/ Hiroyuki Sagawa / Professor
/ Hisasi Morikawa / Professor
/ Ken-ichi Funahashi / Associate Professor
/ Katsutaro Shimizu / Associate Professor
/ A. G. Belyaev / Visiting Researcher
/ Sergei Duzhin / Visiting Researcher
/ Kazuto Asai / Assistant Professor
/ Michio Honma / Assistant Professor
/ Shigeru Watanabe / Assistant Professor
/ Toshiro Watanabe / Assistant Professor
/ Hiroshi kihara / Research Associate
The scope of activities of the Center for Mathematical sciences spans all aspects of education and research in the fields of mathematical sciences. Current research directions in the field of mathematics are joined by the common theme "Geometrical Method in Mathematical Sciences". In the fields of Physics, theoretical research is performed in many-body theories, Nuclear Physics and Quantum Gravity. Together with this, there is a project to develop educational software on quantum physics. The research areas assigned to each co-researcher are as follows:
Refereed Journal Papers
We study the effect of the unique shell-structure as well as the very low particle-threshold on collective modes in drip-line nuclei, first performing the Hartree-Fock (HF) calculation with Skyrme interactions and, then, using the random-phase-approximation (RPA) solved in the coordinate space with the Green's function method. We examine also one-particle resonant states in the HF potential. The properties of both isocalar and isovector monopole giant resonance (GR) are found to change drastically in nuclei around the neutron-drip-line. The characteristic feature of the isovector dipole modes as well as the isoscalar quadrupole modes in drip-line nuclei is also studied.
The very low-energy transition strength unique in neutron drip line nuclei is studied, taking an example of ~$^{28}_{8}O_{20}$~ and performing the Hartree-Fock plus RPA calculation with Skyrme interaction. The most dramatic example is monopole modes, however, an appreciable amount of isovector dipole strength may appear also in the very low excitation energy. Unperturbed response functions are carefully studied, which contain all basic information on the exotic behaviour of the RPA strength function. The low-energy transition strength is induced by the excitations of neutrons, which have smaller binding energies and smaller angular momenta. The neutrons with a few MeV binding energies are sufficient for obtaining this strength, and the phenomena are differentiated from the socalled soft multipole excitations in halo nuclei.
We study the effect of isospin impurity on the super-allowed Fermi $\beta $ decay using microscopic HF and RPA (or TDA) model taking into account CSB and CIB interactions. It is found that the super-allowed transitions between odd-odd $J$=0 nuclei and even-even $J$=0 nuclei are quenched because of the cancellation of the isospin impurity effects of mother and daughter nuclei, while the isospin impurity of N=Z nuclei gives enhancement of the sum rule of Fermi transition probabilities. An implication of the calculated Fermi transition rate on the CVC hypothesis as well as on the unitarity of Cabbibo-Kobayashi-Maskawa mixing matrix is discussed.
Core polarization charges of quadrupole transitions in light neutron drip line nuclei are studied by using a particle-vibration coupling model with HF single particle wave functions and RPA response functions in $^{28}$O. We obtain very small core polarization charges $e _{pol}$(IS)=0.14 and $e _{pol}$(IV)=0.06 as a result of the cancelation between the contributions of low-energy threshold strength and those of giant resonances. It depends crucially on both the property of the one-particle multipole operator and the shell structure around the Fermi level whether the very low-lying threshold strength contributes to the polarization charges of a given multipole constructively or destructively.
We study a relation between the spreading width of the isobaric analog state (IAS) and the isospin mixing probability of the corresponding parent state by using the Feshbach projection method. The formula is applied for calculations of the spreading width of several heavy isotopes and compared with available experimental data. Contributions from isovector monopole (IVM) states are found to be important to explain quantitatively the experimental spreading width. The isospin dependence of the calculated width of several isotopes is also found to be consistent with the experimental observations.
Core polarization charges of quadrupole transitions in proton drip line nuclei, $^{100}_{50}Sn_{50}$ and $^{48}_{28}Ni_{20}$, are estimated, using the Hartree-Fock calculations with Skyrme interactions and the RPA solved in the coordinate space with the Green's function method. The polarization charges of the two nuclei are larger than those of $\ell$-s closed shell nuclei and receive the major contributions from both the lowest-lying 2$^{+}$ state and the giant resonances. The E2 polarization charge estimated for $^{100}_{50}Sn_{50}$ is consistent with the available empirical information obtained from the shell model, analysis of the data on $^{99}_{48}Cd_{51}$, though the estimated $e_{pol}(E2)$ values depend appreciably on Skyrme interactions used.
We analyse mathematically the relationship between the mean field theory network (MFT) model and the continuous-time Hopfield neural network by the use of the theory of dynamical systems. We prove that the set of asymptotically stable fixed points of the asynchronous MFT model coincides with the set of asymptotically stable equilibria of the continuous-time Hopfield neural networks. Therefore, it is shown that the asyncronous MFT model is equivalent to the Hopfield neural network on the nature of the fixed points (or equilibria).
We demonstarite an equivalence between Dirac quantization and reduced phase space quantization. The equivalence of the two quantization methods determines the operator ordering of the Hamiltonian. Some examples of the operator ordering are shown in simple models.
The interacting boson model is extended to describe the spectroscopy of superdeformed bands. Microscopic structure of the model in the second minimum is discussed and superdeformed bosons are introduced as the new building blocks. Solutions of a quadrupole Hamiltonian are implemented through the 1/N expansion method. Effects of the quadrupole parameters on dynamic moment of inertia and electric quadrupole transition rates are discussed and the results are used in a description of superdeformed bands in the Hg-Pb and Gd-Dy regions.
We present a description of the quantum Monte Carlo diagonalization method. This method has been introduced recently as an approach having both the advantage of the quantum Monte Carlo method and that of the direct diagonalization of the Hamiltonian matrix. In addition, the angular momentum projection is implemented so as to remove the degeneracy with regard to magnetic quantum number. We show that with this method the convergence of the eigenvalues is improved and that the wave functions of excited states can be obtained more easily. Moreover, the calculation of transition matrix elements becomes simpler.
The feasibility of shell-model calculations is radically extended by the quantum Monte Carlo diagonalization method with various improvements. The major improvements are made in the sampling for the generation of shell-model basis vectors, and in the restoration of symmetries such as angular momentum and isospin. Consequently, the level structure of low-lying states can be studied with realistic interactions. After testing this method on 24Mg, we present first results for energy levels and E2 properties of 64Ge, indicating its large and gamma-soft deformation.
Refereed Proceeding Papers
Others