Abstract
Reducing the many-fermion problem to a set of single-particle (s.p.) equations, the Kohn–Sham (KS) theory has provided a practical tool to implement
ab initio
calculations of ground-state ...energies and densities in many-electron systems. There have been attempts to extend the KS theory so that it could describe other physical quantities, or it could be applied to other many-fermion systems. By generalizing and reformulating the KS theory in terms of the 1-body density matrix, we expose the minimal composition of the theory that enables the reduction of the many-fermion problem to the s.p. equations. Based on the reformulation, several basic issues are reconsidered. The
v
- and
N
-representabilities for the KS theory are distinguished from those for the Hohenberg-Kohn theorem. Criteria for the extendability of the KS theory are addressed.
The structure of exotic nuclei sheds new light on the linkage of the nuclear structure to the nucleonic interaction. The self-consistent mean-field (SCMF) theories are useful to investigate this ...linkage, which are applicable to many nuclei covering almost the whole range of the nuclear chart without artificial truncation of model space. For this purpose, it is desired to develop effective interaction for the SCMF calculations well connected to the bare nucleonic interaction. Focusing on ground-state properties, I show the results of SCMF calculations primarily with the Michigan-three-range-Yukawa (M3Y)-type semi-realistic interaction, M3Y-P6 and M3Y-P6a to be precise, and discuss in detail how the nucleonic interaction affects the structure of nuclei including those far off the
β
-stability. The central channels of the effective interaction are examined by the properties of the infinite nuclear matter up to the spin dependence and the isospin dependence. While experimental information of the infinite matter is obtained by extrapolating systematic data on finite nuclei in principle, it is not easy to constrain the spin dependence and the isospin dependence without connection to the bare nucleonic interaction. The noncentral channels play important roles in the shell structure of the finite nuclei. The tensor force is demonstrated to affect
Z
- or
N
-dependence of the shell structure and the magic numbers, on which the spin–isospin channel in the central force often acts cooperatively. By using the M3Y-P6 interaction, the prediction of magic numbers is given in a wide range of the nuclear chart, which is consistent with almost all the available data. In relation to the erosion of magic numbers in unstable nuclei, effects of the tensor force on the nuclear deformation are also argued, being opposite between nuclei at the
ℓ
s
- and the
j
j
-closed magicities. Qualitatively consistent with the
3
N
-force effect on the
ℓ
s
-splitting suggested from the chiral effective field theory, the density-dependent LS channel, which is newly introduced in M3Y-P6a, reproduces the observed kinks in the differential charge radii at the
j
j
-closed magic numbers and predicts anti-kinks at the
ℓ
s
-closed magic numbers. The pairing correlation has significant effects on the halos near the neutron drip line. A new mechanism called “unpaired-particle haloing” is disclosed.
Abstract
By applying the angular-momentum projection to the self-consistent axial mean-field solutions with the semi-realistic effective Hamiltonian M3Y-P6, the pairing effects on the pure rotational ...energy of nuclei, i.e. the rotational energy at a fixed intrinsic state, have been investigated. While it was shown at the Hartree–Fock (HF) level that the individual terms of the Hamiltonian contribute to the rotational energy with ratios insensitive to nuclides except for light or weakly-deformed nuclei, the pair correlations significantly change the contributions, even for the well-deformed heavy nuclei. The contribution of the interaction to the rotational energy is found to correlate well with the degree of proximity between nucleons, which is measured via the expectation value that two nucleons exist at the same position. While the nucleons slightly spread as the angular momentum increases at the HF level, accounting for the positive (negative) contribution of the attractive (repulsive) components of the interaction, the pair correlations reduce or invert the effect.
We report, for the first time, the long-awaited detection of diffuse gamma rays with energies between 100 TeV and 1 PeV in the Galactic disk. Particularly, all gamma rays above 398 TeV are observed ...apart from known TeV gamma-ray sources and compatible with expectations from the hadronic emission scenario in which gamma rays originate from the decay of π^{0}'s produced through the interaction of protons with the interstellar medium in the Galaxy. This is strong evidence that cosmic rays are accelerated beyond PeV energies in our Galaxy and spread over the Galactic disk.
Heavy nuclei exhibit a crossover from vibrational to rotational collectivity as the number of neutrons or protons increases from shell closure towards midshell, but the microscopic description of ...this crossover has been a major challenge. We apply the shell model Monte Carlo approach to families of even-even samarium and neodymium isotopes and identify a microscopic signature of the crossover from vibrational to rotational collectivity in the low-temperature behavior of ⟨J(2)⟩(T), where J is the total spin and T is the temperature. This signature agrees well with its values extracted from experimental data. We also calculate the state densities of these nuclei and find them to be in very good agreement with experimental data. Finally, we define a collective enhancement factor from the ratio of the total state density to the intrinsic state density as calculated in the finite-temperature Hartree-Fock-Bogoliubov approximation. The decay of this enhancement factor with excitation energy is found to correlate with the pairing and shape phase transitions in these nuclei.
The influence of the Nambu–Goldstone (NG) mode on the energy-weighted sum (EWS) of the excitation strengths is analyzed within the random-phase approximation (RPA). When a certain symmetry is broken ...at the mean-field level, an NG mode emerges in the RPA, which can be represented by canonical variables forming a two-dimensional Jordan block. A general formula is rederived which separates out the NG-mode contribution to the EWS, via the projection on the subspace directed by the NG mode. As examples, the formula is applied to the E1 excitation and the rotational excitations in nuclei, reinforcing the theoretical consistency of the RPA.
Properties of solutions of the random-phase approximation (RPA) equation are reanalyzed mathematically, where it is defined as a generalized eigenvalue problem of the stability matrix
$\mathsf{S}$
...with the norm matrix
$\mathsf{N}=\mathrm{diag}(1,-1)$
. As well as physical solutions, unphysical solutions are examined in detail, taking the possibility of Jordan blocks of the matrix
$\mathsf{N\,S}$
into consideration. Two types of duality of eigenvectors and basis vectors of the Jordan blocks are pointed out and explored, which disclose many basic properties of the RPA solutions.
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