%Paper: 
%From: "Lynne Orr, U. Rochester, (716)275-8528" <ORR@urhep.pas.rochester.edu>
%Date: Tue, 20 Sep 1994 19:10:53 -0500 (EST)

%
%  ichep.sty appended after \end{document}
%
%  To incorporate postscript figures, uncomment \special statements
%   (there are 3).
%
%
\documentstyle{ichep}
\hoffset 0mm
\voffset 23mm
% Use suitable offset values to centre the output on your own system.
%
% Some examples of definitions used later.
\def\tbar{{\bar{t}}}
\def\tt{t\bar{t}}
\def\to{\rightarrow}
\def\as{\alpha_s}
\def\qq{q\bar{q}}
\def\pp{{\rm p\bar{p}}}
\def\bbar{{\bar{b}}}
\def\qbar{{\bar{q}}}
\def\bb{{b\bar{b}}}
\def\ww{W^+W^-}
\def\GeV{{\rm GeV}}
\def\GeVc{{\rm GeV/c}}
\def\TeV{{\rm TeV}}
\def\gt{\Gamma_t}
\def\bWbW{b W^+ \bar b W^-}
\def\degree{^{\circ}}
\def\cF{{\cal F}}
\def\prod{\cF_{\mbox{\tiny PROD}}}
\def\dec{\cF_{\mbox{\tiny DEC}}}
\def\int{\cF_{\mbox{\tiny INT}}}

\begin{document}



\title{
\vskip -3.5\baselineskip
\begin{flushright}
{\normalsize\rm
UR-1379 \\
 DTP/94/72  \\
ER-40685-829 \\
August 1994 \\}
\end{flushright}
\vskip 2\baselineskip
Soft Jets and Top Mass Measurement at the Tevatron}

\author{Lynne H Orr$^{\dag\ddag\#}$\ and W J Stirling$^{\S\|}$}

\affil{\dag\ Department of Physics and Astronomy, University of Rochester,\\
Rochester, NY 14627, USA\\
\S\ Departments of Physics and Mathematical Sciences, University of Durham,\\
Durham DH1 3LE, UK}


\abstract{
Extra soft jets in top events in $p \bar p$ collisions may arise not only
from gluons radiated off initial state partons or final state $b$ quarks, but
may also be radiated from the $t$ quarks themselves.  We discuss predictions
for distributions of soft gluons in $t \bar t$ production at the Tevatron
and the implications for attempts to measure the top mass by reconstructing
the invariant mass of its decay products.}

\twocolumn[\maketitle]

\fnm{7}{Presented by L H Orr at the XXVII International Conference on High
Energy Physics, Glasgow, July 20-27, 1994; proceedings to be published by
IOP Publishing Ltd.}
\fnm{2}{Work supported in part by the U.S. DOE, grant DE-FG02-91ER40685.}
\fnm{8}{E-mail: orr@urhep.pas.rochester.edu.}
\fnm{4}{E-mail: wjs@hep.durham.ac.uk.}


\section{Introduction}
In $\tt$ production at the Tevatron, the final state particles may be
accompanied by additional soft jets due to gluon radiation.  These soft jets
must be accounted for somehow in attempts to measure the top mass $m_t$ by
momentum reconstruction.  In particular, one would like to know whether
soft jets should be combined with the top's daughter $W$'s and $b$'s in
such reconstructions.  It is obvious that if the gluon has been radiated
off the final $b$ or $\bbar$, the gluon should be included, but if
it was radiated off an intitial state quark, then it should not.  Our
intuition tells us that final-state radiation, as in the former case,
 corresponds to jets near the $b$ or
$\bbar$ direction, and that initial-state radiation, as in
the latter case, corresponds to jets near the beam axis.

This intuitive picture is incomplete, however, because we must also consider
radiation off the top quarks themselves.  Do such gluons belong to the inital
state or the final state?  That this question cannot be answered indicates
that the the initial/final state picture of gluon radiation is too na{\"\i}ve
in the case of the top quark.  Top production and decay must be considered
simultaneously in a treatment of gluon radiation.

In this talk we report results of a study \cite{OS} of soft gluon radiation in
top production and decay in which all diagrams are correctly taken into
account.
Our aims are (i) to determine where the gluons come from and where they go, in
a way that is relevant to $m_t$ measurement, and (ii) to compare the correct
results which those of simple, intuitive models that are in the spirit of
what might be easily implemented in Monte Carlo Simulations.


\section{Soft gluons: formalism and features}

\begin{figure*}
\vspace{14cm}
\vspace{7cm}
\hspace{-2.2cm}
\hspace{-.2in}
%\special{psfile=ichep1.ps}
\vspace{-14.cm}
\caption{
Gluon pseudorapidity distributions in $\tt$ production via
$\qq\to \tt \to \bb \ww $, in $\pp$ collisions at
$\protect\sqrt{s} = 1.8\ \TeV$.
(a) Net distribution and contributions from
production and decay.
(b) Distributions arising from ISR, ISR/FSR, and BB models described in
the text.}
\vspace{-.23cm}
\end{figure*}


We work in the soft approximation ({\it i.e.}, we assume that the gluons
are less energetic than other particle in the event); for a discussion of
the soft gluon formalism in top physics see \cite{KOS}.  We consider
the process $\qq\to\tt\to\bWbW$ with emission of a soft gluon.
The matrix element and phase space factorize so that we can write the
gluon distribution as
\begin{equation}
{1\over d\sigma_0}\ {d\sigma\over{d E_g d\cos\theta_g d\phi_g}}\ = \
{\alpha_s\over 4 \pi^2} \ E_g \ (\prod + \dec +\int),
\end{equation}
where $d\sigma_0$ is the differential cross section for the lowest-order
process (with no gluon).
$\prod$ corresponds to gluons radiated in
association with $\tt$ production, {\it i.e.,} radiated before the $t$ or
$\tbar$ quark goes on shell.
  Similarly, $\dec$ corresponds to gluons
radiated in the decay of the $t$ or $\tbar$.  $\int$ represents the
interferences between the two and depends on the top width $\gt$.
Expressions for $\prod$, $\dec$, and $\int$ can be found in \cite{KOhS}.

The important point is that this production--decay--interference decomposition
provides a gauge--invariant substitute for the initial/final state picture
discussed above.  It
determines for us whether the gluon's momentum should be combined with those
of the $t$ decay products in reconstructing the top quark's four-momentum.
Gluons associated with top production do not contribute to the on-shell top
quark's momentum and should not be included.  Gluons associated with the
decay {\it do} contribute to the top momentum.  For the interference term there
is no such clear interpretation, but in the case of interest here it is
negligible anyway.

Detailed discussions of the properties of this distribution
(Eq.\ 1) can be found in
\cite{OS} and \cite{KOhS}.  Here we merely wish to point out some
physical features of $\prod$ and $\dec$ which have consequences for the
full distributions we see below, and which distinguish the correct distribution
from those in simpler models.  Being associated with $\tt$ production only,
$\prod$ knows nothing about the decay of the top quark, and depends only
on the momenta of the initial $q$ and $\qbar$ and the $t$ and $\tbar$,
as well as that of the gluon itself.  Similarly, $\dec$ knows nothing about
the initial state and depends only on the momenta of the $t$, $\tbar$, $b$,
$\bbar$, and gluon.  Both $\prod$ and $\dec$ can be written as sums of
``color antennae'' which can be interpreted in terms of a pair of quarks
connected by a color string.  These antennae exhibit color coherence, or
the string effect:  more radiation appears between such paired quarks than
outside of them.


\begin{figure*}
\vspace{14cm}
\vspace{7cm}
\hspace{-2.2cm}
\hspace{-.2in}
%\special{psfile=ichep2.ps}
\vspace{-14.cm}
\caption{Distribution in the cosine of the angle between the gluon and the
$b$-quark,  (a) with cuts described in the text and
 (b) with the additional cut $|\eta_g|\leq 1.5$.}
\vspace{-.23cm}
\end{figure*}


\section{Gluon distributions at the Tevatron}
Let us examine soft gluon distributions for $\tt$ production in $\pp$
collisions
at 1.8 TeV center-of-mass energy at the Tevatron.  The results shown are
from \cite{OS}, where a more complete discussion can be found.
We take $m_t=174\ \GeV$
and work at the parton level, considering only the $\qq$ initial state (which
dominates) and using minimal kinematic cuts, which are:
%($|\eta_{b}|,|\eta_{\bbar}|  \leq  1.5;\  |\eta_g| \leq 3.5;\
%10\ \GeV/c \leq p_T^g  \leq  25\ \GeV/c;\
%E_g \leq 100\ \GeV$; and $\Delta R_{bg},\Delta R_{\bbar g} \geq 0.5$).
\begin{eqnarray}
|\eta_{b}|,|\eta_{\bbar}| \> & \leq & \> 1.5 \; ,\nonumber \\
|\eta_g| \> & \leq & \> 3.5 \; ,\nonumber \\
10\ \GeV/c \leq \> & p_T^g & \> \leq  25\ \GeV/c \; ,\nonumber \\
E_g \> & \leq & \> 100\ \GeV \; ,\nonumber \\
\Delta R_{bg},\Delta R_{\bbar g} \> & \geq & \> 0.5 \; .
\label{cuts}
\end{eqnarray}




\subsection{Angular distributions and top momentum reconstruction}
We focus on angular distributions since we are interested in where soft jets
will appear in detectors.  Figure 1(a) shows the gluon pseudorapidity
distribution.  The total (solid line) is shown along with its decomposition
according to Eq.\ 1 into
production (dotted line) and decay (dashed line) contributions.  The
production piece is peaked in the forward direction and centrally suppressed.
This reflects the color antennae connecting the initial-state quarks with the
top quarks.  The decay contribution is peaked in the central region, which
is where the radiating top and bottom quarks tend to be produced.  The net
distribution is only slightly peaked in the center.
Note that,
while gluons at larger rapidities are almost exclusively associated with
production (and hence should be ignored in top momentum reconstruction),
central gluons are nearly as likely to have come from production as from decay.


In Figure 2 we test the second part of our guess (see introduction) by
 examining  to what extent proximity of gluons to the $b$ quark
correlates with having come from the decay contribution.  Fig. 2(a)
shows the distribution in cosine of the angle between the $b$ quark and the
gluon with the same cuts and decomposition as in Fig. 1(a).
The contribution from production is flat, as expected since it contains
no explicit  dependence on the $b$ quark's momentum.  The decay
contribution does increase as the gluon approaches the $b$, leading to
an excess above the production contribution close to the $b$.
The excess is only a slight one, though, and
the result is very sensitive to the cut on $\Delta R$.  Furthermore, no
hadronization effects have been taken into account.  We can improve the
situation by recalling that forward gluons tend to come from production.
If we tighten the gluon pseudorapidity cut to $|\eta_g|<1.5$, we see more
of an excess in decay gluons near the $b$, as shown in Fig.\ 2(b).  Sensitivity
to the $\Delta R$ cut and fragmentation effects remain a problem, however.


\begin{figure*}
\vspace{14cm}
\vspace{7cm}
\hspace{-2.2cm}
\hspace{-.2in}
%\special{psfile=ichep3.ps}
\vspace{-14.cm}
\caption{Forward--backward asymmetry in gluon pseudorapidity distributions in
$\tt$ production.  The cuts are as in Fig.\ 1 with the additional
requirements $\Delta\phi_{\bb}>135\degree$ and $\Delta\phi_{bg}<90\degree$.
The curves correspond to the
(a) total (solid), production (dots) and decay (dashes) distributions, and
to the  distributions for the
(b)  ISR (dots), ISR/FSR (dashes)
and BB (dash-dots) models.}
\vspace{-.23cm}
\end{figure*}


We now return to the pseudorapidity distribution
to compare the correct  distribution in
Fig.~1(a) to those in Fig.~1(b), obtained
from some simpler models that are intuitively appealing and easily implemented
in Monte Carlo simulations.  The ISR model (dotted line)
includes radiation off the initial $\qq$ state only, as if the $q$ and $\qbar$
formed a color singlet.  We might expect this to correspond to the
contribution associated with production, but we see by comparing to the
dotted line in Fig.~1(a) that the ISR model overestimates radiation in the
central region.  In the ISR/FSR model (dashed line) we add to the ISR model
radiation from the final $\bb$
pair as if they too formed a color singlet.  This model corresponds roughly
to the na\"{\i}ve expectation mentioned in the introductory paragraph.
Figure 1(b) shows that
this model overestimates the total radiation and gets the shape wrong.
In the BB model (dot-dashed line) we use the correct color structure but ignore
radiation off the top quark.  This model approximately
reproduces the correct pseudorapidity distribution.  However, it does not
give the correct azimuthal distribution,\cite{OS} and, more important
for $m_t$ reconstruction, does not permit a production--decay decomposition.


\subsection{Color structure and forward-backward asymmetry}

Finally, we discuss briefly a forward-backward asymmetry in the
radiation pattern (for appropriately chosen final states)
that arises from the color
structure of gluon emission in hadronic $\tt$ production.  While not directly
relevant to measurement of the top mass, the asymmetry is interesting because
it is a result of the fact that the top quarks themselves can radiate before
decaying.  It also reveals major differences between the correct distribution
and the simpler models.



This asymmetry arises from the string effect mentioned above.
For example, in $\qq\to\tt$ the $q$--$t$ antenna produces more radiation in the
region between the $t$ and $q$ than, say, between the $t$ and $\qbar$,
resulting in a forward--backward asymmetry in the gluon
radiation.  To avoid cancellation of the effect by an equal and opposite
asymmetry due to the $\qbar$ and $\tbar$, we try to preferentially select
gluons that are more likely to be in the $t$ than the $\tbar$ hemisphere, with
the additional cuts $\Delta \phi_{\bb} > 135\degree$ and
$\Delta \phi_{bg}<90\degree$.

The resulting distribution is shown in Figure
3(a).  A forward--backward asymmetry is evident, and we see from the
decomposition that it comes entirely from the production piece; the decay
knows nothing about the initial quarks' direction.  In Fig.\ 3(b) we show
the same distribution for the three simpler models.  There is no asymmetry
for the ISR and ISR/FSR models because there is no connection between radiation
in the initial and final states.  In contrast, the BB model shows a more
marked asymmetry than the correct distribution because without radiation from
the intermediate top quarks there is a more direct color connection between the
initial and final states.


\section{Summary}

We have shown that the subject of gluon radiation in $\tt$ production and
decay is a complicated one due to the rich color structure of the process.
For purposes of top mass reconstruction, we saw that there is no simple
prescription for dealing with additional soft jets in $\tt$ events, but
that the production--decay decomposition provides some guidance.
A comparison to simpler,
intuitively appealing models such as one might easily
implement in Monte Carlo simulations showed that they
do not reproduce the correct distributions and/or do not allow for the
production--decay decomposition.
Finally, we discussed a forward--backward asymmetry in soft gluon radiation
that illustrates the color structure, including in particular
radiation off the top quarks themselves.


\Bibliography{9}
\bibitem{OS} L.H.~Orr and W.J.~Stirling, DTP/94/60, UR-1365, July 1994.

\bibitem{KOS} V.A.~Khoze,  L.H.~Orr and W.J.~Stirling,
Nucl.~Phys. {\bf B378} (1992) 413.

\bibitem{KOhS} V.A.~Khoze,  J.~Ohnemus and W.J.~Stirling,
\prev{D49}{94}{1237}.

\end{thebibliography}
\end{document}

\section{Introduction}
These instructions are designed to demonstrate the use of the ICHEP style
file to produce Camera-Ready Copy (CRC).  See the accompanying information
document for instructions on obtaining this and other files referred to.
Note that this paper follows its own recommendations as to style and layout.

\subsection{Title page information}
Double-column journal CRC is produced using the \verb"ichep.sty" style file
with standard \LaTeX\ 2.09; it does not require
the new font selection scheme or \LaTeX2e.

The first line of the file should be
\begin{flushleft}
\verb"\documentstyle["{\it optional style files}\verb"]{ichep}"
\end{flushleft}
As shown, optional style files may be included; however
please make sure they do not redefine vital information.
The optional file \verb"iopfts.sty" can be used to obtain the AMS extension
fonts and access to characters such as the Blackboard bold alphabet.
% e.g.\ $\Bbb{ABC}$ if desired   % uncomment this line if iopfts loaded
%                                % as optional style file
At this point any macros specific to the paper may be added or a file
loaded to process figure files. The article content then starts with
the command \verb"\begin{document}".

The title is typeset with the \verb+\title{+{\it Full title\/}\verb+}+
command. Long titles may be split using \verb"\\".  Wherever possible,
mathematics in the title should be printed in a bold font, if a suitable
font is available.

The author(s) names are set with the command
\verb+\author{+{\it author names\/}\verb+}+.  All
authors should be listed together, and symbols or superscripted numbers
used to identify authors from different addresses. For long author lists
\verb"\\" is used to provide appropriate line breaks.

The header information down to and including the abstract is part of a
\LaTeX\ minipage and so any normal footnotes in this area would occur at
the bottom of the minipage and not at the bottom of the full page. To
circumvent this problem footnotes are set by putting, at the
appropriate place in the author list, the standard code for the
symbol and including the actual footnote outside the minipage (i.e.\
after the \verb"\twocolumn" command (see later))
with \verb"\fnm{"{\it Num\/}\verb"}{"{\it Footnote.}\verb"}". {\it Num\/}
is the number for the appropriate symbol (1 = \dag, 2 = \ddag, 3 = \S,
4 = $\|$, 5 = \P, 6 = $^+$, 7 = $^{\tsty*}$, 8 = $\sharp$, 9 = \dag\dag).
Where footnote symbols are also being used for links to addresses, the
standard code for the symbols is used. Thus for an article with
two authors each at a different address and each also with a footnote,
the author field should be:
\begin{flushleft}
\noindent\verb"\author{A J Cox$^{\dag\ddag}$\ and "\\
\verb"Jim Revill$^{\S\|}$}"
\end{flushleft}
and, assuming \dag\ and \S\ are address indicators,
after the \verb"\twocolumn" command the footnote text is coded with:
\begin{flushleft}
\verb"\fnm{2}{"{\it Footnote one.}\verb"}"\\
\verb"\fnm{4}{"{\it Footnote two.}\verb"}"
\end{flushleft}
A footnote to the title is set by adding an asterisk at the end of the
title and  \verb"\fnm{7}{"{\it Footnote.}\verb"}" after the
\verb"\twocolumn" command.

Author(s) addresses are set with the \verb"\affil" or \verb"\address"
command. Multiple addresses should be contained within
one \verb"\affil" command and separated by \verb"\\", e.g.
\begin{flushleft}
\verb"\affil{\dag\ "{\it Address one }\verb"\\"\\
\verb"\S\ "{\it Address two }\verb"}"
\end{flushleft}
There should be no paragraph break between addresses.

If a paper is written by authors on behalf of a collaboration and it is
desired to indicate the group concerned, this is done with a
\verb"\collab{"{\it Text}\verb"}" command after the addresses and before
the abstract.

The abstract is set with the command
\begin{flushleft}
\verb"\abstract{"{\it Text of Abstract.}\verb"}"
\end{flushleft}
The abstract should not make reference to the paper itself, but should
give a concise summary of the main content and conclusions of the paper.
If the abstract contains more than one paragraph, the
paragraphs should be separated with \verb"\cabs" rather than a paragraph
break. After the abstract follows the code
\begin{verbatim}
\twocolumn[\maketitle]
\end{verbatim}
This indicates the start of the two-column material and is followed by any
footnotes to the head (see earlier).

\section{The text}
To divide the text as required into sections, subsections and subsubsections,
use the commands \verb"\section{"{\it title}\verb"}",
\verb"\subsection{"{\it title}\verb"}" and
\verb"\subsubsection{"{\it title}\verb"}". Mathematics in a
section title should appear in bold where possible, and in subsections
it should be bold italic.  The acknowledgments section should be placed at the
end of the main text and before the references.  Its heading can be set with
\verb"\ack" for Acknowledgments or \verb"\ackn" for the singular version,
or \verb"\section*{Acknowledgments}".

\section{Figures}
The basic code for typesetting a figure is
\begin{flushleft}
\verb"\begin{figure}["{\it posn}\verb"]"\\
\verb"\vspace*{"{\it vertical figure space}\verb"}"\\
\verb"\caption{"{\it Figure caption.}\verb"}"\\
\verb"\end{figure}"
\end{flushleft}
A simplified equivalent command is provided (note capital `F'):
\begin{flushleft}
\verb"\Figure{"{\it space}\verb"}{"{\it Caption.}\verb"}["{\it posn}\verb"]"
\end{flushleft}

For single-column figures (\fref{pic1}) the
caption is set to the width of the column and is unjustified.
For a double-column figure (\fref{pic2}) the basic code is the same except that
the \verb"figure*" environment is used instead of \verb"figure".
The double-column code can be simplified to:
\begin{flushleft}
\verb"\widefigure{"{\it space}
\verb"}{"{\it Caption.}\verb"}["{\it posn}\verb"]"
\end{flushleft}
The caption for a double-column figure is set to the same width as
the abstract but unjustified; a short caption will be centred on the page.

\Figure{8pc}{This figure is set using the simplified coding; it should
appear at the top of a column or at the bottom. When single and double
column material are in close proximity careful positioning of figure calls
in the text is necessary to get good results.\label{pic1}}

\widefigure{8pc}{This wide figure has a short caption.\label{pic2}}

In all cases the positioning information is optional, and should normally
only be required where the default \verb"[thb]" does not give
satisfactory results.

Illustrations may be produced using the \LaTeX\ picture environment, by
including a postscript file or pasting a figure into a blank space as
produced in the example above. Illustrations should be original black ink
drawings, or glossy photographic prints of originals. Photocopies are not
normally satisfactory. All figures should be referred to in the text; if the
\LaTeX\ cross-referencing facility is used the commands \verb+\fref{pic1}+,
\verb+\Fref{pic1}+ are available to produce e.g.\ \fref{pic1}, \Fref{pic1}.
The label, e.g.\ \verb"\label{pic1}", is placed in the caption argument.

\section{Tables}
A simplified code for setting a table is available:
\begin{flushleft}
\verb"\begin{table}"\\
\verb"\Table{"{\it cols}\verb"}{"\\
{\it Table headings}\verb" \\"\\
\verb"\hline"\\
{\it Contents of table}\verb" \\"\\
\verb"}\caption{"{\it Table caption.}\verb"}"\\
\verb"\end{table}"
\end{flushleft}
Here {\it cols} specifies the alignment of the columns and the desired
vertical rules.  For example, to obtain five columns aligned left, right,
centred, right, left and vertical rules before the first and second columns
and after the last one, the code is {\it cols\/ }\verb+= |l|rcrl|+. If the
table is wider than a single column, replace \verb"table" by \verb"table*".
The caption appears in the same form as for a figure. Note a common source of
error is failing to add a \verb"\protect" to fragile commands in captions.

\def\e{\epsilon}
\def\add{\hbox{\scriptsize extra}{}}
% Some special symbols are defined.
\begin{table}
\Table{|c|cc|cc|}{
Source: & \multicolumn{2}{c|}{Experiment 1} &
\multicolumn{2}{c|}{Experiment 2} \\
& \multicolumn{2}{c|}{Results} & \multicolumn{2}{c|}{Results}  \\
\hline
Parameter & Max. & Min. & Max. & Min. \\
\hline
$\e_1$ & 6.675 & $-1.613$ & .065 & $-.134$  \\
\hline
$\e_2$ & .032 & $-.150$ & .014 & $-.057$  \\}
\caption{The maximum and minimum values of
the $\e^{\mbox{\protect\add}}_i$
parameter found in the two experiments.\label{tabl1}}
\end{table}

The command \verb"\lineup" allows \verb"\0" to be used as a space
the width of a digit, \verb"\-" to be a left overlapping minus sign and
\verb"\m" to be a phantom minus sign. These commands can be useful in
aligning columns of numbers.  (See the source text for examples of these
points.)  All tables should be referred to in the text and positioned close
to the point of first mention (\tref{tabl1}, \tref{tabl2}).

\begin{table*}
\Table{|llll|llll|}{
(a) & & & & (b)&&& \\
$x$ & $y$ & $A_{\rm m}$ (\%) & $A_{\rm corr}$ (\%) & $x$ & $y$
    & $A_{\rm m}$ (\%) & $A_{\rm corr}$ (\%) \\
\hline
0.005 & 0.850 & \00.900 & \00.938 & 0.005 & 0.850 & \00.686 & \00.781\\
0.015 & 0.756 & \02.600 & \02.551 & 0.008 & 0.800 & \00.663 & \00.662\\
0.025 & 0.666 & \09.000 & \08.932 & 0.010 & 0.750 & \00.604 & \00.573\\
0.035 & 0.599 & \02.500 & \02.456 & 0.050 & 0.700 & \0\-1.352 & \0\-1.832\\
0.050 & 0.528 & \08.100 & \08.060 &       &       &           & \\
} \caption{Some results of the iteration procedure, $E=100\,$GeV.
$A_{\rm m}$ is the `measured' spin asymmetry,
$A_{\rm corr}$ is the radiatively corrected spin asymmetry.
(a) proton data, (b) deuteron data.\label{tabl2}}
\end{table*}

\section{Displayed equations}
Mathematical material may be included in
text in the usual way, e.g.
$\sigtot=\half(b\,\vector{x}.\vector{y} -c\sin \theonetwo -d\sin\thethrfour)$.
%\ $i\Tr\delta x\sin \theta/
%\delta y_{\rm abs}\,{\bf A}= +2A^3{\bf B}{\cal C}+\vec{\cal C}$.
There are also two basic types of displayed equation in the ICHEP style: those
which are centred and those which start full left; these are outlined below.
Short equations are suited to the basic \LaTeX\ \verb+equation+ and
\verb+eqnarray+ enviroments. The code
\begin{verbatim}
\begin{equation}
f^{abc}T^c=[T^a,T^b].
\end{equation}
\end{verbatim}
produces the centred equation
\begin{equation}
f^{abc}T^c=[T^a,T^b].
\end{equation}
The plain \TeX\ command \verb+\eqalign+ is available in this enviroment
for aligning a multiline formula:
\begin{equation}
\eqalign{
f_{abc}T^c&=[T^a,T^b] \cr
          &=T^aT^b-T^bT^c \cr}
\end{equation}
is produced by the code
\begin{verbatim}
\begin{equation}
\eqalign{
f_{abc}T^c&=[T^a,T^b] \cr
          &=T^aT^b-T^bT^c \cr}
\end{equation}
\end{verbatim}
A series of short equations such as:
\begin{eqnarray}
\mbox{BR}(Z^0\to e^+e^-)&=3.37\%\nonumber \\
\mbox{BR}(Z^0\to \mu^+\mu^-)&=3.37\% \\
\mbox{BR}(Z^0\to \tau^+\tau^-)&
=3.36\%\nonumber
\end{eqnarray}
can be produced using the \verb+eqnarray+ enviroment:
\begin{verbatim}
\begin{eqnarray}
\mbox{BR}(Z^0\to e^+e^-)&=3.37\%\nonumber \\
\mbox{BR}(Z^0\to \mu^+\mu^-)&=3.37\% \\
\mbox{BR}(Z^0\to \tau^+\tau^-)&
=3.36\%\nonumber
\end{eqnarray}
\end{verbatim}
Long, turned over, equations such as
\begin{leqnarray}
\label{eq3}
\fl(1-x)^{-1}=1+x+x^2+x^3+x^4 \cr
+x^5+x^6+x^7\cdots
\end{leqnarray}
are suited to the \verb+leqnarray+ enviroment. \Eref{eq3} (\verb+\Eref{eq3}+)
was produced using:
\begin{verbatim}
\begin{leqnarray}
\label{eq3}
\fl(1-x)^{-1}=1+x+x^2+x^3+x^4 \cr
+x^5+x^6+x^7\cdots
\end{eqnarray}
\end{verbatim}
Note the command \verb"\fl" is used to make the first line start full left
and no ampersands are required for the alignment. Ampersands can be used if
there is secondary alignment, for instance for conditions. Using \verb"\cr"
at the end of a line instead of \verb"\\" suppresses the generation of an
equation number for that line.

For papers containing a large number of very long equations the double
column format may not be fully appropriate; to go to a single column
format the command \verb"\onecolumn" is used with \verb"\twocolumn" to
revert to two-column format after the long equations have been set. These
commands should only be used between paragraphs at places where it is
appropriate to end a page as they cause page breaks. \verb"\onecol" and
\verb"\twocol" can be used instead to make breaks and change format where
the break occurs within a paragraph rather than between paragraphs.


\section{References}
Indicate references in the main text by an arabic numeral in square brackets:
this may be done by hand [4], or by using the \LaTeX\
cross referencing facilities, e.g.\ \verb+\cite{higgs}+
to produce \cite{higgs}. The references, listed
in order of first citation, should be placed at the end of the paper under
the heading `References'; do not start a new page. In order to standardize
appearances as much as possible, please adopt the conventions indicated in the
examples below.

\Bibliography{9}
\bibitem{dirac} P.A.M.\ Dirac {\it The
Principles of Quantum Mechanics}, p.136
(Oxford 1987).
\bibitem{strange} M.\ Gell-Mann and A.\ Pais,
Proc. of the Glasgow Conf. on Nuclear and
Meson Phys. 1954, p.342; Eds. E.H. Bellamy
and R.G.\ Moorhouse (Pergamon 1954).
\bibitem{cmass} M.K.\ Gaillard and B.W.\ Lee,
\prev{D10}{74}{897}.
\bibitem{higgs} P.W.\ Higgs,
\prl{12}{64}{132};\ \ib{13}{64}{508};\
and\ \prev{145}{66}{1156}.
\bibitem{psi} J.J.\ Aubert {\it et al.},
\prl{33}{74}{1404}; \\
J.-E.\ Augustin {\it et al.},
\prl{33}{74}{1406}.
\bibitem{top} CDF Collaboration: F.\ Abe {\it
et al.}, Fermilab preprint:
FERMILAB-PUB-94-116-E.
\end{thebibliography}
\vspace{5mm}
\noindent
The  \verb+\Bibliography+ command provided, which generates the
\verb+thebibliography+ enviroment, should be used. A series of macros is
available for the most commonly used journal titles to aid the user and
ensure uniformity. The above example was typeset with the code:
\begin{verbatim}
\Bibliography{9}
\bibitem{dirac} P.A.M.\ Dirac {\it The
Principles of Quantum Mechanics}, p.136
(Oxford 1987).
\bibitem{strange} M.\ Gell-Mann and A.\ Pais,
Proc. of the Glasgow Conf. on Nuclear and
Meson Phys. 1954, p.342; Eds. E.H. Bellamy
and R.G.\ Moorhouse (Pergamon 1954).
\bibitem{cmass} M.K.\ Gaillard and B.W.\ Lee,
\prev{D10}{74}{897}.
\bibitem{higgs} P.W.\ Higgs,
\prl{12}{64}{132};\ \ib{13}{64}{508};\
and\ \prev{145}{66}{1156}.
\bibitem{psi} J.J.\ Aubert {\it et al.},
\prl{33}{74}{1404}; \\
J.-E.\ Augustin {\it et al.},
\prl{33}{74}{1406}.
\bibitem{top} CDF Collaboration: F.\ Abe {\it
et al.}, Fermilab preprint:
FERMILAB-PUB-94-116-E.\end{thebibliography}
\end{verbatim}
\end{document}
%%%%%%%%%%%%%%%%%%%%%%%% ichep.sty follows %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%                                                                      %%%
%%%    INSTITUTE OF PHYSICS PUBLISHING                                   %%%
%%%                                                                      %%%
%%%    ICHEP.STY  LaTeX CRC style file for ICHEP94 conference            %%%
%%%                                                                      %%%
%%%    Copyright 1994 IOP Publishing Ltd                                 %%%
%%%                                                                      %%%
%%%    Permission is hereby given to use this file for                   %%%
%%%    material to be submitted to or published by                       %%%
%%%    Institute of Physics Publishing                                   %%%
%%%                                                                      %%%
%%%    Version 1.2  1 July 1994                                          %%%
%%%                                                                      %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% First we have a character check
%
% ! exclamation mark    " double quote
% # hash                ` opening quote (grave)
% & ampersand           ' closing quote (acute)
% $ dollar              % percent
% ( open parenthesis    ) close paren.
% - hyphen              = equals sign
% | vertical bar        ~ tilde
% @ at sign             _ underscore
% { open curly brace    } close curly
% [ open square         ] close square bracket
% + plus sign           ; semi-colon
% * asterisk            : colon
% < open angle bracket  > close angle
% , comma               . full stop
% ? question mark       / forward slash
% \ backslash           ^ circumflex
%
% ABCDEFGHIJKLMNOPQRSTUVWXYZ
% abcdefghijklmnopqrstuvwxyz
% 1234567890
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\typeout{Document Style `ichep.sty'. IOP camera-ready copy
style file for ICHEP Conference Proceedings}

\let\reset@font\empty

\def\refname{References}
\def\figurename{Figure}
\def\tablename{Table}
\def\abstractname{Abstract}

\def\@ptsize{0}
\@namedef{ds@11pt}{\def\@ptsize{0}}
\@namedef{ds@12pt}{\def\@ptsize{0}}
\def\ds@twoside{\@twosidetrue
           \@mparswitchtrue}

\def\ds@draft{\overfullrule 5\p@}

\newif\if@titlepage \@titlepagefalse
\def\ds@titlepage{\@titlepagetrue}

\def\ds@twocolumn{\@twocolumntrue}

%
\newdimen\mathindent
\newlength{\digitwidth}
\newlength{\indentedwidth}
\newcounter{firstpage}
\newbox{\captionbox}
\newcounter{eqnval}
%
\@twosidetrue
%\@mparswitchtrue
\def\ds@draft{\overfullrule 5\p@}
\@options
%
\def\hexnumber@#1{\ifcase#1 0\or 1\or 2\or 3\or 4\or 5\or 6\or 7\or 8\or
 9\or A\or B\or C\or D\or E\or F\fi}
%
\lineskip 1pt \normallineskip 1pt
\def\baselinestretch{1}
\def\@normalsize{\@setsize\normalsize{12pt}\xpt\@xpt
\abovedisplayskip 10pt plus2pt minus5pt
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus3pt
\belowdisplayshortskip 6pt plus3pt minus3pt}
\def\small{\@setsize\small{11pt}\ixpt\@ixpt
\abovedisplayskip 8.5pt plus 3pt minus 4pt
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus2pt
\belowdisplayshortskip 4pt plus2pt minus 2pt
\def\@listi{\topsep 4pt plus 2pt minus 2pt\parsep 0pt plus 1pt
\itemsep \parsep}}
\def\footnotesize{\@setsize\footnotesize{9.5pt}\viiipt\@viiipt
\abovedisplayskip 6pt plus 2pt minus 4pt
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus 1pt
\belowdisplayshortskip 3pt plus 1pt minus 2pt
\def\@listi{\topsep 3pt plus 1pt minus 1pt\parsep 0pt plus 1pt
\itemsep \parsep}}
\def\scriptsize{\@setsize\scriptsize{8pt}\viipt\@viipt}
\def\tiny{\@setsize\tiny{6pt}\vpt\@vpt}
\def\large{\@setsize\large{14pt}\xiipt\@xiipt}
\def\Large{\@setsize\Large{18pt}\xivpt\@xivpt}
\def\LARGE{\@setsize\LARGE{22pt}\xviipt\@xviipt}
\def\huge{\@setsize\huge{25pt}\xxpt\@xxpt}
\def\Huge{\@setsize\Huge{30pt}\xxvpt\@xxvpt}
\normalsize
\oddsidemargin -3pc
\evensidemargin -3pc
\marginparwidth .75in
\marginparsep 7\p@
\topmargin=-72\p@
\headheight=12\p@
\headsep=12\p@
\footheight=12\p@
\footskip=25\p@

\textheight 55pc
\textwidth 18cm
\indentedwidth 15.9cm
\columnsep 1cm
\columnseprule 0\p@
\mathindent = 2pc

\newcommand{\onecol}{\parfillskip=0pt\par\eject
   \onecolumn\parfillskip=0pt plus1fil\noindent}
\newcommand{\twocol}{\parfillskip=0pt\par\eject
   \twocolumn\parfillskip=0pt plus1fil\noindent}
\footnotesep 6.65\p@
\skip\footins 9\p@ plus 4\p@ minus 2\p@
\floatsep 12\p@ plus 2\p@ minus 2\p@
\textfloatsep 18\p@ plus 2\p@ minus 4\p@
\intextsep 12\p@ plus 2\p@ minus 2\p@
\@maxsep 20\p@
\dblfloatsep 12\p@ plus 2\p@ minus 2\p@
\dbltextfloatsep 18\p@ plus 2\p@ minus 4\p@
\@dblmaxsep 20\p@
\@fptop 0\p@
\@fpsep 8\p@ plus 1fil
\@fpbot 0\p@ plus 1fil
\@dblfptop 0\p@
\@dblfpsep 8\p@ plus 1fil
\@dblfpbot 0\p@
\marginparpush 5\p@

\parskip 0\p@
\parindent 16\p@
\topsep 4\p@ plus 2\p@ minus 2\p@
\partopsep 2\p@ plus 1\p@ minus 1\p@
\itemsep 0\p@ plus 2\p@
\@lowpenalty 51
\@medpenalty 151
\@highpenalty 301
\@beginparpenalty -\@lowpenalty
\@endparpenalty -\@lowpenalty
\@itempenalty -\@lowpenalty

\@noskipsecfalse   % new version

%
\def\section{\@startsection{section}{1}{\z@}{-3.5ex plus -1ex minus
 -.2ex}{2.3ex plus .2ex}{\noindent\reset@font\normalsize\bf\raggedright}}
\def\subsection{\@startsection{subsection}{2}{\z@}{-3.25ex plus -1ex minus
 -.2ex}{1.5ex plus .2ex}{\noindent\reset@font
  \normalsize\it\raggedright\nohyphens}}
\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-3.25ex plus
-1ex minus -.2ex}{-1em}{\reset@font\normalsize\it\nohyphens}}
\def\paragraph{\@startsection
 {paragraph}{4}{\z@}{3.25ex plus 1ex minus .2ex}{-1em}
                                                {\reset@font\normalsize\it}}
\def\subparagraph{\@startsection
 {subparagraph}{4}{\parindent}{3.25ex plus 1ex minus
 .2ex}{-1em}{\reset@font\normalsize\it}}

\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth
     \let\@svsec\@empty\else
     \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname.\hskip 1em}\fi
     \@tempskipa #5\relax
      \ifdim \@tempskipa>\z@
        \begingroup #6\relax
          \noindent{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par}%
        \endgroup
       \csname #1mark\endcsname{#7}\addcontentsline
         {toc}{#1}{\ifnum #2>\c@secnumdepth \else
                      \protect\numberline{\csname the#1\endcsname}\fi
                    #7}\else
        \def\@svsechd{#6\hskip #3\relax  %% \relax added 2 May 90
                   \@svsec #8\csname #1mark\endcsname
                      {#7}\addcontentsline
                           {toc}{#1}{\ifnum #2>\c@secnumdepth \else
                             \protect\numberline{\csname the#1\endcsname}\fi
                       #7}}\fi
     \@xsect{#5}}
%
\def\@ssect#1#2#3#4#5{\@tempskipa #3\relax
   \ifdim \@tempskipa>\z@
     \begingroup #4\noindent{\hskip #1}{\interlinepenalty \@M #5\par}\endgroup
   \else \def\@svsechd{#4\hskip #1\relax #5}\fi
    \@xsect{#3}}


\setcounter{secnumdepth}{3}

\def\appendix{\@@par
 \setcounter{section}{0}
 \setcounter{subsection}{0}
 \setcounter{subsubsection}{0}
 \setcounter{equation}{0}
 \setcounter{figure}{0}
 \setcounter{table}{0}
 \def\thesection{Appendix \Alph{section}}
 \def\theequation{\ifnumbysec
      \Alph{section}.\arabic{equation}\else
      \Alph{section}\arabic{equation}\fi}
 \def\thetable{\ifnumbysec
      \Alph{section}\arabic{table}\else
      A\arabic{table}\fi}
 \def\thefigure{\ifnumbysec
      \Alph{section}\arabic{figure}\else
      A\arabic{figure}\fi}}



\labelsep 4\p@

\leftmargini 16\p@
\leftmarginii 18\p@
\leftmarginiii 16\p@
\leftmarginiv 14\p@
\leftmarginv 10\p@
\leftmarginvi 10\p@
\leftmargin\leftmargini
\labelwidth\leftmargini\advance\labelwidth-\labelsep
\parsep 0\p@ plus 1\p@
\def\@listI{\leftmargin\leftmargini \parsep 4\p@ plus2\p@ minus\p@
\topsep 8\p@ plus2\p@ minus4\p@
\itemsep 4\p@ plus2\p@ minus\p@}

\let\@listi\@listI
\@listi

\def\@listii{\leftmargin\leftmarginii
 \labelwidth\leftmarginii\advance\labelwidth-\labelsep
 \topsep 3\p@ plus 1\p@ minus 1\p@
 \parsep 0\p@ plus 1\p@
 \itemsep \parsep}
\def\@listiii{\leftmargin\leftmarginiii
 \labelwidth\leftmarginiii\advance\labelwidth-\labelsep
 \topsep 2\p@ plus 1\p@ minus 1\p@
 \parsep \z@ \partopsep 1\p@ plus 0\p@ minus 1\p@
 \itemsep \topsep}
\def\@listiv{\leftmargin\leftmarginiv
 \labelwidth\leftmarginiv\advance\labelwidth-\labelsep}
\def\@listv{\leftmargin\leftmarginv
 \labelwidth\leftmarginv\advance\labelwidth-\labelsep}
\def\@listvi{\leftmargin\leftmarginvi
 \labelwidth\leftmarginvi\advance\labelwidth-\labelsep}

\pretolerance=5000
\tolerance=8000
\hbadness=5000
\vbadness=5000
%
\def\labelenumi{\theenumi}
\def\theenumi{\arabic{enumi}}
\def\labelenumii{\theenumii}
\def\theenumii{\alpha{enumii}}
\def\p@enumii{\theenumi.}
\def\labelenumiii{\theenumiii.}
\def\theenumiii{\arabic{enumiii}}
\def\p@enumiii{\p@enumii.\theenumii}
\def\labelenumiv{\theenumiv.}
\def\theenumiv{\arabic{enumiv}}
\def\p@enumiv{\p@enumiii.\theenumiii}

\def\labelitemi{$\m@th\bullet$}
\def\labelitemii{\bf --}
\def\labelitemiii{$\m@th\ast$}
\def\labelitemiv{$\m@th\cdot$}

\def\verse{\let\\=\@centercr
 \list{}{\itemsep\z@ \itemindent -1.5em\listparindent \itemindent
 \rightmargin\leftmargin\advance\leftmargin 1.5em}\item[]}
\let\endverse\endlist
\def\quotation{\list{}{\listparindent 1.5em
 \itemindent\listparindent
 \rightmargin\leftmargin\parsep 0\p@ plus 1\p@}\item[]}
\let\endquotation=\endlist
\def\quote{\list{}{\rightmargin\leftmargin}\item[]}
\let\endquote=\endlist

\def\descriptionlabel#1{\hspace\labelsep \bf #1}
\def\description{\list{}{\labelwidth\z@ \itemindent-\leftmargin
 \let\makelabel\descriptionlabel}}
\let\enddescription\endlist
%
\def\enumerate{\ifnum \@enumdepth >3 \@toodeep\else
      \advance\@enumdepth \@ne
      \edef\@enumctr{enum\romannumeral\the\@enumdepth}\list
      {\csname label\@enumctr\endcsname}{\usecounter
        {\@enumctr}\def\makelabel##1{##1\hss}}\fi}
%
\def\itemize{\ifnum \@itemdepth >3 \@toodeep\else \advance\@itemdepth \@ne
\edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%
\list{\csname\@itemitem\endcsname}{\def\makelabel##1{##1\hss}\topsep=3pt
  \parsep=0pt\listparindent=0pt\itemsep=0pt\partopsep=0pt\rightmargin=0pt
  }\fi}
%
\newenvironment{leqnarray}{\begin{leqnarray}}{\end{leqnarray}}
\def\leqnarray{\stepcounter{equation}\let\@currentlabel=\theequation
\global\@eqnswtrue
\global\@eqcnt\z@\tabskip\mathindent\let\\=\@eqncr
\abovedisplayskip\topsep\ifvmode\advance\abovedisplayskip\partopsep\fi
\belowdisplayskip\abovedisplayskip
\belowdisplayshortskip\abovedisplayskip
\abovedisplayshortskip\abovedisplayskip
$$\halign to
\columnwidth\bgroup\@eqnsel$\displaystyle\tabskip\z@
 {##{}}$&\global\@eqcnt\@ne
                    $\displaystyle{{}##{}}$\hfil    %\hfil delete before 2nd $
 &\global\@eqcnt\tw@ $\displaystyle{{}##}$\hfil
 \tabskip\@centering&\llap{##}\tabskip\z@\cr}
%
\def\endleqnarray{\@@eqncr\egroup
 \global\advance\c@equation\m@ne$$\global\@ignoretrue }
%
\arraycolsep 5\p@
\tabcolsep=6\p@
\arrayrulewidth .4\p@
\doublerulesep 2\p@
\tabbingsep \labelsep
\skip\@mpfootins = \skip\footins
\fboxsep = 3\p@
\fboxrule = .4\p@
\def\titlepage{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
     \else \newpage \fi \thispagestyle{myheadings}\c@page\z@}

\def\endtitlepage{\if@restonecol\twocolumn \else \newpage \fi}

\newcounter {section}
\newcounter {subsection}[section]
\newcounter {subsubsection}[subsection]
\newcounter {paragraph}[subsubsection]
\newcounter {subparagraph}[paragraph]



\def\thesection {\arabic{section}}
\def\thesubsection {\thesection.\arabic{subsection}}
\def\thesubsubsection {\thesubsection .\arabic{subsubsection}}
\def\theparagraph {\thesubsubsection.\arabic{paragraph}}
\def\thesubparagraph {\theparagraph.\arabic{subparagraph}}
\def\@chapapp{Section}


\def\@pnumwidth{1.55em}
\def\@tocrmarg {2.55em}
\def\@dotsep{4.5}
\setcounter{tocdepth}{2}


\def\tableofcontents{\@restonecolfalse\if@twocolumn\@restonecoltrue
 \onecolumn\fi\section*{Contents}{}\thispagestyle{empty}
 \@starttoc{toc}\if@restonecol\twocolumn\fi}
%
\def\l@section{\@dottedtocline{1}{1.5em}{2.3em}}
\def\l@subsection{\@dottedtocline{2}{3.8em}{3.2em}}
\def\l@subsubsection{\@dottedtocline{3}{7.0em}{4.1em}}
\def\l@paragraph{\@dottedtocline{4}{10em}{5em}}
\def\l@subparagraph{\@dottedtocline{5}{12em}{6em}}
\def\listoffigures{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
 \fi\section*{List of Figures\@mkboth
 {LIST OF FIGURES}{LIST OF FIGURES}}\@starttoc{lof}\if@restonecol\twocolumn
 \fi}
\def\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}
\def\listoftables{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
 \fi\section*{List of Tables\@mkboth
 {LIST OF TABLES}{LIST OF TABLES}}\@starttoc{lot}\if@restonecol\twocolumn
 \fi}
\let\l@table\l@figure
%
% Redefinition to remove dotted lines from \@dottedtocline
%
\def\@dottedtocline#1#2#3#4#5{\ifnum #1>\c@tocdepth \else
  \vskip \z@ plus .2\p@
  {\leftskip #2\relax \rightskip \@tocrmarg \parfillskip -\rightskip
    \parindent #2\relax\@afterindenttrue
   \interlinepenalty\@M
   \leavevmode
   \@tempdima #3\relax \advance\leftskip \@tempdima
   \hbox{}\hskip -\leftskip
    #4\nobreak\hfill \nobreak \hbox to\@pnumwidth{\hfil
   \rm #5}\@@par}\fi}

\def\footnoterule{}%
\setcounter{footnote}{0}
\@addtoreset{footnote}{page}
\long\def\@makefntext#1{\parindent 1em\noindent
 \makebox[1em][l]{\footnotesize\rm$\m@th{\fnsymbol{footnote}}$}%
 \footnotesize\rm #1}
\def\@makefnmark{\hbox{${\fnsymbol{footnote}}\m@th$}}
\def\@thefnmark{\fnsymbol{footnote}}
\def\footnote{\@ifnextchar[{\@xfootnote}{\stepcounter{\@mpfn}%
     \begingroup\let\protect\noexpand
       \xdef\@thefnmark{\thempfn}\endgroup
     \@footnotemark\@footnotetext}}
\def\@fnsymbol#1{\ifcase#1\or \dagger\or \ddagger\or \S\or
   \|\or \P\or ^{+}\or ^{\tsty *}\or \sharp
   \or \dagger\dagger \else\@ctrerr\fi\relax}
\newcommand\ftnote[1]{\setcounter{footnote}{#1}%
   \addtocounter{footnote}{-1}\footnote}
\newcommand{\fnm}[1]{\setcounter{footnote}{#1}\footnotetext}
%
\def\center{\trivlist\topsep=0\p@\partopsep=0\p@
   \parsep=0\p@\itemsep=0\p@\centering\item[]}
%
\newenvironment{indented}{\begin{indented}}{\end{indented}}
\def\indented{\list{}{\itemsep=0\p@\labelsep=0\p@\itemindent=0\p@
   \labelwidth=0\p@\leftmargin=1.5cm\rightmargin=1.5cm
   \topsep=0\p@\partopsep=0\p@
   \parsep=0\p@\listparindent=0\p@}\rm}

\let\endindented=\endlist
%
\def\catchline{\hfill}

\def\cpyrtline{\hfill}
%
\def\maketitle{\thispagestyle{myheadings}%
   \vspace*{1.8cm}
   \begin{center}\@title\end{center}
   \vspace*{1.1cm}
   \normalsize\rm
   \begin{center}\@author\end{center}
   \begin{center}\@address\end{center}
   \@collab
   \@abstract}
%
%  Title
%
\def\title#1{\def\@title{\exhyphenpenalty=10000\hyphenpenalty=10000
    \Large\bf#1\par}}
\def\shortitle#1{\def\@shorttitle{#1}}
\let\paper=\title
%
% Authors
%
\renewcommand{\author}[1]{\def\@author{{\large #1\par}}}
%
% Affiliation
%
\newcommand{\address}[1]{\def\@address{\rm #1\par}}
\let\affil=\address
%
\newcommand{\collab}[1]{\def\@collab{\begin{center}%
   {\large\rm #1}\par
   \end{center}}}
%
% Default
%
\def\@collab{}
%
% Abstract
%
\def\abstract#1{\def\@abstract{\begin{center}
{\bf\abstractname}\end{center}%
\begin{indented}
\item[]#1\par
\end{indented}
\vspace{2cm minus1cm}}}%
%
\def\endabstract{}
%
% Command for second and subsequent paragraphs in abstract
%
\def\cabs{\\\hspace*{16\p@}}
%
\def\nosections{\vspace{30\p@ plus12\p@ minus12\p@}
    \noindent\ignorespaces}
%
\def\ack{\ifletter\bigskip\noindent\ignorespaces\else
    \section*{Acknowledgments}\fi}
\def\ackn{\ifletter\bigskip\noindent\ignorespaces\else
    \section*{Acknowledgment}\fi}
%
\newif\ifnumbysec
\def\theequation{\ifnumbysec
      \arabic{section}.\arabic{equation}\else
      \arabic{equation}\fi}
\def\eqnobysec{\numbysectrue\@addtoreset{equation}{section}}
%
\def\eqalign#1{\null\vcenter{\def\\{\cr}\openup\jot\m@th
  \ialign{\strut\hfil$\displaystyle{##{}}$&$\displaystyle{{}##}$\hfil
      \crcr#1\crcr}}\,}
%
\def\eqalignno#1{\displ@y \tabskip\z@skip
  \halign to\if@twocolumn\columnwidth\else\displaywidth\fi
   {\hfil$\@lign\displaystyle{##}$%
    \tabskip\z@skip
    &$\@lign\displaystyle{{}##}$\hfill\tabskip\@centering
    &\llap{$\@lign\hbox{\rm##}$}\tabskip\z@skip\crcr
    #1\crcr}}
%
\def\numparts{\addtocounter{equation}{1}%
     \setcounter{eqnval}{\value{equation}}%
     \setcounter{equation}{0}%
     \def\theequation{\ifnumbysec
     \arabic{section}.\arabic{eqnval}{\it\alph{equation}}%
     \else\arabic{eqnval}{\it\alph{equation}}\fi}}

\def\endnumparts{\def\theequation{\ifnumbysec
     \arabic{section}.\arabic{equation}\else
     \arabic{equation}\fi}%
     \setcounter{equation}{\value{eqnval}}}
%
\def\cases#1{%
     \left\{\,\vcenter{\def\\{\cr}\normalbaselines\openup1\jot\m@th%
     \ialign{\strut$\displaystyle{##}\hfil$&\tqs
     \rm##\hfil\crcr#1\crcr}}\right.}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  Floats
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  \c@topnumber            : Number of floats allowed at the top of a column.
%
\setcounter{topnumber}{4}
%
%  \topfraction            : Fraction of column that can be devoted to floats.
%
\def\topfraction{1}
%
%  \c@dbltopnumber, \dbltopfraction : Same as above, but for double-column
%                          floats.
%
\setcounter{dbltopnumber}{4}
\def\dbltopfraction{1}
%
%  \c@bottomnumber, \bottomfraction : Same as above for bottom of page.
%
\setcounter{bottomnumber}{2}
\def\bottomfraction{.8}
%
%  \c@totalnumber          : Number of floats allowed in a single column,
%                          including in-text floats.
%
\setcounter{totalnumber}{5}
%
%  \textfraction         : Minimum fraction of column that must contain text.
%
\def\textfraction{0}
%
%  \floatpagefraction    : Minimum fraction of page that must be taken
%                          up by float page.
%
\def\floatpagefraction{.8}
%
%  \dblfloatpagefraction : Same as above, for double-column floats.
%
\def\dblfloatpagefraction{.8}
%
\newcounter{figure}
\def\thefigure{\@arabic\c@figure}
\def\figure{\let\@makecaption\@makeonecolcaption\@float{figure}}
\let\endfigure\end@float
%
\@namedef{figure*}{\let\@makecaption\@makewidecaption
      \@dblfloat{figure}}
\@namedef{endfigure*}{\end@dblfloat}
%
\def\@makewidecaption#1#2{\vspace{10\p@}%
     \sbox{\captionbox}{\noindent\footnotesize\rm\raggedright{\bf #1.} #2}%
     \ifdim\wd\captionbox > \indentedwidth
     \begin{indented}
     \item[]\footnotesize\rm\raggedright{\bf #1.} #2\par
     \end{indented}%
     \else
     \hbox to \hsize{\hfil\box\captionbox\hfil}\fi}
%
\def\@makeonecolcaption#1#2{\vspace{10pt}%
     \parbox{\columnwidth}{\noindent
     \footnotesize\rm\raggedright{\bf #1.} #2}\par}
%
%
% The document style must define the following.
%
%    \fps@TYPE   : The default placement specifier for floats of type TYPE.
%
\def\fps@figure{tb}
\def\fps@table{tb}
%
%    \ftype@TYPE : The type number for floats of type TYPE.
%
\def\ftype@figure{1}
\def\ftype@table{2}
%
%    \ext@TYPE   : The file extension indicating the file on which the
%                  contents list for float type TYPE is stored.  For example,
%                  \ext@figure = 'lof'.
%
\def\ext@table{aux}
\def\ext@figure{aux}
%
%    \fnum@TYPE  : A macro to generate the figure number for a caption.
%                  For example, \fnum@TYPE == Figure \thefigure.
%
\def\fnum@table{\tablename~\thetable}
\def\fnum@figure{\figurename~\thefigure}
%
%    \@makecaption{NUM}{TEXT} : A macro to make a caption, with NUM the value
%                  produced by \fnum@... and TEXT the text of the caption.
%                  It can assume it's in a \parbox of the appropriate width.
%
\newcommand{\Figure}[2]{\def\figspace{\vspace*{#1}}%
    \def\figcap{\caption{#2}}%
    \futurelet\next\@figplace}
\def\@figplace{\ifx\next[\let\next=\@figpl
                 \else\let\next=\@fignopl\fi\next}
\def\@figpl[#1]{\begin{figure}[#1]
   \figspace
   \figcap
   \end{figure}}
\def\@fignopl{\begin{figure}
   \figspace
   \figcap
   \end{figure}}
%
\newcommand{\widefigure}[2]{\def\figspace{\vspace*{#1}}%
    \def\figcap{\caption{#2}}%
    \futurelet\next\@wfigplace}
\def\@wfigplace{\ifx\next[\let\next=\@wfigpl
                 \else\let\next=\@wfignopl\fi\next}
\def\@wfigpl[#1]{\begin{figure*}[#1]
   \figspace
   \figcap
   \end{figure*}}
\def\@wfignopl{\begin{figure*}
   \figspace
   \figcap
   \end{figure*}}
%
% \@float{TYPE}[PLACEMENT] : This macro begins a float environment for a
%     single-column float of type TYPE with PLACEMENT as the placement
%     specifier.  The default value of PLACEMENT is defined by \fps@TYPE.
%     The environment is ended by \end@float.
%     E.g., \figure == \@float{figure}, \endfigure == \end@float.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  Tables
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newcounter{table}
%
\def\thetable{\@arabic\c@table}
\def\table{\let\@makecaption\@makeonecolcaption
    \footnotesize\rm\@float{table}}
\let\endtable\end@float
%
\@namedef{table*}{\let\@makecaption\@makewidecaption
   \footnotesize\rm
   \@dblfloat{table}}
\@namedef{endtable*}{\end@dblfloat}
%
\def\tabular{\def\@halignto{}\@tabular}
\def\endtabular{\crcr\egroup\egroup $\egroup}
\expandafter \let \csname endtabular*\endcsname = \endtabular
%
\newsavebox{\tablebox}
%
\newcommand{\Table}[2]{\begin{center}
    \lineup
    \begin{tabular}{#1}%
    \hline
    #2
    \hline
    \end{tabular}
    \end{center}}
%
\newcommand{\tabnote}[1]{\begin{indented}
     \item[]\footnotesize\rm\raggedright #1\par
     \end{indented}}
%
% Definitions for centring headings over several columns
% \centre{4}{Results for helium} will centre
% Results for helium over four columns
% \crule{4} will produce a rule centred over four columns
% to go below a centred heading
%
\newcommand{\centre}[2]{\multicolumn{#1}{c}{#2}}
\newcommand{\crule}[1]{\multispan{#1}{\hrulefill}}
%
\def\lineup{\def\0{\hbox{\phantom{\footnotesize\rm 0}}}%
    \def\m{\hbox{$\phantom{-}$}}%
    \def\-{\llap{$-$}}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% References
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newcommand{\Bibliography}[1]{\section*{References}\par\numrefs{#1}}
\newcommand{\References}[1]{\section*{References}\footnotesize\rm}
%
\def\thebibliography#1{\list
 {\hfil[\arabic{enumi}]}{\topsep=0\p@\parsep=0\p@
 \partopsep=0\p@\itemsep=0\p@
 \labelsep=5\p@\itemindent=0\p@                %-10
 \settowidth\labelwidth{\footnotesize[#1]}%
 \leftmargin\labelwidth
 \advance\leftmargin\labelsep
% \advance\leftmargin -\itemindent
 \usecounter{enumi}}%
 \def\newblock{\ }
 \sloppy\clubpenalty4000\widowpenalty4000
 \sfcode`\.=1000\footnotesize\rm\relax}
\let\endthebibliography=\endlist
%
\def\numrefs#1{\begin{thebibliography}{#1}}
\def\endnumrefs{\end{thebibliography}}
\let\endbib=\endnumrefs

\mark{{}{}}

\def\ps@headings{\let\@mkboth\markboth
 \def\@oddfoot{}%
 \def\@evenfoot{}%
 \def\@evenhead{\makebox[\mathindent][l]{\normalsize\rm \thepage}%
  \normalsize\it\rightmark\hfill}%
 \def\@oddhead{\makebox[\mathindent][r]{\hfill}{\normalsize\it\leftmark}\hfill
  \normalsize\rm\thepage}%
}%

\def\ps@myheadings{\let\@mkboth\markboth
 \def\@oddhead{\catchline}%
 \def\@oddfoot{\cpyrtline}%
 \def\@evenhead{}%
 \def\@evenfoot{}%
}


\def\today{\ifcase\month\or
 January\or February\or March\or April\or May\or June\or
 July\or August\or September\or October\or November\or December\fi
 \space\number\day, \number\year}

\def\@begintheorem#1#2{\rm \trivlist \item[\hskip \labelsep{\it #1\ #2.}]}
\def\@opargbegintheorem#1#2#3{\rm \trivlist
      \item[\hskip \labelsep{\it #1\ #2\ (#3).}]}

\let\scap=\sc
\renewcommand{\sc}{\protect\scriptsize}
\newcommand{\itsc}{\protect\scriptsize\it}
\newcommand{\bfsc}{\protect\scriptsize\bf}
\def\p@LaTeX{{L\kern-.3em\lower.1em\hbox{$^{\rm A}$}\kern-.15em%
    T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}}
%
\newcommand{\nohyphens}{\hyphenpenalty=10000\exhyphenpenalty=10000}
\newcommand{\fl}{\hspace*{-\mathindent}}
\newcommand{\Tr}{\mathop{\rm Tr}\nolimits}
\newcommand{\tr}{\mathop{\rm tr}\nolimits}
\newcommand{\Or}{\mathop{\rm O}\nolimits}
\newcommand{\lshad}{[\![}
\newcommand{\rshad}{]\!]}
\newcommand{\case}[2]{{\textstyle\frac{#1}{#2}}}
\def\pt(#1){({\it #1\/})}
\newcommand{\dsty}{\displaystyle}
\newcommand{\tsty}{\textstyle}
\newcommand{\ssty}{\scriptstyle}
\newcommand{\sssty}{\scriptscriptstyle}
\def\lo#1{\llap{${}#1{}$}}
\def\eql{\llap{${}={}$}}
\def\lsim{\llap{${}\sim{}$}}
\def\lsimeq{\llap{${}\simeq{}$}}
\def\lequiv{\llap{${}\equiv{}$}}
%
\def\;{\protect\psemicolon}
\def\psemicolon{\relax\ifmmode\mskip\thickmuskip\else\kern .3333em\fi}
%
\newcommand{\eref}[1]{(\ref{#1})}
\newcommand{\sref}[1]{section~\ref{#1}}
\newcommand{\fref}[1]{figure~\ref{#1}}
\newcommand{\tref}[1]{table~\ref{#1}}
\newcommand{\Eref}[1]{Equation~(\ref{#1})}
\newcommand{\Sref}[1]{Section~\ref{#1}}
\newcommand{\Fref}[1]{Figure~\ref{#1}}
\newcommand{\Tref}[1]{Table~\ref{#1}}

\newcommand{\opencirc}{\raisebox{2\p@}{\;\circle{5}}}
\newcommand{\opensqr}{\mbox{$\Box$}}
\newcommand{\fullcirc}{\raisebox{-2\p@}{\Large$\bullet$}}
\newcommand{\fullsqr}{\mbox{\vrule height6pt width6pt}}
\newcommand{\dotted}
                 {\mbox{${\mathinner{\cdotp\cdotp\cdotp\cdotp\cdotp\cdotp}}$}}
\newcommand{\dashed}{\mbox{-\; -\; -\; -}}
\newcommand{\broken}{\mbox{-- -- --}}
\newcommand{\longbroken}{\mbox{--- --- ---}}
\newcommand{\chain}{\mbox{--- $\cdot$ ---}}
\newcommand{\dashddot}{\mbox{--- $\cdot$ $\cdot$ ---}}
\newcommand{\full}{\mbox{------}}
%
\newcommand{\etal}{{\it et al\/}\ }
\newcommand{\nonum}{\item[]}
%
% abbreviations for IOPP journals
%
\newcommand{\CQG}{{\em Class. Quantum Grav.} }
\newcommand{\HPP}{{\em High Perform. Polym.} }              % added 4/5/93
\newcommand{\IP}{{\em Inverse Problems\/} }
\newcommand{\JHM}{{\em J. Hard Mater.} }                    % added 4/5/93
\newcommand{\JPA}{{\em J. Phys. A: Math. Gen.} }
\newcommand{\JPB}{{\em J. Phys. B: At. Mol. Phys.} }      %1968-87
\newcommand{\jpb}{{\em J. Phys. B: At. Mol. Opt. Phys.} } %1988 and onwards
\newcommand{\JPC}{{\em J. Phys. C: Solid State Phys.} }   %1968--1988
\newcommand{\JPCM}{{\em J. Phys.: Condens. Matter\/} }    %1989 and onwards
\newcommand{\JPD}{{\em J. Phys. D: Appl. Phys.} }
\newcommand{\JPE}{{\em J. Phys. E: Sci. Instrum.} }
\newcommand{\JPF}{{\em J. Phys. F: Met. Phys.} }
\newcommand{\JPG}{{\em J. Phys. G: Nucl. Phys.} }         %1975--1988
\newcommand{\jpg}{{\em J. Phys. G: Nucl. Part. Phys.} }   %1989 and onwards
\newcommand{\MSMSE}{{\em Modelling Simulation Mater. Sci. Eng.} }
\newcommand{\MST}{{\em Meas. Sci. Technol.} }              %1990 and onwards
\newcommand{\NET}{{\em Network\/} }
\newcommand{\NL}{{\em Nonlinearity\/} }
\newcommand{\NT}{{\em Nanotechnology} }
\newcommand{\PAO}{{\em Pure Appl. Optics\/} }
\newcommand{\PM}{{\em Physiol. Meas.} }                        % added 4/5/93
\newcommand{\PMB}{{\em Phys. Med. Biol.} }
\newcommand{\PPCF}{{\em Plasma Phys. Control. Fusion\/} }      % added 4/5/93
\newcommand{\PSST}{{\em Plasma Sources Sci. Technol.} }
\newcommand{\QO}{{\em Quantum Opt.} }
\newcommand{\RPP}{{\em Rep. Prog. Phys.} }
\newcommand{\SLC}{{\em Sov. Lightwave Commun.} }               % added 4/5/93
\newcommand{\SST}{{\em Semicond. Sci. Technol.} }
\newcommand{\SUST}{{\em Supercond. Sci. Technol.} }
\newcommand{\WRM}{{\em Waves Random Media\/} }
%
% Other commonly quoted journals
%
\newcommand{\AC}{{\em Acta Crystallogr.} }
\newcommand{\AM}{{\em Acta Metall.} }
\newcommand{\AP}{{\em Ann. Phys., Lpz.} }
\newcommand{\APNY}{{\em Ann. Phys., NY\/} }
\newcommand{\APP}{{\em Ann. Phys., Paris\/} }
\newcommand{\CJP}{{\em Can. J. Phys.} }
\newcommand{\JAP}{{\em J. Appl. Phys.} }
\newcommand{\JCP}{{\em J. Chem. Phys.} }
\newcommand{\JJAP}{{\em Japan. J. Appl. Phys.} }
\newcommand{\JP}{{\em J. Physique\/} }
\newcommand{\JPhCh}{{\em J. Phys. Chem.} }
\newcommand{\JMMM}{{\em J. Magn. Magn. Mater.} }
\newcommand{\JMP}{{\em J. Math. Phys.} }
\newcommand{\JOSA}{{\em J. Opt. Soc. Am.} }
\newcommand{\JPSJ}{{\em J. Phys. Soc. Japan\/} }
\newcommand{\JQSRT}{{\em J. Quant. Spectrosc. Radiat. Transfer\/} }
\newcommand{\NC}{{\em Nuovo Cimento\/} }
\newcommand{\NIM}{{\em Nucl. Instrum. Methods\/} }
\newcommand{\NP}{{\em Nucl. Phys.} }
\newcommand{\PL}{{\em Phys. Lett.} }
\newcommand{\PR}{{\em Phys. Rev.} }
\newcommand{\PRL}{{\em Phys. Rev. Lett.} }
\newcommand{\PRS}{{\em Proc. R. Soc.} }
\newcommand{\PS}{{\em Phys. Scr.} }
\newcommand{\PSS}{{\em Phys. Status Solidi\/} }
\newcommand{\PTRS}{{\em Phil. Trans. R. Soc.} }
\newcommand{\RMP}{{\em Rev. Mod. Phys.} }
\newcommand{\RSI}{{\em Rev. Sci. Instrum.} }
\newcommand{\SSC}{{\em Solid State Commun.} }
\newcommand{\ZP}{{\em Z. Phys.} }
%

\def\ap#1#2#3 {Ann. Phys. (NY) {\bf#1} (19#2) #3}
\def\apj#1#2#3 {Astrophys. J. {\bf#1} (19#2) #3}
\def\apjl#1#2#3 {Astrophys. J. Lett. {\bf#1} (19#2) #3}
\def\app#1#2#3 {Acta. Phys. Pol. {\bf#1} (19#2) #3}
\def\ar#1#2#3 {Ann. Rev. Nucl. Part. Sci. {\bf#1} (19#2) #3}
\def\cpc#1#2#3 {Computer Phys. Comm. {\bf#1} (19#2) #3}
\def\err#1#2#3 {{\it Erratum} {\bf#1} (19#2) #3}
\def\ib#1#2#3 {{\it ibid.} {\bf#1} (19#2) #3}
\def\jmp#1#2#3 {J. Math. Phys. {\bf#1} (19#2) #3}
\def\ijmp#1#2#3 {Int. J. Mod. Phys. {\bf#1} (19#2) #3}
\def\jetp#1#2#3 {JETP Lett. {\bf#1} (19#2) #3}
\def\jpg#1#2#3 {J. Phys. G. {\bf#1} (19#2) #3}
\def\mpl#1#2#3 {Mod. Phys. Lett. {\bf#1} (19#2) #3}
\def\nat#1#2#3 {Nature (London) {\bf#1} (19#2) #3}
\def\nc#1#2#3 {Nuovo Cim. {\bf#1} (19#2) #3}
\def\nim#1#2#3 {Nucl. Instr. Meth. {\bf#1} (19#2) #3}
\def\np#1#2#3 {Nucl. Phys. {\bf#1} (19#2) #3}
\def\pcps#1#2#3 {Proc. Cam. Phil. Soc. {\bf#1} (#2) #3}
\def\pl#1#2#3 {Phys. Lett. {\bf#1} (19#2) #3}
\def\prep#1#2#3 {Phys. Rep. {\bf#1} (19#2) #3}
\def\prev#1#2#3 {Phys. Rev. {\bf#1} (19#2) #3}
\def\prl#1#2#3 {Phys. Rev. Lett. {\bf#1} (19#2) #3}
\def\prs#1#2#3 {Proc. Roy. Soc. {\bf#1} (19#2) #3}
\def\ptp#1#2#3 {Prog. Th. Phys. {\bf#1} (19#2) #3}
\def\ps#1#2#3 {Physica Scripta {\bf#1} (19#2) #3}
\def\rmp#1#2#3 {Rev. Mod. Phys. {\bf#1} (19#2) #3}
\def\rpp#1#2#3 {Rep. Prog. Phys. {\bf#1} (19#2) #3}
\def\sjnp#1#2#3 {Sov. J. Nucl. Phys. {\bf#1} (19#2) #3}
\def\spj#1#2#3 {Sov. Phys. JEPT {\bf#1} (19#2) #3}
\def\spu#1#2#3 {Sov. Phys.-Usp. {\bf#1} (19#2) #3}
\def\zp#1#2#3 {Zeit. Phys. {\bf#1} (19#2) #3}
%
\ps@headings \pagenumbering{arabic} \onecolumn


