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\documentclass[10pt]{iopart}
% Uncomment next line if AMS fonts required
%\usepackage{iopams}  
\usepackage{epsfig}
\begin{document}

\title{QCD effects to Bjorken 
unpolarized sum rule for $\nu N$ deep-inelastic scattering} 
%publication in an Institute of Physics Publishing journal using \LaTeXe}

\author{S.I. Alekhin\dag\ and A.L. Kataev\ddag  
%\footnote[1]{( romneya.robertson@iop.org)}
%\footnote[2]{(kataev@ms2.inr.ac.ru)
}

\address{\dag\ Institute of High Energy Physics, 
Protvino, Russia}
%House, Temple Back, Bristol BS1 6BE, UK}
%\ead{alekhin@sirius.ihep.su}

\address{\ddag\ Institute for Nuclear Research of the Academy 
of Sciences of Russia, 117312, Moscow, Russia} 
%Institute of Physics Publishing, 
%Dirac House, Temple Back, Bristol BS1 6BE, UK}
\ead{alekhin@sirius.ihep.su;~kataev@ms2.inr.ac.ru}

\begin{abstract}
The possibility of the first measurement 
of Bjorken unpolarized sum rule for $F_1$ structure function 
of $\nu N$ deep-inelastic scattering at Neutrino Factories is commented. 
The brief summary of various theoretical contributions
to this  sum rule is given. Using the next-to-leading set 
of parton distributions functions, we simulate the expected $Q^2$-behavior 
and emphasize that its measurement can allow 
to determine the value of the QCD strong coupling constant $\alpha_s$ 
with reasonable theoretical uncertainty, dominated by the 
ambiguity in the existing estimates of  
the twist-4 non-perturbative $1/Q^2$-effect.



\end{abstract}

%Uncomment for PACS numbers title message
%\pacs{00.00, 20.00, 42.10}

% Uncomment for Submitted to journal title message
%\submitto{\JPA}

% Comment out if separate title page not required
%\maketitle

The Bjorken unpolarized sum rule 
for $F_1$ structure function of $\nu N$ DIS, which was  theoretically
derived 
quite long ago in the classical work of Ref.~\cite{Bjorken:1968dy}, 
is still remaining experimentally unchecked.
However, at Neutrino Factories, due to large variation of 
$y=E_{had}/E_{\nu}\leq 1/(1+\frac{xM_W}{2E_{\nu}})$ it might  be possible 
to extract from the data for differential cross-sections data 
of $\nu N$ DIS  all 6 structure functions, including\
namely $xF_1^{\nu N}$, $xF_1^{\overline{\nu} N}$. 


The direct measurement of  $F_1^{\nu N}$ SF is allowing to perform  
the first experimental determination of the Bjorken unpolarized sum rule, 
which has the following theoretical expression 
\begin{equation}
\label{Bj}
I_1(Q^2)=
 \int_0^{1}dx\bigg[F_1^{\nu n}(x,Q^2)-F_1^{\nu p}(x,Q^2)
\bigg]=1-\frac{2}{3}\frac{\alpha_s}{\pi}-...+O(\frac{1}{Q^2}) 
\end{equation}
The Bjorken unpolarized sum rule is related to the 
Adler isospin sum rule $I_2(Q^2)=\int_0^1(dx/2x)[F_2^{\nu n}(x,Q^2)-
F_2^{\nu p}(x,Q^2)]=1$ by the following relation $I_1(Q^2)=I_2+I_L(Q^2)$,
where $I_L(Q^2)=\int_0^1(dx/x)[F_L^{\nu p}(x,Q^2)-F_L^{\nu n}(x,Q^2)]$ 
is the Callan-Gross relation for $\nu N$ DIS, which contains 
perturbative QCD corrections 
and higher-twist terms, responsible for difference between 
the Bjorken unpolarized sum rule and the explicit Adler sum rule. 
In the $\overline{MS}$-scheme the massless  
perturbative QCD expression for $I_1$, 
namely $I_1^{PT}$,
is known analytically up to order $O(\alpha_s^3)$ corrections.
The leading order (LO), next-to-leading 
order (NLO) and next-to-next-to-leading order  corrections 
were subsequently  calculated in Refs.\cite{Altarelli:1978id},
\cite{Gorishnii:1983gs} and Ref.\cite{Larin:1990zw} respectively.
The numerical estimates of the order  $O(\alpha_s^4)$-contributions
are also available \cite{Kataev:1995vh,Samuel:1995jc}. 
Moreover, in Ref.\cite{Blumlein:1998sh}
the  heavy-quark mass dependence of 
$I_1$ was calculated  to the level of $\alpha_s^2$-terms.
More recently, in Ref.\cite{Broadhurst:2002bi}  
the renormalon contributions to Eq.(1)  were evaluated. They indicate that the 
leading non-perturbative contribution to $I_1$ should be of order 
$O(1/Q^2)$. 

Indeed, with taking into account the non-perturbative twist-4 contributions,
one can write down theoretical expression  
for  $I_1$ as
\begin{equation}
I_1(Q^2)=I_1^{PT}(Q^2)-\frac{8}{9}\frac{<<O>>}{Q^2} +O(\frac{1}{Q^4})
\end{equation}    
where 
%\begin{equation}
$2p_{\mu}<<O>>=<p|O_{\mu}|p>$, 
$O_{\mu}=\overline{u}\tilde{G}_{\mu\nu}\gamma_{\nu}\gamma_{5}u-
\overline{d}\tilde{G}_{\mu\nu}\gamma_{\nu}\gamma_{5}d$
%\end{equation}
and  $\tilde{G}_{\mu\nu}=(\epsilon_{\mu\nu\alpha\beta}/2)G_{\mu\nu}^a
(\lambda^a/2)$ \cite{Shuryak:1981kj}. The numerical value of the twist-4 
term  was calculated in Ref.\cite{Braun:1986ty} with the help of 3-point 
functions QCD sum rules formalism. The result of this work is
$<<O>>=0.15\pm 0.07$ GeV$^2$, where we take for the theoretical error 
the conservative 
estimate 50$\%$.

\begin{figure}
\centerline{\epsfig{file=bsr.ps,width=10cm,height=6.5cm}}
\caption{The perturbative contribution (dashes), 
the target mass correction (dots), and 
to the high-twist contribution (dashed dots) to $I_1(Q^2)$;
full curve give the sum of all these terms.}
\label{fig:bsr}
\end{figure}

\begin{figure}
\begin{center}
\epsfig{file=bsrerr.ps,width=10cm,height=6.5cm}
\caption{The theoretical errors in $\alpha_{\rm s}$ extracted from the Bjorken 
sum rule (dashes: the error due to high-twist contribution; 
dots: the error due to target mass correction; 
full curve: combination of both).}
\end{center}
\label{fig:bsrerr}
\end{figure}

The $Q^2$-behavior of $I_1^{PT}$ in the NLO is given in Fig.\ref{fig:bsr} 
together with the high-twist contribution of Eq.(2) and the target 
mass (TMC)
correction term calculated using the parton distributions functions 
(PDFs) of Ref.\cite{Alekhin:2001ch}.
One can see that the main uncertainty in $I_1(Q^2)$ comes from 
the high-twist contribution, which rises at low $Q^2$. 
The theoretical error in the $\alpha_s(Q)$ value determined from the 
measurement of $I_1(Q^2)$ reads 
\begin{equation}
\Delta\alpha_s(M_Z)=\Delta I_1(Q^2)\bigg[\frac{dI_1(Q^2)}{d\alpha_s(Q^2)}
\frac{d\alpha_s(Q^2)}{d\alpha_s(M_Z)}\bigg]^{-1}, 
\end{equation}
where $\Delta I_1(Q^2)$ is the corresponding 
theoretical uncertainty in $I_1(Q^2)$.
The errors in $\alpha_s(Q^2)$ due to uncertainties in the high-twist 
term and the TMC are given in Fig.2  
(the latter is determined by the PDFs uncertainties).
At $Q^2=4$ GeV$^2$ and $Q^2=10$ GeV$^2$ the total theoretical error in 
$\alpha_s$ is 
\begin{equation}
\label{uns}
\Delta^{HT}\alpha_s(M_Z)=0.012~~~~~and~~~~ \Delta^{HT}\alpha_s(M_Z)=0.007
\end{equation}
correspondingly.

To conclude, the first experimental determination of the Bjorken unpolarized 
sum rule, which will be possible at Neutrino Factories, can be considered
as an additional source of precise determination of $\alpha_s$, provided 
the twist-4 contributions are known with less ambiguities. Moreover, turning 
the problems around and  fixing $\alpha_s(M_Z)$-value in the available 
perturbative expression for the Bjorken unpolarized sum rule,  
one can try to extract from the analysis of low $Q^2$-data of 
Neutrino Factories  the independent estimates of the corresponding 
twist-4 contributions. 
Another problem, which can be of interest for the future program of 
Neutrino Factories, is the study of nuclear corrections to this still 
unmeasured sum rule of $\nu N$ DIS (for the discussions see 
Ref.\cite{Mangano:2001mj}).

{\bf Acknowledgments} 
We are grateful to S.A. Kulagin for discussions.
The work was supported by RFBR Grant N 00-02-17432.
One of us (ALK) wishes to thank the OC of NuFact'02 Workshop for 
hospitality in London. His research was also supported by 
RFBR Grant N 02-01-00601.

\section*{References}
\begin{thebibliography}{99}
%\cite{Bjorken:1968dy}
\bibitem{Bjorken:1968dy}
J.~D.~Bjorken,
%``Asymptotic Sum Rules At Infinite Momentum,''
Phys.\ Rev.\  {\bf 179} (1969) 1547.
%%CITATION = PHRVA,179,1547;%%
%\cite{Mangano:2001mj}
\bibitem{Mangano:2001mj}
M.~L.~Mangano {\it et al.},
``Physics at the front-end of a neutrino factory: A quantitative  appraisal,''
CERN-TH-2001-131, Report of the nuDIS Working Group for the ECFA-CERN 
Neutrino-Factory study [hep-ph/0105155].
%%CITATION = HEP-PH 0105155;%%
%\cite{Altarelli:1978id}
\bibitem{Altarelli:1978id}
G.~Altarelli, R.~K.~Ellis and G.~Martinelli,
%``Leptoproduction And Drell-Yan Processes Beyond The Leading Approximation In Chromodynamics,''
Nucl.\ Phys.\ B {\bf 143} (1978) 521
[Erratum-ibid.\ B {\bf 146} (1978) 544].
%%CITATION = NUPHA,B143,521;%%
%\cite{Gorishnii:1983gs}
\bibitem{Gorishnii:1983gs}
K.~G.~Chetyrkin, S.~G.~Gorishny, S.~A.~Larin and  F.~V.~Tkachov
%``Higher QCD Corrections To The Bjorken Sum Rule,''
Phys.\ Lett.\ B {\bf 137} (1984) 230.
%%CITATION = PHLTA,B137,230;%%
%\cite{Larin:1990zw}
\bibitem{Larin:1990zw}
S.~A.~Larin, F.~V.~Tkachov and J.~A.~Vermaseren,
%``The Alpha(S**3) Correction To The Bjorken Sum Rule,''
Phys.\ Rev.\ Lett.\  {\bf 66} (1991) 862.
%%CITATION = PRLTA,66,862;%%
%\cite{Kataev:1995vh}
\bibitem{Kataev:1995vh}
A.~L.~Kataev and V.~V.~Starshenko,
%``Estimates of the higher order QCD corrections to R(s), R(tau) and deep inelastic scattering sum rules,''
Mod.\ Phys.\ Lett.\ A {\bf 10} (1995) 235.
%%CITATION = HEP-PH 9502348;%%
%\cite{Samuel:1995jc}
\bibitem{Samuel:1995jc}
M.~A.~Samuel, J.~R.~Ellis and M.~Karliner,
%``Comparison of the Pade approximation method to perturbative QCD calculations,''
Phys.\ Rev.\ Lett.\  {\bf 74} (1995) 4380.
%%CITATION = HEP-PH 9503411;%%
%\cite{Blumlein:1998sh}
\bibitem{Blumlein:1998sh}
J.~Blumlein and W.~L.~van Neerven,
%``Heavy flavour contributions to the deep inelastic sum rules,''
Phys.\ Lett.\ B {\bf 450} (1999) 417.
%%CITATION = HEP-PH 9811351;%%
\cite{Broadhurst:2002bi}
\bibitem{Broadhurst:2002bi}
D.~J.~Broadhurst and A.~L.~Kataev,
%``Bjorken unpolarized and polarized sum rules: Comparative analysis of  large-N(F) expansions,''
Phys.\ Lett.\ B {\bf 544} (2002) 154
[hep-ph/0207261].
%%CITATION = HEP-PH 0207261;%%
%\cite{Shuryak:1981kj}
\bibitem{Shuryak:1981kj}
E.~V.~Shuryak and A.~I.~Vainshtein,
%``Theory Of Power Corrections To Deep Inelastic Scattering In Quantum Chromodynamics. 1. Q**2 Effects,''
Nucl.\ Phys.\ B {\bf 199} (1982) 451.
%%CITATION = NUPHA,B199,451;%%
%\cite{Braun:1986ty}
\bibitem{Braun:1986ty}
V.~M.~Braun and A.~V.~Kolesnichenko,
%``Power Corrections To Bjorken And Gross-Llewellyn Smith Sum Rules In QCD,''
Nucl.\ Phys.\ B {\bf 283} (1987) 723.
%%CITATION = NUPHA,B283,723;%%
%\cite{Alekhin:1996za}

\bibitem{Alekhin:2001ch}
S.~I.~Alekhin,
Phys.\ Rev.\ D {\bf 63} (2001) 094022
[hep-ph/0011002].
%%CITATION = HEP-PH 0011002;%%
\end{thebibliography}
\end{document}







\subsection{Equation numbers, sections, subsections, figures and 
tables}


  
\section{Figures and figure captions}
Figures may be included in an article as encapsulated PostScript files or
using the \LaTeX\ picture environment. Alternatively authors may send in 
high quality printed versions of their figures (fair copies) and 
attach copies of the fair copies to each 
typescript. The fair copies should be in black 
Indian ink or printing on tracing paper, plastic or white card or 
paper, or glossy photographs.

Each figure should have a brief caption describing it and, if 
necessary, interpreting the various lines and symbols on the figure. 
As much lettering as possible should be removed from the figure itself and 
included in the caption. If a figure has parts, these should be 
labelled ($a$), ($b$), ($c$), etc. 
\Tref{blobs} gives the definitions for describing symbols and lines often
used within figure captions (more symbols are available
when using the optional packages loading the AMS extension fonts).

\begin{table}
\caption{\label{blobs}Control sequences to describe lines and symbols in figure 
captions.}
\begin{indented}
\item[]\begin{tabular}{@{}lllll}
\br
Control sequence&Output&&Control sequence&Output\\
\mr
\verb"\dotted"&\dotted        &&\verb"\opencircle"&\opencircle\\
\verb"\dashed"&\dashed        &&\verb"\opentriangle"&\opentriangle\\
\verb"\broken"&\broken&&\verb"\opentriangledown"&\opentriangledown\\
\verb"\longbroken"&\longbroken&&\verb"\fullsquare"&\fullsquare\\
\verb"\chain"&\chain          &&\verb"\opensquare"&\opensquare\\
\verb"\dashddot"&\dashddot    &&\verb"\fullcircle"&\fullcircle\\
\verb"\full"&\full            &&\verb"\opendiamond"&\opendiamond\\
\br
\end{tabular}
\end{indented}
\end{table}

Unless the figures files are incorporated into the text 
the captions should be listed at the end of the article.

\subsection{Figure captions where figure files are not available}
The command \verb"\Figures" starts a new page and an unnumbered section
with the heading `Figure captions'. 
The captions should then be set with the commands:
\begin{verbatim}
\begin{figure}
\caption{\label{label}Figure caption.}
\end{figure}
\end{verbatim}
or more simply
\begin{verbatim}
\Figure{\label{label}Figure caption.}                                         
\end{verbatim}
The caption should finish with a full stop and the printed version will be 
indented as in Institute of Physics Publishing single-column journals.

\subsection{Inclusion of graphics files}
If graphics files are available as encapsulated PostScript (EPS) files 
(or are created within the \LaTeX\ picture environment) they may
be included within the body of the text at an appropriate point using a
standard graphics inclusion package. Authors should ensure EPS files meet
the following criteria.
\begin{itemize}
\item The Bounding Box should indicate the area of the figure 
with a minimum of white space around it and not the dimensions of the
page.
\item Any fonts used should be from the standard PostScript set (Times,
Helvetica, Courier and Symbol).
\item Scanned images should be of 600 dpi resolution for line art (black
and white) and 150 dpi resolution for grayscale or colour.
\item Captions and labels (e.g.\ Figure 1) should not be included in the
EPS file although part letters (e.g.\ ($a$)) are acceptable provided they
are placed close or within the boundary of the figure. 
\end{itemize}

The precise coding required will depend on the graphics package being used
and the printer driver. We use a printer driver compatible with DVIPS but
authors should avoid using special effects generated by including verbatim
PostScript code within the \LaTeX\ file with specials other than the
standard figure inclusion ones.

Using the epsf package figures can be included using code such as:
\begin{verbatim}
\begin{figure}
\begin{center}
\epsfbox{file.eps}
\end{center}
\caption{\label{label}Figure caption}
\end{figure}
\end{verbatim}


\clearpage

\appendix
\section{List of macros for formatting text, figures and tables}


\begin{table}[hb]
\caption{Macros available for use in text. Parameters in square brackets 
are optional.}
\footnotesize\rm
\begin{tabular}{@{}*{7}{l}}
\br
Macro name&Purpose\\
\mr
\verb"\title[#1]{#2}"&Title of article and short title (optional)\\
\verb"\paper[#1]{#2}"&Title of paper and short title (optional)\\
\verb"\letter{#1}"&Title of Letter to the Editor\\
\verb"\comment[#1]{#2}"&Title of Comment and short title (optional)\\
\verb"\topical[#1]{#2}"&Title of Topical Review and short title 
(optional)\\
\verb"\review[#1]{#2}"&Title of review article and short title (optional)\\
\verb"\note[#1]{#2}"&Title of Note and short title (optional)\\
\verb"\prelim[#1]{#2}"&Title of Preliminary Communication \& short title\\
\verb"\author{#1}"&List of all authors\\
\verb"\article[#1]{#2}{#3}"&Type and title of other articles and 
short title (optional)\\
\verb"\address{#1}"&Address of author\\
\verb"\pacs{#1}"&PACS classification codes\\
\verb"\pacno{#1}"&Single PACS classification code\\
\verb"\ams{#1}"&American Mathematical Society classification code\\
\verb"\submitto{#1}"&`Submitted to' message\\
\verb"\maketitle"&Creates title page\\
\verb"\begin{abstract}"&Start of abstract\\
\verb"\end{abstract}"&End of abstract\\
\verb"\nosections"&Inserts space before text when no sections\\
\verb"\section{#1}"&Section heading\\
\verb"\subsection{#1}"&Subsection heading\\
\verb"\subsubsection{#1}"&Subsubsection heading\\
\verb"\appendix"&Start of appendixes\\
\verb"\ack"&Acknowledgments heading\\
\verb"\References"&Heading for reference list\\
\verb"\begin{harvard}"&Start of alphabetic reference list\\
\verb"\end{harvard}"&End of alphabetic reference list\\
\verb"\begin{thebibliography}{#1}"
&Start of numeric reference list\\
\verb"\end{thebibliography}"&End of numeric reference list\\
\verb"\etal"&\etal for text and reference lists\\
\verb"\dash"&Rule for repeated authors in alphabetical reference list\\
\verb"\nonum"&Unnumbered entry in numerical reference list\\
\br
\end{tabular}
\end{table}


\begin{table}
\caption{Macros defined within {\tt iopart.cls}
for use with figures and tables.}
\begin{indented}
\item[]\begin{tabular}{@{}l*{15}{l}}
\br
Macro name&Purpose\\
\mr
\verb"\Figures"&Heading for list of figure captions\\
\verb"\Figure{#1}"&Figure caption\\
\verb"\Tables"&Heading for tables and table captions\\
\verb"\Table{#1}"&Table caption\\
\verb"\fulltable{#1}"&Table caption for full width table\\
\verb"\endTable"&End of table created with \verb"\Table"\\
\verb"\endfulltab"&End of table created with \verb"\fulltable"\\
\verb"\endtab"&End of table\\
\verb"\br"&Bold rule for tables\\
\verb"\mr"&Medium rule for tables\\
\verb"\ns"&Small negative space for use in table\\
\verb"\centre{#1}{#2}"&Centre heading over columns\\
\verb"\crule{#1}"&Centre rule over columns\\
\verb"\lineup"&Set macros for alignment in columns\\
\verb"\m"&Space equal to width of minus sign\\
\verb"\-"&Left overhanging minus sign\\
\verb"\0"&Space equal to width of a digit\\
\br
\end{tabular}
\end{indented}
\end{table}


\clearpage
\section{Control sequences for journal
abbreviations}
\label{jlabs}
\begin{table}[hb]
\caption{\label{jlab1}Abbreviations for the IOPP journals.}
\begin{indented}
\item[]
\begin{tabular}{@{}lll}
\br
Macro name&{\rm Short form of journal title}&Years relevant\\
\mr
{\it Current journals}\\
\mr
\verb"\CQG"&Class. Quantum Grav.\\
\verb"\CTM"&Combust. Theory Modelling\\
\verb"\EJP"&Eur. J. Phys.\\
\verb"\HPP"&High Performance Polymers\\
\verb"\IP"&Inverse Problems\\
\verb"\JHEP"&J. High Energy Phys.&1999 and onwards\\
\verb"\JMM"&J. of Michromech. and Microeng.\\
\verb"\JOA"&J. Opt. A: Pure and Applied Opt.&1998 and onwards\\
\verb"\JOB"&J. Opt. B: Quantum and Semiclass. Opt.&1999 and onwards\\
\verb"\JPA"&J. Phys. A: Math. Gen.\\
\verb"\jpb"&J. Phys. B: At. Mol. Opt. Phys.&1988 and onwards\\
\verb"\JPCM"&J. Phys: Condens. Matter&1989 and onwards\\
\verb"\JPD"&J. Phys. D: Appl. Phys.\\
\verb"\JPF"&J. Phys. F: Met. Phys.\\
\verb"\jpg"&J. Phys. G: Nucl. Part. Phys.&1989 and onwards\\
\verb"\MSMSE"&Modelling Simul. Mater. Sci. Eng.\\
\verb"\MST"&Meas. Sci. Technol.&1990 and onwards\\
\verb"\NET"&Network:Comput. Neural Syst.\\
\verb"\NJP"&New J. Phys.&1999 and onwards\\
\verb"\NL"&Nonlinearity\\
\verb"\NT"&Nanotechnology\\
\verb"\PM"&Physiol. Meas.\\
\verb"\PMB"&Phys. Med. Biol.\\
\verb"\PPCF"&Plasma Physics and Controlled Fusion\\
\verb"\PSST"&Plasma Sources Sci. Technol.\\
\verb"\PUS"&Public Understand. Sci.\\
\verb"\RPP"&Rep. Prog. Phys.\\%\cite{Bjorken:1968dy}
%\bibitem{Bjorken:1968dy}
%J.~D.~Bjorken,
%``Asymptotic Sum Rules At Infinite Momentum,''
%Phys.\ Rev.\  {\bf 179} (1969) 1547.
%%CITATION = PHRVA,179,1547;%%
\verb"\SST"&Semicond. Sci. Technol.\\
\verb"\SUST"&Supercond. Sci. Technol.\\
\verb"\WRM"&Waves in Random Media\\
\mr
{\it No Longer Published}\\
\mr
\verb"\BIO"&Bioimaging&1998\\
\verb"\DSE"&Distributed Systems Eng.&1993--1999\\
\verb"\JO"&J. Opt.&1970--1998\\
\verb"\JPB"&J. Phys. B: At. Mol. Phys.&1968--1987\\
\verb"\JPC"&J. Phys. C: Solid State Phys.&1968--1988\\
\verb"\JPE"&J. Phys. E: Sci. Instrum.&1968--1989\\
\verb"\JPG"&J. Phys. G: Nucl. Phys.&1975--1988\\
\verb"\PAO"&Pure and Applied Opt.&1992--1998\\
\verb"\QO"&Quantum Opt.&1989--1994\\
\verb"\QSO"&Quantum and Semiclass. Opt.&1995--1998\\
\br
\end{tabular}
\end{indented}
\end{table}



\begin{table}

\caption{\label{jlab2}Abbreviations for some more 
common non-IOPP journals.}
\begin{indented}
\item[]\begin{tabular}{@{}ll}
\br
Macro name&{\rm Short form of journal}\\
\mr
\verb"\AC"&Acta Crystallogr.\\
\verb"\AM"&Acta Metall.\\
\verb"\AP"&Ann. Phys., Lpz\\
\verb"\APNY"&Ann. Phys., NY\\
\verb"\APP"&Ann. Phys., Paris\\
\verb"\CJP"&Can. J. Phys.\\
\verb"\GRG"&Gen. Rel. Grav.\\
\verb"\JAP"&J. Appl. Phys.\\
\verb"\JCP"&J. Chem. Phys.\\
\verb"\JJAP"&Japan. J. Appl. Phys.\\
\verb"\JMMM"&J. Magn. Magn. Mater.\\
\verb"\JMP"&J. Math. Phys.\\
\verb"\JOSA"&J. Opt. Soc. Am.\\
\verb"\JP"&J. Physique\\
\verb"\JPhCh"&J. Phys. Chem.\\
\verb"\JPSJ"&J. Phys. Soc. Japan\\
\verb"\JQSRT"&J. Quant. Spectrosc. Radiat. Transfer\\
\verb"\NC"&Nuovo Cimento\\
\verb"\NIM"&Nucl. Instrum. Methods\\
\verb"\NP"&Nucl. Phys.\\
\verb"\PF"&Phys. Fluids\\
\verb"\PL"&Phys. Lett.\\
\verb"\PR"&Phys. Rev.\\
\verb"\PRL"&Phys. Rev. Lett.\\
\verb"\PRS"&Proc. R. Soc.\\
\verb"\PS"&Phys. Scr.\\
\verb"\PSS"&Phys. Status Solidi\\
\verb"\PTRS"&Phil. Trans. R. Soc.\\
\verb"\RMP"&Rev. Mod. Phys.\\
\verb"\RSI"&Rev. Sci. Instrum.\\
\verb"\SSC"&Solid State Commun.\\
\verb"\SPJ"&Sov. Phys.--JETP\\
\verb"\ZP"&Z. Phys.\\
\br
\end{tabular}
\end{indented}
\end{table}
\end{document}


