We present a newly enhanced version of the Monte Carlo shell-model (MCSM) method by incorporating the conjugate gradient method and energy-variance extrapolation. This new method enables us to perform large-scale shell-model calculations that the direct diagonalization method cannot reach. This new-generation framework of the MCSM provides us with a powerful tool to perform very advanced large-scale shell-model calculations on current massively parallel computers such as the K computer. We discuss the validity of this method in ab initio calculations of light nuclei, and propose a new method to describe the intrinsic wave function in terms of the shell-model picture. We also apply this new MCSM to the study of neutron-rich Cr and Ni isotopes using conventional shell-model calculations with an inert ⁴⁰Ca core and discuss how the magicity of N=28,40,50 remains or is broken.

We study the double Gamow-Teller (DGT) strength distribution of ${}^{48}\mathrm{Ca}$ with state-of-the-art large-scale nuclear shell model calculations. Our analysis shows that the centroid energy of the DGT giant resonance depends mostly on the isovector pairing interaction, while the resonance width is more sensitive to isoscalar pairing. Pairing correlations are also key in neutrinoless $\beta \beta$ ($0\nu \beta \beta$) decay. We find a simple relation between the centroid energy of the ${}^{48}\mathrm{Ca}$ DGT giant resonance and the $0\nu \beta \beta$ decay nuclear matrix element. More generally, we observe a very good linear correlation between the DGT transition to the ground state of the final nucleus and the $0\nu \beta \beta$ decay matrix element. The correlation, which originates on the dominant short-range character of both transitions, extends to heavier systems including several $\beta \beta$ emitters and also holds in energy-density functional results. Our findings suggest that DGT experiments can be a very valuable tool to obtain information on the value of $0\nu \beta \beta$ decay nuclear matrix elements.

Subjecting a physical system to extreme conditions is one of the means often used to obtain a better understanding and deeper insight into its organization and structure. In the case of the atomic nucleus, one such approach is to investigate isotopes that have very different neutron-to-proton (N/Z) ratios than in stable nuclei. Light, neutron-rich isotopes exhibit the most asymmetricN/Zratios and those lying beyond the limits of binding, which undergo spontaneous neutron emission and exist only as very short-lived resonances (about 10⁻²¹ s), provide the most stringent tests of modern nuclear-structure theories. Here we report on the first observation of²⁸O and²⁷O through their decay into²⁴O and four and three neutrons, respectively. The²⁸O nucleus is of particular interest as, with theZ = 8 andN = 20 magic numbers^1,2, it is expected in the standard shell-model picture of nuclear structure to be one of a relatively small number of so-called ‘doubly magic’ nuclei. Both²⁷O and²⁸O were found to exist as narrow, low-lying resonances and their decay energies are compared here to the results of sophisticated theoretical modelling, including a large-scale shell-model calculation and a newly developed statistical approach. In both cases, the underlying nuclear interactions were derived from effective field theories of quantum chromodynamics. Finally, it is shown that the cross-section for the production of²⁸O from a²⁹F beam is consistent with it not exhibiting a closedN = 20 shell structure.

In this Letter, we present mass-ratio measurements on highly charged Yb 42 + ions with a precision of 4 × 10 − 12 and isotope-shift measurements on Yb + on the S 2 1 / 2 → D 5 / 2 2 and S 2 1 / 2 → F 7 / 2 2 transitions with a precision of 4 × 10 − 9 for the isotopes Yb 168 , 170 , 172 , 174 , 176 . We present a new method that allows us to extract higher-order changes in the nuclear charge distribution along the Yb isotope chain, benchmarking nuclear structure calculations. Additionally, we perform a King plot analysis to set bounds on a fifth force in the keV / c 2 to MeV / c 2 range coupling to electrons and neutrons.

We present an overview of the advanced Monte Carlo shell model (MCSM), including its recent applications to no-core shell-model calculations and to large-scale shell-model calculations (LSSM) in the usual sense. For the ab initio no-core MCSM we show recent methodological developments, which include the evaluation of energy eigenvalues in an infinitely large model space by an extrapolation method. As an example of the application of the no-core MCSM, the cluster structure of Be isotopes is discussed. Regarding LSSM applications, the triple shape coexistence in ⁶⁸ Ni and ⁷⁰ Ni and the shape transition of Zr isotopes are clarified with the visualization of the intrinsic deformation of the MCSM wave function. General aspects of the code development of the MCSM on massively parallel computers are also briefly described.

We propose a variational calculation scheme utilizing the superposition of the angular-momentum, parity, number projected quasiparticle vacua, that is especially suitable for applying to medium-heavy nuclei in shell-model calculations. We derive a formula for the energy variance with quasiparticle vacua and apply the energy-variance extrapolation to the present scheme for further precise estimation of the exact shell-model energy. The validity of the method is presented for the shell-model calculation of ${}^{132}\mathrm{Ba}$ in the $50\le Z,N\le 82$ model space. We also discuss the feasibility of this scheme in the case of the ${}^{150}\mathrm{Nd}$ in the $50\le Z\le 82$ and $82\le Z\le 126$ model space and demonstrate that its neutrinoless double-$\beta$-decay matrix element is obtained showing good convergence.