function d=dipole_elementRb87D1line(Fl,ml,Fu,mu)
% Fl, ml  are F and m quantum numbers of lower state
% Fu, mu  are F and m quantum numbers of upper state
% F is total momentum and m is projection
	d.left   = 0; %default return value
	d.linear = 0; %default return value
	d.right  = 0; %default return value
	if ( mu==(ml+1) )
		% sigma plus polarization
		% ------ Fl=2 -> Fu=2 --------
		if ( (ml==-2) & (Fl==2) & (Fu==2) )
			d.right=sqrt(1/6);
		endif
		if ( (ml==-1) & (Fl==2) & (Fu==2) )
			d.right=sqrt(1/4);
		endif
		if ( (ml== 0) & (Fl==2) & (Fu==2) )
			d.right=sqrt(1/4);
		endif
		if ( (ml== 1) & (Fl==2) & (Fu==2) )
			d.right=sqrt(1/6);
		endif
		if ( (ml== 2) & (Fl==2) & (Fu==2) )
			d.right=0;
		endif
		% ------ Fl=2 -> Fu=1 --------
		if ( (ml==-2) & (Fl==2) & (Fu==1) )
			d.right=sqrt(1/2);
		endif
		if ( (ml==-1) & (Fl==2) & (Fu==1) )
			d.right=sqrt(1/4);
		endif
		if ( (ml== 0) & (Fl==2) & (Fu==1) )
			d.right=sqrt(1/12);
		endif
		if ( (ml== 1) & (Fl==2) & (Fu==1) )
			d.right=0;
		endif
		if ( (ml== 2) & (Fl==2) & (Fu==1) )
			d.right=0;
		endif
		% ------ Fl=1 -> Fu=2 --------
		if ( (ml==-1) & (Fl==1) & (Fu==2) )
			d.right = -sqrt(1/12);
		endif
		if ( (ml== 0) & (Fl==1) & (Fu==2) )
			d.right = -sqrt(1/4);
		endif
		if ( (ml== 1) & (Fl==1) & (Fu==2) )
			d.right = -sqrt(1/2);
		endif
		% ------ Fl=1 -> Fu=1 --------
		if ( (ml==-1) & (Fl==1) & (Fu==1) )
			d.right = -sqrt(1/12);
		endif
		if ( (ml== 0) & (Fl==1) & (Fu==1) )
			d.right = -sqrt(1/12);
		endif
		if ( (ml== 1) & (Fl==1) & (Fu==1) )
			d.right = 0;
		endif
	endif
	if ( mu==(ml+0) )
		% pi polarization
		% ------ Fl=2 -> Fu=2 --------
		if ( (ml==-2) & (Fl==2) & (Fu==2) )
			d.linear=-sqrt(1/3);
		endif
		if ( (ml==-1) & (Fl==2) & (Fu==2) )
			d.linear=-sqrt(1/12);
		endif
		if ( (ml== 0) & (Fl==2) & (Fu==2) )
			d.linear=0;
		endif
		if ( (ml== 1) & (Fl==2) & (Fu==2) )
			d.linear=sqrt(1/12);
		endif
		if ( (ml== 2) & (Fl==2) & (Fu==2) )
			d.linear=sqrt(1/3);
		endif
		% ------ Fl=2 -> Fu=1 --------
		if ( (ml==-2) & (Fl==2) & (Fu==1) )
			d.linear = 0;
		endif
		if ( (ml==-1) & (Fl==2) & (Fu==1) )
			d.linear=sqrt(1/4);
		endif
		if ( (ml== 0) & (Fl==2) & (Fu==1) )
			d.linear=sqrt(1/3);
		endif
		if ( (ml== 1) & (Fl==2) & (Fu==1) )
			d.linear=sqrt(1/4);
		endif
		if ( (ml== 2) & (Fl==2) & (Fu==1) )
			d.linear = 0;
		endif
		% ------ Fl=1 -> Fu=2 --------
		if ( (ml==-1) & (Fl==1) & (Fu==2) )
			d.linear =  sqrt(1/4);
		endif
		if ( (ml== 0) & (Fl==1) & (Fu==2) )
			d.linear =  sqrt(1/2);
		endif
		if ( (ml== 1) & (Fl==1) & (Fu==2) )
			d.linear =  sqrt(1/4);
		endif
		% ------ Fl=1 -> Fu=1 --------
		if ( (ml==-1) & (Fl==1) & (Fu==1) )
			d.linear =  sqrt(1/12);
		endif
		if ( (ml== 0) & (Fl==1) & (Fu==1) )
			d.linear = 0;
		endif
		if ( (ml== 1) & (Fl==1) & (Fu==1) )
			d.linear = -sqrt(1/12);
		endif
	endif
	if ( mu==(ml-1) )
		% sigma minus polarization
		% ------ Fl=2 -> Fu=2 --------
		if ( (ml==-2) & (Fl==2) & (Fu==2) )
			d.left = 0;
		endif
		if ( (ml==-1) & (Fl==2) & (Fu==2) )
			d.left = -sqrt(1/6);
		endif
		if ( (ml== 0) & (Fl==2) & (Fu==2) )
			d.left = -sqrt(1/4);
		endif
		if ( (ml== 1) & (Fl==2) & (Fu==2) )
			d.left = -sqrt(1/4);
		endif
		if ( (ml== 2) & (Fl==2) & (Fu==2) )
			d.left = -sqrt(1/6);
		endif
		% ------ Fl=2 -> Fu=1 --------
		if ( (ml==-2) & (Fl==2) & (Fu==1) )
			d.left = 0;
		endif
		if ( (ml==-1) & (Fl==2) & (Fu==1) )
			d.left = 0;
		endif
		if ( (ml== 0) & (Fl==2) & (Fu==1) )
			d.left =  sqrt(1/12);
		endif
		if ( (ml== 1) & (Fl==2) & (Fu==1) )
			d.left =  sqrt(1/4);
		endif
		if ( (ml== 2) & (Fl==2) & (Fu==1) )
			d.left =  sqrt(1/2);
		endif
		% ------ Fl=1 -> Fu=2 --------
		if ( (ml==-1) & (Fl==1) & (Fu==2) )
			d.left = -sqrt(1/2);
		endif
		if ( (ml== 0) & (Fl==1) & (Fu==2) )
			d.left = -sqrt(1/4);
		endif
		if ( (ml== 1) & (Fl==1) & (Fu==2) )
			d.left = -sqrt(1/12);
		endif
		% ------ Fl=1 -> Fu=1 --------
		if ( (ml==-1) & (Fl==1) & (Fu==1) )
			d.left = 0;
		endif
		if ( (ml== 0) & (Fl==1) & (Fu==1) )
			d.left =  sqrt(1/12);
		endif
		if ( (ml== 1) & (Fl==1) & (Fu==1) )
			d.left =  sqrt(1/12);
		endif
	endif
endfunction



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