Search for Cold Dark Matter and Solar Neutrinos with GENIUS and GENIUS-TF
I.V. Krivosheina
Nishnii-Novgorod
Russia
Max-Planck-Institut f\"ur Kernphysik
P.O. Box 10 39 80
D-69029 Heidelberg
Germany
The new project GENIUS will cover a wide range of the parameter space of predictions of SUSY for neutralinos as cold dark matter. Further it has the potential to be a real-time detector for low-energy ($pp$ and $^7$Be) solar neutrinos. A GENIUS Test Facility has just been funded and will come into operation by end of 2002.
IK-st-file.tex
%\documentclass{article}
%\documentclass[twoside]{article}
%\documentclass[12pt,twoside]{article}

%\usepackage{fleqn,espcrc1}
%\usepackage{fleqn,espcrc2,epsf}
%\documentstyle[twoside,fleqn,espcrc2]{article}
%\usepackage{graphicx}
%\usepackage{epsfig}
%\usepackage[figuresright]{rotating}

%\documentstyle[epsf,iopconf1]{article}
%\documentstyle{article}
%\documentstyle[sprocl,epsf]{article}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[twoside,12pt]{article}
\usepackage{epsfig}

\def\Journal#1#2#3#4{{#1} {#2} (#4) #3 }
\def\NCA{{\em Nuovo Cimento} A}
\def\PHYS{{\em Physica}}
\def\NPA{{\em Nucl. Phys.} A}
\def\MATH{{\em J. Math. Phys.}}
\def\PRO{{\em Prog. Theor. Phys.}}
\def\NPB{{\em Nucl. Phys.} B}
\def\PLA{{\em Phys. Lett.} A}
\def\PLB{{\em Phys. Lett.} B}
\def\PLD{{\em Phys. Lett.} D}
\def\PL{{\em Phys. Lett.}}
\def\PRL{\em Phys. Rev. Lett.}
\def\PREV{\em Phys. Rev.}
\def\PREP{\em Phys. Rep.}
\def\PRA{{\em Phys. Rev.} A}
\def\PRD{{\em Phys. Rev.} D}
\def\PRC{{\em Phys. Rev.} C}
\def\PRB{{\em Phys. Rev.} B}
\def\ZPC{{\em Z. Phys.} C}
\def\ZPA{{\em Z. Phys.} A}
\def\ANNP{\em Ann. Phys. (N.Y.)}
\def\RMP{{\em Rev. Mod. Phys.}}
\def\CHEM{{\em J. Chem. Phys.}}
\def\INT{{\em Int. J. Mod. Phys.} E}
\def\r{\vec r}
\def\R{\vec R}
\def\p{\vec p}
\def\P{\vec P}
\def\q{\vec q}
\def\ss{\mbox{\boldmath $\sigma$}}

\newcommand{\ba}[1]{\begin{eqnarray} \label{(#1)}}
\newcommand{\ea}{\end{eqnarray}}
\newcommand{\nn}{\nonumber}
\newcommand{\rf}[1]{(\ref{(#1)})}

\newcommand{\ttbs}{\char'134}
\newcommand{\AmS}{{\protect\the\textfont2
  A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}}

%
%\def \KK {H.V.~Klapdor-Kleingrothaus}
\def \znbb {$0\nu\beta\beta$}
\def \tnbb {$2\nu\beta\beta$}
\def \Rpv{R_{P} \hspace{-0.9em}/\;\:}%\hspace{0.8em}}
\def\rp{$R_p \hspace{-1em}/\;\:$}
\def \emass {\langle m_{\nu} \rangle}
\font\eightrm=cmr8

%\input{psfig}

%\bibliographystyle{unsrt} %for BibTeX - sorted numerical labels by
                          %order of first citation.

%\arraycolsep1.5pt

% A useful Journal macro
\def\Journal#1#2#3#4{{#1} {\bf #2}, #3 (#4)}

% Some useful journal names
\def\NCA{\em Nuovo Cimento}
\def\NIM{\em Nucl. Instrum. Methods}
\def\NIMA{{\em Nucl. Instrum. Methods} {\bf A}}
\def\NPB{{\em Nucl. Phys.} {\bf B}}
\def\PLB{{\em Phys. Lett.} {\bf  B}}
\def\PRL{\em Phys. Rev. Lett.}
\def\PRD{{\em Phys. Rev.} {\bf D}}
\def\ZPC{{\em Z. Phys.} {\bf C}}

% Some other macros used in the sample text
\def\st{\scriptstyle}
\def\sst{\scriptscriptstyle}
\def\mco{\multicolumn}
\def\epp{\epsilon^{\prime}}
\def\vep{\varepsilon}
\def\ra{\rightarrow}
\def\ppg{\pi^+\pi^-\gamma}
\def\vp{{\bf p}}
\def\ko{K^0}
\def\kb{\bar{K^0}}
\def\al{\alpha}
\def\ab{\bar{\alpha}}
\def\be{\begin{equation}}
\def\ee{\end{equation}}
\def\bea{\begin{eqnarray}}
\def\eea{\end{eqnarray}}
\def\CPbar{\hbox{{\rm CP}\hskip-1.80em{/}}}%temp replacemt due to no font
\def \KK {H.V.~Klapdor-Kleingrothaus}
\hyphenation{author another created financial paper re-commend-ed Post-Script}

\def \lsim {~\mbox{${}^< \hspace*{-9pt} _\sim$}~}
\def \gsim {~\mbox{${}^> \hspace*{-9pt} _\sim$}~}
\def \leql {~\ ^< \hspace*{-7pt} _=~\ }
\def \geql {~\ ^> \hspace*{-7pt} _=~\ }


\topmargin-2.8cm
\oddsidemargin-1cm
\evensidemargin-1cm
\textwidth18.5cm
\textheight27.0cm
\begin{document}


\title{Search for Cold Dark Matter and Solar Neutrinos 
	with GENIUS and GENIUS-TF}


\author{I.V. Krivosheina
\\
Radiophysical Research Institute (NIRFI),
	Nishnii-Novgorod, Russia,
\\ 
	Max-Planck-Institut f\"ur Kernphysik,
	P.O. Box 10 39 80, D-69029 Heidelberg,
\\ 
	Germany, E-mail: irina@gustav.mpi-hd.mpg}

\maketitle

%%%%%%%%%%%%%%%%%%%%%%%%%% ABSTRACT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{abstract}
	The new project 
	GENIUS will cover a wide range of the parameter 
	 space of predictions of SUSY for neutralinos as cold dark matter. 
	 Further it has the potential to be a real-time detector 
	 for low-energy ($pp$ and $^7$Be) solar neutrinos. 
	 A GENIUS Test Facility has just been funded and will 
	 come into operation by end of 2002.
\end{abstract}
%%%%%%%%%%%%%%%%%%%%%%%%%% end ABSTRACT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%% Introduction %%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}

	Concerning solar neutrino physics, present information on 
	possible $\nu$ oscillations relies on 0.2\% of the solar neutrino flux.
	The total $pp$ neutrino flux has not been measured and also no 
	real-time information is available for the latter.
	Concerning the search for cold dark matter, direct detection of 
	the latter by underground detectors remains 
	indispensable. 
	
	The GENIUS project proposed in 1997  
\cite{KK-Bey97,GEN-prop,KK60Y,KK-InJModPh98,KK-J-PhysG98} 
	as the first third generation $\beta\beta$ detector, 
	could attack all of these problems with an unprecedented sensitivity. 
	 GENIUS will allow real time detection 
	of low-energy solar neutrinos with a threshold of 19 keV.
	   For the further potential of GENIUS for other beyond 
	SM physics, such 
	as double beta decay, SUSY, compositeness, leptoquarks, 
	   violation of Lorentz invariance and equivalence principle, 
	   etc we refer to  
\cite{KK-Erice01,KK-SprTracts00,KK-InJModPh98,KK60Y,KK-WEIN98,KK-Neutr98}.

	


%%%%%%%%% Fig. 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
                      
\begin{figure}[t]% Figure 1
%\begin{center}
%\begin{minipage}[t]{8 cm}
%\hspace{-2.cm}
\epsfig{file=Neu00-sol-neutr-Bach.eps,scale=0.4}
%\epsfig{file=Sol-Neutr-Sp-Bach.eps,scale=0.4}
\hspace{.5cm}
\includegraphics*[scale=0.45]
{pp_7be-new.eps}
\caption[]{%Figure 12. 
       Left: 
	The sensitivity (thresholds) of different running and projected 
	solar neutrino detectors (see 
\protect\cite{HomP-Bach} and home-page
	HEIDELBERG NON-ACCELERATOR PARTICLE PHYSICS 
	GROUP: $http://www.mpi-hd.mpg.de/non\_acc/$). 
	Right:
	Simulated spectrum of low-energy solar neutrinos 
       (according to SSM) for the GENIUS detector 
       (1 tonne of Ge) (from  
\protect\cite{KK01}, 
	and estimated background).
%\label{pp_7be-new}
\label{fig:sol-neutr-Bach}}
%\end{center}
%\end{minipage}
\end{figure}


%%%%%%%%%%%%%%%%%%%%%%%%% sect. 1 %%%%%%%%%%%%%%%%%%%%

\section{GENIUS and Low-Energy Solar Neutrinos}


	GENIUS which has been proposed for solar $\nu$ detection 
	in 1999  
%\cite{Kla98d}
\cite{BKK-SolN,GEN-prop}
	, could be the first detector measuring 
		the {\em full}\ $pp$ (and $^7$Be) 
		neutrino flux in real time 
(Fig.~\ref{fig:sol-neutr-Bach}).


	The main idea of GENIUS, originally proposed for double beta and dark 
	matter search 
\cite{KK-Bey97,KK-J-PhysG98,KK-Neutr98,KK-WEIN98,KK-InJModPh98,KK-SprTracts00}
  is to achieve an extremely low radioactive background 
	(factor of $>$  1000 smaller than in the HEIDELBERG-MOSCOW 
	experiment) by using 'naked' detectors in liquid nitrogen.  


	While for cold 
	dark matter search 100 kg of {\it natural} Ge detectors 
	are sufficient, GENIUS as a solar neutrino detector would contain 
	1-10 tons of enriched $^{70}{Ge}$ or $^{73}{Ge}$.

	That Ge detectors in liquid nitrogen operate excellently, has been 
	demonstrated in the Heidelberg low-level laboratory  
\cite{KK-J-PhysG98,Bau98}
	and the overall feasibility of the project has been shown in 
\cite{GEN-prop,KK-J-PhysG98,KK-NOW00,LowNu2}.

	The potential of GENIUS to measure the spectrum of low-energy solar 
	neutrinos in real time has been studied by  
\cite{BKK-SolN,GEN-prop,LowNu2}. 
	The detection reaction is elastic neutrino-electon scattering 
	$\nu ~+~ e^- \longrightarrow~ \nu~ +~e^-$. 

	The maximum electron recoil energy is 261 keV for the pp neutrinos 
	and 665 keV for the $^{7}{Be}$ neutrinos. 
%\cite{Bach89}. 
	The recoil electrons can be detected through their ionization 
	in a HP Ge detector with an energy resolution of 0.3$\%$. GENIUS 
	can measure only (like BOREXINO, and others) but with much better 
	energy resolution) the energy distribution of the recoiling electrons, 
	and not directly determine the energy of the incoming neutrinos. 
	The dominant part of the signal in GENIUS is produced by $pp$ 
	neutrinos (66$\%$) and $^{7}{Be}$ neutrinos (33$\%$). The detection 
	rates for the $pp$ and $^{7}{Be}$ fluxes are according to the 
	Standard Solar Model  
\cite{BacBasPins98}
	$R_{pp}$ = 35 SNU = 1.8  events/day ton~ (18 events/day 10 tons) 
	and~ $R_{^{7}{Be}}$~ = 13 SNU~ = 0.6 events/day ton~ 
	(6 events/day 10 tons)~(1 SNU = ${10}^{-36}$/s target atom). 


	To measure the low-energy solar $\nu$ flux with a signal to 
	background ratio of 3:1, the required background rate is 
	about 1 $\times~ {10}^{-3}$ events/kg y keV in this energy range. 
	This is about a factor of 10 smaller than what is required for 
	the application of GENIUS for cold dark matter search. This can 
	be achieved if the liquid nitrogen shielding is increased to at 
	least 13 m in diameter and production of the Ge detectors is 
	performed underground (see 
\cite{BKK-SolN,LowNu2}). 


	Another source of background 
	is coming from   
	2$\nu\beta\beta$ decay of $^{76}{Ge}$, which is contained in 
	{\it natural} Ge with 7.8$\%$. Using enriched 
	$^{70}{Ge}$ or $^{73}{Ge}$ ($>$85$\%$) 
	as detector material, the abundance of the $\beta\beta$ emitter 
	can be reduced up to a factor of 1500. In this case the $pp$-signal 
	will not be disturbed by 2$\nu\beta\beta$ decay (see 
\cite{LowNu2}). 

	The expected spectrum of the low-energy signal in the SSM is 
	shown in 
Fig. ~\ref{fig:sol-neutr-Bach} (right part).  

	After the unfavouring of the SMA solution by 
	Superkamiokande, it is important to 
	differentiate between the LMA and the LOW solution. Here 
	due to its relatively high counting rate, GENIUS will be able to test  
	in particular the LOW solution of the solar $\nu$ problem by the 
	expected day/night variation of the flux (see 
\cite{KK-NOW00,LowNu2}).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Section 6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

%%%%%%%%%%%%%%%%%%%%  fig. 2 ****************************

%\clearpage
\begin{figure}
\begin{center}
\epsfig{file=All-Exper-KK-B-EL-TRANSP.eps,scale=0.4}
\end{center}
\caption[]{%Figure 9. 
       WIMP-nucleon cross section limits in pb for scalar interactions as 
       function of the WIMP mass in GeV. 
       Shown are contour lines of present experimental limits (solid lines) 
       and of projected experiments (dashed lines). 
       Also shown is the region of evidence published by DAMA. 
       The theoretical expectations are shown by two scatter plots, 
	- for accelerating and for non-accelerating Universe (from  
\cite{BedKK00,BedKK-01}) and by the grey region (from  
\cite{EllOliv-DM00}). 
	{\em Only}\ GENIUS will be able to probe the shown range 
       also by the signature from seasonal modulations.
\label{fig:Bedn-Wp2000}}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%  end fig. 2 ***************************

\section{GENIUS and Cold Dark Matter Search}
 
	GENIUS would already in a first step, with 100 kg of 
		{\it natural} Ge detectors, cover a significant part of the 
		MSSM parameter space for prediction of neutralinos 
		as cold dark matter 
(Fig.~\ref{fig:Bedn-Wp2000}) 
	(see, e.g. 
\cite{BedKK00,BedKK-01,EllOliv-DM00})
	For this purpose the background in the energy range 
		$< 100$~keV has to be reduced to 
		$10^{-2}$ (events/kg y keV). 
	At this level solar neutrinos as source of background 
	are still negligible. 
Fig.~\ref{fig:Bedn-Wp2000} 
	shows together with the expected sensitivity of GENIUS, 
	for this background, predictions for neutralinos as dark matter by 
	two models, one basing on supergravity  
\cite{EllOliv-DM00}, another basing on the MSSM with more 
     relaxed unification conditions  
\cite{BedKK00,BedKK-01}.

	     The sensitivity of GENIUS for Dark Matter corresponds to 
	     that obtainable with a 1 km$^3$ AMANDA detector for 
	     {\it indirect} detection (neutrinos from annihilation 
	     of neutralinos captured at the Sun) (see  
\cite{Eds99}). 
	Interestingly both experiments would probe different neutralino 
	compositions: GENIUS mainly gaugino-dominated neutralinos, 
	AMANDA mainly neutralinos with comparable gaugino and 
	Higgsino components (see Fig. 38 in  
\cite{Eds99}). 
     It should be stressed that, together with DAMA, GENIUS will be 
     {\em the only}\ future Dark Matter experiment, which would be able to 
     positively identify a dark matter signal by the seasonal 
     modulation signature. 
     This {\it cannot} be achieved, for example, by the CDMS experiment.

\section{GENIUS-TF}

	As a first step of GENIUS, a small test facility, GENIUS-TF, 
	is at present under installation in the Gran Sasso 
	Underground Laboratory 
\cite{GENIUS-TF}.
	With about 40 kg of natural Ge detectors operated 
	in liquid nitrogen, GENIUS-TF could test the DAMA seasonal 
	modulation signature for dark matter. 
	No other experiment running, like CDMS, IGEX, etc., 
	or projected at present, will have this potential 
\cite{KK-LP01}.
	Up to summer 2001, already six 2.5 kg Germanium detectors with 
	an extreme low-level threshold of $\sim$500 eV have been produced.
	
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Section 6 %%%%%%%%%%%%%%%%%%%%%%%%





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%THE BIBLIOGR>%%%%%%%%%%%%%%%%%
\begin{thebibliography}{99}




\bibitem{KK60Y}%{3}	
		H.V. Klapdor-Kleingrothaus, 
		{\sf "60 Years of Double Beta Decay"}, {\it World Scientific, 
		Singapore} (2001) 1253~p.


\bibitem{Bau98}%{6}
 	L.~Baudis, G.~Heusser, B.~Majorovits, Y.~Ramachers, H.~Strecker and 
 	H.V.~Klapdor--Kleingrothaus, {\it hep-ex/} {\bf 9811040} and 
	{\it Nucl. Instr. Meth.} {\bf A 426}, 425 (1999).


\bibitem{BKK-SolN}%{7}
	L. Baudis and H.V. Klapdor-Kleingrothaus, 
	{\it Eur. Phys. J.} {\bf A 5}, 441-443  (1999) and in 
	Proceedings of the 2nd Int. Conf. on Particle 
	Physics Beyond the Standard Model BEYOND'99, 
	Castle Ringberg, Germany, 6-12 June 1999, 
	edited by H.V. Klapdor-Kleingrothaus and I.V. Krivosheina, 
	{\it IOP Bristol}, 1023 - 1036 (2000).

\bibitem{KK01}%{8}	
		H.V. Klapdor-Kleingrothaus et al., 
		to be publ. 2001 
		and ${\it http://www.mpi-hd.mpg.de/non\_acc/}$


%%%%%%%%%% Rom 2001, LP01, Erice 2001 %%%%%%%%%%%%%%%%%
\bibitem{KK-LP01}
	H.V. Klapdor-Kleingrothaus, 
	in Proc. of the XX Lepton Photon Symposium (LP01), 
	July 23 - 28, 2001, Rome, Italy, 
	{\it World Scientific, Singapore} (2002) 

\bibitem{KK-Erice01}
	H.V. Klapdor-Kleingrothaus, 
	in Proc. of the Erice School on Nuclear Physics about Neutrinos, 
	ed. A. Faessler,  
	{\it Progress in Particle and Nuclear Physics} {\bf 48} (2002).

%%%%%%%%%%%%%%%% BEY97 %%%%%%%%%%%%%%%%%%%%%%%
 	
\bibitem{KK-Bey97}%{17}
	H.V. Klapdor-Kleingrothaus in Proceedings of BEYOND'97, 
	First International Conference on Particle Physics 
	Beyond the Standard Model, Castle Ringberg, Germany, 
	8-14 June 1997, 
     edited by H.V. Klapdor-Kleingrothaus and H. P\"as, 
	{\it IOP Bristol} 485-531 (1998)  
%	and {\it Int. J. Mod. Phys.} {\bf A 13} (1998) 3953, and 
%     {\it J. Phys.} {\bf G 24} (1998) 483-516.

%%%%%%%%%%%%%%%%%%%%% BEY99 %%%%%%%%%%%%%%%%%%%%%%%%

\bibitem{GEN-prop}%{18}
	H.V. Klapdor-Kleingrothaus et al. 
	{\it MPI-Report} {\bf MPI-H-V26-1999} and 
	{\it Preprint: hep-ph/}{\bf 9910205} and in 
	Proceedings of the 2nd Int. Conf. on Particle 
	Physics Beyond the Standard Model BEYOND'99, 
	Castle Ringberg, Germany, 6-12 June 1999, 
	edited by H.V. Klapdor-Kleingrothaus and I.V. Krivosheina, 
	{\it IOP Bristol}, 915 - 1014 (2000).

%%%%%%%%%%%%% NEUTRINO98 %%%%%%%%%%%%%
\bibitem{KK-Neutr98}%{19}
	H.V. Klapdor-Kleingrothaus, in Proc. of 18th Int. 
	Conf. on Neutrino Physics and Astrophysics (NEUTRINO 98), 
	Takayama, Japan, 4-9 Jun 1998, (eds) Y. Suzuki et al. 
	{\it Nucl. Phys. Proc. Suppl.} {\bf 77}, 357 - 368 (1999).   

%%%%%%%%%%%%%%%%%%%%5 WEIN98 %%%%%%%%%%%%%%%%%%%%%%%

\bibitem{KK-WEIN98}%{20}
	H.V. Klapdor-Kleingrothaus, in Proc. of WEIN'98, 
	"Physics Beyond the Standard Model", Proceedings of the Fifth Intern.  
	WEIN Conference, P. Herczeg, C.M. Hoffman and 
	H.V. Klapdor-Kleingrothaus (Editors), 
	{\it World Scientific, Singapore}, 275-311 (1999).


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% NOW 2000 %%%%%%%%%%%%%

\bibitem{KK-NOW00}%{22}
	H.V. Klapdor-Kleingrothaus, in Proc. of Int. Conference 
	NOW2000 - "Origins of Neutrino Oscillations", 
	{\it Nucl. Phys.} {\bf B} (2001) ed. G. Fogli and 
	{\it Preprint: hep-ph/}{\bf 0102277}, 
	{\it Preprint: hep-ph/}{\bf 0102276}. 

%%%%%%%%%%%%%%%%%%%%%%%%%% NOON 2000 and LowNu2000 %%%%%%%%%%%%%%%%%


\bibitem{LowNu2}%{24}
	H.V. Klapdor-Kleingrothaus, in 
	Proc. Int. Workshop on Low Energy Solar Neutrinos, LowNu2, 
	December 4 and 5 (2000) Tokyo, Japan, 
	ed: Y. Suzuki, World Scientific, Singapore (2001), home page: 
	{\it http://www-sk.icrr.u-tokyo.ac.jp/neutlowe/2/transparency/
index.html}

%%%%%%%%%%%%% Journ %%%%%%%%%%%%%%%%

\bibitem{KK-J-PhysG98}%{27}
	H.V. Klapdor-Kleingrothaus, J. Hellmig and M. Hirsch, 
	{\it J. Phys.} {\bf G 24}, 483 (1998).

\bibitem{KK-InJModPh98}%{28}
	H.V. Klapdor-Kleingrothaus, {\it Int. J. Mod. Phys.} {\bf A 13}, 3953  
	(1998).
%	and {\it J. Phys.} {\bf G 24} (1998) 483--516.

\bibitem{KK-SprTracts00}%{29}
	H.V. Klapdor-Kleingrothaus, {\it Springer Tracts in Modern Physics}, 
	{\bf 163}, 69-104 (2000), 
	{\it Springer-Verlag, Heidelberg, Germany} (2000).

%%%%%%%%%%%%%%%% Dark Matter %%%%%%%%%%%


\bibitem{BedKK00}%{31}
	V.A. Bednyakov and H.V. Klapdor-Kleingrothaus, 
	{\it Phys. Rev.} {\bf D 62} (2000) 043524/1-9 and {\it hep-ph/}
	{\bf 9908427}. 

\bibitem{BedKK-01}%{32}
	V.A. Bednyakov and H.V. Klapdor-Kleingrothaus, 
	{\it Preprint: hep-ph/}{\bf 0011233} (2000) and  
	{\it Phys. Rev.} {\bf D 63} (2001) 095005.

\bibitem{EllOliv-DM00}%{33}
	J. Ellis, A. Ferstl and K.A. Olive, {\it Phys. Lett.} {\bf B 481},  
	304--314 (2000) and {\it Preprint: hep-ph/}{\bf 0001005} 
	and {\it Preprint: hep-ph/}{\bf 0007113}.

\bibitem{Eds99}%{34}
	J. Edsj\"o, Neutralinos as dark matter - can we see them? 
	Seminar given in the theory group, Department of Physics, 
	Stockholm University, October 12, 1999, home page: 
	{\it http://www.physto.se/edsjo/}

\bibitem{GENIUS-TF}
	H.V. Klapdor-Kleingrothaus, L. Baudis, A. Dietz, 
	G. Heusser, I.V. Krivosheina, B. Majorovits and 
	H. Strecker, hep-ex/0012022, Subm. for Publ. (2001).	

%%%%%%%%%%%%%%% Solar Neutrinos Bahcall %%%%%%%%%

\bibitem{HomP-Bach}%{35}
	see: {\it http://www.sns.ias.edu.jnb/}

\bibitem{Bach89}%{36}
	J.N. Bahcall, {\it Neutrino Astrophysics}, Cambridge Univ. 
	Press (1989). 

\bibitem{BacBasPins98}%{39}
	J.N. Bahcall, S. Basu and M. Pinsonneault, 
	{\it Phys. Lett.} {\bf B 433}, 1 (1998).


\end{thebibliography}        






\end{document}
examp.tex
\documentclass[twoside,12pt]{article}
\usepackage{epsfig}

\def\Journal#1#2#3#4{{#1} {#2} (#4) #3 }
\def\NCA{{\em Nuovo Cimento} A}
\def\PHYS{{\em Physica}}
\def\NPA{{\em Nucl. Phys.} A}
\def\MATH{{\em J. Math. Phys.}}
\def\PRO{{\em Prog. Theor. Phys.}}
\def\NPB{{\em Nucl. Phys.} B}
\def\PLA{{\em Phys. Lett.} A}
\def\PLB{{\em Phys. Lett.} B}
\def\PLD{{\em Phys. Lett.} D}
\def\PL{{\em Phys. Lett.}}
\def\PRL{\em Phys. Rev. Lett.}
\def\PREV{\em Phys. Rev.}
\def\PREP{\em Phys. Rep.}
\def\PRA{{\em Phys. Rev.} A}
\def\PRD{{\em Phys. Rev.} D}
\def\PRC{{\em Phys. Rev.} C}
\def\PRB{{\em Phys. Rev.} B}
\def\ZPC{{\em Z. Phys.} C}
\def\ZPA{{\em Z. Phys.} A}
\def\ANNP{\em Ann. Phys. (N.Y.)}
\def\RMP{{\em Rev. Mod. Phys.}}
\def\CHEM{{\em J. Chem. Phys.}}
\def\INT{{\em Int. J. Mod. Phys.} E}
\def\r{\vec r}
\def\R{\vec R}
\def\p{\vec p}
\def\P{\vec P}
\def\q{\vec q}
\def\ss{\mbox{\boldmath $\sigma$}}
\newcommand{\be}{\begin{equation}}
\newcommand{\ee}{\end{equation}}
\newcommand{\bea}{\begin{eqnarray}}
\newcommand{\eea}{\end{eqnarray}}
\newcommand{\nn}{\nonumber}
\topmargin-2.8cm
\oddsidemargin-1cm
\evensidemargin-1cm
\textwidth18.5cm
\textheight27.0cm
\begin{document}

\title{
Two-Body Correlations in Nuclear Systems
}

\author{H.\ M\"uther
\\
Institut f\"ur Theoretische Physik,\\ Universit\"at T\"ubingen,
T\"ubingen, Germany
\\
\\
A. Polls\\
Departament d'Estructura i Constituents de la Mat\`eria\\
Universitat de Barcelona,
E-08028 Barcelona, Spain}

\maketitle

\begin{abstract} Correlations in the nuclear wave-function beyond the mean-field 
or Hartree-Fock approximation are very important to describe basic properties of
nuclear structure. Various approaches to account for such correlations are
described and compared to each other. This includes the hole-line expansion, the
coupled cluster or ``exponential S'' approach, the self-consistent evaluation of
Greens functions, variational approaches using correlated basis functions and
recent developments employing quantum Monte-Carlo techniques. Details of these 
correlations are explored and their sensitivity to the underlying 
nucleon-nucleon interaction. Special
attention is paid to the attempts to investigate these correlations in
exclusive nucleon knock-out experiments induced by electron scattering.
Another important issue of nuclear structure physics is the role of relativistic
effects as contained in phenomenological mean field models.  The sensitivity of 
various nuclear structure observables on these
relativistic features are investigated. The report includes the discussion of
nuclear matter as well as finite nuclei.
\end{abstract}
%\eject
%\tableofcontents
\section{Introduction}
One of the central challenges of theoretical nuclear physics is the attempt to
describe the basic properties of nuclear systems in terms of a realistic
nucleon-nucleon (NN) interaction. Such an attempt typically contains two major
steps. In the first step one has to consider a specific model for the NN
interaction. This could be a model which is inspired by the
quantum-chromo-dynamics\cite{faes0}, a meson-exchange or One-Boson-Exchange
model\cite{rupr0,nijm0} or a purely phenomenological ansatz in terms of
two-body spin-isospin operators multiplied 
by local potential
functions\cite{argo0,urbv14}. Such models are considered as a realistic
description of the NN interaction, if the adjustment of parameters within the
model yields a good fit to the NN scattering data at energies below the
threshold for pion production as well as energy and other observables of the
deuteron.

After the definition of the nuclear hamiltonian,
 the second
step implies the solution of the many-body problem of $A$ nucleons interacting
in terms of such a realistic two-body NN interaction. The simplest approach to
this many-body problem of interacting fermions one could think of would be the
mean field or Hartree-Fock approximation. This procedure yields very good
results for the bulk properties of nuclei, binding energies and radii, 
if one employs simple phenomenological NN forces like e.g.~the Skyrme forces, 
which are adjusted to describe such nuclear structure data\cite{skyrme}.
However, employing realistic NN interactions the Hartree-Fock approximation
fails very badly: it leads to unbound nuclei\cite{art99}. 


\begin{figure}[tb]
%\epsfysize=9.0cm
\begin{center}
\begin{minipage}[t]{8 cm}
\epsfig{file=emblem.ps,scale=0.5}
\end{minipage}
\begin{minipage}[t]{16.5 cm}
\caption{Cartoon of a nucleus, displaying the size of the nucleons as compared
to the typical distance to nearest neighbors. Also indicated are the internal
structure of nucleons and mesons.\label{fig1}}
\end{minipage}
\end{center}
\end{figure}

The calculation scheme discussed so far, determine the interaction of two
nucleons in the vacuum in a first step and then solve the many-body problem of
nucleons interacting by such realistic potentials in a second step, is of course
based on the picture that nucleons are elementary particles with properties,
which are not affected by the presence of other nucleons in the nuclear medium. 
One knows, of course, that this is a rather simplified picture: nucleons are
built out of quarks and their properties might very well be influenced by the
surrounding medium. A cartoon of this feature is displayed in Fig.~\ref{fig1}.

\section{Many-Body Approaches}
\subsection{\it Hole - Line Expansion \label{sec:holeline}}
As it has been discussed already above one problem of nuclear structure
calculations based on realistic NN interactions is to deal with the strong
short-range components contained in all such interactions. This problem is 
evident in particular when
so-called hard-core potentials are employed, which are infinite for relative
distances smaller than the radius of the hard core $r_c$. The matrix elements
of such a potential $V$ evaluated for an uncorrelated two-body wave function
$\Phi (r)$ diverges since $\Phi (r)$ is different from zero also for relative
distances $r$ smaller than the hard-core radius $r_c$ (see the schematic picture
in Fig.~\ref{fig3}. A way out of this problem is to account for the two-body
correlations induced by the NN interaction in the correlated wave function
$\Psi (r)$ or by defining an effective operator, which acting on the
uncorrelated wave function $\Phi (r)$ yields the same result as the bare
interaction $V$ acting on $\Psi (r)$. This concept is well known for example in
dealing with the scattering matrix $T$, which is defined by
\be
<\Phi \vert T \vert \Phi > = <\Phi \vert V \vert \Psi > \; . \label{eq:tmat}
\ee
As it is indicated in the schematic Fig.~\ref{fig3}, the correlations tend to 
enhance the amplitude
of the correlated wave function $\Psi$ relative to the uncorrelated one
at distances $r$ for which the interaction is attractive. A reduction of
the amplitude is to be expected for small distances for which $V(r)$ is
repulsive. From this discussion we see that the
correlation effects tend to make the matrix elements of $T$ more attractive
than those of the bare potential $V$.  For two nucleons in the vacuum the $T$
matrix can be determined by solving a Lippmann-Schwinger equation
\bea
T \vert \Phi > &= &V \left\{ \vert \Phi > + \frac{1}{\omega  - H_0 +
i\epsilon } V \vert \Psi >\right\}\nonumber \\
& = &  \left\{ V + V \frac{1 }{\omega  - H_0 +i\epsilon } T\right\} \vert 
\Phi >\, . \label{eq:lipschw}
\eea

\begin{figure}[tb]
%\epsfysize=9.0cm
\begin{center}
\begin{minipage}[t]{8 cm}
\epsfig{file=fig3.eps,scale=0.7}
\end{minipage}
\begin{minipage}[t]{16.5 cm}
\caption{Schematic picture of a NN interaction with hard core and its effect on
the correlated NN wave function $\Psi(r)$. \label{fig3}}
\end{minipage}
\end{center}
\end{figure}

Therefore it seems quite natural to define the single-particle potential $U$ in
analogy to the Hartree-Fock definition with the bare interaction $V$ replaced
by the corresponding $G$-matrix. To be more precise, the Brueckner-Hartree-Fock
(BHF) definition of $U$ is given by
\be
<\alpha \vert U \vert \beta> = \cases{ \sum_{\nu \le F} <\alpha \nu \vert
\frac{1} {2} \left( G(\omega_{\alpha \nu}) + G(\omega_{\beta \nu}) \right)
\vert \beta \nu >, & if $\alpha$ and $\beta$ $\le F$ \cr \sum_{\nu \le F}
<\alpha \nu \vert G(\omega_{\alpha \nu}) \vert \beta \nu >, & if $\alpha\le F$
and $\beta > F$ \cr 0 & if $\alpha$ and $\beta$ $>F$, \cr}\, . \label{eq:ubhf}
\ee               

\subsection{\it Many-Body Theory in Terms of Green's Functions
\label{subsec:green}}
 
The two-body approaches discussed so far, the hole-line expansion as well as the
CCM, are essentially restricted to the evaluation of ground-state properties.
The Green's function approach, which  will
shortly be introduced in this section
also yields results for dynamic properties like e.g.~the single-particle
spectral function which is closely related to the cross section of particle
knock-out and pick-up reactions. It is based on the time-dependent
perturbation expansion and also assumes a separation of the total hamiltonian
into an single-particle part $H_0$ and a perturbation $H_1$. 
A more detailed description can be found e.g.~in the textbook
of Fetter and Walecka\cite{fetwal}. 

\section{Effects of Correlations derived from Realistic Interactions}
\subsection{\it Models for the NN Interaction\label{sec:nninter}}
 
In our days there is a general agreement between physicists working on this
field, that quantum chromo dynamics (QCD) provides the basic theory of
the strong
interaction. Therefore also the roots of the strong interaction between two
nucleons must be hidden in QCD. For nuclear structure calculations, however, one
needs to determine the NN interaction at low energies and momenta, a region in
which one cannot treat QCD by means of perturbation theory. On the other hand,
the
system of two interacting nucleons is by far too complicate to be treated by
means of lattice QCD calculations. Therefore one has to consider
phenomenological models for the NN interaction.   

With the OBE ansatz one can now solve the Blankenbecler--Sugar or a
corresponding scattering equation and adjust the parameter of the OBE model to
reproduce the empirical NN scattering phase shifts as well as binding energy and
other observables for the deuteron. Typical sets of parameters resulting from
such fits are listed in table~\ref{tab:obe}.
 
\begin{table}
\begin{center}
\begin{minipage}[t]{16.5 cm}
\caption{Parameters of the realistic OBE potentials Bonn $A$, $B$ and $C$ (see
table A.1 of \protect{\cite{rupr0}}).
The second column displays the type of
meson: pseudoscalar (ps), vector (v) and scalar (s) and the third its
isospin $T_{\rm iso}$.}
\label{tab:obe}
\end{minipage}
\begin{tabular}{rrrr|rr|rr|rr}
\hline
&&&&&&&&&\\[-2mm]
&&&&\multicolumn{2}{c}{Bonn A}&\multicolumn{2}{c}{Bonn
B}&\multicolumn{2}{c}{Bonn C}\\
Meson &&$T_{\rm iso}$&$m_{\alpha}$&$g^2_{\alpha}/4\pi$&$\Lambda_{\alpha}$
&$g^2_{\alpha}/4\pi$&$\Lambda_{\alpha}$&$g^2_{\alpha}/4\pi$&$\Lambda_{\alpha}$\\
&&&[MeV]&&[MeV]&[MeV]&[MeV]\\
&&&&&&&&&\\[-2mm]
\hline
&&&&&&&&&\\[-2mm]
$\pi$ & ps & 1 & 138.03 & 14.7 & 1300 & 14.4 & 1700 & 14.2 & 3000\\[2mm]
$\eta$ & ps & 0 & 548.8 & 4 & 1500 & 3 & 1500 & 0 & -\\[2mm]
$\rho$ & v & 1 & 769 & 0.86$^{\rm a}$ & 1950 & 0.9$^{\rm a}$ & 1850 &
1.0$^{\rm a}$ & 1700 \\[2mm]       
$\omega$ & v & 0 & 782.6 & 25$^{\rm a}$ & 1350 & 24.5$^{\rm a}$ & 1850 &
24$^{\rm a}$ & 1400\\[2mm]
$\delta$ & s & 1 & 983 & 1.3 & 2000 & 2.488 & 2000 & 4.722 & 2000\\[2mm]
$\sigma^{\rm b}$ & s & 0 & 550$^{\rm b}$ & 8.8 & 2200 & 8.9437 & 1900 & 8.6289 &
1700\\
&&&(710-720)$^{\rm b}$ & 17.194 & 2000 & 18.3773 & 2000 & 17.5667 & 2000\\
&&&&&&&&&\\[-2mm]\hline
\end{tabular}
%noalign{\smallskip\hrule}\cr}
\begin{minipage}[t]{16.5 cm}
\vskip 0.5cm
\noindent
$^{\rm a}$ The tensor coupling constants are $f_{\rho}$=6.1 $g_{\rho}$
and $f_{\omega}$ = 0. \\
$^{\rm b}$ The $\sigma$ parameters in the first line apply for NN channels
with isospin 1, while those in the second line refer to isospin 0 channels. In
this case the masses for the $\sigma$ meson of 710 (Bonn A) and 720 MeV (Bonn B
and C) were considered.
\end{minipage}
\end{center}
\end{table}     

\subsection{\it Ground state Properties of Nuclear Matter and Finite Nuclei}
 
In the first part of this section we would like to discuss the convergence of
the many-body approaches and compare results for nuclear matter as obtained from
various calculation schemes presented in section 2.
The convergence of the hole-line expansion for nuclear matter has been
investigated during the last few years in particular by the group in
Catania\cite{song1,song2}. Continuing the earlier work of Day\cite{day81} they
investigated the effects of the three-hole-line contributions for various
choices of the auxiliary potential $U$ (see Eq.~\ref{eq:ubhf}). In particular
they considered the standard or conventional choice, which assumes a
single-particle potential $U=0$ for single-particle states above the Fermi level,
and the so-called ``continuous choice''. This continuous choice supplements the definition of the
auxiliary potential of the hole states in Eq.~(\ref{eq:ubhf}) with a
corresponding definition (real part of the BHF self-energy) also for the
particle states with momenta above the Fermi momentum, $k >k_F$. In this way
one does not have any gap in the single-particle spectrum at $k=k_F$. 

\section{Conclusion}
 
The main aim of this review has been to demonstrate that nuclear systems
are very intriguing many-body systems.  They are non-trivial
systems in the sense that they require the treatment of correlations beyond the
mean field or Hartree-Fock approximation. Therefore, from the point of view of
many-body
theory, they can be compared to other quantum many-body systems like liquid He,
electron gas, clusters of atoms etc. A huge amount of experimental data is
available for real nuclei with finite number of particles as well as for the
infinite limit of nuclear matter or the matter of a neutron star.    

\begin{thebibliography}{99}
\itemsep -2pt 
\bibitem{faes0} A. Valcarce, A. Buchmann, F. Fern\'andez, and Amand Faessler,
\Journal{\PRC} {51}{1480} {1995} 
\bibitem{rupr0} R. Machleidt, \Journal{\em Adv. Nucl. Phys.}{19}{189}{1989}
\bibitem{nijm0} M.M. Nagels, T.A. Rijken, and J.J. de Swart, \Journal{\PRD} 
{17} {768} {1978}
\bibitem{argo0} R.B. Wiringa, R.A. Smith, and T.L. Ainsworth, \Journal{\PRC}
{29} {1207} {1984}
\bibitem{urbv14} I.E. Lagaris and V.R. Pandharipande, \Journal{\NPA}{359} 
{331} {1981}
\bibitem{skyrme} M. Brack, C. Guet, and H.-B, Hakansson, \Journal {\PREP}{123}
{275}{1985}
\bibitem{art99} H. M\"uther and A. Polls, \Journal{\PRC} {}{in press}{1999}, 
preprint nucl-th/9908002.
\bibitem{fetwal} A.L. Fetter and J.D. Walecka, {\it Quantum Theory of Many 
Particle Systems} (McGraw-Hill New York, 1971)
\bibitem{song1} H.Q. Song, M. Baldo, U. Lombardo, and G. Giansiracusa,
\Journal{\PLB} {411}{237}{1997}
\bibitem{song2} H.Q. Song, M. Baldo, G. Giansiracusa, annd U. Lombardo, 
\Journal{\PRL} {81} {1584}{1998}
\bibitem{day81} B.D. Day, \Journal{\PRC} {24}{1203}{1981}

\end{thebibliography}
\end{document}

hep-ph0206149.extracted_bib
\begin{thebibliography}{99}




\bibitem{KK60Y}%{3}	
		H.V. Klapdor-Kleingrothaus, 
		{\sf "60 Years of Double Beta Decay"}, {\it World Scientific, 
		Singapore} (2001) 1253~p.


\bibitem{Bau98}%{6}
 	L.~Baudis, G.~Heusser, B.~Majorovits, Y.~Ramachers, H.~Strecker and 
 	H.V.~Klapdor--Kleingrothaus, {\it hep-ex/} {\bf 9811040} and 
	{\it Nucl. Instr. Meth.} {\bf A 426}, 425 (1999).


\bibitem{BKK-SolN}%{7}
	L. Baudis and H.V. Klapdor-Kleingrothaus, 
	{\it Eur. Phys. J.} {\bf A 5}, 441-443  (1999) and in 
	Proceedings of the 2nd Int. Conf. on Particle 
	Physics Beyond the Standard Model BEYOND'99, 
	Castle Ringberg, Germany, 6-12 June 1999, 
	edited by H.V. Klapdor-Kleingrothaus and I.V. Krivosheina, 
	{\it IOP Bristol}, 1023 - 1036 (2000).

\bibitem{KK01}%{8}	
		H.V. Klapdor-Kleingrothaus et al., 
		to be publ. 2001 
		and ${\it http://www.mpi-hd.mpg.de/non\_acc/}$


%%%%%%%%%% Rom 2001, LP01, Erice 2001 %%%%%%%%%%%%%%%%%
\bibitem{KK-LP01}
	H.V. Klapdor-Kleingrothaus, 
	in Proc. of the XX Lepton Photon Symposium (LP01), 
	July 23 - 28, 2001, Rome, Italy, 
	{\it World Scientific, Singapore} (2002) 

\bibitem{KK-Erice01}
	H.V. Klapdor-Kleingrothaus, 
	in Proc. of the Erice School on Nuclear Physics about Neutrinos, 
	ed. A. Faessler,  
	{\it Progress in Particle and Nuclear Physics} {\bf 48} (2002).

%%%%%%%%%%%%%%%% BEY97 %%%%%%%%%%%%%%%%%%%%%%%
 	
\bibitem{KK-Bey97}%{17}
	H.V. Klapdor-Kleingrothaus in Proceedings of BEYOND'97, 
	First International Conference on Particle Physics 
	Beyond the Standard Model, Castle Ringberg, Germany, 
	8-14 June 1997, 
     edited by H.V. Klapdor-Kleingrothaus and H. P\"as, 
	{\it IOP Bristol} 485-531 (1998)  
%	and {\it Int. J. Mod. Phys.} {\bf A 13} (1998) 3953, and 
%     {\it J. Phys.} {\bf G 24} (1998) 483-516.

%%%%%%%%%%%%%%%%%%%%% BEY99 %%%%%%%%%%%%%%%%%%%%%%%%

\bibitem{GEN-prop}%{18}
	H.V. Klapdor-Kleingrothaus et al. 
	{\it MPI-Report} {\bf MPI-H-V26-1999} and 
	{\it Preprint: hep-ph/}{\bf 9910205} and in 
	Proceedings of the 2nd Int. Conf. on Particle 
	Physics Beyond the Standard Model BEYOND'99, 
	Castle Ringberg, Germany, 6-12 June 1999, 
	edited by H.V. Klapdor-Kleingrothaus and I.V. Krivosheina, 
	{\it IOP Bristol}, 915 - 1014 (2000).

%%%%%%%%%%%%% NEUTRINO98 %%%%%%%%%%%%%
\bibitem{KK-Neutr98}%{19}
	H.V. Klapdor-Kleingrothaus, in Proc. of 18th Int. 
	Conf. on Neutrino Physics and Astrophysics (NEUTRINO 98), 
	Takayama, Japan, 4-9 Jun 1998, (eds) Y. Suzuki et al. 
	{\it Nucl. Phys. Proc. Suppl.} {\bf 77}, 357 - 368 (1999).   

%%%%%%%%%%%%%%%%%%%%5 WEIN98 %%%%%%%%%%%%%%%%%%%%%%%

\bibitem{KK-WEIN98}%{20}
	H.V. Klapdor-Kleingrothaus, in Proc. of WEIN'98, 
	"Physics Beyond the Standard Model", Proceedings of the Fifth Intern.  
	WEIN Conference, P. Herczeg, C.M. Hoffman and 
	H.V. Klapdor-Kleingrothaus (Editors), 
	{\it World Scientific, Singapore}, 275-311 (1999).


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% NOW 2000 %%%%%%%%%%%%%

\bibitem{KK-NOW00}%{22}
	H.V. Klapdor-Kleingrothaus, in Proc. of Int. Conference 
	NOW2000 - "Origins of Neutrino Oscillations", 
	{\it Nucl. Phys.} {\bf B} (2001) ed. G. Fogli and 
	{\it Preprint: hep-ph/}{\bf 0102277}, 
	{\it Preprint: hep-ph/}{\bf 0102276}. 

%%%%%%%%%%%%%%%%%%%%%%%%%% NOON 2000 and LowNu2000 %%%%%%%%%%%%%%%%%


\bibitem{LowNu2}%{24}
	H.V. Klapdor-Kleingrothaus, in 
	Proc. Int. Workshop on Low Energy Solar Neutrinos, LowNu2, 
	December 4 and 5 (2000) Tokyo, Japan, 
	ed: Y. Suzuki, World Scientific, Singapore (2001), home page: 
	{\it http://www-sk.icrr.u-tokyo.ac.jp/neutlowe/2/transparency/
index.html}

%%%%%%%%%%%%% Journ %%%%%%%%%%%%%%%%

\bibitem{KK-J-PhysG98}%{27}
	H.V. Klapdor-Kleingrothaus, J. Hellmig and M. Hirsch, 
	{\it J. Phys.} {\bf G 24}, 483 (1998).

\bibitem{KK-InJModPh98}%{28}
	H.V. Klapdor-Kleingrothaus, {\it Int. J. Mod. Phys.} {\bf A 13}, 3953  
	(1998).
%	and {\it J. Phys.} {\bf G 24} (1998) 483--516.

\bibitem{KK-SprTracts00}%{29}
	H.V. Klapdor-Kleingrothaus, {\it Springer Tracts in Modern Physics}, 
	{\bf 163}, 69-104 (2000), 
	{\it Springer-Verlag, Heidelberg, Germany} (2000).

%%%%%%%%%%%%%%%% Dark Matter %%%%%%%%%%%


\bibitem{BedKK00}%{31}
	V.A. Bednyakov and H.V. Klapdor-Kleingrothaus, 
	{\it Phys. Rev.} {\bf D 62} (2000) 043524/1-9 and {\it hep-ph/}
	{\bf 9908427}. 

\bibitem{BedKK-01}%{32}
	V.A. Bednyakov and H.V. Klapdor-Kleingrothaus, 
	{\it Preprint: hep-ph/}{\bf 0011233} (2000) and  
	{\it Phys. Rev.} {\bf D 63} (2001) 095005.

\bibitem{EllOliv-DM00}%{33}
	J. Ellis, A. Ferstl and K.A. Olive, {\it Phys. Lett.} {\bf B 481},  
	304--314 (2000) and {\it Preprint: hep-ph/}{\bf 0001005} 
	and {\it Preprint: hep-ph/}{\bf 0007113}.

\bibitem{Eds99}%{34}
	J. Edsj\"o, Neutralinos as dark matter - can we see them? 
	Seminar given in the theory group, Department of Physics, 
	Stockholm University, October 12, 1999, home page: 
	{\it http://www.physto.se/edsjo/}

\bibitem{GENIUS-TF}
	H.V. Klapdor-Kleingrothaus, L. Baudis, A. Dietz, 
	G. Heusser, I.V. Krivosheina, B. Majorovits and 
	H. Strecker, hep-ex/0012022, Subm. for Publ. (2001).	

%%%%%%%%%%%%%%% Solar Neutrinos Bahcall %%%%%%%%%

\bibitem{HomP-Bach}%{35}
	see: {\it http://www.sns.ias.edu.jnb/}

\bibitem{Bach89}%{36}
	J.N. Bahcall, {\it Neutrino Astrophysics}, Cambridge Univ. 
	Press (1989). 

\bibitem{BacBasPins98}%{39}
	J.N. Bahcall, S. Basu and M. Pinsonneault, 
	{\it Phys. Lett.} {\bf B 433}, 1 (1998).


\end{thebibliography}