The correlation is from the off-diagonal terms of the residual interaction, which is the TBME of the shell model. Consider following Hamiltonian of these nuclei

the correlation energy between the two neutrons is the term . Be aware that this is a residual interaction, not the nucleon-nucleon interaction .

Thus,

,

where is mean field.

The separation energies is proportional to the terms

Thus, the neutron-neutron correlation energy is

For 18O, MeV, and MeV, thus, MeV.

In the shell model calculation, the single particle energy of the 1d5/2 and 2s1/2 neutron are -4.143 MeV and -3.27 MeV respectively. The residual interaction is

The eigenenergy of the ground state of 18O is -10.539 on top of 16O.

The non-correlated binding energy of 18O is 2*-4.143 = -8.286 MeV.

Therefore, the theoretical correlated energy is 2.258 MeV.

### Like this:

Like Loading...

## Leave a Reply