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 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 18 O, 134 Te and 135 I using the same input V low−k have been performed. For cut-off momentum Λ in the vicinity of 2 f m −1 , our calculated low-lying spectra for these nuclei are in good agreement with experiments, and are weakly dependent on Λ. 21.60.Cs; 21.30.Fe; 27.80.+j A fundamental problem in nuclear physics has been the determination of the effective nucleon-nucleon (N N ) interaction used in the nuclear shell model, which has been successful in describing a variety of nuclear properties. There have been a number of successful approaches [1][2][3][4] for this determination, ranging from empirical fits of experimental data, to deriving it microscopically from the bare N N potential. Despite impressive quantitative successes, the traditional microscopic approach suffers the fate of being "model dependent" owing to the fact that there is no unique V N N to start from. Moreover, as the Brueckner G matrix has traditionally been the starting point, one obtains different input interactions for nuclei in different mass regions as a result of the Pauli blocking operator.In this work, we propose a different approach to shell model effective interactions that is motivated by the recent applications of effective field theory (EFT) and the renormalization group (RG) to low energy nuclear systems [5][6][7][8].Our aim is to remove some of the model dependence that arises at short distances in the various V N N models, and also to eliminate the mass dependence one finds in the G matrix approach, thus allowing the same interaction to be used in different nuclear regions such as those for 18 O and 134 Te. A central theme of the RG-EFT approach is that physics in the infrared region is insensitive to the details of the short distance dynamics. One can therefore have infinitely many theories that differ substantially at small distances, but still give the same low energy physics if they possess the same symmetries and the "correct" long-wavelength structure [5,8]. The fact that the various meson models for V N N share the same one pion tail, but differ significantly in how they treat the shorter distance pieces illustrates this explicitly as they give the same phase shifts and deuteron binding energy. In RG language, the short distance pieces of V N N are like irrelevant operators since their detailed form can not be resolved from low energy data.Motivated by these observations, we would like to derive a low-momentum NN potential V low−k by integrating out the high momentum components of different models of V N N i...

A review is presented of the development and current status of nuclear shell-model calculations, in which the two-body effective interaction between valence nucleons is derived from the free nucleon-nucleon potential. The significant progress made in this field within the last decade is emphasized, in particular as regards the so-called Vlow-k approach to the renormalization of the bare nucleon-nucleon interaction. In the last part of the review, we first give a survey of realistic shell-model calculations from early to present days. Then, we report recent results for neutron-rich nuclei near doubly magic Sn-132, and for the whole even-mass N = 82 isotonic chain. These illustrate how shell-model effective interactions derived from modern nucleon-nucleon potentials are able to provide an accurate description of nuclear structure properties

This paper discusses the derivation of an effective shell-model hamiltonian starting from a realistic nucleon-nucleon potential by way of perturbation theory. More precisely, we present the state of the art of this approach when the starting point is the perturbative expansion of theQ-box vertex function. Questions arising from diagrammatics, intermediate-states and orderby-order convergences, and their dependence on the chosen nucleon-nucleon potential, are discussed in detail, and the results of numerical applications for the p-shell model space starting from chiral next-to-next-to-next-to-leading order potentials are shown. Moreover, an alternative graphical method to derive the effective hamiltonian, based on theẐ-box vertex function recently introduced by Suzuki et al., is applied to the case of a non-degenerate (0+2) ω model space. Finally, our shell-model results are compared with the exact ones obtained from no-core shell-model calculations.