Exercise on Qualitative SCF

The n,l states sequence in SCF potential
is influenced by the centrifugal barrier


0. What is SCF
1. what is the  centrifugal barrier
2. why are then the low-l-values energetically favoured?

3. sketch this or fetch the figures at the address
http://web.ift.uib.no/AMOS/PHYS261/2006.09.27_task/   (eps available)
http://web.ift.uib.no/AMOS/PHYS261/2006.09.27_task/Compare_potentials.html

  (plots of -Z/r + L(L+1)/(r*r)
   and
 -(Z-1)/r (exp(-alpha*r)) - 1/r   + L(L+1)/(r*r)

4. explain the approximation formula  -(Z-1)/r (exp(-alpha*r)) - 1/r


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%  Matlab program for the figures
%  -Z/r + L(L+1)/(r*r)
%   and
%  -(Z-1)/r (exp(-alpha*r)) - 1/r   + L(L+1)/(r*r)
figure(1), hold off
r=0.2:0.05:6;
plot (r,-1./r,'k-',r,-1./r+1*(1+1)/2./r.^2,'r-',r,-1./r+2*(2+1)/2./r.^2,'b-')
hold on,plot([0 6],[0 0],'k:')
set(gca,'xlim',[0,4],'ylim',[-2,2])
gtext('L=0')  %  place by mouse
gtext('L=1')  %  place by mouse
gtext('L=2')  %  place by mouse
%  To save the picture, run
%   print -depsc 'coulomb_pot.eps'

figure(2)
alf=0.1;
plot (r,-1./r,'b:',r,-1./r.*exp(-alf*r),'k-',r,-1./r.*exp(-alf*r)+1*(1+1)/2./r.^2,'b-')
hold on,plot([0 6],[0 0],'k:')
set(gca,'xlim',[0,4],'ylim',[-2,2])
gtext('L=0')  %  place by mouse
gtext('L=1')  %  place by mouse
%  To save the picture, run
%  figure(2); print -depsc 'hartree_pot.eps'