%
% $Id: aipcheck.tex,v 1.4 2001/01/31 20:46:55 latex3 Exp $
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Testing for potential problems with this class
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newif\ifproblem
\newif\iftimesok

\typeout{***********************************************}
\typeout{*}
\typeout{* Testing if all files required for the aipproc}
\typeout{* class are available ...}
\typeout{*}
\typeout{***********************************************}

\typeout{*}
\typeout{* Looking for LaTeX2e ... }
\ifx\documentclass\undefined
 \typeout{*}
 \typeout{* Sorry this is a fatal error:}
 \typeout{*}
 \typeout{* The aipproc class can only be used with LaTeX2e which is}
 \typeout{* the standard LaTeX since 1994!}
 \typeout{*}
 \typeout{* Please make sure that your version of LaTeX is up-to-date}
 \typeout{* before attempting to use this class.}
 \typeout{*}
 \expandafter\stop
\else
 \typeout{* ... ok }
\fi

\typeout{*}
\typeout{* Looking for aipproc.cls ... }
\IfFileExists{aipproc.cls}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Sorry this is a fatal error:}
     \typeout{*}
     \typeout{* Before you can use the aipproc class you have to unpack}
     \typeout{* it from the documented source.}
     \typeout{*}
     \typeout{* Run LaTeX on the file 'aipproc.ins', e.g.,}
     \typeout{*}
     \typeout{* \space\space latex aipproc.ins}
     \typeout{*}
     \typeout{* or whatever is necessary on your installation to process}
     \typeout{* a file with LaTeX. This should unpack a number of files for you:}
     \typeout{*}
     \typeout{* aipproc.cls \space and \space aip-*.clo}
     \typeout{*}
     \typeout{* After that retry processing this guide.}
     \typeout{*}
     \stop
}

\typeout{*}
\typeout{* Looking for fixltx2e.sty ... }
\IfFileExists{fixltx2e.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found, trying fix2col.sty instead ... }
     \typeout{*}
     \IfFileExists{fix2col.sty}
	 {
	  \typeout{* ... ok }
	 }
	 {
	  \typeout{* ... not found! }
	  \typeout{*}
	  \typeout{* Sorry this is a fatal error:}
	  \typeout{*}
	  \typeout{* Your LaTeX distribution contains neither fixltx2e.sty}
	  \typeout{* nor fix2col.sty.}
	  \typeout{*}
	  \typeout{* This means that it is either too old or incompletely}
	  \typeout{* installed.}
	  \typeout{*}
	  \typeout{* fixltx2e.sty is part of the standard LaTeX distribution}
	  \typeout{* since 1999; fix2col.sty is an earlier version of this}
	  \typeout{* package.}
	  \typeout{*}
	  \typeout{* Best solution is to get the latest LaTeX distribution.}
	  \typeout{* If this is impossible for you, download fix2col.sty.}
	  \typeout{* You can get this software from a CTAN host.}
          \typeout{* Refer to http://www.tug.org to find such an archive on}
          \typeout{* the net.}
	  \typeout{*}
	  \typeout{* After you have updated your LaTeX distribution}
	  \typeout{* retry processing this guide.}
	  \stop
     }
}

\typeout{*}
\typeout{* Looking for fontenc.sty ... }
\IfFileExists{fontenc.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Sorry this is a fatal error:}
     \typeout{*}
     \typeout{* The fontenc package, which is part of standard LaTeX}
     \typeout{* (base distribution) has to be installed at the site to}
     \typeout{* run the aipproc class.}
     \typeout{*}
     \typeout{* The fact that it cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* improperly.}
     \typeout{*}
     \typeout{* Please make sure that your version of LaTeX is okay}
     \typeout{* before attempting to use this class. The LaTeX distribution}
     \typeout{* contains the file "ltxcheck.tex" which can be used to}
     \typeout{* test the basic functionality and integrity of your installation.}
     \typeout{*}
     \stop
    }

\typeout{*}
\typeout{* Looking for calc.sty ... }
\IfFileExists{calc.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Sorry this is a fatal error:}
     \typeout{*}
     \typeout{* The calc package, which is part of standard LaTeX}
     \typeout{* (tool distribution) has to be installed at the site}
     \typeout{* to run the aipproc class.}
     \typeout{*}
     \typeout{* The fact that it cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts.}
     \typeout{*}
     \typeout{* Please make sure that the tools distribution of LaTeX}
     \typeout{* is installed before attempting to use this class.}
     \typeout{*}
     \typeout{* (You might be able to get calc.sty separately for your}
     \typeout{* installation if you are unable to upgrade to a recent}
     \typeout{* distribution for some reason.)}
     \typeout{*}
     \stop
    }

\typeout{*}
\typeout{* Looking for varioref.sty ... }
\IfFileExists{varioref.sty}
    {
     \typeout{* ... ok }
     \gdef\variorefoptionifavailable{varioref,}
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Problem detected:}
     \typeout{*}
     \typeout{* The varioref package, which is part of standard LaTeX}
     \typeout{* (tool distribution) is not installed at this site.}
     \typeout{*}
     \typeout{* The fact that it cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts.}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but }
     \typeout{* you cannot make use of the options "varioref" or "nonvarioref".}
     \typeout{*}
     \typeout{* Please also note that the aipguide.tex documentation}
     \typeout{* normally uses the "varioref" option to show its}
     \typeout{* effects (which  will now fail).}
     \typeout{*}
     \typein{* Type <return> to continue ...}
     \problemtrue
     \gdef\variorefoptionifavailable{}
     \let\vpageref\pageref
     \let\vref\ref
    }

\typeout{*}
\typeout{* Looking for times.sty ... }
\IfFileExists{times.sty}
    {
     \begingroup
% load times and forget it immediately again
       \RequirePackage{times}
       \global\expandafter\let\csname ver@times.sty\endcsname\relax    
       \long\def\next{ptm}
       \ifx\rmdefault\next
         \typeout{* ... ok }
         \gdef\psnfssproblemoption{}
         \endgroup
         \timesoktrue
       \else
         \endgroup
     \typeout{* ... obsolete! }
     \typeout{*}
     \typeout{* Serious problem detected:}
     \typeout{*}
     \typeout{* The times package, which is part of standard LaTeX}
     \typeout{* (psnfss distribution) is obsolete at this site.}
     \typeout{*}
     \typeout{* The fact that it contains incorrect code either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts with old files remaining!}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but}
     \typeout{* you have to specify the option "cmfonts" which result in}
     \typeout{* documents which are not conforming to the AIP layout specification!}
     \typeout{*}
     \typeout{* You can also try using the class in the following way:}
     \typeout{*}
     \typeout{* \space\space \string\documentclass[cmfonts]{aipproc}}
     \typeout{* \space\space \string\usepackage{times}}
     \typeout{* \space\space ...}
     \typeout{*}
     \typeout{* With luck this will result in Times Roman output but chances}
     \typeout{* are that you will get a larger number of error messages in}
     \typeout{* which case you have to remove the \string\usepackage declaration.}
     \typeout{*}
     \typein{* Type <return> to continue ...}
          \problemtrue
          \gdef\psnfssproblemoption{cmfonts}
          \def\textdegree{$^\circ$}            % used below but now
                                               % not setup
       \fi
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Serious problem detected:}
     \typeout{*}
     \typeout{* The times package, which is part of standard LaTeX}
     \typeout{* (psnfss distribution) can not be found.}
     \typeout{*}
     \typeout{* The fact that this package cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts!}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but }
     \typeout{* you have to specify the option "cmfonts" which result in}
     \typeout{* documents which are not conforming to the AIP layout specification!}
     \typeout{*}
     \typein{* Type <return> to continue ...}
     \problemtrue
     \gdef\psnfssproblemoption{cmfonts,}
    }

\iftimesok % don't bother testing other font options if times already
           % bad

\typeout{*}
\typeout{* Looking for t1ptm.fd or T1ptm.fd ... }
\IfFileExists{t1ptm.fd}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found, trying T1ptm.fd ... }
     \IfFileExists{T1ptm.fd}
          {
           \typeout{* ... ok }
          }
          {
           \typeout{* ... not found}
           \typeout{* Serious problem detected:}
           \typeout{*}
           \typeout{* The times package, which is part of standard LaTeX}
           \typeout{* (psnfss distribution) is available but the corresponding}
           \typeout{* .fd file (defining how to load Times Roman) is missing.}
           \typeout{*}
           \typeout{* The fact that this package is only partially installed}
           \typeout{* means that you LaTeX installation is unable to use Times}
           \typeout{* Roman fonts!}
           \typeout{*}
           \typeout{* You can use the aipproc class without this package but }
           \typeout{* you have to specify the option "cmfonts" which result in}
           \typeout{* documents which are not conforming to the AIP layout}
           \typeout{* specification!}
           \typeout{*}
           \typein{* Type <return> to continue ...}
           \problemtrue
           \timesokfalse
           \gdef\psnfssproblemoption{cmfonts,}
          }
    }

\fi


\newcommand\CheckFDFile[3]{%
  \typeout{*}
  \typeout{* Looking for #1#3.fd or #2#3.fd ... }
  \IfFileExists{#1#3.fd}
    {
     \typeout{* ... ok }
    }
    {
     \IfFileExists{#2#3.fd}
      {
       \typeout{* ... ok }
      }
      {\problemtrue
       \typeout{* ... not found! }
      }
    }
}

\iftimesok % don't bother testing other font options if Times already bad

\typeout{*}
\typeout{* Looking for mathptm.sty ... }
\IfFileExists{mathptm.sty}
    {
     \typeout{* ... ok }
     \CheckFDFile{ot1}{OT1}{ptmcm}
     \CheckFDFile{oml}{OML}{ptmcm}
     \CheckFDFile{oms}{OMS}{pzccm}
     \CheckFDFile{omx}{OMX}{psycm}
     \ifproblem
      \typeout{*}
      \typeout{* Problem detected:}
      \typeout{*}
      \typeout{* The mathptm package, which is part of standard LaTeX}
      \typeout{* (psnfss distribution) was found but some or all of its}
      \typeout{* support files describing which fonts to load are missing!}
      \typeout{*}
      \typeout{*}
      \typeout{* The fact that this package is only partially installed}
      \typeout{* means that the mathptm package cannot be used!}
      \typeout{*}
      \typeout{* You can use the aipproc class without this package but }
      \typeout{* you have to specify the option "nomathfonts" so that}
      \typeout{* math formulas will be typeset using Computer Modern.}
      \typeout{*}
      \typein{* Type <return> to continue ...}
      \problemtrue
      \gdef\psnfssproblemoption{nomathfonts,}
     \fi
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Problem detected:}
     \typeout{*}
     \typeout{* The mathptm package, which is part of standard LaTeX}
     \typeout{* (psnfss distribution) can not be found.}
     \typeout{*}
     \typeout{* The fact that this package cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts!}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but }
     \typeout{* you have to specify the option "nomathfonts" so that}
     \typeout{* math formulas will be typeset using Computer Modern.}
     \typeout{*}
     \typein{* Type <return> to continue ...}
     \problemtrue
     \gdef\psnfssproblemoption{nomathfonts,}
    }

\typeout{*}
\typeout{* Looking for mathtime.sty ... }
\IfFileExists{mathtime.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* The mathime package can not be found.}
     \typeout{*}
     \typeout{* This is not a serious problem because this package is}
     \typeout{* only of interest if you own the commerical MathTime fonts.}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but }
     \typeout{* you cannot use the "mathtime" option of the class.}
     \typeout{*}
     \typein{* Type <return> to continue ...}
     \problemtrue
    }
\else
\fi % iftimesok

\typeout{*}
\typeout{* Looking for graphicx.sty ... }
\IfFileExists{graphicx.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Problem detected:}
     \typeout{*}
     \typeout{* The graphics package, which is part of standard LaTeX}
     \typeout{* (graphics distribution) can not be found.}
     \typeout{*}
     \typeout{* The fact that this package cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts!}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but }
     \typeout{* you cannot use commands like \protect\includegraphics
                or \protect\resizebox}
     \typeout{* in this case.}
     \typeout{*}
     \typeout{* Please note that you will get a further error message below}
     \typeout{* about: "graphicx.sty not found" because the class will try}
     \typeout{* to load this package! Type return in response to that error.}
     \typeout{*}
     \typeout{* As a result the illustrations in aipguide will look strange.}
     \typeout{*}
     \typein{* Type <return> to continue ...}

     \gdef\resizebox##1##2{}
     \gdef\includegraphics{\textbf{graphics package missing:}}
     \problemtrue
    }

\typeout{*}
\typeout{* Looking for textcomp.sty ... }
\IfFileExists{textcomp.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Problem detected:}
     \typeout{*}
     \typeout{* The textcomp package, which is part of standard LaTeX}
     \typeout{* (base distribution) can not be found.}
     \typeout{*}
     \typeout{* The fact that this package cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts!}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but }
     \typeout{* you will always get the error: "textcomp.sty not found"}
     \typeout{* because the class will try to load this package!}
     \typeout{* Type return in response to that error.}
     \typeout{*}
     \typein{* Type <return> to continue ...}

     \def\textdegree{$^\circ$}         % used below but now
                                       % not set up
     \problemtrue
    }


\typeout{*}
\typeout{* Looking for url.sty ... }
\IfFileExists{url.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Problem detected:}
     \typeout{*}
     \typeout{* The url package, which should be part of a good LaTeX}
     \typeout{* distribution, can not be found.}
     \typeout{*}
     \typeout{* Without this package you will not be able to use the \string\url}
     \typeout{* command. Try to download this package from a CTAN  host.}
     \typeout{* Refer to http://www.tug.org to find such an archive on}
     \typeout{* the net.}
     \typeout{*}
     \typein{* Type <return> to continue ...}

     \problemtrue
    }



\typeout{*}
\typeout{* Looking for natbib.sty ... }
\IfFileExists{natbib.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Serious problem detected:}
     \typeout{*}
     \typeout{* The natbib package, which should be part of a good LaTeX}
     \typeout{* distribution, can not be found.}
     \typeout{*}
     \typeout{* Without this package you will not be able to use certain}
     \typeout{* citation styles. See the aipguide documentation!}
     \typeout{*}
     \typeout{* Especially the layout for ARLO requires this package!}
     \typeout{*}
     \typeout{* Try to download this package from a CTAN  host.}
     \typeout{* Refer to http://www.tug.org to find such an archive on}
     \typeout{* the net.}
     \typeout{*}
     \typein{* Type <return> to continue ...}

     \problemtrue
    }


\typeout{*}
\typeout{* ... finished testing}
\typeout{*}
\ifproblem
\typeout{* The tests have reveiled some problems in your TeX installation.}
\typeout{*}
\typeout{* Please review the above comments carefully and read the file}
\typeout{* README for further information.}
\typeout{*}
\typeout{*****************************************************************}
\typein{* Type <return> to continue ...}
\else
\typeout{****************************************************************}
\typeout{*}
\typeout{* The tests have reveiled no problems in your TeX installation.}
\typeout{*}
\typeout{****************************************************************}
\fi


% if this file is run standalone stop otherwise continue
\def\next{aipcheck}
\edef\currjob{\jobname}
\edef\next{\meaning\next}
\edef\currjob{\meaning\currjob}
\ifx\currjob\next
  \expandafter\stop
\fi

\endinput
%%%=======================================================
%%% =
%%% = Sample file for the class "aipproc"
%%% =
%%%=======================================================

\input{aipcheck.tex}

%\typeout{}
%\typeout{**********************************************}
%\typeout{*}
%\typeout{* Here you can type in any options for the class.}
%\typeout{* A full list of supported options is described in}
%\typeout{* the aipguide documentation.}
%\typeout{*}
%\typeout{* Or you may simply press the <RETURN> key in which}
%\typeout{* case the file is processed with the standard settings.}
%\typeout{*}
%\typeout{**********************************************}
%\typeout{}
%\typein[\selectedoptions]{Any options to the class?}
%\ifx\empty\selectedoptions
  \def\selectedoptions{final}
%\fi

\documentclass[
   \selectedoptions
  ]
  {aipproc}

\newcommand\sample{%
 Infandum, regina, iubes renovare dolorem, Troianas ut opes et
 lamen\-ta\-bile regnum cruerint Danai; quaeque ipse miserrima vidi, et
 quorum pars magna fui. Quis talia fando Myrmidonum Dolopumve aut duri
 miles Ulixi temperet a lacrimis? \smallsample
}

\newcommand\smallsample{%
 Et iam nox umida caelo praecipitat,
 suadentque cadentia sidera somnos.
 Sed si tantus amor casus cognoscere
 nostros et breviter Troiae supremum audire laborem, quamquam animus
 meminisse horret, luctuque refugit, incipiam.
}

%\typeout{}
%\typeout{**********************************************}
%\typeout{*}
%\typeout{* Type in the layout style name to be used:}
%\typeout{*}
%\typeout{* `6x9' for AIP proceedings 6x9 inch single column}
%\typeout{* `8x11single' for AIP proceedings 8x11 inch single column}
%\typeout{* `8x11double' for AIP proceedings 8x11 inch double column}
%\typeout{* `arlo' for Acoustics Research Letters Online}
%\typeout{*}
%\typeout{* ATTENTION:}
%\typeout{*}
%\typeout{* \space Typesetting the guide with different styles might
%                  produce}
%\typeout{* \space errors if the .aux file is kept between runs!}
%\typeout{*}
%\typeout{**********************************************}
%\typeout{}
%\typein[\selectedlayoutstyle]{What layout?}
%\layoutstyle\selectedlayoutstyle
\layoutstyle{6x9}

\SetInternalRegister\hbadness{8000} % pseudo latin isn't breaking very well :-)

% We need something to show special stuff for ARLO only.
%
\newcommand\doingARLO[2][]{%
  \ifx\mmref\undefined #1\else #2\fi
}
  
\begin{document}

%
%ESTAS SON ALGUNAS DE MIS PROPIAS DEFINICIONES !!!
%
\def\bsig{\mbox{\boldmath $\sigma$}}                          
\def\bsig{\mbox{\boldmath $\Sigma$}}
\def\bgam{\mbox{\boldmath $\gamma$}}
\def\bgam{\mbox{\boldmath $\Gamma$}}
\def\bphi{\mbox{\boldmath $\phi$}}
\def\bphi{\mbox{\boldmath $\Phi$}}
\def\btau{\mbox{\boldmath $\tau$}}
\def\btau{\mbox{\boldmath $\Tau$}}
\def\btau{\mbox{\boldmath $\partial$}}
\def\Delc{{\Delta}_{\circ}}
\def\bp{\mid {\bf p} \mid}
\def\al{\alpha}
\def\bet{\beta}
\def\gam{\gamma}
\def\del{\delta}
\def\Del{\Delta}
\def\te{\theta}
\def\nua{{\nu}_{\alpha}}
\def\nui{{\nu}_i}
\def\nuj{{\nu}_j}
\def\nue{{\nu}_e}
\def\num{{\nu}_{\mu}}
\def\nut{{\nu}_{\tau}}
\def\2te{2{\theta}}
\def\chic#1{{\scriptscriptstyle #1}}
\def\chicl{{\chic L}}
\def\lam{\lambda}
\def\SU{SU(2)_{\chic L} \otimes U(1)_{\chic Y}}
\def\Lam{\Lambda}
\def\sig{\sigma}
\def\'#1{\ifx#1i\accent19\i\else\accent19#1\fi}
\def\O{\Omega}
\def\o{\omega}
\def\s{\sigma}
\def\D{\Delta}
\def\d{\delta}
\def\df{\rm d}
\def\8{\infty}
\def\ld{\lambda}
\def\eps{\epsilon}
\def\ref#1{$^{#1}$}
\def\chicl{{\chic L}}
\def\lam{\lambda}
\def\SU{SU(2)_{\chic L} \otimes U(1)_{\chic Y}}
\def\Lam{\Lambda}
\def\sig{\sigma}
\def\'#1{\ifx#1i\accent19\i\else\accent19#1\fi}
\def\O{\Omega}
\def\o{\omega}
\def\s{\sigma}
\def\D{\Delta}
\def\d{\delta}
\def\df{\rm d}
\def\8{\infty}
\def\ld{\lambda}
\def\eps{\epsilon}
\def\ref#1{$^{#1}$}
%\def\'#1{\ifx#1i\accent19\i\else\accent19#1\fi}

\title 
      []
      {Neutrinos and Nucleosynthesis in Supernova}

%\classification{13.15.+g, 13.10.+q, 13.40.Gp, 25.30.Pt}
%\keywords{anapole moment of neutrino; charge radius of neutrino; 
%electromagnetic properties of neutrino}

\author{U. Solis, J. C. D'Olivo and  L. G. Cabral-Rosetti}
{address={{\it Departamento de F{\'\i}sica de Altas Energ{\'\i}as, Instituto 
de Ciencias Nucleares,\\
Universidad Nacional Autnoma de Mxico (ICN-UNAM), Circuito Exterior, C.U., 
Apartado Postal 70-543, 04510 Mxico, D.F., Mxico.}\\
},
  email={solis@nuclecu.unam.mx, dolivo@nuclecu.unam.mx, luis@nuclecu.unam.mx,},
  thanks={}
}
%\fi

% \copyrightholder{?????????}
\copyrightyear  {2002}

\begin{abstract}
The type II supernova is considered as a candidate site for the production of 
heavy elements. The nucleosynthesis occurs in an intense neutrino flux, we 
calculate the electron fraction in this environment\ \footnote{Contribution 
to the Proceeedings of the {\it Mexican School of Astrophysics} ({\bf EMA}), 
Guanajuato, M\'exico, July 31 - August 7, 2002.}.
\end{abstract}

\date{\today}

\maketitle

\section{Nucleosynthesis in Supernova}

A star lives a luminous life by burning $H$ into successively heavier elements. 
However, as the Fe group nuclei near mass number $A=56$ are most tightly bound, 
no more nuclear binding energy can be released to power the star by burning Fe. 
Therefore, heavy elements beyond Fe have to be made by process other than normal 
stellar burning. One such process is the rapid neutron capture process, or the 
r-process. 

One starts with some nuclei and lots of neutrons, the nuclei rapidly capture 
these neutrons to make very neutron-rich unstable progenitor nuclei. After neutron 
capture stops, the progenitor nuclei successively beta-decay towards stability 
and become the r-process nuclei observed in nature. This process is responsible for 
approximately half the natural abundance of nuclei with mass number $A>100$ 
\cite{Quian}.

There is as yet no consensus for the site or sites of r-process nucleosynthesis. 
The high neutron densities $10^{20}$ $cm^3$ and temperatures of $10^9$ K 
associated with r-process suggest astrophysical sites as core-collapse type II or 
Ib supernovae. The most plausible environment yet proposed is the neutrino-heated 
ejecta from the nascent neutron star. Close to the neutron star, the temperature 
is several Mev and the atmosphere is essentially dissociated into neutrons and 
protons. As the neutrinos emitted by the neutron star free-stream through this 
atmosphere, some of the $\nu_e$ and  ${\overline{\nu}_e}$ are captured by the 
nucleons and their energy is deposited in the atmosphere. The atmosphere is heated 
and, as a result, it expands away from the neutron star and eventually develops 
into a mass outflow, a {\it neutrino-driven wind} \cite{Caldwell}. After the shock 
wave has propagated out to several hundred kilometers, condition behind the shock 
at 100 to 200 km are suitable for neutrino heating. The neutrino heating blows a 
hot bubble above the proton-neutron star.

\section{Neutrino-Nucleon Interaction}

Neutrinos and antineutrinos of all three flavors are emitted by the neutron star 
producided in a supernova. The individual neutrino species has approximately the 
same luminosity but very diferent average energy. As the neutrinos diffuse out of 
the neutron star, they thermally decouple from the neutron star matter at different 
radii due to the diference in their ability to exchange energy with such matter.  
Neutrinos species of all flavors have identical neutral current interactions but, 
due to energy threshold effects, the $\nu_{\mu}$, $\nu_{\tau}$, and their antiparticles 
lack the charged current capture reactions analogous to 
%
\begin{eqnarray}
\label{e.1}
\nu_e + n \rightarrow p + e \\
\ \ \ \ \ \ \ \ \ \ n + e^+ \rightarrow p + {\overline{\nu}_e}.
\end{eqnarray}
%
%\begin{equation}
% \nu_e + n \rightarrow p + e \\              
% \bar{\nu_ e} + p \rightarrow n + e^+.   
%\end{equation}

The result is that $\nu_{\tau}$, $\nu_{\mu}$, and their antiparticles, have 
indentical spectra and decouple at a higher density, and thus temperature, than 
the electron neutrinos and antineutrinos \cite{Nunokawa1}.

We require the neutron-to-nuclei ratio $R>100$ to effect a good r-process yield 
for heavy nuclear species, but the models with conventional equations of state for 
nuclear matter all give smaller values of $R$. In all models $R$ is  determined 
by the net neutron-proton ratio; the entropy-per-baryon in the ejecta, $s$; and 
the dynamic expansion time scale, $t_{dyn}$ . The neutron-to-proton ratio is 
$n/p =  Y_e^{-1}-1$, where $Y_e$ is the number of electrons per baryon. The r-process 
is only possible when $Y_e<0.5$ at freeze-out from nuclear statistical equilibrium. 
The value of $Y_e$ in the region above the neutrinosphere is determined by the 
interactions in Eq. (1) and (2). We can write the rate of change of $Y_e$ with time as
%
\begin{equation}
\frac{dY_e}{dt} = \lambda_1 - \lambda_2 Y_e,
\end{equation}
\noindent
where $\lambda_1= \lambda_{n \nu_e}+ \lambda_{e^+ n}$ and $\lambda_2 = \lambda_1 
+ \lambda_{n \bar{\nu_e}} +\lambda_{e p}$, are the rates 
in (1) and (2), (see Ref\cite{Nunokawa2}).

\section{Electron Fraction}
The general solution to the above equation is given by 
%
\begin{equation}
%\begin{center}
Y_e = \frac{\lambda_1}{\lambda_2} - \int_0^t I(t,t^{'}) 
\left[\frac{d}{dt^{'}}(\frac{\lambda_1(t^{'})}{\lambda_2(t^{'})})\right] dt^{'} , 
%\end{center}
\end{equation}
%
\noindent
with the integrating factor given by 
%
\begin{equation}
I(t,t^{'})= e^{-\int_{t^{'}}^t \lambda_2(t{''})dt{''}}
%I(t,t^{'})= e^{-\int_{t^{'}}^t \lambda_2(t{''})dt{''}}.
\end{equation}
%
\noindent
and  $\lambda_1/ \lambda_2 \equiv Y_{eq}$. The functional form for the weak-interaction 
rates are given by theory $V-A$, for example: 
%
\begin{equation}
\lambda_{\nu n} = A\int^{\infty}_0 dp_{\nu}p_{\nu}^2 p_e^2 (1-f_e)Pf_{\nu},
\end{equation} 
%
\noindent
where $A=\frac{{G_{\chic F}}^2}{2 {\pi}^3}({g_V}^2+3{g_A}^2)$, $G_{\chic F}$ is the Fermi 
coupling constant, $f$ is the distribution of neutrinos or electrons, and P is a factor 
of probability ($<1$). The normalized energy spectrum of each neutrino species, electron 
and positron is given by Fermi-Dirac distributions, but in this work, we assume that 
can be approximated by a Maxwell-Boltzmann distribution, following Bernstein 
\cite{Bernstein} and Enqvist \cite{Enqvist}.

We changed to the variable $y=\Delta m/T$ and the solution is function of the temperature, 
the integrating factor now becomes 
%
\begin{equation}
I(y,y^{'})= e^{-\int_{y^{'}}^y \left[\frac{dt^{''}}{dy^{''}}\right]\lambda_2(y{''})dy{''}}.
\end{equation}
%
To evaluate the integrating factor we assume the neutrino-driven wind model, the radius 
of an outflowing mass element is related to time $t$ by 
$r=r_o exp\left\{ {(t-t_o)/t_{dyn}} \right\}$ this implies an outflow velocity proporcional 
to the radius, $v=r/t_{dyn}$ \cite{Meyer}. In the model, $\rho \, \alpha \,  r^{-3}$ and 
$T \, \alpha \, r^{-1}$. We set $T_n = T_p  = T_e= T_{e^+}=T$, but we assume that the 
neutrino and antineutrino 
temperatures remain nearly constant. We finally compute the integrals in the solution for 
a range of $y$ values, we obtain the curve for $Y_e(y)$ and $P$. Numerical supernova 
neutrino transport calculations show that $T_{\overline{\nu}_e}= 5.1$ Mev, 
$T_{\nu_e} = 4.5$ Mev and we set for $t_{dyn} =0.3$ s. Neutrino oscillations add a new 
complication to the diagnostic of supernova neutrinos,  the factor $P$ will be the 
survival probability of the electron neutrinos and antineutrinos.
%
\begin{figure}
\includegraphics[height=.27\textheight]{fig1.eps}
\caption{
In (a), the electron fraction $Y_e$ and $Y_{eq}$ is plotted against 
$y=(m_n - m_p)/T$ without convertion of neutrinos. In (b), $Y_e$ and $Y_{eq}$ 
but for $P=1.0,0.8,0.5,0.3$.}
\label{vertex}
\end{figure}
%
\section{Conclusions}
The main goal in this work has been to calculate the electron fraction in a simple and 
accurate analytical form. We think that analytical prescription may be useful to 
simplify the calculation and to help the understanding of the physics involucred. In the 
future we will include the effects of the convertion of neutrinos.  

\begin{theacknowledgments}
This work was supported in part by the {\it Programa de Apoyo a
Proyectos de Investigacin e Inovacin Tecnolgica} ({\bf PAPIIT}) de
la {\bf DGAPA-UNAM} {\it No. de Proyecto}: {\sc IN109001} and in part
by {\bf CONACYT} under proyect No I37307-E.
\end{theacknowledgments}

\begin{thebibliography}{10}
%
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%
\bibitem{Caldwell}D. O. Caldwell, G. M. Fuller, Y. Quian 
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%
\bibitem{Nunokawa1}H. Nunokawa {\it Nucl. Phys. Proc. Suppl.} 
{\bf 95}, 193 (2001).
%
\bibitem{Nunokawa2}H. Nunokawa, Y. Quian, A. Rossi, 
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\bibitem{Bernstein}J. Bernstein, S. Brown, G. Feinberg 
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\bibitem{Enqvist}K. Enqvist, K. Kainulainen, J. Maalampi 
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\bibitem{Meyer}B. S. Meyer, G. C. McLaughlin and G. M. 
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\end{thebibliography}

\end{document}




