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We explore the effect of the imaginary part of the self-energy,$Im\Sigma(\vec{k},\omega)$, having a single pole, $\Omega(\vec{k},\omega)$,with spectral weight, $\alpha(\vec{k})$, and quasi-particle lifetime,$\Gamma(\vec{k})$, on the density of states. We solve the set of parameters,$\Omega(\vec{k},\omega$), $\alpha(\vec{k})$, and $\Gamma(\vec{k})$ by means ofthe moment approach (exact sum rules) of Nolting. Our choice for$\Sigma(k,\omega)$, satisfies the Kramers - Kronig relationship automatically.Due to our choice of the self - energy, the system is not a Fermi liquid forany value of the interaction, a result which is also true in the momentapproach of Nolting without lifetime effects. By increasing the value of thelocal interaction, $U/W$, at half-filling ($\rho = 1/2$), we go from aparamagnetic metal to a paramagnetic insulator, (Mott metal - insulatortransition ($MMIT$)) for values of $U/W$ of the order of $U/W \geq 1$ ($W$ isthe band width) which is in agreement with numerical results for finitelattices and for infinity dimensions ($D = \infty$). These results settle downthe main weakness of the spherical approximation of Nolting: a finite gap forany finite value of the interaction, i.e., an insulator for any finite value of$U/W$. Lifetime effects are absolutely indispensable. Our scheme works betterthan the one of improving the narrowing band factor, $B(\vec{k})$, beyond thespherical approximation of Nolting.Comment: 5 pages and 5 ps figures (included

The Mott metal - insulator transition in the two-dimensional Hubbard model at half-filling with lifetime effects within the moment approach