On stable pair potentials with an attractive tail, remarks on two papers by A. G. Basuev

We revisit two old and apparently little known papers by Basuev [2] [3] and show that the results contained there yield strong improvements on current lower bounds of the convergence radius of the Mayer series for continuous particle systems interacting via a very large class of stable and tempered potentials which includes the Lennard-Jones type potentials. In particular we analyze the case of the classical Lennard-Jones gas under the light of the Basuev scheme and, using also some new results [33] on this model recently obtained by one of us, we provide a new lower bound for the Mayer series convergence radius of the classical Lennard-Jones gas which improves by a factor of the order $10^5$ on the current best lower bound recently obtained in [17].