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A low momentum nucleon-nucleon (NN) potential $V_{low-k}$ is derived frommeson exhange potentials by integrating out the model dependent high momentummodes of $V_{NN}$. The smooth and approximately unique $V_{low-k}$ is used asinput for shell model calculations instead of the usual Brueckner $G$ matrix.Such an approach eliminates the nuclear mass dependence of the inputinteraction one finds in the $G$ matrix approach, allowing the same inputinteraction to be used in different nuclear regions. Shell model calculationsof $^{18}$O and $^{134}$Te using the {\bf same} input $V_{low-k}$ have beenperformed. For cut-off momentum $\Lambda$ in the vicinity of 2 $fm^{-1}$, ourcalculated low-lying spectra for these nuclei are in good agreement withexperiments, and are weakly dependent on $\Lambda$.Comment: 13 pages, 4 figures. Changes made emphasizing the renormalization  group and effective field theory connections to comply with referee's  comment

Low momentum nucleon-nucleon potential and shell model effective interactions