Exotic neutron-rich medium-mass nuclei with realistic nuclear forces

Abstract

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-

Nonempirical Interactions for the Nuclear Shell Model: An Update

“…Soon after their introduction to nuclear physics, EFT and RG methods also revitalized efforts to systematically derive shell model interactions (130,131). From a practical perspective, this offered a convenient way to confront RG-evolved chiral two-plus three-nucleon interactions with the wealth of available spectroscopic data, using existing shell model codes (132)(133)(134)(135)(136)(137)(138)(139)(140)(141)(142)(143)(144). At the conceptual level, these interactions validate the independent-particle picture underlying the shell model.…”

“…(5) would be comparable to the corresponding energy denominators, and the Taylor series (5) might converge slowly, if at all. However, for a modest spread of energies (∼10 MeV), this does not appear to be a problem (138,144).…”

Impact of off-diagonal cross-shell interaction on 14 C

“…+ states in the even-even nuclei [6,7]. Many effective Hamiltonians are well defined considering the observed binding energies and levels, while some of them have realistic basis.…”

Roles of nuclear weak rates on the evolution of degenerate cores in stars

“…The Urca density can not be clearly assigned for the weak rates for SDPF-M. This shortcoming can be improved for the effective interaction obtained by EKK (extended Kuo-Krenciglowa) method [24], which can properly treat Q-box calculations in two-major shells without divergence problems [25]. Energy levels in 31 Mg are well reproduced, and more important roles of p-h excitations are noticed compared with the SDPF-M case.…”

“…The Urca density determined by the Q-value of the reaction is found to be log 10 ρY e = 8.92 and 8.78 for 23 Ne- 23 Na and 25 Na- 25 Mg pairs, respectively. Double e-capture reactions on 24 Mg or 20 Ne, which are succeeded by e-capture on 24 Na or 20 F, respectively, are important for heating the core in later stages of the stellar evolution [12,13]. Electroncapture, β-decay and ν energy loss rates as well as energy production rates by γ emissions are tabulated for sd-shell nuclei using a fine grid for density and temperature in [13].…”