epsf.tex
%%% ====================================================================
%%%   This file is freely redistributable and placed into the
%%%   public domain by Tomas Rokicki.
%%%  @TeX-file{
%%%     author          = "Tom Rokicki",
%%%     version         = "2.7k",
%%%     date            = "19 July 1997",
%%%     time            = "10:00:05 MDT",
%%%     filename        = "epsf.tex",
%%%     address         = "Tom Rokicki
%%%                        Box 2081
%%%                        Stanford, CA 94309
%%%                        USA",
%%%     telephone       = "+1 415 855 9989",
%%%     email           = "rokicki@cs.stanford.edu (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "PostScript, TeX",
%%%     supported       = "yes",
%%%     abstract        = "This file contains macros to support the inclusion
%%%                        of Encapsulated PostScript files in TeX documents.",
%%%     docstring       = "This file contains TeX macros to include an
%%%                        Encapsulated PostScript graphic.  It works
%%%                        by finding the bounding box comment,
%%%                        calculating the correct scale values, and
%%%                        inserting a vbox of the appropriate size at
%%%                        the current position in the TeX document.
%%%
%%%                        To use, simply say
%%%
%%%                        \input epsf % somewhere early on in your TeX file
%%%
%%%                        % then where you want to insert a vbox for a figure:
%%%                        \epsfbox{filename.ps}
%%%
%%%                        Alternatively, you can supply your own
%%%                        bounding box by
%%%
%%%                        \epsfbox[0 0 30 50]{filename.ps}
%%%
%%%                        This will not read in the file, and will
%%%                        instead use the bounding box you specify.
%%%
%%%                        The effect will be to typeset the figure as
%%%                        a TeX box, at the point of your \epsfbox
%%%                        command. By default, the graphic will have
%%%                        its `natural' width (namely the width of
%%%                        its bounding box, as described in
%%%                        filename.ps). The TeX box will have depth
%%%                        zero.
%%%
%%%                        You can enlarge or reduce the figure by
%%%                        saying
%%%
%%%                          \epsfxsize=<dimen> \epsfbox{filename.ps}
%%%                        or
%%%                          \epsfysize=<dimen> \epsfbox{filename.ps}
%%%
%%%                        instead. Then the width of the TeX box will
%%%                        be \epsfxsize and its height will be scaled
%%%                        proportionately (or the height will be
%%%                        \epsfysize and its width will be scaled
%%%                        proportionately).
%%%
%%%                        The width (and height) is restored to zero
%%%                        after each use, so \epsfxsize or \epsfysize
%%%                        must be specified before EACH use of
%%%                        \epsfbox.
%%%
%%%                        A more general facility for sizing is
%%%                        available by defining the \epsfsize macro.
%%%                        Normally you can redefine this macro to do
%%%                        almost anything.  The first parameter is
%%%                        the natural x size of the PostScript
%%%                        graphic, the second parameter is the
%%%                        natural y size of the PostScript graphic.
%%%                        It must return the xsize to use, or 0 if
%%%                        natural scaling is to be used.  Common uses
%%%                        include:
%%%
%%%                           \epsfxsize  % just leave the old value alone
%%%                           0pt         % use the natural sizes
%%%                           #1          % use the natural sizes
%%%                           \hsize      % scale to full width
%%%                           0.5#1       % scale to 50% of natural size
%%%                           \ifnum #1>\hsize\hsize\else#1\fi
%%%                                       % smaller of natural, hsize
%%%
%%%                        If you want TeX to report the size of the
%%%                        figure (as a message on your terminal when
%%%                        it processes each figure), say
%%%                        `\epsfverbosetrue'.
%%%
%%%                        If you only want to get the bounding box
%%%                        extents, without producing any output boxes
%%%                        or \special{}, then say
%%%                        \epsfgetbb{filename}.  The extents will be
%%%                        saved in the macros \epsfllx \epsflly
%%%                        \epsfurx \epsfury in PostScript units of
%%%                        big points.
%%%
%%%                        Revision history:
%%%
%%%                        ---------------------------------------------
%%%                        epsf.tex macro file:
%%%                        Originally written by Tomas Rokicki of
%%%                        Radical Eye Software, 29 Mar 1989.
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Don Knuth, 3 Jan 1990.
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Tomas Rokicki, 18 Jul 1990.
%%%                        Accept bounding boxes with no space after
%%%                        the colon.
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Nelson H. F. Beebe
%%%                        <beebe@math.utah.edu>, 03 Dec 1991 [2.0].
%%%                        Add version number and date typeout.
%%%
%%%                        Use \immediate\write16 instead of \message
%%%                        to ensure output on new line.
%%%
%%%                        Handle nested EPS files.
%%%
%%%                        Handle %%BoundingBox: (atend) lines.
%%%
%%%                        Do not quit when blank lines are found.
%%%
%%%                        Add a few percents to remove generation of
%%%                        spurious blank space.
%%%
%%%                        Move \special output to
%%%                        \epsfspecial{filename} so that other macro
%%%                        packages can input this one, then change
%%%                        the definition of \epsfspecial to match
%%%                        another DVI driver.
%%%
%%%                        Move size computation to \epsfsetsize which
%%%                        can be called by the user; the verbose
%%%                        output of the bounding box and scaled width
%%%                        and height happens here.
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Nelson H. F. Beebe
%%%                        <beebe@math.utah.edu>, 05 May 1992 [2.1].
%%%                        Wrap \leavevmode\hbox{} around \vbox{} with
%%%                        the \special so that \epsffile{} can be
%%%                        used inside \begin{center}...\end{center}
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Nelson H. F. Beebe
%%%                        <beebe@math.utah.edu>, 09 Dec 1992 [2.2].
%%%                        Introduce \epsfshow{true,false} and
%%%                        \epsfframe{true,false} macros; the latter
%%%                        suppresses the insertion of the PostScript,
%%%                        and instead just creates an empty box,
%%%                        which may be handy for rapid prototyping.
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Nelson H. F. Beebe
%%%                        <beebe@math.utah.edu>, 14 Dec 1992 [2.3].
%%%                        Add \epsfshowfilename{true,false}.  When
%%%                        true, and \epsfshowfalse is specified, the
%%%                        PostScript file name will be displayed
%%%                        centered in the figure box.
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Nelson H. F. Beebe
%%%                        <beebe@math.utah.edu>, 20 June 1993 [2.4].
%%%                        Remove non-zero debug setting of \epsfframemargin,
%%%                        and change margin handling to preserve EPS image
%%%                        size and aspect ratio, so that the actual
%%%                        box is \epsfxsize+\epsfframemargin wide by
%%%                        \epsfysize+\epsfframemargin high.
%%%                        Reduce output of \epsfshowfilenametrue to
%%%                        just the bare file name.
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Nelson H. F. Beebe
%%%                        <beebe@math.utah.edu>, 13 July 1993 [2.5].
%%%                        Add \epsfframethickness for control of
%%%                        \epsfframe frame lines.
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Nelson H. F. Beebe
%%%                        <beebe@math.utah.edu>, 02 July 1996 [2.6]
%%%                        Add missing initialization \epsfatendfalse;
%%%                        the lack of this resulted in the wrong
%%%                        BoundingBox being picked up, mea culpa, sigh...
%%%                        ---------------------------------------------
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Nelson H. F. Beebe
%%%                        <beebe@math.utah.edu>, 25 October 1996 [2.7]
%%%                        Update to match changes in from dvips 5-600
%%%                        distribution: new user-accessible macros:
%%%                        \epsfclipon, \epsfclipoff, \epsfdrafton,
%%%                        \epsfdraftoff, change \empty to \epsfempty.
%%%                        ---------------------------------------------
%%%                        
%%%                        Modified to avoid verbosity, give help.
%%%                        --kb@cs.umb.edu, for Texinfo.
%%%  }
%%% ====================================================================
%
\ifx\epsfannounce\undefined \def\epsfannounce{\immediate\write16}\fi
 \epsfannounce{This is `epsf.tex' v2.7k <10 July 1997>}%
%
\newread\epsffilein    % file to \read
\newif\ifepsfatend     % need to scan to LAST %%BoundingBox comment?
\newif\ifepsfbbfound   % success?
\newif\ifepsfdraft     % use draft mode?
\newif\ifepsffileok    % continue looking for the bounding box?
\newif\ifepsfframe     % frame the bounding box?
\newif\ifepsfshow      % show PostScript file, or just bounding box?
\epsfshowtrue          % default is to display PostScript file
\newif\ifepsfshowfilename % show the file name if \epsfshowfalse specified?
\newif\ifepsfverbose   % report what you're making?
\newdimen\epsfframemargin % margin between box and frame
\newdimen\epsfframethickness % thickness of frame rules
\newdimen\epsfrsize    % vertical size before scaling
\newdimen\epsftmp      % register for arithmetic manipulation
\newdimen\epsftsize    % horizontal size before scaling
\newdimen\epsfxsize    % horizontal size after scaling
\newdimen\epsfysize    % vertical size after scaling
\newdimen\pspoints     % conversion factor
%
\pspoints = 1bp        % Adobe points are `big'
\epsfxsize = 0pt       % default value, means `use natural size'
\epsfysize = 0pt       % ditto
\epsfframemargin = 0pt % default value: frame box flush around picture
\epsfframethickness = 0.4pt % TeX's default rule thickness
%
\def\epsfbox#1{\global\def\epsfllx{72}\global\def\epsflly{72}%
   \global\def\epsfurx{540}\global\def\epsfury{720}%
   \def\lbracket{[}\def\testit{#1}\ifx\testit\lbracket
   \let\next=\epsfgetlitbb\else\let\next=\epsfnormal\fi\next{#1}}%
%
% We use \epsfgetlitbb if the user specified an explicit bounding box,
% and \epsfnormal otherwise.  Because \epsfgetbb can be called
% separately to retrieve the bounding box, we move the verbose
% printing the bounding box extents and size on the terminal to
% \epsfstatus.  Therefore, when the user provided the bounding box,
% \epsfgetbb will not be called, so we must call \epsfsetsize and
% \epsfstatus ourselves.
%
\def\epsfgetlitbb#1#2 #3 #4 #5]#6{%
   \epsfgrab #2 #3 #4 #5 .\\%
   \epsfsetsize
   \epsfstatus{#6}%
   \epsfsetgraph{#6}%
}%
%
\def\epsfnormal#1{%
    \epsfgetbb{#1}%
    \epsfsetgraph{#1}%
}%
%
\newhelp\epsfnoopenhelp{The PostScript image file must be findable by
TeX, i.e., somewhere in the TEXINPUTS (or equivalent) path.}%
%
\def\epsfgetbb#1{%
%
%   The first thing we need to do is to open the
%   PostScript file, if possible.
%
    \openin\epsffilein=#1
    \ifeof\epsffilein
        \errhelp = \epsfnoopenhelp
        \errmessage{Could not open file #1, ignoring it}%
    \else                       %process the file
        {%                      %start a group to contain catcode changes
            % Make all special characters, except space, to be of type
            % `other' so we process the file in almost verbatim mode
            % (TeXbook, p. 344).
            \chardef\other=12
            \def\do##1{\catcode`##1=\other}%
            \dospecials
            \catcode`\ =10
            \epsffileoktrue         %true while we are looping
            \epsfatendfalse     %[02-Jul-1996]: add forgotten initialization
            \loop               %reading lines from the EPS file
                \read\epsffilein to \epsffileline
                \ifeof\epsffilein %then no more input
                \epsffileokfalse %so set completion flag
            \else                %otherwise process one line
                \expandafter\epsfaux\epsffileline:. \\%
            \fi
            \ifepsffileok
            \repeat
            \ifepsfbbfound
            \else
                \ifepsfverbose
                    \immediate\write16{No BoundingBox comment found in %
                                    file #1; using defaults}%
                \fi
            \fi
        }%                      %end catcode changes
        \closein\epsffilein
    \fi                         %end of file processing
    \epsfsetsize                %compute size parameters
    \epsfstatus{#1}%
}%
%
% Clipping control:
\def\epsfclipon{\def\epsfclipstring{ clip}}%
\def\epsfclipoff{\def\epsfclipstring{\ifepsfdraft\space clip\fi}}%
\epsfclipoff % default for dvips is OFF
%
% The special that is emitted by \epsfsetgraph comes from this macro.
% It is defined separately to allow easy customization by other
% packages that first \input epsf.tex, then redefine \epsfspecial.
% This macro is invoked in the lower-left corner of a box of the
% width and height determined from the arguments to \epsffile, or
% from the %%BoundingBox in the EPS file itself.
%
% This version is for dvips:
\def\epsfspecial#1{%
     \epsftmp=10\epsfxsize
     \divide\epsftmp\pspoints
     \ifnum\epsfrsize=0\relax
       \special{PSfile=\ifepsfdraft psdraft.ps\else#1\fi\space
                llx=\epsfllx\space
                lly=\epsflly\space
                urx=\epsfurx\space
                ury=\epsfury\space
                rwi=\number\epsftmp
                \epsfclipstring
               }%
     \else
       \epsfrsize=10\epsfysize
       \divide\epsfrsize\pspoints
       \special{PSfile=\ifepsfdraft psdraft.ps\else#1\fi\space
                llx=\epsfllx\space
                lly=\epsflly\space
                urx=\epsfurx\space
                ury=\epsfury\space
                rwi=\number\epsftmp\space
                rhi=\number\epsfrsize
                \epsfclipstring
               }%
     \fi
}%
%
% \epsfframe macro adapted from the TeXbook, exercise 21.3, p. 223, 331.
% but modified to set the box width to the natural width, rather
% than the line width, and to include space for margins and rules
\def\epsfframe#1%
{%
  \leavevmode                   % so we can put this inside
                                % a centered environment
  \setbox0 = \hbox{#1}%
  \dimen0 = \wd0                                % natural width of argument
  \advance \dimen0 by 2\epsfframemargin         % plus width of 2 margins
  \advance \dimen0 by 2\epsfframethickness      % plus width of 2 rule lines
  \vbox
  {%
    \hrule height \epsfframethickness depth 0pt
    \hbox to \dimen0
    {%
      \hss
      \vrule width \epsfframethickness
      \kern \epsfframemargin
      \vbox {\kern \epsfframemargin \box0 \kern \epsfframemargin }%
      \kern \epsfframemargin
      \vrule width \epsfframethickness
      \hss
    }% end hbox
    \hrule height 0pt depth \epsfframethickness
  }% end vbox
}%
%
\def\epsfsetgraph#1%
{%
   %
   % Make the vbox and stick in a \special that the DVI driver can
   % parse.  \vfil and \hfil are used to place the \special origin at
   % the lower-left corner of the vbox.  \epsfspecial can be redefined
   % to produce alternate \special syntaxes.
   %
   \leavevmode
   \hbox{% so we can put this in \begin{center}...\end{center}
     \ifepsfframe\expandafter\epsfframe\fi
     {\vbox to\epsfysize
     {%
        \ifepsfshow
            % output \special{} at lower-left corner of figure box
            \vfil
            \hbox to \epsfxsize{\epsfspecial{#1}\hfil}%
        \else
            \vfil
            \hbox to\epsfxsize{%
               \hss
               \ifepsfshowfilename
               {%
                  \epsfframemargin=3pt % local change of margin
                  \epsfframe{{\tt #1}}%
               }%
               \fi
               \hss
            }%
            \vfil
        \fi
     }%
   }}%
   %
   % Reset \epsfxsize and \epsfysize, as documented above.
   %
   \global\epsfxsize=0pt
   \global\epsfysize=0pt
}%
%
%   Now we have to calculate the scale and offset values to use.
%   First we compute the natural sizes.
%
\def\epsfsetsize
{%
   \epsfrsize=\epsfury\pspoints
   \advance\epsfrsize by-\epsflly\pspoints
   \epsftsize=\epsfurx\pspoints
   \advance\epsftsize by-\epsfllx\pspoints
%
%   If `epsfxsize' is 0, we default to the natural size of the picture.
%   Otherwise we scale the graph to be \epsfxsize wide.
%
   \epsfxsize=\epsfsize{\epsftsize}{\epsfrsize}%
   \ifnum \epsfxsize=0
      \ifnum \epsfysize=0
        \epsfxsize=\epsftsize
        \epsfysize=\epsfrsize
        \epsfrsize=0pt
%
%   We have a sticky problem here:  TeX doesn't do floating point arithmetic!
%   Our goal is to compute y = rx/t. The following loop does this reasonably
%   fast, with an error of at most about 16 sp (about 1/4000 pt).
%
      \else
        \epsftmp=\epsftsize \divide\epsftmp\epsfrsize
        \epsfxsize=\epsfysize \multiply\epsfxsize\epsftmp
        \multiply\epsftmp\epsfrsize \advance\epsftsize-\epsftmp
        \epsftmp=\epsfysize
        \loop \advance\epsftsize\epsftsize \divide\epsftmp 2
        \ifnum \epsftmp>0
           \ifnum \epsftsize<\epsfrsize
           \else
              \advance\epsftsize-\epsfrsize \advance\epsfxsize\epsftmp
           \fi
        \repeat
        \epsfrsize=0pt
      \fi
   \else
     \ifnum \epsfysize=0
       \epsftmp=\epsfrsize \divide\epsftmp\epsftsize
       \epsfysize=\epsfxsize \multiply\epsfysize\epsftmp
       \multiply\epsftmp\epsftsize \advance\epsfrsize-\epsftmp
       \epsftmp=\epsfxsize
       \loop \advance\epsfrsize\epsfrsize \divide\epsftmp 2
       \ifnum \epsftmp>0
          \ifnum \epsfrsize<\epsftsize
          \else
             \advance\epsfrsize-\epsftsize \advance\epsfysize\epsftmp
          \fi
       \repeat
       \epsfrsize=0pt
     \else
       \epsfrsize=\epsfysize
     \fi
   \fi
}%
%
% Issue some status messages if the user requested them
%
\def\epsfstatus#1{% arg = filename
   \ifepsfverbose
     \immediate\write16{#1: BoundingBox:
                  llx = \epsfllx\space lly = \epsflly\space
                  urx = \epsfurx\space ury = \epsfury\space}%
     \immediate\write16{#1: scaled width = \the\epsfxsize\space
                  scaled height = \the\epsfysize}%
   \fi
}%
%
%   We still need to define the tricky \epsfaux macro. This requires
%   a couple of magic constants for comparison purposes.
%
{\catcode`\%=12 \global\let\epsfpercent=%\global\def\epsfbblit{%BoundingBox}}%
\global\def\epsfatend{(atend)}%
%
%   So we're ready to check for `%BoundingBox:' and to grab the
%   values if they are found.
%
%   If we find a line
%
%   %%BoundingBox: (atend)
%
%   then we ignore it, but set a flag to force parsing all of the
%   file, so the last %%BoundingBox parsed will be the one used.  This
%   is necessary, because EPS files can themselves contain other EPS
%   files with their own %%BoundingBox comments.
%
%   If we find a line
%
%   %%BoundingBox: llx lly urx ury
%
%   then we save the 4 values in \epsfllx, \epsflly, \epsfurx, \epsfury.
%   Then, if we have not previously parsed an (atend), we flag completion
%   and can stop reading the file.  Otherwise, we must keep on reading
%   to end of file so that we find the values on the LAST %%BoundingBox.
\long\def\epsfaux#1#2:#3\\%
{%
   \def\testit{#2}%             % save second character up to just before colon
   \ifx#1\epsfpercent           % then first char is percent (quick test)
       \ifx\testit\epsfbblit    % then (slow test) we have %%BoundingBox
            \epsfgrab #3 . . . \\%
            \ifx\epsfllx\epsfatend % then ignore %%BoundingBox: (atend)
                \global\epsfatendtrue
            \else               % else found %%BoundingBox: llx lly urx ury
                \ifepsfatend    % then keep parsing ALL %%BoundingBox lines
                \else           % else stop after first one parsed
                    \epsffileokfalse
                \fi
                \global\epsfbbfoundtrue
            \fi
       \fi
   \fi
}%
%
%   Here we grab the values and stuff them in the appropriate definitions.
%
\def\epsfempty{}%
\def\epsfgrab #1 #2 #3 #4 #5\\{%
   \global\def\epsfllx{#1}\ifx\epsfllx\epsfempty
      \epsfgrab #2 #3 #4 #5 .\\\else
   \global\def\epsflly{#2}%
   \global\def\epsfurx{#3}\global\def\epsfury{#4}\fi
}%
%
%   We default the epsfsize macro.
%
\def\epsfsize#1#2{\epsfxsize}%
%
%   Finally, another definition for compatibility with older macros.
%
\let\epsffile=\epsfbox
\endinput

liebend.tex
\documentstyle[a4wide,epsf,11pt,titlepage]{article}

\pagestyle{myheadings}

\setcounter{tocdepth}{1}
\newcounter{nref}
\setcounter{nref}{0}
\newcommand{\bbib}{%
  \renewcommand{\refname}{\large\bf References}%
  \begin{thebibliography}{99}%
  \setcounter{enumiv}{\thenref}}
\newcommand{\ebib}{%
  \end{thebibliography}%
  \setcounter{nref}{\arabic{enumiv}}}
\newcommand{\head}[3]{%
  \setcounter{nref}{0}%
  \thispagestyle{empty}%
  \section*{\LARGE\bf #1}%
  \stepcounter{section}%
  \addcontentsline{toc}{section}{#1}%
  \large\itshape%
  #2\\\vspace{0.1pt}\\%
  #3%
  \normalsize\upshape%
  \bigskip}

\begin{document}

%----------------------------------------------------------------------

\head{The Importance of Neutrino Opacities for the Accretion Luminosity
in Spherically Symmetric Supernova Models}
     {M.\ Liebend\"orfer$^{1,2}$, O.~E.~B.\ Messer$^{1,2,3}$, A.\ Mezzacappa$^{1}$, W.~R.\ Hix$^{1,2,3}$, F.-K. Thielemann$^{4}$, K. Langanke$^{5}$}
     {$^1$ Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN\-37831 \\
      $^2$ Department of Physics and Astronomy, University of Tennessee, Knoxville, TN\-37996 \\
      $^3$ Joint Institute for Heavy Ion Research, Oak Ridge National 
                Laboratory, Oak Ridge, TN\-37831 \\
      $^4$ Department of Physics and Astronomy, University of Basel, CH\-4056 Basel \\
      $^5$ Institut for Fysik og Astronomi, \r{A}rhus Universitet, DK\-8000 \r{A}rhus C}

\subsection*{General Relativistic Boltzmann Neutrino Transport}
Spherically symmetric simulations of stellar core collapse and postbounce
evolution do not lead to explosions if they are based on ``standard''
\cite{liebend.Bruenn_85,liebend.Lattimer_Swesty_91}
nuclear and weak interaction microphysics. This widely anticipated
statement achieved a completely new level of justification with
the technically complete and self-consistent treatment of neutrino
transport in the highly dynamical evolution after core collapse and
bounce \cite{liebend.Rampp_Janka_00,liebend.Mezzacappa_et_al_01}
in general relativity
\cite{liebend.Bruenn_DeNisco_Mezzacappa_01,liebend.Liebendoerfer_et_al_01}.
Multidimensional models for core collapse supernovae, which allow
non stratified hydrodynamics at the cost of reliable neutrino transport,
present the neglect of convection as a plausible cause for the failure
to reproduce supernova explosions in spherical symmetry (e.g. see Ref.
\cite{liebend.Janka_Kifonidis_Rampp_01} and references therein).
In our spherically symmetric models, neutrino
absorption adds only weakly to the entropy of the shock-dissociated
material after shock stagnation because of high infall velocities.
Nevertheless, spherically symmetric models provide a field for
further studies: The realistic neutron star structure and the accurate
evolution of angle- and energy-resolved neutrino distribution functions
enable the investigation of the influence of nuclear and weak interaction
physics on the models. Complete implicit radiation hydrodynamics also
provides insight into many tightly coupled processes with strong feedback
in the evolution of a core collapse supernova.

In the following, we compare the postbounce evolution of five
different initial stellar progenitors, simulated with general
relativistic three-flavor Boltzmann neutrino transport. The chosen
progenitors have masses of $13$ M$_{\odot}$ and $20$ M$_{\odot}$
\cite{liebend.Nomoto_Hashimoto_88}; and $15$ M$_{\odot}$, $25$
M$_{\odot}$, and $40$ M$_{\odot}$ \cite{liebend.Woosley_Weaver_95}. We
present in Fig. 1 the shock position for these different models as a
function of time, as solid lines. We find similar trajectories for all
progenitors, with a shock radius maximum around $150$ km. We also plot the
shock position in terms of enclosed mass in Fig. 2b: Before the existence
of a shock during core collapse, we plot the deleptonization-dependent
position of the sonic point where the shock will form after bounce. In a
later stage, the gradient of the shock trajectory reflects the accretion
rate given by the radial density profile of the progenitor star. Also
shown are the electron neutrino luminosities and rms energies in
Fig. 2a. Among the chosen progenitors, which represent the full progenitor mass
range of expected type II events, the most striking feature is
the clear separation into a quantitatively similar evolution up to the
electron neutrino burst and a distinctively different one afterwards.

\begin{figure}[ht]
  \centerline{\epsfxsize=0.9\textwidth\epsffile{liebend1.ps}}
  \caption{Shown in solid lines are the shock trajectories with standard input physics. Dash-dotted is the shock trajectory of the 20 solar mass
progenitor with nucleon strangeness content included. The experimental dashed
trajectories (based on transport with lowest angular resolution) show explosions
as a function of parametrized isoenergetic scattering on free nucleons.}
\end{figure}

\subsection*{Feedback in the Deleptonization during Core Collapse} When
the inner core of the progenitors reach the Chandrasekhar mass, they
have comparable density and temperature profiles. The electron fraction
determines the location of the sonic point at the surface of the inner
core, which is causally connected by electron pressure (Fig. 2b). During
collapse, the electron fraction decreases by electron capture on nuclei
and protons until trapped neutrinos block further deleptonization.
A regulation mechanism establishes similar electron fractions in all
models \cite{liebend.Bruenn_85,liebend.Messer_et_al_02}: The small
abundance of free protons, $Y_p$, is given by the Lattimer-Swesty equation
of state as a function of the electron fraction, $Y_e$. The sensitivity
$d\ln (Y_p)/dY_e\sim 30$ is large enough that a small deviation, $\Delta
Y_e=0.01$, from a ``normal'' $Y_e$-evolution changes the proton abundance,
and therewith the number of electron captures on free protons, by a
third. This negative feedback drives the electron fraction back to the
``norm''-evolution whenever electron captures on free protons dominate.
In our simulations, capture on heavy nuclei is suppressed as soon as the
$N=40$ shell is closed \cite{liebend.Bruenn_85}. Thus, the described
self-regulation sets in at this point, leading to very small differences
in the evolution of the different progenitors up to shock breakout.
The extent to which this regulation survives extension of electron
capture rates to heavier nuclei, when these rates are computed
with improved nuclear shell models, remains to be investigated.

\begin{figure}[ht]
  \centerline{\epsfxsize=0.45\textwidth\epsffile{liebend2.ps}
                      \epsfxsize=0.45\textwidth\epsffile{liebend3.ps}}
  \caption{The left hand side shows the electron neutrino luminosities
(solid) and rms energies (dashed). On the right hand side are the
accretion energy rate (solid) and the sonic point/mass trajectories in
enclosed mass (dashed).} \end{figure}

\subsection*{Accretion Luminosities and Neutrino Opacities}
The accretion luminosity, which dominates over the core diffusion luminosity
soon after shock stall, is produced by
the compression of infalling material at the surface of the PNS. The
available energy can roughly be estimated by the rate of infalling
material, multiplied by the gravitational potential at the neutrino
sphere. The result is an energy deposition rate that qualitatively
relates the modulation in the observable neutrino luminosities to
accretion rates (Fig. 2ab), i.e. to variations in the initial density
profiles of the progenitor stars. A relation of this kind might be
linked to analytical supernova models that present conditions for
shock revival as a function of independent luminosities and accretion
rates \cite{liebend.Burrows_Goshy_93,liebend.Janka_01}. The
main influence of nuclear input physics to the evolution of the shock
position resides in how the high density equation of state determines
the size of the PNS on the one hand, and how the neutrino opacities
at moderate densities ($\sim 10^{13}$ g/cm$^3$) affect the 
energy loss rate by neutrino emission on the other:

Indeed, reduced isoenergetic scattering opacities at moderate densities
have led to explosions in spherical symmetry and suggested a search for
an exploration of the physical limits. However, a physically
justifiable opacity reduction by taking into account the strangeness
content of nucleons (see e.g. \cite{liebend.Kolbe_et_al_92}) did not
produce explosions, even if it had a positive effect in exploratory runs
(Fig. 1). A detailed discussion of the degrees of freedom in the nuclear
input in this regime has been given in Ref. \cite{liebend.Horowitz_02}. A
parameter study with decreased opacities beyond physical limits (Fig. 1)
shows an interesting side effect: In exploding models, we find
electron fractions close to $0.5$ in the inner layers of ejecta
as soon as the electron degeneracy is lifted in the neutrino heated, expanding
material. The electron fraction changes during mass ejection will be
considered in upcoming nucleosynthesis calculations of supernova yields
\cite{liebend.Hauser_et_al_02}.

With standard opacities at moderate densities, the microphysics
above nuclear densities affects the postbounce
evolution more by influencing the size and stability of
the PNS than by influencing the diffusive neutrino flux. A more compact PNS
puts the accretion/heating cycle deeper into the gravitational
potential, resulting in higher infall velocities and luminosities
\cite{liebend.Bruenn_DeNisco_Mezzacappa_01,liebend.Liebendoerfer_et_al_01}.
An explosion-enhancing effect from the deeper gravitational potential
can only be obtained if the PNS contraction is fast enough to produce
very high luminosities before the heating region has adjusted to the
smaller PNS radius, or if the outer layers are kept at a distance
by a yet unidentified mechanism. PNS convection may provide
a more visible consequence of changes in the high density physics
\cite{liebend.Keil_Janka_Mueller_96,liebend.Mezzacappa_et_al_98}.
However, a definitive conclusion regarding the effect of convection
below and around the neutrino sphere awaits a more refined equation
of state and the inclusion of detailed multidimensional neutrino transport.

\subsection*{Acknowledgements}
M.L. is supported by the National Science Foundation under contract 
AST-9877130.
O.E.B.M. is supported by funds from the DoE HENP
Scientific Discovery through Advanced Computing Program. 
A.M. is supported at the Oak Ridge National Laboratory, managed by
UT-Battelle, LLC, for the U.S. Department of Energy under contract
DE-AC05-00OR22725.
W.R.H. is supported by NASA under contract NAG5-8405 and by funds 
from the Joint Institute for Heavy Ion Research and a DoE HENP
PECASE Award.
F.-K.T. is supported in part by the Swiss National Science Foundation 
under contract 20-61822.00.
K. L. is supported in part by the Danish Research Council.
We thank the Institute for Nuclear Theory at the University of
Washington for its hospitality and the Department of Energy for
partial support.
Our simulations were carried out on the National Energy Research
Supercomputer Center Cray SV-1. 

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