  Within the infinite series of ring (or bubble) diagram approximation for the
electronic self-energy as appropriate for the long-range Coulomb interaction,
we calculate the density-dependent T=0 Fermi liquid quasiparticle effective
mass renormalization in two dimensional (2D) electron systems in the
random-phase-approximation (RPA). We find that the quasiparticle effective mass
increases very strongly with increasing $r_s$, exhibiting an unexpected
divergence at a critical $r_s$ value ($\sim 16$ in the ideal 2D system). We
discuss the possibility for and the consequences of such an interaction induced
effective mass divergence as the electron density decreases, and critically
comment on the likely theoretical scenarios which could lead to such a low
density effective mass divergence in electron liquids.
