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The 2017 Event Horizon Telescope (EHT) observations of the central source in M87 have led to the first measurement of the size of a black-hole shadow. This observation offers a new and clean gravitational test of the black-hole metric in the strong-field regime. We show analytically that spacetimes that deviate from the Kerr metric but satisfy weak-field tests can lead to large deviations in the predicted black-hole shadows that are inconsistent with even the current EHT measurements. We use numerical calculations of regular, parametric, non-Kerr metrics to identify the common characteristic among these different parametrizations that control the predicted shadow size. We show that the shadow-size measurements place significant constraints on deviation parameters that control the second post-Newtonian and higher orders of each metric and are, therefore, inaccessible to weak-field tests. The new constraints are complementary to those imposed by observations of gravitational waves from stellar-mass sources.

A novel shape evolution in the Sn isotopes by the state-of-the-art application of the Monte Carlo shell model calculations is presented in a unified way for the ^{100-138}Sn isotopes. A large model space consisting of eight single-particle orbits for protons and neutrons is taken with the fixed Hamiltonian and effective charges, where protons in the 1g_{9/2} orbital are fully activated. While the significant increase of the B(E2;0_{1}^{+}→2_{1}^{+}) value, seen around ^{110}Sn as a function of neutron number (N), has remained a major puzzle over decades, it is explained as a consequence of the shape evolution driven by proton excitations from the 1g_{9/2} orbital. A second-order quantum phase transition is found around N=66, connecting the phase of such deformed shapes to the spherical pairing phase. The shape and shell evolutions are thus described, covering topics from the Gamow-Teller decay of ^{100}Sn to the enhanced double magicity of ^{132}Sn.

We present the nuclear matrix element for the neutrinoless double-beta decay of ^{48}Ca based on large-scale shell-model calculations including two harmonic oscillator shells (sd and pf shells). The excitation spectra of ^{48}Ca and ^{48}Ti, and the two-neutrino double-beta decay of ^{48}Ca are reproduced in good agreement to the experimental data. We find that the neutrinoless double-beta decay nuclear matrix element is enhanced by about 30% compared to pf-shell calculations. This reduces the decay lifetime by almost a factor of 2. The matrix-element increase is mostly due to pairing correlations associated with cross-shell sd-pf excitations. We also investigate possible implications for heavier neutrinoless double-beta decay candidates.

Gamow-Teller (GT) transitions in atomic nuclei are sensitive to both nuclear shell structure and effective residual interactions. The nuclear GT excitations were studied for the mass number A = 42, 46, 50, and 54 "f-shell" nuclei in ((3)He, t) charge-exchange reactions. In the (42)Ca → (42)Sc reaction, most of the GT strength is concentrated in the lowest excited state at 0.6 MeV, suggesting the existence of a low-energy GT phonon excitation. As A increases, a high-energy GT phonon excitation develops in the 6-11 MeV region. In the (54)Fe → (54)Co reaction, the high-energy GT phonon excitation mainly carries the GT strength. The existence of these two GT phonon excitations are attributed to the 2 fermionic degrees of freedom in nuclei.

Collinear laser spectroscopy was performed on Ga (Z=31) isotopes at ISOLDE, CERN. A gas-filled linear Paul trap (ISCOOL) was used to extend measurements towards very neutron-rich isotopes (N=36-50). A ground state (g.s.) spin I=1/2 is measured for 73Ga, being near degenerate with a 3/2{-} isomer (75  eV≲E{ex}≲1  keV). The 79Ga g.s., with I=3/2, is dominated by protons in the πf{5/2} orbital and in 81Ga the 5/2{-} level becomes the g.s. The data are compared to shell-model calculations in the f{5/2}pg{9/2} model space, calling for further theoretical developments and new experiments.

Novel simple properties of the monopole component of effective nucleon-nucleon interactions are presented, leading to the so-called monopole-based universal interaction. Shell structures are shown to change as functions of N and Z, consistent 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.

Recent experimental characterization of the subshell closure at N=32 in the Ca, Ti, and Cr isotones has stimulated shell-model calculations that indicated the possibility that the N=34 isotones of these same elements could exhibit characteristics of a shell closure, namely, a high energy for the first excited 2(+) level. To that end, we have studied the decay of 56Sc produced in fragmentation reactions and identified new gamma rays in the daughter N=34 isotone 56Ti. The first 2(+) level is found at an energy of 1127 keV, well below the expected position that would indicate the presence of an N=34 shell closure in 56Ti.

The magic numbers in exotic nuclei are discussed, and their novel origin is shown to be the spin-isospin dependent part of the nucleon-nucleon interaction in nuclei. The importance and robustness of this mechanism is shown in terms of meson exchange, G-matrix, and QCD theories. In neutron-rich exotic nuclei, magic numbers such as N = 8, 20, etc. can disappear, while N = 6, 16, etc. arise, affecting the structure of the lightest exotic nuclei to nucleosynthesis of heavy elements.

The transition from spherical to deformed shapes is studied in terms of large-scale shell-model calculations for Ba isotopes as a function of valence nucleon number with fixed single-particle space and Hamiltonian. A new version of the Monte Carlo shell model is introduced so as to incorporate pairing correlations efficiently, by utilizing condensed pair bases. The energy levels and electromagnetic matrix elements are described in agreement with experiments throughout the transitional region. The orbital M1 sum rule is calculated as a measure of the deformation evolution, and the Q-phonon picture is shown to be reasonable from spherical to deformed nuclei.