Novel simple properties of the monopole component of the effective nucleon-nucleon interaction are presented, leading to the so-called monopole-based universal interaction. Shell structures are shown to change as functions of N and Z consistently with experiments. Some key cases of this shell evolution are discussed, clarifying the effects of central and tensor forces. The validity of the present tensor force is examined in terms of the low-momentum interaction V lowk and the Q box formalism.

We study boron, carbon, nitrogen and oxygen isotopes with a newly constructed shell-model Hamiltonian developed from monopole-based-universal interaction (VMU ). The present Hamiltonian can reproduce well the ground-state energies, energy levels, electric quadrupole properties and spin properties of these nuclei in full psd model space including (0 − 3) ω excitations. Especially, it correctly describes the drip lines of carbon and oxygen isotopes and the spins of the ground states of 10 B and 18 N while some former interactions such as WBP and WBT fail. We point out that the inclusion of 2 ω excitations is important in reproducing some of these properties. In the present (0 + 2) ω calculations small but constant E2 effective charges appear to work quite well. As the inclusion of the 2 ω model space makes rather minor change, this seems to be related to the smallness of 4 He core. Similarly, the spin g factors are very close to free values. The applicability of tensor and spin-orbit forces in free space, which are taken in the present Hamiltonian, is examined in shell model calculations.

Background: Effective interactions, either derived from microscopic theories or based on fitting selected properties of nuclei in specific mass regions, are widely used inputs to shell-model studies of nuclei. The commonly used unperturbed basis functions are given by the harmonic oscillator. Until recently, most shell-model calculations have been confined to a single oscillator shell like the sd shell or the pf shell. Recent interest in nuclei away from the stability line requires, however, larger shell-model spaces. Because the derivation of microscopic effective interactions has been limited to degenerate models spaces, there are both conceptual and practical limits to present shell-model calculations that utilize such interactions. Purpose: The aim of this work is to present a novel microscopic method to calculate effective nucleon-nucleon interactions for the nuclear shell model. Its main difference from existing theories is that it can be applied not only to degenerate model spaces but also to nondegenerate model spaces. This has important consequences, in particular for intershell matrix elements of effective interactions. Methods:The formalism is presented in the form of a many-body perturbation theory based on the recently developed extended Kuo-Krenciglowa method. Our method enables us to microscopically construct effective interactions not only in one oscillator shell but also for several oscillator shells. Results: We present numerical results using effective interactions within (i) a single oscillator shell (a so-called degenerate model space) like the sd shell or the pf shell and (ii) two major shells (nondegenerate model space) like the sdf 7 p 3 shell or the pf g 9 shell. We also present energy levels of several nuclei that have two valence nucleons on top of a given closed-shell core. Conclusions: Our results show that the present method works excellently in shell-model spaces that comprise several oscillator shells, as well as in a single oscillator shell. We show, in particular, that the microscopic intershell interactions are much more attractive than has been expected by degenerate perturbation theory. The consequences for shell-model studies are discussed.

We present the first application of the newly developed EKK theory of the effective nucleonnucleon interaction to shell-model studies of exotic nuclei, including those where conventional approaches with fitted interactions encounter difficulties. This EKK theory enables us to derive the interaction suitable for several major shells (sd+pf in this work). By using such an effective interaction obtained from the Entem-Machleidt QCD-based χN 3 LO interaction and the Fujita-Miyazawa three-body force, the energies, E2 properties and spectroscopic factors of low-lying states of neutronrich Ne, Mg and Si isotopes are nicely described, as the first shell-model description of the "island of inversion" without fit of the interaction. The long-standing question as to how particle-hole excitations occur across the sd-pf magic gap is clarified with distinct differences from the conventional approaches. The shell evolution is shown to appear similarly to earlier studies. Introduction. -The nuclear shell model [1, 2] provides a unified and successful description of both stable and exotic nuclei, as a many-body framework which can be related directly to nuclear forces. Exotic nuclei are located far from the β-stability line on the Segrè chart, exhibiting very short life times, mainly due to an unbalanced ratio of proton (Z) and neutron (N ) numbers. Exotic nuclei differ remarkably in some other aspects from their stable counterparts, providing us with new insights in understanding atomic nuclei and nuclear forces [3][4][5]. As experimental data on exotic nuclei are, in general, less abundant compared to stable nuclei, theoretical calculations, interpretations and predictions play an ever increasing role.Shell-model (SM) calculations handle the nuclear forces in terms of two-body matrix elements (TBMEs). In the early days, TBMEs were empirically determined in order to reproduce certain observables. A well-known example is the effective interaction for p-shell nuclei by Cohen and Kurath [6]. A breakthrough towards more microscopically-derived TBMEs was achieved by Kuo and Brown for sd-shell nuclei [7]. Although basic features of the nucleon-nucleon (N N ) force for the SM calculation are included in these effective interactions, empirical adjustments of TBMEs were needed in order to reproduce various observables [8][9][10].These effective interactions were all derived for a Hilbert space represented by the degrees of freedom of one major (oscillator) shell. As we move towards ex-

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