Low momentum nucleon-nucleon potential and shell model effective interactions

A low momentum nucleon-nucleon (NN) potential $V_{low-k}$ is derived from meson exhange potentials by integrating out the model dependent high momentum modes of $V_{NN}$. The smooth and approximately unique $V_{low-k}$ is used as input for shell model calculations instead of the usual Brueckner $G$ matrix. Such an approach eliminates the nuclear mass dependence of the input interaction one finds in the $G$ matrix approach, allowing the same input interaction to be used in different nuclear regions. Shell model calculations of $^{18}$O and $^{134}$Te using the {\bf same} input $V_{low-k}$ have been performed. For cut-off momentum $\Lambda$ in the vicinity of 2 $fm^{-1}$, our calculated low-lying spectra for these nuclei are in good agreement with experiments, and are weakly dependent on $\Lambda$.