Ground state of 113Sn from shell model The shell model predicts that the ground state of 113Sn with 63 neutrons would have J=5/2+. But the ground state is taken to be 1/2+. What is the reason behind that? Has it got something to do with pairing energy?
 A: There are, of course, limitations to the independent particle model (IPM) version of the shell model.
First of all, the configuration you get from the shell model depends on the assumed ordering of the single-particle orbits. If one uses single-particle orbits calculated for 208Pb, then the ordering for neutron orbits above N=50 is 1g7/2, 2d5/2, 2d3/2, 3s1/2, and filling with 13 neutrons leads to a hole in the 2d5/2 and a 5/2+ ground state. However, if one uses orbits calculated for 112Sn, the ordering is 2d5/2, 1g7/2, 3s1/2, 1d3/2, leading to an unpaired 1g7/2 neutron and a 7/2+ ground state. (These of course depend also on the specific form of the potential used to calculate the states).
Second, the spacing between the orbits is quite small, and so neglecting the residual interaction between the 13 valence neutrons is not a good approximation.
In this specific case, my guess would be that the 1g7/2 and 3s1/2 orbits lie very close to one another in energy, so that exciting from the 1g7/2 to the 3s1/2 does not cost much energy. If 112Sn is slightly deformed (say for example oblate, i.e. pancake-shaped), it's possible that adding a neutron to the 3s1/2 results in more overlap with the rest of the valence neutrons than adding the final 1g7/2 would. The last 1g7/2 orbit to be filled will be the most prolate, or cigar-shaped, and thus have a small overlap with the other neutrons, while the 3s1/2 is spherical, and so would have a somewhat larger overlap.
EDIT: There is also a pairing argument which can be made. The attractive pairing energy increases in magnitude with increasing $\ell$, and so if the 1g7/2 and 3s1/2 are close in energy, with 3s1/2 below the 1g7/2 it can become energetically favorable to promote the odd neutron from the 3s1/2 to the 1g7/2 in order to gain pairing energy.
Note that one of these arguments applies if the 3s1/2 is above the 1g7/2, and the other applies if the ordering is reversed.
