We systematically investigate the existence of exotic torus isomers and their precession motions for a series of $N=Z$ even-even nuclei from $^{28}$Si to $^{56}$Ni. We analyze the microscopic shell structure of the torus isomer and discuss why the to
rus shape is generated beyond the limit of large oblate deformation. We use the cranked three-dimensional Hartree-Fock (HF) method with various Skyrme interactions in a systematic search for high-spin torus isomers. We use the three-dimensional time-dependent Hartree-Fock (TDHF) method for describing the precession motion of the torus isomer. We obtain high-spin torus isomers in $^{36}$Ar, $^{40}$Ca, $^{44}$Ti, $^{48}$Cr, and $^{52}$Fe. The emergence of the torus isomers is associated with the alignments of single-particle angular momenta, which is the same mechanism as found in $^{40}$Ca. It is found that all the obtained torus isomers execute the precession motion at least two rotational periods. The moment of inertia about a perpendicular axis, which characterizes the precession motion, is found to be close to the classical rigid-body value. The high-spin torus isomer of $^{40}$Ca is not an exceptional case. Similar torus isomers exist widely in nuclei from $^{36}$Ar to $^{52}$Fe and they execute the precession motion. The torus shape is generated beyond the limit of large oblate deformation by eliminating the $0s$ components from all the deformed single-particle wave functions to maximize their mutual overlaps.
We investigate the precession motion of the exotic torus configuration in high-spin excited states of $^{40}$Ca. For this aim, we use the three-dimensional time-dependent Hartree-Fock (TDHF) method. Although the high-spin torus isomer is a unique qua
ntum object characterized by the alignment of angular momenta of independent single-particle motions, we find that the obtained moment of inertia for rotations about an axis perpendicular to the symmetry axis is close to the rigid-body value. We also analyze the microscopic structure of the precession motion using the random-phase approximation (RPA) method for high-spin states. In the RPA calculation, the precession motion of the torus isomer is generated by coherent superposition of many one-particle-one-hole excitations across the sloping Fermi surface that strongly violates the time-reversal symmetry. By comparing results of the TDHF and the RPA calculations, we find that the precession motion obtained by the TDHF calculation is a pure collective motion well decoupled from other collective modes.
We investigate the possibility of the existence of the exotic torus configuration in the high-spin excited states of $^{40}$Ca. We here consider the spin alignments about the symmetry axis. To this end, we use a three-dimensional cranked Skyrme Hartr
ee-Fock method and search for stable single-particle configurations. We find one stable state with the torus configuration at the total angular momentum $J=$ 60 $hbar$ and an excitation energy of about 170 MeV in all calculations using various Skyrme interactions. The total angular momentum J=60 $hbar$ consists of aligned 12 nucleons with the orbital angular momenta $Lambda=+4$, +5, and +6 for spin up-down neutrons and protons. The obtained results strongly suggest that a macroscopic amount of circulating current breaking the time-reversal symmetry emerges in the high-spin excited state of $^{40}$Ca.
We investigate the existence of weakly coupled gas-like states comprised of three $alpha$ particles around an $^{16}$O core in $^{28}$Si. We calculate the excited states in $^{28}$Si using the multi-configuration mixing method based on the $^{16}$O +
3$alpha$ cluster model. We also include the $^{16}$O + $^{12}$C and $^{24}$Mg + $alpha$ basis wave functions prepared by the generator coordinate method. To identify the gas-like states, we calculate the isoscalar monopole transition strengths and the overlap of the obtained states with the geometrical cluster wave function and the Tohsaki-Horiuchi-Schuck-R{o}pke (THSR) wave function. The results show that the obtained fourth and twelfth states significantly overlap with the THSR wave function. These two states clearly coexist with the $^{16}$O + $^{12}$C cluster states, emerging at similar energies. The calculated isoscalar monopole strengths between those two states are significantly large, indicating that the states are members of the excitation mode. Furthermore, the calculated root-mean-squared (RMS) radii for these states also suggest that a layer of gas-like three $alpha$ particles could exist around the surface of the $^{16}$O core, which can be described as a two-dimensional gas in the intermediate state before the Hoyle-like three $alpha$ states emerge.
We investigate the linear-chain configurations of four-$alpha$ clusters in $^{16}$O using a Skyrme cranked Hartree-Fock method and discuss the relationship between the stability of such states and angular momentum. We show the existence of a region o
f angular momentum (13-18 $hbar$) where the linear chain configuration is stabilized. For the first time we demonstrate that stable exotic states with a large moment of inertia ($hbar^2/2Theta$ $sim$ 0.06-0.08 MeV) can exist.
We have studied gas-like states of $alpha$ clusters around an $^{16}$O core in $^{24}$Mg based on a microscopic $alpha$-cluster model. This study was performed by introducing a Monte Carlo technique for the description of the THSR (Tohsaki Horiuchi S
chuck R{o}pke) wave function, and the coupling effect to other low-lying cluster states was taken into account. A large isoscalar monopole ($E0$) transition strength from the ground to the gas-like state is discussed. The gas-like state of two $alpha$ clusters in $^{24}$Mg around the $^{16}$O core appears slightly below the 2$alpha$-threshold e
We use very deep near-infrared (NIR) imaging data obtained in MOIRCS Deep Survey (MODS) to investigate the evolution of the galaxy stellar mass function back to z~3. The MODS data reach J=24.2, H=23.1, K=23.1 (5sigma, Vega magnitude) over 103 arcmin^
2 (wide) and J=25.1, H=23.7, K=24.1 over 28 arcmin^2 (deep) in the GOODS-North region. The wide and very deep NIR data allow us to measure the number density of galaxies down to low stellar mass (10^9-10^10 Msun) even at high redshift with high statistical accuracy. The normalization of the mass function decreases with redshift and the integrated stellar mass density becomes ~ 8-18% of the local value at z~2 and ~ 4-9% at z~3, which are consistent with results of previous studies in general fields. Furthermore, we found that the low-mass slope becomes steeper with redshift from alpha ~- 1.3 at z~1 to alpha ~- 1.6 at z~3, and that the evolution of the number density of low-mass (10^9-10^10 Msun) galaxies is weaker than that of M* (~10^11 Msun) galaxies. This indicates that the contribution of low-mass galaxies to the total stellar mass density has been significant at high redshift. The steepening of the low-mass slope with redshift is opposite trend expected from the stellar mass dependence of the specific star formation rate reported in previous studies. The present result suggests that the hierarchical merging process overwhelmed the effect of the stellar mass growth by star formation and was very important for the stellar mass assembly of these galaxies at 1<~z<~3.
