Low momentum nucleon-nucleon potential and shell model effective interactions

A low momentum nucleon-nucleon (NN) potential V_low-k is derived from meson exchange potentials by integrating out the model dependent high momentum modes of VNN. 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 ¹⁸O, ¹³⁴Te, and ¹³⁵I using the same input V_low-k have been performed. For cut-off momentum {Λ} 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 {Λ}.