We explore the effect of the imaginary part of the self-energy,
ImΣ(k,ω), having a single pole, Ω(k,ω),
with spectral weight, α(k), and quasi-particle lifetime,
Γ(k), on the density of states. We solve the set of parameters,
Ω(k,ω), α(k), and Γ(k) by means of
the moment approach (exact sum rules) of Nolting. Our choice for
Σ(k,ω), satisfies the Kramers - Kronig relationship automatically.
Due to our choice of the self - energy, the system is not a Fermi liquid for
any value of the interaction, a result which is also true in the moment
approach of Nolting without lifetime effects. By increasing the value of the
local interaction, U/W, at half-filling (ρ=1/2), we go from a
paramagnetic metal to a paramagnetic insulator, (Mott metal - insulator
transition (MMIT)) for values of U/W of the order of U/W≥1 (W is
the band width) which is in agreement with numerical results for finite
lattices and for infinity dimensions (D=∞). These results settle down
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
U/W. Lifetime effects are absolutely indispensable. Our scheme works better
than the one of improving the narrowing band factor, B(k), beyond the
spherical approximation of Nolting.Comment: 5 pages and 5 ps figures (included