">|; 

$key = q/displaystyleleft.vphantom{-frac{E_r}{kT}}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="$\displaystyle \left.\vphantom{-\frac{E_r}{kT}}\right)$">|; 

$key = q/displaystyle{frac{{hbar^2}}{{2mu_2r^2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img245.png"
 ALT="$\displaystyle {\frac{{\hbar^2}}{{2\mu_2r^2}}}$">|; 

$key = q/bf{chi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$ \bf\chi$">|; 

$key = q/cal{H};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$ \cal {H}$">|; 

$key = q/displaystyle{frac{{dq_i}}{{dt}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="$\displaystyle {\frac{{dq_i}}{{dt}}}$">|; 

$key = q/displaystyle{frac{{partial^3U}}{{partialR_ipartialR_jpartialR_k}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$\displaystyle {\frac{{\partial^3 U }}{{\partial R_i\partial R_j\partial R_k}}}$">|; 

$key = q/displaystylesum_{{AB}}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$\displaystyle \sum_{{AB}}^{}$">|; 

$key = q/displaystyleleft.vphantom{-frac{pi}{4}x^2}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img274.png"
 ALT="$\displaystyle \left.\vphantom{- \frac{\pi}{4}x^2}\right)$">|; 

$key = q/displaystyle{frac{{sinetadeta}}{{2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="$\displaystyle {\frac{{\sin\eta d\eta}}{{2}}}$">|; 

$key = q/includegraphics[scale=0.3]{figuresslashfig5_5.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="390" HEIGHT="262" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img293.png"
 ALT="\includegraphics[scale=0.3]{figures/fig5_5.eps}">|; 

$key = q/displaystyleleft.vphantom{frac{p_1}{r_2}+frac{p_2}{r_1}}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img231.png"
 ALT="$\displaystyle \left.\vphantom{ \frac{p_1}{r_2} + \frac{p_2}{r_1}}\right)$">|; 

$key = q/displaystyleoverline{{mu}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img282.png"
 ALT="$\displaystyle \overline{{\mu}}$">|; 

$key = q/displaystyle{frac{{gamma_1s_1}}{{2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$\displaystyle {\frac{{\gamma_1s_1}}{{2}}}$">|; 

$key = q/displaystyleomega_{1}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img206.png"
 ALT="$\displaystyle \omega_{1}^{}$">|; 

$key = q/displaystyleoverline{{mu}}^{{3}}_{{}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img285.png"
 ALT="$\displaystyle \overline{{\mu}}^{{3}}_{{}}$">|; 

$key = q/displaystyle{frac{{pi}}{{2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img271.png"
 ALT="$\displaystyle {\frac{{\pi}}{{2}}}$">|; 

$key = q/Phi_{{nu'}}^{*};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$ \Phi_{{\nu'}}^{*}$">|; 

$key = q/displaystyle{frac{{partialH({{bf{q,p})}}{{partialp_i}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="$\displaystyle {\frac{{\partial H({\bf q,p})}}{{\partial p_i}}}$">|; 

$key = q/displaystyleleft.vphantom{frac{partial^2U}{partialR_ipartialR_j}}right)_{{0}}^{{}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$\displaystyle \left.\vphantom{\frac{\partial^2 U}{\partial R_i\partial R_j}}\right)_{{0}}^{{}}$">|; 

$key = q/nu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$ \nu$">|; 

$key = q/overline{{E}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img275.png"
 ALT="$ \overline{{E}}$">|; 

$key = q/displaystylepsi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img265.png"
 ALT="$\displaystyle \psi$">|; 

$key = q/displaystyle{frac{{l^2}}{{2mu_1R^2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img235.png"
 ALT="$\displaystyle {\frac{{l^2}}{{2\mu_1R^2}}}$">|; 

$key = q/displaystylesum_{{A}}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$\displaystyle \sum_{{A}}^{}$">|; 

$key = q/displaystyleomega_{3}^{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img198.png"
 ALT="$\displaystyle \omega_{3}^{2}$">|; 

$key = q/displaystyleint_{0}^{{2pi}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="$\displaystyle \int_{0}^{{2\pi}}$">|; 

$key = q/scriptstylealpha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img227.png"
 ALT="$\scriptstyle \alpha$">|; 

$key = q/displaystylebeta_{0}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img209.png"
 ALT="$\displaystyle \beta_{0}^{}$">|; 

$key = q/displaystyleleft.vphantom{R^2frac{partial}{partialR}}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img244.png"
 ALT="$\displaystyle \left.\vphantom{ R^2\frac{\partial}{\partial R}}\right)$">|; 

$key = q/displaystyleint_{{theta=0}}^{{pi}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img136.png"
 ALT="$\displaystyle \int_{{\theta=0}}^{{\pi}}$">|; 

$key = q/includegraphics[scale=0.5]{figuresslashfig5_6.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="456" HEIGHT="452" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img294.png"
 ALT="\includegraphics[scale=0.5]{figures/fig5_6.eps}">|; 

$key = q/displaystyledelta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="$\displaystyle \delta$">|; 

$key = q/displaystylechi_{nu}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$\displaystyle \chi_{\nu}^{}$">|; 

$key = q/displaystylemu^{2}_{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img278.png"
 ALT="$\displaystyle \mu^{2}_{}$">|; 

$key = q/displaystylesum_{n}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img213.png"
 ALT="$\displaystyle \sum_{n}^{}$">|; 

$key = q/displaystylexi_{4}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img142.png"
 ALT="$\displaystyle \xi_{4}^{}$">|; 

$key = q/displaystyleomega_{2}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img207.png"
 ALT="$\displaystyle \omega_{2}^{}$">|; 

$key = q/displaystylesigma^{2}_{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img173.png"
 ALT="$\displaystyle \sigma^{2}_{}$">|; 

$key = q/displaystyleoverline{{chi}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img151.png"
 ALT="$\displaystyle \overline{{\chi}}$">|; 

$key = q/displaystylecal{H};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$\displaystyle \cal {H}$">|; 

$key = q/displaystyle{frac{{E_{v_1,v_2,v_3}}}{{kT}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img124.png"
 ALT="$\displaystyle {\frac{{E_{v_1,v_2,v_3}}}{{kT}}}$">|; 

$key = q/displaystyle{frac{{p_2}}{{r_1}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img230.png"
 ALT="$\displaystyle {\frac{{p_2}}{{r_1}}}$">|; 

$key = q/displaystylemu_{1}^{{-1}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img239.png"
 ALT="$\displaystyle \mu_{1}^{{-1}}$">|; 

$key = q/displaystylexi_{1}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img139.png"
 ALT="$\displaystyle \xi_{1}^{}$">|; 

$key = q/displaystylecal{T};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$\displaystyle \cal {T}$">|; 

$key = q/scriptstylenu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$\scriptstyle \nu$">|; 

$key = q/displaystyle{frac{{hbar^2}}{{2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img249.png"
 ALT="$\displaystyle {\frac{{\hbar^2}}{{2}}}$">|; 

$key = q/chi^{2}_{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img171.png"
 ALT="$ \chi^{2}_{}$">|; 

$key = q/omega_{i}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img199.png"
 ALT="$ \omega_{i}^{}$">|; 

$key = q/alpha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$ \alpha$">|; 

$key = q/displaystyleleft.vphantom{frac{1}{pimu}}right)^{{{1slash2}}}_{{}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$\displaystyle \left.\vphantom{ \frac{1}{\pi\mu}}\right)^{{{1/2}}}_{{}}$">|; 

$key = q/xi_{9}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img168.png"
 ALT="$ \xi_{9}^{}$">|; 

$key = q/displaystyleleft(vphantom{frac{partial^3U}{partialR_ipartialR_jpartialR_k}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$\displaystyle \left(\vphantom{ \frac{\partial^3 U }{\partial R_i\partial R_j\partial R_k}}\right.$">|; 

$key = q/displaystyleepsilon_{k}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img259.png"
 ALT="$\displaystyle \epsilon_{k}^{}$">|; 

$key = q/displaystylehbar;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img186.png"
 ALT="$\displaystyle \hbar$">|; 

$key = q/displaystyleleft(vphantom{frac{1}{mu_1R^2}+frac{1}{mu_2r^2}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img250.png"
 ALT="$\displaystyle \left(\vphantom{ \frac{1}{\mu_1R^2} + \frac{1}{\mu_2r^2}}\right.$">|; 

$key = q/xi_{i}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img145.png"
 ALT="$ \xi_{i}^{}$">|; 

$key = q/displaystyleomega_{i}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img205.png"
 ALT="$\displaystyle \omega_{i}^{}$">|; 

$key = q/displaystyle{frac{{p_1}}{{r_2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img229.png"
 ALT="$\displaystyle {\frac{{p_1}}{{r_2}}}$">|; 

$key = q/displaystyle{frac{{x}}{{2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img286.png"
 ALT="$\displaystyle {\frac{{x}}{{2}}}$">|; 

$key = q/displaystylexi_{5}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img143.png"
 ALT="$\displaystyle \xi_{5}^{}$">|; 

$key = q/displaystyle{frac{{d^2U(R)}}{{dR^2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$\displaystyle {\frac{{d^2U(R)}}{{dR^2}}}$">|; 

$key = q/displaystylebf{R);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$\displaystyle \bf R)$">|; 

$key = q/displaystyleleft.vphantom{frac{N_T-N_r}{N_TN_r}}right)^{{1slash2}}_{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img183.png"
 ALT="$\displaystyle \left.\vphantom{ \frac{N_T-N_r}{N_TN_r}}\right)^{{1/2}}_{}$">|; 

$key = q/displaystylePhi_{nu}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$\displaystyle \Phi_{\nu}^{}$">|; 

$key = q/gamma_{i}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$ \gamma_{i}^{}$">|; 

$key = q/displaystylenu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$\displaystyle \nu$">|; 

$key = q/displaystyleleft(vphantom{frac{N_T-N_r}{N_TN_r}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img181.png"
 ALT="$\displaystyle \left(\vphantom{ \frac{N_T-N_r}{N_TN_r}}\right.$">|; 

$key = q/displaystyleomega_{2}^{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img197.png"
 ALT="$\displaystyle \omega_{2}^{2}$">|; 

$key = q/displaystyleint_{{x_0}}^{x};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img158.png"
 ALT="$\displaystyle \int_{{x_0}}^{x}$">|; 

$key = q/displaystyleleft.vphantom{frac{m_2+m_3}{m_2m_3}}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img224.png"
 ALT="$\displaystyle \left.\vphantom{ \frac{m_2+m_3}{m_2m_3} }\right)$">|; 

$key = q/displaystyle{frac{{m_1(m_2+m_3)r_1^2+m_3(m_1+m_2)r_2^2-2m_1m_3r_1r_2cosalpha}}{{2m_1m_2m_3r_1^2r_2^2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="382" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img226.png"
 ALT="$\displaystyle {\frac{{m_1(m_2+m_3)r_1^2 + m_3(m_1+m_2)r_2^2 -2m_1m_3r_1r_2\cos\alpha}}{{2m_1m_2m_3r_1^2r_2^2}}}$">|; 

$key = q/displaystyle{frac{{dphi}}{{2pi}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="$\displaystyle {\frac{{d\phi}}{{2\pi}}}$">|; 

$key = q/displaystyle{frac{{pi}}{{4}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img273.png"
 ALT="$\displaystyle {\frac{{\pi}}{{4}}}$">|; 

$key = q/xi_{8}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img167.png"
 ALT="$ \xi_{8}^{}$">|; 

$key = q/displaystylebf{q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$\displaystyle \bf q$">|; 

$key = q/displaystyleleft(vphantom{frac{1-{overline{chi}}}{N_T}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img174.png"
 ALT="$\displaystyle \left(\vphantom{ \frac{1-{\overline{\chi}}}{N_T}}\right.$">|; 

$key = q/displaystyleint_{0}^{{pi}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="$\displaystyle \int_{0}^{{\pi}}$">|; 

$key = q/displaystyleleft.vphantom{frac{m_1+m_2}{m_1m_2}}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img221.png"
 ALT="$\displaystyle \left.\vphantom{ \frac{m_1+m_2}{m_1m_2}}\right)$">|; 

$key = q/displaystyleapprox;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img152.png"
 ALT="$\displaystyle \approx$">|; 

$key = q/displaystylealpha_{k}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img192.png"
 ALT="$\displaystyle \alpha_{k}^{}$">|; 

$key = q/displaystyleleft.vphantom{2muoverline{mu}+pi{overline{mu}}^3frac{x}{2}}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img287.png"
 ALT="$\displaystyle \left.\vphantom{ 2\mu\overline{\mu} +\pi {\overline{\mu}}^3\frac{x}{2}}\right)$">|; 

$key = q/includegraphics[scale=0.6]{figuresslashfig2_3.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="484" HEIGHT="543" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="\includegraphics[scale=0.6]{figures/fig2_3.eps}">|; 

$key = q/displaystyleinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$\displaystyle \infty$">|; 

$key = q/Delta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$ \Delta$">|; 

$key = q/displaystylerho;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img270.png"
 ALT="$\displaystyle \rho$">|; 

$key = q/displaystylesum_{{i=1}}^{N};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img190.png"
 ALT="$\displaystyle \sum_{{i=1}}^{N}$">|; 

$key = q/displaystyleint_{{gamma=0}}^{{2pi}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img135.png"
 ALT="$\displaystyle \int_{{\gamma=0}}^{{2\pi}}$">|; 

$key = q/displaystyle{frac{{1}}{{mu_2r^2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img252.png"
 ALT="$\displaystyle {\frac{{1}}{{\mu_2r^2}}}$">|; 

$key = q/includegraphics[scale=0.8]{figuresslashfig1_3.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="460" HEIGHT="239" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="\includegraphics[scale=0.8]{figures/fig1_3.eps}">|; 

$key = q/displaystylemu_{2}^{{-1}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img240.png"
 ALT="$\displaystyle \mu_{2}^{{-1}}$">|; 

$key = q/displaystylechi_{k}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img258.png"
 ALT="$\displaystyle \chi_{k}^{}$">|; 

$key = q/Phi_{{nu'}}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$ \Phi_{{\nu'}}^{}$">|; 

$key = q/displaystyleleft.vphantom{frac{1-{overline{chi}}}{N_r}}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img179.png"
 ALT="$\displaystyle \left.\vphantom{ \frac{1-{\overline{\chi}}}{N_r}}\right)$">|; 

$key = q/displaystyleleft.vphantom{-frac{hbar^2}{2mu}nabla^2+U({{bf{q})}right];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img264.png"
 ALT="$\displaystyle \left.\vphantom{-\frac{\hbar^2}{2\mu}\nabla^2 +U({\bf q})}\right]$">|; 

$key = q/bf{R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$ \bf R$">|; 

$key = q/displaystylesum_{{i,j}}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$\displaystyle \sum_{{i,j}}^{}$">|; 

$key = q/displaystylexi_{6}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img144.png"
 ALT="$\displaystyle \xi_{6}^{}$">|; 

$key = q/rightarrow;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$ \rightarrow$">|; 

$key = q/displaystyleoverline{{mu}}^{2}_{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img289.png"
 ALT="$\displaystyle \overline{{\mu}}^{2}_{}$">|; 

$key = q/displaystyle{frac{{partial}}{{partialtheta}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img255.png"
 ALT="$\displaystyle {\frac{{\partial}}{{\partial\theta}}}$">|; 

$key = q/displaystylesum_{{i=1}}^{{N_T}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img148.png"
 ALT="$\displaystyle \sum_{{i=1}}^{{N_T}}$">|; 

$key = q/displaystyle{frac{{1-{overline{chi}}}}{{N_r}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img178.png"
 ALT="$\displaystyle {\frac{{1-{\overline{\chi}}}}{{N_r}}}$">|; 

$key = q/displaystyleleft(vphantom{frac{d^2U(R)}{dR^2}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$\displaystyle \left(\vphantom{\frac{d^2U(R)}{dR^2}}\right.$">|; 

$key = q/displaystyleleft[vphantom{-frac{hbar^2}{2mu}nabla^2+U({{bf{q})}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img261.png"
 ALT="$\displaystyle \left[\vphantom{-\frac{\hbar^2}{2\mu}\nabla^2 +U({\bf q})}\right.$">|; 

$key = q/displaystylexi_{i}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img156.png"
 ALT="$\displaystyle \xi_{i}^{}$">|; 

$key = q/includegraphics[scale=0.3]{figuresslashfig2_5.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="272" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="\includegraphics[scale=0.3]{figures/fig2_5.eps}">|; 

$key = q/displaystyle{frac{{1}}{{pimu}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="$\displaystyle {\frac{{1}}{{\pi\mu}}}$">|; 

$key = q/pi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img172.png"
 ALT="$ \pi$">|; 

$key = q/displaystyle{frac{{1}}{{2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="$\displaystyle {\frac{{1}}{{2}}}$">|; 

$key = q/displaystyle{frac{{p_r^2}}{{2mu_2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img234.png"
 ALT="$\displaystyle {\frac{{p_r^2}}{{2\mu_2}}}$">|; 

$key = q/cal{C};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$ \cal {C}$">|; 

$key = q/mu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="$ \mu$">|; 

$key = q/displaystylePsi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$\displaystyle \Psi$">|; 

$key = q/displaystyle{frac{{E_r}}{{kT}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="$\displaystyle {\frac{{E_r}}{{kT}}}$">|; 

$key = q/displaystyleoint_{{C_k}}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img187.png"
 ALT="$\displaystyle \oint_{{C_k}}^{}$">|; 

$key = q/xi_{{10}}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img169.png"
 ALT="$ \xi_{{10}}^{}$">|; 

$key = q/displaystyle{frac{{partialH({{bf{q,p})}}{{partialq_i}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="$\displaystyle {\frac{{\partial H({\bf q,p})}}{{\partial q_i}}}$">|; 

$key = q/epsilon;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$ \epsilon$">|; 

$key = q/includegraphics[scale=0.3]{figuresslashfig5_4.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="376" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img292.png"
 ALT="\includegraphics[scale=0.3]{figures/fig5_4.eps}">|; 

$key = q/displaystyleint;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="$\displaystyle \int$">|; 

$key = q/sigma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$ \sigma$">|; 

$key = q/displaystylesigma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$\displaystyle \sigma$">|; 

$key = q/displaystylesum_{{ABC}}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$\displaystyle \sum_{{ABC}}^{}$">|; 

$key = q/displaystylephi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="$\displaystyle \phi$">|; 

$key = q/includegraphics[scale=0.8]{figuresslashfig1_1.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="529" HEIGHT="313" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="\includegraphics[scale=0.8]{figures/fig1_1.eps}">|; 

$key = q/displaystyle{frac{{p_i^2}}{{2m_i}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="$\displaystyle {\frac{{p_i^2}}{{2m_i}}}$">|; 

$key = q/includegraphics[scale=0.4]{figuresslashfig1_2.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="520" HEIGHT="259" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="\includegraphics[scale=0.4]{figures/fig1_2.eps}">|; 

$key = q/displaystyle{frac{{2}}{{kT}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="$\displaystyle {\frac{{2}}{{kT}}}$">|; 

$key = q/displaystylePhi_{{nu'}}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$\displaystyle \Phi_{{\nu'}}^{}$">|; 

$key = q/displaystyleoverline{{chi}}^{2}_{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img180.png"
 ALT="$\displaystyle \overline{{\chi}}^{2}_{}$">|; 

$key = q/displaystyleleft(vphantom{frac{2J_i}{omega_i}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img201.png"
 ALT="$\displaystyle \left(\vphantom{\frac{2J_i}{\omega_i}}\right.$">|; 

$key = q/mu_{2}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img238.png"
 ALT="$ \mu_{2}^{}$">|; 

$key = q/displaystyleDelta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$\displaystyle \Delta$">|; 

$key = q/displaystylesum_{{i,j,k}}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$\displaystyle \sum_{{i,j,k}}^{}$">|; 

$key = q/xi_{j}^{i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img155.png"
 ALT="$ \xi_{j}^{i}$">|; 

$key = q/displaystyleleft(vphantom{frac{1}{pimu}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$\displaystyle \left(\vphantom{ \frac{1}{\pi\mu}}\right.$">|; 

$key = q/displaystyleleft(vphantom{sum_{i=1}^Np_idq_i}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img189.png"
 ALT="$\displaystyle \left(\vphantom{ \sum_{i=1}^N p_idq_i}\right.$">|; 

$key = q/displaystyle{frac{{dgamma}}{{2pi}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="$\displaystyle {\frac{{d\gamma}}{{2\pi}}}$">|; 

$key = q/alpha_{k}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img193.png"
 ALT="$ \alpha_{k}^{}$">|; 

$key = q/displaystylexi_{6}^{i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img150.png"
 ALT="$\displaystyle \xi_{6}^{i}$">|; 

$key = q/displaystyleleft.vphantom{frac{d^2U(R)}{dR^2}}right)_{{{R=R_e}}}^{{}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$\displaystyle \left.\vphantom{\frac{d^2U(R)}{dR^2}}\right)_{{{R=R_e}}}^{{}}$">|; 

$key = q/displaystyle{frac{{2J_i}}{{omega_i}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img202.png"
 ALT="$\displaystyle {\frac{{2J_i}}{{\omega_i}}}$">|; 

$key = q/displaystylemu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="$\displaystyle \mu$">|; 

$key = q/infty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$ \infty$">|; 

$key = q/displaystyleSigma_{g}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$\displaystyle \Sigma_{g}^{}$">|; 

$key = q/displaystylesum_{{i=1}}^{3};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$\displaystyle \sum_{{i=1}}^{3}$">|; 

$key = q/displaystylesum_{l}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img211.png"
 ALT="$\displaystyle \sum_{l}^{}$">|; 

$key = q/displaystyle{frac{{2b}}{{b_{max}^2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img129.png"
 ALT="$\displaystyle {\frac{{2b}}{{b_{max}^2}}}$">|; 

$key = q/displaystyle{frac{{T_{po}}}{{pihbar}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img215.png"
 ALT="$\displaystyle {\frac{{ T_{po}}}{{\pi \hbar}}}$">|; 

$key = q/displaystyle{frac{{partial^2U}}{{partialR_ipartialR_j}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$\displaystyle {\frac{{\partial^2 U}}{{\partial R_i\partial R_j}}}$">|; 

$key = q/displaystyle{frac{{1}}{{N_{v_1}N_{v_2}N_{v_3}}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img122.png"
 ALT="$\displaystyle {\frac{{1}}{{N_{v_1}N_{v_2}N_{v_3}}}}$">|; 

$key = q/displaystylexi_{2}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img140.png"
 ALT="$\displaystyle \xi_{2}^{}$">|; 

$key = q/beta_{0}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img210.png"
 ALT="$ \beta_{0}^{}$">|; 

$key = q/displaystyleleft.vphantom{frac{partial^3U}{partialR_ipartialR_jpartialR_k}}right)_{{0}}^{{}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$\displaystyle \left.\vphantom{ \frac{\partial^3 U }{\partial R_i\partial R_j\partial R_k}}\right)_{{0}}^{{}}$">|; 

$key = q/displaystyle{frac{{sinthetadtheta}}{{2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="$\displaystyle {\frac{{\sin \theta d\theta}}{{2}}}$">|; 

$key = q/includegraphics[scale=0.3]{figuresslashfig5_3.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="390" HEIGHT="161" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img291.png"
 ALT="\includegraphics[scale=0.3]{figures/fig5_3.eps}">|; 

$key = q/displaystylesum_{{j=1}}^{{infty}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img216.png"
 ALT="$\displaystyle \sum_{{j=1}}^{{\infty}}$">|; 

$key = q/displaystylebf{r;R);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$\displaystyle \bf r;R)$">|; 

$key = q/displaystylepi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="$\displaystyle \pi$">|; 

$key = q/overline{{mu}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img277.png"
 ALT="$ \overline{{\mu}}$">|; 

$key = q/displaystyleomega_{3}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img208.png"
 ALT="$\displaystyle \omega_{3}^{}$">|; 

$key = q/chi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="$ \chi$">|; 

$key = q/displaystyle{frac{{1}}{{sintheta}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img254.png"
 ALT="$\displaystyle {\frac{{1}}{{\sin\theta}}}$">|; 

$key = q/displaystyleleft.vphantom{-frac{E_{v_1,v_2,v_3}}{kT}}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img125.png"
 ALT="$\displaystyle \left.\vphantom{-\frac{E_{v_1,v_2,v_3}}{kT}}\right)$">|; 

$key = q/mu_{1}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img237.png"
 ALT="$ \mu_{1}^{}$">|; 

$key = q/displaystyle{frac{{sineta}}{{2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img130.png"
 ALT="$\displaystyle {\frac{{\sin\eta}}{{2}}}$">|; 

$key = q/displaystyle{frac{{p_1p_2cosalpha}}{{m_2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img225.png"
 ALT="$\displaystyle {\frac{{p_1p_2\cos\alpha}}{{m_2}}}$">|; 

$key = q/displaystylelambda_{i}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img159.png"
 ALT="$\displaystyle \lambda_{i}^{}$">|; 

$key = q/includegraphics[scale=0.4]{figuresslashfig3_1.ps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="520" HEIGHT="333" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img194.png"
 ALT="\includegraphics[scale=0.4]{figures/fig3_1.ps}">|; 

$key = q/displaystyleleft(vphantom{frac{partial^2U}{partialR_ipartialR_j}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$\displaystyle \left(\vphantom{\frac{\partial^2 U}{\partial R_i\partial R_j}}\right.$">|; 

$key = q/displaystyleleft(vphantom{frac{m_1+m_2}{m_1m_2}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img219.png"
 ALT="$\displaystyle \left(\vphantom{ \frac{m_1+m_2}{m_1m_2}}\right.$">|; 

$key = q/displaystyleleft(vphantom{frac{sqrtpi}{2}overline{mu}x}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img280.png"
 ALT="$\displaystyle \left(\vphantom{\frac{\sqrt \pi}{2} \overline{\mu}x}\right.$">|; 

$key = q/delta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$ \delta$">|; 

$key = q/displaystyle{frac{{d[A]}}{{dt}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="$\displaystyle {\frac{{d[A]}}{{dt}}}$">|; 

$key = q/displaystyle{frac{{2b'}}{{b_{max}^2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img163.png"
 ALT="$\displaystyle {\frac{{2b'}}{{b_{max}^2}}}$">|; 

$key = q/displaystyleomega_{1}^{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img196.png"
 ALT="$\displaystyle \omega_{1}^{2}$">|; 

$key = q/displaystyleleft.vphantom{1-tanhfrac{gamma_1s_1}{2}}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$\displaystyle \left.\vphantom{ 1- \tanh\frac{\gamma_1s_1}{2} }\right)$">|; 

$key = q/displaystyleleft.vphantom{sum_{i=1}^Np_idq_i}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img191.png"
 ALT="$\displaystyle \left.\vphantom{ \sum_{i=1}^N p_idq_i}\right)$">|; 

$key = q/displaystylealpha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$\displaystyle \alpha$">|; 

$key = q/displaystylesum_{{i,j,k=1,2,3}}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="$\displaystyle \sum_{{i,j,k=1,2,3}}^{}$">|; 

$key = q/displaystylembox{R_4,R_5,R_6,Ï„Î¿Ï…Ï„ÏÎ¹Î±Ï„Î¿Î¼Î¹ÎºÎ¿ÏÎ¼Î¿ÏÎ¯Î¿Ï…};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="$\displaystyle \mbox{$R_4$, $R_5$, $R_6$, Ï„Î¿Ï… Ï„ÏÎ¹Î±Ï„Î¿Î¼Î¹ÎºÎ¿Ï Î¼Î¿ÏÎ¯Î¿Ï… }$">|; 

$key = q/displaystyleint_{{delta=0}}^{{2pi}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img138.png"
 ALT="$\displaystyle \int_{{\delta=0}}^{{2\pi}}$">|; 

$key = q/alpha_{{po}}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img218.png"
 ALT="$ \alpha_{{po}}^{}$">|; 

$key = q/displaystyle{frac{{m_1+m_2}}{{m_1m_2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img220.png"
 ALT="$\displaystyle {\frac{{m_1+m_2}}{{m_1m_2}}}$">|; 

$key = q/displaystyle{frac{{N_r}}{{N_T}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img153.png"
 ALT="$\displaystyle {\frac{{N_r}}{{N_T}}}$">|; 

$key = q/displaystylegamma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="$\displaystyle \gamma$">|; 

$key = q/displaystylesum_{{po}}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img214.png"
 ALT="$\displaystyle \sum_{{po}}^{}$">|; 

$key = q/displaystylenabla^{2}_{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img263.png"
 ALT="$\displaystyle \nabla^{2}_{}$">|; 

$key = q/displaystyle{frac{{{overline{chi^2}}-{overline{chi}^2}}}{{N_T}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img170.png"
 ALT="$\displaystyle {\frac{{{\overline{\chi^2}} -{\overline{\chi}^2}}}{{N_T}}}$">|; 

$key = q/displaystyleint_{0}^{b};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img162.png"
 ALT="$\displaystyle \int_{0}^{b}$">|; 

$key = q/displaystyleleft(vphantom{r^2frac{partial}{partialr}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img247.png"
 ALT="$\displaystyle \left(\vphantom{ r^2\frac{\partial}{\partial r}}\right.$">|; 

$key = q/cal{T};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$ \cal {T}$">|; 

$key = q/displaystyle{frac{{partialpsi({{bf{q},t)}}{{partialt}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img260.png"
 ALT="$\displaystyle {\frac{{\partial\psi({\bf q},t)}}{{\partial t}}}$">|; 

$key = q/displaystylesqrt{{1slash2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$\displaystyle \sqrt{{1/2}}$">|; 

$key = q/displaystylexi_{3}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img141.png"
 ALT="$\displaystyle \xi_{3}^{}$">|; 

$key = q/displaystyle{frac{{sqrtpi}}{{2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img281.png"
 ALT="$\displaystyle {\frac{{\sqrt \pi}}{{2}}}$">|; 

$key = q/includegraphics[scale=0.6]{figuresslashfig4_2.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="509" HEIGHT="543" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img267.png"
 ALT="\includegraphics[scale=0.6]{figures/fig4_2.eps}">|; 

$key = q/displaystylebf{R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$\displaystyle \bf R$">|; 

$key = q/displaystyle{frac{{1}}{{2pi}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img131.png"
 ALT="$\displaystyle {\frac{{1}}{{2\pi}}}$">|; 

$key = q/displaystylephi_{i}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img204.png"
 ALT="$\displaystyle \phi_{i}^{}$">|; 

$key = q/displaystyle{frac{{partial}}{{partialR}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img242.png"
 ALT="$\displaystyle {\frac{{\partial}}{{\partial R}}}$">|; 

$key = q/displaystyleint_{{eta=0}}^{{pi}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img134.png"
 ALT="$\displaystyle \int_{{\eta=0}}^{{\pi}}$">|; 

$key = q/displaystyleleft(vphantom{-frac{E_{v_1,v_2,v_3}}{kT}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img123.png"
 ALT="$\displaystyle \left(\vphantom{-\frac{E_{v_1,v_2,v_3}}{kT}}\right.$">|; 

$key = q/displaystyleint_{0}^{{b_max}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img133.png"
 ALT="$\displaystyle \int_{0}^{{b_max}}$">|; 

$key = q/phi_{k}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img195.png"
 ALT="$ \phi_{k}^{}$">|; 

$key = q/includegraphics[scale=0.5]{figuresslashfig3_2.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="514" HEIGHT="452" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img212.png"
 ALT="\includegraphics[scale=0.5]{figures/fig3_2.eps}">|; 

$key = q/displaystyle{frac{{hbar^2}}{{2mu_1R^2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img241.png"
 ALT="$\displaystyle {\frac{{\hbar^2}}{{2\mu_1R^2}}}$">|; 

$key = q/displaystyle{frac{{sinalpha}}{{m_2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img232.png"
 ALT="$\displaystyle {\frac{{\sin\alpha}}{{m_2}}}$">|; 

$key = q/displaystylealpha^{2}_{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$\displaystyle \alpha^{2}_{}$">|; 

$key = q/displaystyle{frac{{1-{overline{chi}}}}{{N_T}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img175.png"
 ALT="$\displaystyle {\frac{{1-{\overline{\chi}}}}{{N_T}}}$">|; 

$key = q/displaystyleleft.vphantom{frac{2J_i}{omega_i}}right)^{{1slash2}}_{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img203.png"
 ALT="$\displaystyle \left.\vphantom{\frac{2J_i}{\omega_i}}\right)^{{1/2}}_{}$">|; 

$key = q/displaystylesqrt{{1slash6}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$\displaystyle \sqrt{{1/6}}$">|; 

$key = q/includegraphics[scale=0.5]{figuresslashfig2_6.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="424" HEIGHT="452" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="\includegraphics[scale=0.5]{figures/fig2_6.eps}">|; 

$key = q/includegraphics[scale=0.7]{figuresslashtccc_current.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="534" HEIGHT="409" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="\includegraphics[scale=0.7]{figures/tccc_current.eps}">|; 

$key = q/displaystylesqrt{{1slash3}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$\displaystyle \sqrt{{1/3}}$">|; 

$key = q/displaystylesum_{{i=1}}^{{12}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="$\displaystyle \sum_{{i=1}}^{{12}}$">|; 

$key = q/displaystyle{frac{{partial}}{{partialr}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img246.png"
 ALT="$\displaystyle {\frac{{\partial}}{{\partial r}}}$">|; 

$key = q/displaystylebf{r,R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$\displaystyle \bf r,R$">|; 

$key = q/displaystyleeta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="$\displaystyle \eta$">|; 

$key = q/displaystyleSigma^{+}_{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$\displaystyle \Sigma^{+}_{}$">|; 

$key = q/displaystyle{frac{{exp[ij(S_{po}slashhbar-alpha_{po}pislash2)]}}{{[det(M_{po}^j-1)]^{1slash2}}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img217.png"
 ALT="$\displaystyle {\frac{{\exp[ij(S_{po}/ \hbar - \alpha_{po} \pi/2)]}}{{[det(M_{po}^j-1)]^{1/2}}}}$">|; 

$key = q/displaystyleleft.vphantom{r^2frac{partial}{partialr}}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img248.png"
 ALT="$\displaystyle \left.\vphantom{ r^2\frac{\partial}{\partial r}}\right)$">|; 

$key = q/rho;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img276.png"
 ALT="$ \rho$">|; 

$key = q/displaystylePi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="$\displaystyle \Pi$">|; 

$key = q/Lambda_{i}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img161.png"
 ALT="$ \Lambda_{i}^{}$">|; 

$key = q/Phi_{nu}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$ \Phi_{\nu}^{}$">|; 

$key = q/includegraphics[scale=0.4]{figuresslashfig5_1.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="325" HEIGHT="362" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img268.png"
 ALT="\includegraphics[scale=0.4]{figures/fig5_1.eps}">|; 

$key = q/phi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img200.png"
 ALT="$ \phi$">|; 

$key = q/displaystylesum_{{jgeqi}}^{3};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$\displaystyle \sum_{{j\geq i}}^{3}$">|; 

$key = q/displaystyleLambda_{i}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img157.png"
 ALT="$\displaystyle \Lambda_{i}^{}$">|; 

$key = q/displaystyleleft(vphantom{-frac{pi}{4}x^2}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img272.png"
 ALT="$\displaystyle \left(\vphantom{- \frac{\pi}{4}x^2}\right.$">|; 

$key = q/displaystyleleft.vphantom{frac{sqrtpi}{2}overline{mu}x}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img283.png"
 ALT="$\displaystyle \left.\vphantom{\frac{\sqrt \pi}{2} \overline{\mu}x}\right)$">|; 

$key = q/displaystyleepsilon;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="10" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$\displaystyle \epsilon$">|; 

$key = q/displaystyleleft(vphantom{frac{p_1}{r_2}+frac{p_2}{r_1}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img228.png"
 ALT="$\displaystyle \left(\vphantom{ \frac{p_1}{r_2} + \frac{p_2}{r_1}}\right.$">|; 

$key = q/displaystyleleft(vphantom{frac{m_2+m_3}{m_2m_3}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img222.png"
 ALT="$\displaystyle \left(\vphantom{ \frac{m_2+m_3}{m_2m_3} }\right.$">|; 

$key = q/displaystyleleft(vphantom{1-tanhfrac{gamma_1s_1}{2}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$\displaystyle \left(\vphantom{ 1- \tanh\frac{\gamma_1s_1}{2} }\right.$">|; 

$key = q/displaystyleint_{0}^{1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img146.png"
 ALT="$\displaystyle \int_{0}^{1}$">|; 

$key = q/displaystylerightarrow;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$\displaystyle \rightarrow$">|; 

$key = q/displaystyleleft.vphantom{frac{1-{overline{chi}}}{N_T}}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img176.png"
 ALT="$\displaystyle \left.\vphantom{ \frac{1-{\overline{\chi}}}{N_T}}\right)$">|; 

$key = q/displaystyleleft(vphantom{frac{1-{overline{chi}}}{N_r}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img177.png"
 ALT="$\displaystyle \left(\vphantom{ \frac{1-{\overline{\chi}}}{N_r}}\right.$">|; 

$key = q/displaystylecal{C};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$\displaystyle \cal {C}$">|; 

$key = q/displaystyleleft(vphantom{R^2frac{partial}{partialR}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img243.png"
 ALT="$\displaystyle \left(\vphantom{ R^2\frac{\partial}{\partial R}}\right.$">|; 

$key = q/lambda_{i}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img160.png"
 ALT="$ \lambda_{i}^{}$">|; 

$key = q/displaystyle{frac{{p_R^2}}{{2mu_1}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img233.png"
 ALT="$\displaystyle {\frac{{p_R^2}}{{2\mu_1}}}$">|; 

$key = q/displaystyle{frac{{m_2+m_3}}{{m_2m_3}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img223.png"
 ALT="$\displaystyle {\frac{{m_2+m_3}}{{m_2m_3}}}$">|; 

$key = q/displaystylenu{^prime};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$\displaystyle \nu{^\prime}$">|; 

$key = q/displaystyle{frac{{E_{J,m}}}{{kT}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img127.png"
 ALT="$\displaystyle {\frac{{E_{J,m}}}{{kT}}}$">|; 

$key = q/includegraphics[scale=0.4,angle=0]{figuresslashfig2_4.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="520" HEIGHT="360" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="\includegraphics[scale=0.4,angle=0]{figures/fig2_4.eps}">|; 

$key = q/displaystyleleft(vphantom{sinthetafrac{partial}{partialtheta}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img256.png"
 ALT="$\displaystyle \left(\vphantom{ \sin\theta\frac{\partial}{\partial\theta}}\right.$">|; 

$key = q/xi_{7}^{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img166.png"
 ALT="$ \xi_{7}^{}$">|; 

$key = q/displaystyleint_{{phi=0}}^{{2pi}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img137.png"
 ALT="$\displaystyle \int_{{\phi=0}}^{{2\pi}}$">|; 

$key = q/displaystyle{frac{{1}}{{mu_1R^2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img251.png"
 ALT="$\displaystyle {\frac{{1}}{{\mu_1R^2}}}$">|; 

$key = q/displaystyle{frac{{sintheta}}{{2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img132.png"
 ALT="$\displaystyle {\frac{{\sin\theta}}{{2}}}$">|; 

$key = q/displaystyleint_{0}^{{b_{max}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="$\displaystyle \int_{0}^{{b_{max}}}$">|; 

$key = q/includegraphics[scale=0.4]{figuresslashfig5_2.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="394" HEIGHT="362" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img269.png"
 ALT="\includegraphics[scale=0.4]{figures/fig5_2.eps}">|; 

$key = q/displaystyleprod_{{i=1}}^{N};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$\displaystyle \prod_{{i=1}}^{N}$">|; 

$key = q/includegraphics[scale=0.4]{figuresslashfig4_1.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="327" HEIGHT="420" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img266.png"
 ALT="\includegraphics[scale=0.4]{figures/fig4_1.eps}">|; 

$key = q/scriptstylemu;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img279.png"
 ALT="$\scriptstyle \mu$">|; 

$key = q/displaystyleleft(vphantom{2muoverline{mu}+pi{overline{mu}}^3frac{x}{2}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img284.png"
 ALT="$\displaystyle \left(\vphantom{ 2\mu\overline{\mu} +\pi {\overline{\mu}}^3\frac{x}{2}}\right.$">|; 

$key = q/displaystyleleft.vphantom{frac{1}{mu_1R^2}+frac{1}{mu_2r^2}}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img253.png"
 ALT="$\displaystyle \left.\vphantom{ \frac{1}{\mu_1R^2} + \frac{1}{\mu_2r^2}}\right)$">|; 

$key = q/displaystyleleft.vphantom{-mux-frac{pi}{4}overline{mu}^2x^2}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img290.png"
 ALT="$\displaystyle \left.\vphantom{ -\mu x-\frac{\pi}{4}\overline{\mu}^2 x^2}\right)$">|; 

$key = q/displaystyle{frac{{2bdb}}{{b_{max}^2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="$\displaystyle {\frac{{2bdb}}{{b_{max}^2}}}$">|; 

$key = q/displaystyle{frac{{ddelta}}{{2pi}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="$\displaystyle {\frac{{d\delta}}{{2\pi}}}$">|; 

$key = q/displaystyle{frac{{hbar^2}}{{2mu}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img262.png"
 ALT="$\displaystyle {\frac{{\hbar^2}}{{2\mu}}}$">|; 

$key = q/displaystylesqrt{{2slash3}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$\displaystyle \sqrt{{2/3}}$">|; 

$key = q/displaystyleleft(vphantom{{frac{2}{kT}}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="$\displaystyle \left(\vphantom{ {\frac{2}{kT}}}\right.$">|; 

$key = q/includegraphics[scale=0.5]{figuresslashfig2_1.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="542" HEIGHT="465" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="\includegraphics[scale=0.5]{figures/fig2_1.eps}">|; 

$key = q/displaystyleSigma^{{-}}_{g};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$\displaystyle \Sigma^{{-}}_{g}$">|; 

$key = q/displaystylesum_{{i=4}}^{6};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="$\displaystyle \sum_{{i=4}}^{6}$">|; 

$key = q/displaystyleint_{0}^{{infty}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="$\displaystyle \int_{0}^{{\infty}}$">|; 

$key = q/displaystyle{frac{{b^2}}{{b_{max}^2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img164.png"
 ALT="$\displaystyle {\frac{{b^2}}{{b_{max}^2}}}$">|; 

$key = q/displaystyleSigma_{g}^{{-}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="$\displaystyle \Sigma_{g}^{{-}}$">|; 

$key = q/displaystyletheta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="$\displaystyle \theta$">|; 

$key = q/displaystyle{frac{{j^2}}{{2mu_2r^2}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img236.png"
 ALT="$\displaystyle {\frac{{j^2}}{{2\mu_2r^2}}}$">|; 

$key = q/displaystyleoint;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img185.png"
 ALT="$\displaystyle \oint$">|; 

$key = q/overline{{chi}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img154.png"
 ALT="$ \overline{{\chi}}$">|; 

$key = q/includegraphics[scale=0.6]{figuresslashfig2_2.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="462" HEIGHT="180" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="\includegraphics[scale=0.6]{figures/fig2_2.eps}">|; 

$key = q/displaystyle{frac{{pib_{max}^2}}{{N_T}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img147.png"
 ALT="$\displaystyle {\frac{{\pi b_{max}^2}}{{N_T}}}$">|; 

$key = q/displaystylebf{r;R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$\displaystyle \bf r;R$">|; 

$key = q/displaystyleleft(vphantom{-frac{E_{J,m}}{kT}}right.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img126.png"
 ALT="$\displaystyle \left(\vphantom{-\frac{E_{J,m}}{kT}}\right.$">|; 

$key = q/displaystylesqrt{xi};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img165.png"
 ALT="$\displaystyle \sqrt{\xi}$">|; 

$key = q/displaystyleleft.vphantom{sinthetafrac{partial}{partialtheta}}right);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img257.png"
 ALT="$\displaystyle \left.\vphantom{ \sin\theta\frac{\partial}{\partial\theta}}\right)$">|; 

1;

