% This is an example LaTeX file, to illustrate the use of this
% text handling program to write laboratory reports.
% This is only an example which you can use as a guide if you
% wish. Everyone has a style of their own, and this is NOT intended
% as a rigid scheme which MUST be followed.
% If you wish to use this template, you should copy it into you own
% directory structure, and use the editor you prefer ( on unixg you could
% use Emacs, or vi ) to produce your own version.
% This file is the LaTeX text file.
% To make a printed copy you must do the following:
% 1) make sure your source file has the proper extension .tex;
% here we will call the source file ex.tex
% 2) process the source file by: latex ex.tex
% 3) This will produce some secondary files with extensions .aux, .log, and
% .dvi If you are incorporating graphics, the graphics must be in files in
% your current directory, anmd the graphics files must be encoded
% as PostScript files, each graphics file having the extension .ps ( More
% on how to generate suitable graphics files later.)
% 4) If you are at a workstation terminal such as one of the Sun's in the
% lab you will be working in an environment call X11. You can then
% preview the document by typing : xdvi ex
% which will produce a display of your document on the terminal. It will no
% show any graphics which you may have incorporated into the document.
% 5) When you have a satisfactory .dvi file you can convert it to a
% PostScript file suitable for printing on printers with PostScript
% capabilities, such as the Laser Jet attached to the 409Lab Suns.
% To convert to PostScript type : dvips -o ex.dvi >ex.ps
% This will produce a PostScript file ex.ps which can be previewed by
% typing : gs ex.ps
% This will give a screen preview of your document as it will be printed
% including graphics.
% The latex source now begins
%Skeleton document for P 409 Oct 30 1992 B.L. White
\documentstyle[11pt]{article}
\textwidth=6.35in
\topmargin=-.05in
\oddsidemargin=0.1in
\textheight=8.45in
\renewcommand{\baselinestretch}{1.0}
\begin{document}
%
% 4 particles
%
\newcommand{\fp} {\mbox{$4\pi$}}
\newcommand{\qqqq} {\mbox{$qq\bar{q}\bar{q}$}}
\newcommand{\pppp} {\mbox{$\pi^+\pi^-\pi^+\pi^-$}}
\newcommand{\ppkk} {\mbox{$\pi^+\pi^-K^+K^-$}}
\newcommand{\kkpp} {\mbox{$K^+K^-\pi^+\pi^-$}}
\newcommand{\pkpp} {\mbox{$\pi^\pm K^\mp\pi^+\pi^-$}}
\newcommand{\pkkz} {\mbox{$\pi^\pm K^\mp K^0$}}
\newcommand{\phppp} {\mbox{$\phi\pi^+\pi^-\pi^0$}}
\newcommand{\kkppp} {\mbox{$K^+K^-\pi^+\pi^-\pi^0$}}
%
% JPC
%
\newcommand{\jpc} {\mbox{${\mbox J}^{\mbox{\small PC}}$}}
\newcommand{\lj} {\mbox{$^{2S+1}L_J$}}
%
\newcommand{\ssz} {\mbox{$^1S_0$}}
\newcommand{\tso} {\mbox{$^3S_1$}}
\newcommand{\spo} {\mbox{$^1P_1$}}
\newcommand{\tpz} {\mbox{$^3P_0$}}
\newcommand{\tpo} {\mbox{$^3P_1$}}
\newcommand{\tpt} {\mbox{$^3P_2$}}
\newcommand{\tpzot} {\mbox{$^3P_{0,1,2}$}}
\newcommand{\tpzt} {\mbox{$^3P_{0,2}$}}
\newcommand{\tpj} {\mbox{$^3P_J$}}
% for the math mode
\newcommand{\sszm} {^1S_0}
\newcommand{\tsom} {^3S_1}
\newcommand{\spom} {^1P_1}
\newcommand{\tpzm} {^3P_0}
\newcommand{\tpom} {^3P_1}
\newcommand{\tptm} {^3P_2}
\newcommand{\tpzotm} {^3P_{0,1,2}}
\newcommand{\tpztm} {^3P_{0,2}}
\newcommand{\tpjm} {^3P_J}
%
% diverse
%
\newcommand{\q} {\mbox{Q$^2$}}
\newcommand{\chs} {\mbox{$\chi^2$}}
\newcommand{\pbgas} {\mbox{$\bar{\mbox{p}}$-Gas}}
\newcommand{\pblx} {\mbox{$\bar{\mbox{p}}$-LX}}
\newcommand{\pbgasdata} {\mbox{$\bar{\mbox{p}}$-Gas data}}
\newcommand{\pblxdata} {\mbox{$\bar{\mbox{p}}$-LX data}}
\newcommand{\dedx} {dE/dx}
\newcommand{\br} {branching ratio}
\newcommand{\h} {\mbox{$H_2$}}
\newcommand{\half} {\mbox{$\frac{1}{2}$}}
\newcommand{\scale} {\mbox{$\times 10^{-5}$}}
\newcommand{\sca}[1] {\mbox{$\times 10^{#1}$}}
\newcommand{\hs}[1] {\hspace{#1}}
\newcommand{\mc} {\multicolumn}
\newcommand{\phinn} {\mbox{$\varphi_{NN}$}}
\newcommand{\bl} {\mbox{\ }}
\newcommand{\pbarp}{\overline{p} p}
\newcommand{\qbarq}{\overline{q} q}
\newcommand{\pp}{\pi^+\pi^-}
\newcommand{\KK}{K^+K^-}
\newcommand{\KzKzb}{K^0\overline{K}^0}
\newcommand{\KSKS}{K_SK_S}
\newcommand{\KSKL}{K_SK_L}
\newcommand{\Htwo}{H_2}
\newcommand{\spa}{\hspace{1.in}}
\newcounter{fig}
\newcommand{\upfig}{\addtocounter{fig}{1}\thefig}
\begin{center}
\huge
FIRST OBSERVATION OF A BIGGS PARTICLE\\
\vspace{0.7in}
\large
B.L.White \\
\vspace{0.4in}
{\em Physics 409 Laboratory\\
Department of Physics\\
University of British Columbia\\
Vancouver B.C\\
Canada V6T 2A6\\
\vspace{0.7in}
\today\\}
\end{center}
\pagebreak
\begin{abstract}
In the abstract we put the barest information about what we did and what
were the results. No explanations or theory or descriptions of apparatus
etc are necessary or relevant. If the reader wishes to know about these
he/she knows that they will be found in the paper. The abstract is used to
allow the reader to decide whether the paper is interesting to him. There
are journals such as 'Physics Abstracts' which publish titles and abstracts
from a wide range of journals, which can be searched on CD-ROM in the Science
Division of the Main library.\\
Having read the abstract, the reader will frequently then jump to the
'Summary' or 'Conclusions' section, and only then decide whether or not to
read the paper. When you have finished composing your report, look at the
abstract and conclusions sections to see if they provide the required
information to encourage the reader to go further.
\end{abstract}
\pagebreak
\section{Introduction}
The introduction should give a brief description of the place of the work
to be described in the general context of physics. You should refer to
previous work where the papers may assist the reader to evaluate your claims
as to the possible significance of the work you are going to describe.\\
This means talking in terms familiar to an educated physicist who may not
be familiar with work in this particular area. The context will include a
discussion of theory and of experimental method and apparatus but not at the
level of detail to be found in the sections devoted to those topics later in
the report. This discussion will place the present work in context with
respect to existing theory and experiment, ( with references like this
\cite{ahmad84.1} ) and will state what improvements and advances are
anticipated and have been achieved as a result of the present work. \\
Of course in a student laboratory this context will often be different
from that in a research laboratory but you should nevertheless make the
attempt to deal with the contextual question.\\ The introduction should
contain as its last section a description of the layout of the report - what
the subsequent sections contain: this is a further guide to the reader as to
whether he/she should continue reading and where the details the reader may
be seeking are to be found.\\
\section{Theory}
Here you review in detail the salient points of the theory. You don't do a step by step reproduction of the standard theory to be found in texts or published documents, but you do
\begin{itemize}
\item Write down the beginning fundamental theoretical equations
\item Set down any essential steps leading from the fundamentals to
\item the set of equations essential to your work.
\end{itemize}
It is fairly common in experimental papers to place the theory in other sections rather than in a section of its own. For instance, some background theory might appear in the introduction and theory associated with how you manipulate the data might occur in the section on Method or one on Data Analysis and Discussion.
\subsection{Mathematical expressions}
In this and other sections you will find the LaTeX equation writing tools
very useful. As an example: \\
\underline{Relativistic Notation}
The normal space co-ordinates are written as
\[ x_{1}, \ x_{2}, \ x_{3}. \]
Einstein's interpretation of the Michelson-Morley experiment was that the speed of light
is the same to all observers. This concept can be expressed mathematically by introducing
time as a fourth dimension, ie.
\[ x_{4} \ = \ ict. \]
An invariant distance $ dS $ can be defined such that
\[ \begin{array}{lrl}
& dS^{2} \ & = \ -(dx_{\lambda})^{2} \\
& & = \ c^{2} dt^{2} \ - \ dx_{1}^{2} - dx_{2}^{2} - dx_{3}^{2}.\\
& & = c^{2} dt^{2} \{ 1 \ - \ \frac{ dx_{1}^{2} + dx_{2}^{2}
+ dx_{3}^{2} }{c^{2}dt^{2} } \} \\
& & = \ ( 1 - \frac{v^{2}}{c^{2}})c^{2}dt^{2} \\
& & = ( 1 - \beta^{2} )c^{2}dt^{2} \\
& & = \ \frac{c^{2}}{\gamma^{2}} dt^{2} \\
{\rm where } & & \\
& \beta^{2} \ & = \ \frac{dx_{1}^{2} + dx_{2}^{2} +
dx_{3}^{2} }{ c^{2}dt^{2}} \ = \ \frac{v^{2}}{c^{2}} \\
{\rm and } & & \\
& \gamma \ & = \ \frac{1}{\sqrt{1 - \beta^{2}}}
\end{array} \]
As $ dS $ is a Lorentz invariant we can introduce a dimensionless velocity
\[ u_{\lambda} = \frac{dx_{\lambda} }{dS} = \frac{\gamma}{c} \frac{
dx_{\lambda} }{dt} \]
such that \[ u_{\lambda}^{2} \ = \ -1 \]
Using this definition of the four velocity we can define the four
momentum
\[ p_{\lambda} \ = \ mc u_{\lambda} \]
\[ \begin{array}{rl}
{\rm such \ that} & \\
{\bf p}_{i} \ & = \ mc\frac{\gamma}{c}\frac{ {\bf dx}_{i} }{dt}
= m\gamma {\bf v_{i} } \hspace{.5cm} i= 1,2,3 \\
{\rm and} & \\
p_{4} \ & = \ mc \frac{\gamma}{c}\frac{dx_{4}}{dt} = \frac{i}{c}
\gamma mc^{2} \ = \ \frac{i}{c} E \\
{\rm as} & \\
u_{\lambda}^{2} \ & = \ -1 \\
-p_{\lambda}^{2} \ & = \ m^{2}c^{2} \ =
\ \frac{E^{2}}{c^{2}} -{\bf p}_{i}^{2} \\
{\rm or} & \\
E^{2} - {\bf p}^{2} c^{2} \ & = \ m^{2}c^{4}
\end{array} \]
where the convention is that a four vector is written in
normal type and a three component vector is written in boldface..\\
This is the end of the math typesetting example.\\
\subsection{newcommands}
At the beginning of the document you will have noticed a section containing numerous 'newcommands' These enable you to define shorthand sequences for
frequently used structures; whether you bother with such things depends
on the length of the dopcument and the number of times you will use
the newcommands\\
As an example: the chisquared\\
\begin{center}
\chs \\
\end{center}
expression used in statistics has been prepared as a newcommand above.\\
\section{Method}
Here you describe how the measurements were made. This will frequently involve you in discussing which experimental factors affect the precision of the final results and how you dealt with them. At this point one distinguishes
between:
\begin{itemize}
\item random or statistical errors, and how you minimised them and how you determined their values,
\item systematic errors ( of calibration etc ) which cannot be determined by
repeated measurements.
\end{itemize}
At this point you also discuss all effects which although not directly part
of the physics you are studying, may possibly have a significant role to
play in the results.
experiment. The rule is- if you can identify a possible factor, you must
specifically find the magnitude of the effect it may have, and then classify it as either ignorably small, or include it in the subsequent analysis. Much ingenious effort goes into planning improvements on experiments in which various factors which could contribute to the error of the measurements are diminished or eliminated. \\
It frequently happens that several different classes of measurement are made in one experiment. These are best dealt with using subsections:
\subsection{ Class One}
Include description of class 1 method. The subsectioning would then
continue on into other sections of the report.\\
\subsection{ Class Two}
You will note that the latex compiler automatically numbers
sections and subsections ( and subsubsections etc)
\section{Apparatus}
A diagram of essentials of mechanical details, block diagrams of
instruments and interrelated equipment, and detailed circuit diagrams of
important parts of the electronics where such things are important. The
Apparatus section can often be simply included as part of the Methods section.
\\
To draw diagrams which may be incorporated into the report as in the example below you can use any drawing or drafting program which produces output
files for PostScript. ( they will have an extension .ps)
\\
\section{Measurements}
The results of your raw measurements as collected in your lab notebook are collected, and summarised here. Often the raw results will be shown in graphical
or tabular form. (see below)\\
\begin{picture}(350,230)(-72,0)
\special{psfile=satdat.ps hscale=50 vscale=50 voffset=-100 hsize=300 vsize=220}
\end{picture}
\subsection{Arrays}
Arrays organise data neatly but don't provide boxes and lines to guide
the eye.\\
\[ \begin{array}{clcr}
a+b+c & uv & x-y & 27 \\
a+b & u+v & z & 134 \\
a & 3u+vw & xyz & 2,978
\end{array} \]
\subsection{Tables}
These are often the best way to show numerical data. If the data is
available in a machine readable form you can use your editor to incorporate
it into the document and format it for LaTeX printing.\\
\begin{center}
\begin{tabular}{||r|r|r|r||} \hline
integer& square & cube & sqrt \\ \hline\hline
1 & 1 & 1 & 1.0000 \\ \hline
2 & 4 & 8 & 1.4142 \\ \hline
3 & 9 & 27 & 1.7321 \\ \hline
4 & 16 & 64 & 2.0000 \\ \hline
5 & 25 & 125 & 2.2361 \\ \hline
6 & 36 & 216 & 2.4495 \\ \hline
7 & 49 & 343 & 2.6458 \\ \hline
8 & 64 & 512 & 2.8284 \\ \hline
9 & 81 & 729 & 3.0000 \\ \hline
10 & 100 & 1000 & 3.1623 \\ \hline
\end{tabular}
\end{center}
\section{Data Analysis and Discussion}
The raw data is converted into a form suitable for comparison with theory;
eg for the LRC experiment, the data is fitted placed into a form where it can
be fitted with curves whose
shapes can be characterised by resonant freqencies, bandwidths etc.
Here you confront your results ( as extracted from the raw data )
with theory, and state to what extent your work supports
the theory, or perhaps supports one theory more strongly than others. The
comparison of theory and experiment is done precisely, with emphasis on the
difference between theory and experiment ( the residuals ) and how large these
residuals are compared with carefully established errors for both theory and
experiment.\\
\section{Conclusions}
Important section where you concisely summarise your work and what it means
and to what extent it has achieved the aims set out in the introduction.
If further work and improvements are suggested by the present work, you
may mention this.\\
\section{Acknowledgements}
Where you thank those who have helped and or provided support, but whose
contribution does not qualify for co-authorship.\\
Thanks to Mr. William Walker for ... and to the Government and citizens
of BC for ...
etc. Usual in research papers, not obligatory for student reports.\\
\pagebreak
\begin{thebibliography}{bizot}
\bibitem{ahmad84.1}
S. Ahmad, C. Amsler, R. Armenteros, E. Auld, D. Axen, G. Beer,
J.C. Bizot, M. Caria, M. Comyn, W. Dahme, B. Delcourt, K. Erdman,
P. Eschtruth, U. Gastaldi, M. Heel, R. Howard, J. Jeanjean,
H. Kalinowsky, F. Kayser, E. Klempt, R. Landua, H. Nguyen,
L. Robertson, C. Sabev, R. Schneider, O. Schreiber, U. Straumann,
P. Truol, B. White and W.R. Wodrich. "PROTONIUM SPECTROSCOPY AND
IDENTIFICATION OF P-WAVE AND S-WAVE INITIAL STATES OF $\pbarp$
ANNIHILATIONS
AT REST WITH THE ASTERIX EXPERIMENT AT LEAR." "Physics at LEAR with
Low-Energy Cooled Antiprotons" Eds. Ugo Gastaldi and Robert Klapisch
(Plenum Publishing Corporation, 1984) p109-141.
\end{thebibliography}
\end{document}