The rapid shape change in Zr isotopes near neutron number N=60 is identified to be caused by type II shell evolution associated with massive proton excitations to its 0g_{9/2} orbit, and is shown to be a quantum phase transition. Monte Carlo shell-model calculations are carried out for Zr isotopes of N=50-70 with many configurations spanned by eight proton orbits and eight neutron orbits. Energy levels and B(E2) values are obtained within a single framework in good agreement with experiment, depicting various shapes in going from N=50 to 70. The novel coexistence of prolate and triaxial shapes is suggested.

The shapes of neutron-rich exotic Ni isotopes are studied. Large-scale shell model calculations are performed by advanced Monte Carlo Shell Model (MCSM) for the pf -g 9/2 -d 5/2 model space. Experimental energy levels are reproduced well by a single fixed Hamiltonian. Intrinsic shapes are analyzed for MCSM eigenstates. Intriguing interplays among spherical, oblate, prolate and γunstable shapes are seen, including shape fluctuations, E(5)-like situation, the magicity of doublymagic 56,68,78 Ni, and the coexistence of spherical and strongly deformed shapes. Regarding the last point, strong deformation and change of shell structure can take place simultaneously, being driven by the combination of the tensor force and changes of major configurations within the same nucleus.

We present a newly enhanced version of the Monte Carlo Shell Model 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 most-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 the conventional shell-model calculations with an inert 40 Ca core and discuss how the magicity of N = 28, 40, 50 remains or is broken. * )

We first review the shell evolution in exotic nuclei driven by nuclear forces. We then demonstrate that the underlying mechanism played by the balance of the tensor and central components in the effective nucleon-nucleon interaction is crucial when describing shape coexistence. This effect will be referred to as type II shell evolution, while the shell evolution passing through a series of isotopes or isotones is denoted as type I. We describe type II shell evolution in some detail for the case of the 68 Ni nucleus as an example. We present how the fission dynamics can be related to enhanced deformation triggered by type II shell evolution, at its initial stage. It is suggested that the island of stability may be related to the suppression of this mechanism.

We propose a thick-restart block Lanczos method, which is an extension of the thick-restart Lanczos method with the block algorithm, as an eigensolver of the large-scale shell-model calculations. This method has two advantages over the conventional Lanczos method: the precise computations of the near-degenerate eigenvalues, and the efficient computations for obtaining a large number of eigenvalues. These features are quite advantageous to compute highly excited states where the eigenvalue density is rather high. A shell-model code, named KSHELL, equipped with this method was developed for massively parallel computations, and it enables us to reveal nuclear statistical properties which are intensively investigated by recent experimental facilities. We describe the algorithm and performance of the KSHELL code and demonstrate that the present method outperforms the conventional Lanczos method.

Atomic nuclei exhibit single-particle and collective degrees of freedom, making them susceptible to variations in size and shape when adding or removing nucleons. The rare cases where dramatic changes in shape occur with the removal of only a single nucleon are key for pinpointing the components of the nuclear interaction driving nuclear deformation. Laser spectroscopy probes the nuclear charge distribution, revealing attometer-scale variations and highlighting sensitivity to the proton (Z) and neutron (N) configurations of the nucleus. The lead isotopes, which possess a closed proton shell (Z = 82), are spherical and steadily shrink with decreasing N. A surprisingly different story was observed for their close neighbours, the mercury isotopes (Z = 80) almost half a century ago 1, 2 : Whilst the even-mass isotopes follow the trend seen for lead, the odd-mass isotopes 181,183,185 Hg exhibit a striking increase in charge radius. This dramatic 'shape staggering' between evenand odd-mass isotopes remains a unique feature of the nuclear chart. Here we present the extension of laser spectroscopy results that reach 177 Hg. An unprecedented combination of state-of-theart techniques including resonance laser ionization, nuclear spectroscopy and mass spectrometry, has established 181 Hg as the shape-staggering endpoint. Accompanying this experimental tour de force, recent computational advances incorporating the largest valence space ever used have been exploited to provide Monte-Carlo Shell Model calculations, in remarkable agreement with the experimental observations. Thus, microscopic insight into the subtle interplay of nuclear interactions that give rise to this phenomenon has been obtained, identifying the shape-driving orbitals. Although shape staggering in the mercury isotopes is a unique and localized feature in the nuclear chart, the underlying mechanism that has now been uncovered nicely describes the duality of single-particle and collective degrees of freedom in atomic nuclei.

Characterisation of the few doubly magic nuclei, known and predicted, provides a benchmark for our knowledge of the fundamental forces that drive the evolution of shell closures with proton-to-neutron asymme

Background: Type II shell evolution has recently been identified as a microscopic cause for nuclear shape coexistence.