(1) We are in the I=1 case with an electrical field, 2 levels can be found if eta = 0, 3 if eta !=0, we can thus conclude that eta !=0, which means that the nucleus is not axially symmetric.
Moreover since the m=-1 level has higher energy than the m=1 level, the electric field gradient is negative.
However, I find something strange about the figure, I would expect that the mi=0 is the lowest state, or is the field gradient so big that the mi=1 goes so much down when eta !=0 that it crosses the mi=0?
(2) at low temperature all nuclei will be in the lowest energy state, due to the boltzmann distribution, which is in this case the mi=1 state
correction: I misinterpreted the E on the slide, I taught it was an electrical field, but we have a magnetic field, by studying the deltaE’s one could get information on the magnetic field that is applied and on the dipole moment of the nuclei