| dc.description |
We explore the effect of the self-energy, , having a single pole, , with spectral weight and quasi-particle lifetime , on the density of states. We obtain the set of parameters , , and by means of the moment approach (exact sum rules) of Nolting. Due to our choice of self-energy, the system is not a Fermi liquid for any value of the interaction, a result which also holds in the moment approach of Nolting without lifetime effects. Our self-energy satisfies the Kramers - Kronig relationships since it is analytic in one of the complex half-planes. By increasing the value of the local interaction, , at half-filling , there is a transition from a paramagnetic metal to a paramagnetic insulator (a Mott metal - insulator transition) for values of of the order of (W is the bandwidth) which is in agreement with numerical results for finite lattices and for an infinite number of dimensions . These results expose the main weakness of the spherical approximation of Nolting: a finite gap for any finite value of the interaction, i.e., an insulator for any finite value of . Lifetime effects are absolutely indispensable to making our scheme work better than that based on improving the narrowing band factor, , beyond that obtained from the spherical approximation of Nolting. |
