Center for Mathematical Sciences

Hiroyuki Sagawa Professor	Noriaki Kamiya Professor	Ken-ichi Funahashi Associate Professor	Katsutaro Shimizu Associate Professor
Toshiro Watanabe Associate Professor	Michio Honma Associate Professor	Kazuto Asai Assistant Professor	Hiroshi Kihara Assistant Professor
Takao Maeda Assistant Professor	Shigeru Watanabe Assistant Professor	Jerome Margueron Visiting Researcher	Jing Peng Visiting Researcher

The scope of activities of the Center for Mathematical Sciences spans all aspects of research and education in the fields of mathematical sciences. Our current researches in the field of mathematics are devoted to various subjects and problems arising in both pure and applied mathematics: non-associative algebras, neural networks, unimodality problems, algebraic combinatorics, spherical functions, homotopy theory, and arithmetic theory. In the fields of physics, theoretical research is performed in many-body theories, nuclear physics, quantum gravity and quantum mechanics of constrain system. There has been also a project to develop educational textbooks and software for mechanics, electromagnetism and quantum mechanics. The research areas assigned to each co-researcher are as follows: Prof. H. Sagawa studies the physics of the many-body system of including nuclei, microclusters and quantum information theory. Prof. N. Kamiya studies the theory of non-associative algebras and a structure theory of algebras from triple systems Prof. K. Funahashi researches the theory of the neural networks and function theory of several complex variables from a geometrical viewpoint Prof. K. Shimizu advances the traditional quantum theory and creates the geometrical theory of quantum gravity Prof. T. Watanabe generalizes the unimodality problems of 1-dimensional infinitely divisible distributions to multi-dimensional cases in the use of analytical methods Prof. K. Asai researches combinatorial identities for generalized Young tableaux, and also, several generating functions arising from algebraic combinatorics Prof. M. Honma researches the microscopic structures and dynamics of the nuclei by the algebraic methods and geometrical models performing the quantitative analysis by the large-scale numeric calculations Prof. H. Kihara studies homotopy theory and its applications to various areas of mathematics Prof. T. Maeda studies arithmetic of elliptic curves and modular forms and their applications Prof. S. Watanabe studies geometrical interpretations of generating functions for spherical functions on homogeneous spaces

Refereed Journal Papers

[k-asai-01:2007]	Kazuto Asai. Homogeneous partial differential equations for superpositions of indeterminate functions of several variables. Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya Mathematics (English edition), 72(6), 2008.
	The article is concerned with homogeneous PDEs satised by some superpositions of indeterminate functions of several variables. For a tree type or a special type of superposition, we determine essentially all PDEs satis ed by the superposition, where those PDEs represent a necessary and suffcient condition for an analytic function to be written locally as an analytic superposition of that type. Furthermore, the representability of a real analytic function as a superposition of that type does not depend on whether real analytic functions or C&rho functions are used in the superposition, where &rho is a constant determined by the structure of the superposition. In addition, we prove that the function u dened by un = xua + yub + zuc + 1 is not generally representable as a superposition f(g(x, y); h(y, z)) of a twice differentiable function f and differentiable functions g, h in any real domain, and not representable as such a superposition of analytic functions f, g, h in any complex domain.
[kamiya-01:2007]	N.Kamiya. A new class of nonassociative algebras with involution. Proc.Japan Acad. Ser A., 2008.
	This is a new clas in non associative algebras, that is, In math. Physics, These methods are useful methods, and construction.
[kamiya-02:2007]	N.Kamiya. A geometrical characterization from triple systems. PADGE 2007, 2007.
	This article is a construction of exceptional Lie algebras from triple systems.
[kamiya-03:2007]	N. Kamiya and and H. Aoki S. Mori. Composition algebras and a generalization of Pytagoras theorem. RIMS, Kyoto Univ.2008, 2008.
	In this paper, we consider a generalization of Pytagoras theorem from view point of nonassociative algebras (in Japanese).
[kamiya-04:2007]	N.Kamiya and S.Okubo. Some construction of Lie superalgebras from triple systems and extended Dynkin diagrams. RIMS, Kyoto Univ. surikaiseki koukyuroku,2007, 1562:1-9, 2007.
	In This paper, we study to Lie superalgebras with Dynkin dyagrams.
[kamiya-05:2007]	N.Kamiya. On triple systems and Extended Dynkin diagrams of Lie superalgebras. Journal of generalized Lie algebras and its application, Sweden, 2008.
	This article is a correspondence of triple systems and Extended Dynkin diagrams.
[m-honma-01:2007]	A. N. Deacon, S. J. Freeman, R. V. Janssens, M. P. Carpenter M. Honma, P. Chowdhury, T. Lauritsen, C. J. Lister, D. Seweryniak, J. F. Smith, S. L. Tabor, B. J. Varley, F. R. Xu, and S. Zhu. Yrast structures in the neutron-rich isotopes 59,60Fe and the role of the g9/2 orbital. Phys. Rev. C, 76:054303/1-16, 2007.
	TThe structure of the neutron-rich isotopes 59,60Fe has been studied with the Gammasphere detector array using fusion-evaporation reactions. Level schemes for these nuclei are presented which have been extended to spins of �` 20h. Both isotopes exhibit regular, near-yrast gamma-decay sequences which are generated by the intrusion of the g9/2 orbital into the fp shell-model space. Lower-spin, natural-parity levels are discussed within the context of shell-model calculations using the GXPF1A interaction in the full fp model space. Experimental features of the high-spin bands are compared with total Routhian surface calculations.
[m-honma-02:2007]	S. Zhu and R. V. F. Janssens and B. Fornal and S. J. Freeman and M. Honma and R. Broda and M. P. Carpenter and A. N. Deacon and B. P. Kay and F. G. Kondev and W. Krölas and J. Kozemczak and A. Larabeee and T. Lauritsen and S. N. Liddick and C. J. Lister and P. F. Mantica and T. Otsuka and T. Pawïat and A. Robinson and D. Seweryniak and J. F. Smith and D. Steppenbeck and B. E. Tomlin and J. Wrzesinski and X. Wang. Oneparticle excitations outside the 54Ti semi-magic core: The 55V and 55Ti yrast structures. Phys. Lett. B, 650:135-140, 2007.
	The level structures of 55V and 55Ti, the two nuclei with a single nucleon outside the semi-magic 5422Ti32 core, have been investigated in order to provide new tests of full pf-shell calculations with the GXPF1A interaction. The addition of a proton does not appear to affect the N = 32 shell gap signicantly, although comparisons between calculations and experiment at high spins (I&pai; ≥ 21/2- ) indicate the need for a larger model space for an accurate description of the data in this regime. The energy separation between the νp1/2 and νf5/2 orbitals in neutron-rich Ti isotopes is not large enough to result in an N = 34 shell gap. However, comparisons between the 55Ti data and the calculations argue for the presence of a sizable N = 34 gap in 54Ca.
[m-honma-03:2007]	C. Dossat and N. Adimi and F. Aksouh and F. Becker and A. Bey and B. Blank and C. Borcea and R. Borcea and A. Boston and M. Caamano and G. Canchel and M. Chartier and D. Cortina and S. Czajkowski and G. de France and F. de Oliveira Santos and A. Fleury and G. Georgiev and J. Giovinazzo and S. GréSvy and R. Grzywacz and M. Hellström and M. Honma and Z. Janas and D. Karamanis and J. Kurcewicz and M. Lewitowicz and M.J. López Jiménez and C. Mazzocchi and I. Matea and V. Maslov and P. Mayet and C. Moore and M. Pfützner and M.S. Pravikoff and M. Stanoiu and I. Stefan and J.C. Thomas. The decay of proton-rich nuclei in the mass A = 36 - 56 region. Nucl. Phys. A, 792:18-86, 2007.
	In a series of experiments at the SISSI/LISE3 facility of GANIL conducted between 1999 and 2004, we have collected decay information for proton-rich nuclei between 36Ca and 56Zn. The data allowed us to study the decay properties of 26 nuclei. The main experimental information obtained for all nuclei is their β-decay half-life and their total β-delayed proton emission branching ratio. For many nuclei, individual proton groups and &gammma; rays were identified and allowed us to establish first partial decay schemes for some of the nuclei studied. In addition, mass-excess values have been determined for some of the nuclei by means of the isobaric multiplet mass equation. For 50Ni, the decay via β-delayed two-proton emission could be tentatively identified. The decay of 49Ni allowed for the first time to identify the first 2+ state in 48Fe. The experimental data are confronted to model predictions for the half-life and the mass-excess values.
[m-honma-04:2007]	XB. Fornal, R. V. F. Janssens, R. Broda, N. Marginean, S. Beghini, L. Corradi, M. P. Carpenter, G. De Angelis, F. Della Vedova, E. Farnea, E. Fioretto, A. Gadea, B. Guiot, M. Honma, W. Królas, T. Lauritsen, S. Lunardi, P. F. Mantica, P. Mason, G. Montagnoli, D. R. Napoli, T. Otsuka, T. Pawlat, G. Pollarolo, F. Scarlassara, A. M. Stefanini, D. Seweryniak, S. Szilner, C. A. Ur, M. Trotta, J. J. Valiente-Dobón, J. Wrzesinski, and S. Zhu. Yrast structure of the neutron-rich N = 31 isotones 51Ca and 52Sc. Phys. Rev. C, 77:014304/1-7, 2007.
	The low-lying yrast states in the 51Ca and 52Sc nuclei were investigated to obtain information on the evolution of the p1/2 and f5/2 neutron single-particle orbitals in neutron-rich nuclei near proton number Z = 20. Level structures associated with neutron excitations into these two orbitals and with proton excitations across the Z = 20 shell gap were identified. Shell-model calculations with the recently proposed GXPF1A interaction account reasonably well for the fp-shell states. The energy separation between the νp1/2 and νf5/2 orbitals in the Ca isotopes appears to be overestimated by the GXPF1A Hamiltonian.
[m-honma-05:2007]	N. J. Stone and K. van Esbroeck and J. Rikovska Stone and M. Honma and T. Giles and M. Veskovic and G. White and A. Wohr and V. I. Mishin and V. N. Fedoseyev and U. Köster and P. F. Mantica and W. B. Walters. Nuclear dipole moment of 71Cu from online β-NMR measurements. Phys. Rev. C, 77:014315/1-3, 2008.
	On-line β-NMR measurements on nuclei oriented at low temperatures of the magnetic dipole moment of 71Cu (N = 42) are reported, with the result μ(71Cu) = +2.28(1) nuclear magneton (n.m.). The value shows a significant difference from μ(67Cu) = +2.54(2) n.m., revealing asymmetry with respect to N = 40. This effect presents a challenge to theoretical interpretation.
[sagawa-01:2007]	J. Margueron, H. Sagawa, and K. Hagino. BCS-BEC crossover of neutron pairs in symmetric andasymmetric nuclear matters. Phys. Rev. C, 76:064316/1-11, 2007.
	We propose new types of density dependent contact pairinginteraction which reproduce the pairing gaps in symmetric and neutronmatters obtained bya microscopic treatment based on the nucleon-nucleon interaction. These interactions are able to simulate the pairing gaps ofeither the bare interaction or theinteraction screened by the medium polarization effects. It is shown that the medium polarization effects cannot be cast into thedensity power law function usually introduced together with the contact interactionand require the introduction of another isoscalar term. The BCSBEC crossover of neutrons pairs in symmetricand asymmetric nuclear matters is studied by using thesecontact interactions. It is shown that the bare and screened pairing interactionslead to different features of the BCS-BEC crossover in symmetricnuclear matter. For the screened pairing interaction, a two-neutron BECstate is formed in symmetric matter at kFn �` 0.2 fm-1(neutron density ρn = ρ0 �` 10-3).Contrarily the bare interaction does not form the BEC state atany neutron densities.
[sagawa-02:2007]	C.M. Campbell, N. Aoi, D. Bazin, M.D. Bowen, B.A. Brown, J.M. Cook, D.-C. Dinca, A. Gade, T. Glasmacher, M. Horoi, S. Kanno, T. Motobayashi, L.A. Riley, H. Sagawa, H. Sakurai, K. Starosta, H. Suzuki, S. Takeuchi, J.R. Terry, K. Yoneda, and H. Zwahlen. Quadrupole collectivity in silicon isotopes approaching neutronnumber N = 28. Phys. Lett. B, 652:169-173, 2007.
	Quadrupole deformation parameters, �\β 2,(p,p)�\, have been deduced for 36, 38, 40Si frommeasured inelastic proton-scattering cross sections. Due to the strong Z =14 subshellgap, low-lying quadrupole collectivity in these nuclei is attributed to theexcitationof valence neutrons. Enhanced collectivity at N = 26 indicates a reduced.
[sagawa-03:2007]	K. Hagino and H. Sagawa. Dipole excitation and geometry of borromean nuclei. Phys. Rev. C, 76:047302 /1-4, 2007.
	We analyze the Coulomb breakup cross sections of 11Li and 6He nucleiusing a threebody model with a density-dependent contactinteraction. We show that the concentration of the B(E1) strengthnear the threshold can be well reproduced with this model. With the help of the calculated B(E1) value, we extract theroot-meansquare (rms) distance between the core nucleus andthe center of mass of two valence neutrons without resorting tothe sum rule, which may suffer from unphysical Pauli forbiddentransitions. Together with the empirical rms distancebetween the neutrons obtainedfrom the matter radius study and also fromthe three-body correlation study in the break-up reaction, we convert these rms distances to the mean openingangle between the valence neutrons from the core nucleus. We nd that the obtainedmean opening angles in 11Li and 6He agree with thethree-body model predictions.
[sagawa-04:2007]	H. Sagawa, Satoshi Yoshida, Guo-Mo Zengand Jian-Zhong Gu, and Xi-Zhen Zhang. Isospin dependence of incompressibility in relativistic andnonrelativistic mean field calculations. Phys. Rev. C, 76:034327/1-8, 2007.
	The isospin dependence of incompressibility is investigated in theSkyrme Hartree-Fock (SHF) and relativistic mean field (RMF) models. The correlations between the nuclear matter incompressibility andthe isospin dependent term of the nite nucleus incompressibilityis elucidated by usingthe Thomas-Fermi approximation. The Coulomb term is also studied by using various different SkyrmeHamiltonians and RMF Lagrangians. Microscopic HF+random phase approximation (RPA) calculationsare performed with Skyrme interactions for 208Pb and Sn isotopes to study the strength distributions of ISGMR. The symmetry term of nuclear incompressibility is extractedto be Kτ = - (500�}50) MeV from the recent experimental data ofisoscalargiant monopole resonances (ISGMR) in Sn isotopes.
[sagawa-05:2007]	H. Esbensen, K. Hagino, P. Mueller, and H. Sagawa. Charge Radius and Dipole Response of 11Li. Phys. Rev. C, 76:024302/1-6, 2007.
	We investigate the consistency of the measured charge radius and dipole response of 11Li within a three-body model. We show how these observables are related to the mean square distance between the 9Li core and the center of mass of the two valence neutrons. In this representation, we find by consideration the effect ofsmaller corrections that the discrepancy between the results of twomeasurements is of the order of 1.5σ.
[sagawa-06:2007]	WenHui Long, Hiroyuki Sagawa, Nguyen Van Giai, and Jie Meng. Shell structure and ρ-tensor correlations in densitydependent relativistic Hartree- Fock theory. Phys. Rev. C, 76:034314/1-11, 2007.
	A new effective interaction PKA1 with ρ-tensor couplings for the densitydependent relativistic Hartree-Fock(DDRHF) theory is presented. It is obtained by fitting selected empiricalground state and shell structureproperties. It provides satisfactory descriptions of nuclear matter and theground state properties of finite nuclei atthe same quantitative level as recent DDRHF and relativistic mean field(RMF) models. Significant improvementin the single-particle spectra is also found due to the inclusion of ρ-tensor couplings. As a result, PKA1 curesa common disease of the existing DDRHF and RMF Lagrangians, namely, theartificial shells at 58 and 92,and recovers the realistic subshell closure at 64. Moreover, the properspin-orbit splittings and well-conservedpseudospin symmetry are obtained with the new effective interaction PKA1. Due to the extra binding introducedby the ρ-tensor correlations, the balance between the nuclear attractionsand the repulsions is changed, and thisconstitutes the physical reason for the improvement of the nuclear shellstructure.
[sagawa-07:2007]	WenHui Long, H. Sagawa, Jie Meng, and Nguyen Van Giai. Evolution of Nuclear Shell Structure due to pion exchange. Europhysics Letters, 82:12001/1-6, 2008.
	The evolution of nuclear shell structure is investigated for the first timewithindensitydependent relativistic Hartree-Fock theory and the role of π -exchange potential is studiedin detail. The energy differences between the neutron orbits υ 1h9/2, υ 1i13/2 in the N = 82isotones and between the proton ones π1g7/2, π1h11/2 in the Z = 50 isotopes are extracted asa function of neutron excess N �\ Z. A kink around Z = 58 for the N = 82isotones is found asan effect of pion correlations. It is shown that the inclusion ofπ-couplingplays a central role toprovide substantial isospin dependence of the energy differences. Inparticular, the tensor part ofthe π- coupling has an important effect on the characteristic isospindependence observed in recentexperiments.
[sagawa-08:2007]	H. Sagawa, Satoshi Yoshida, Xian-Rong Zhou, K. Yako, and H. Sakai. Charge Exchange Spin-DipoleExcitations on 90Zr and 208Pb and Neutron MatterEquation of State. Phys. Rev. C, 76:024301/1-12, 2007.
	Charge exchange spin-dipole (SD) excitationsof 90Zr and 208Pbare studied by using a SkyrmeHartree-Fock(HF) + Random Phase approximation (RPA).The calculated spin-dipole strength distributionsare compared with experimentaldata obtained by 90Zr (p,n) 90Nb and 90Zr (n,p) 90Nb reactions. The model-independent SD sum rule values of various Skyrmeinteractions are studied in comparison with the experimental values in orderto determine the neutron skin thickness of 90Zr. The pressure ofthe neutron matter equation of state (EOS) and the nuclearmatter symmetry energy are discussed in terms ofthe neutron skin thickness and peak energies of SD strength distributions.
[sagawa-09:2007]	Xian-Rong Zhou, H.-J. Schulze, H. Sagawa, and En-Guang Zhao. Hypernuclei in the Deformed Skyrme Hartree-Fock approach. Phys. Rev. C, 76:034312/1-9, 2007.
	The properties of Λ hypernuclei in a broad mass region are studied byusing adeformed Hartree-Fock approach using realisticnucleonic Skyrme forces, pairing correlations, and a microscopicallydetermined lambda-nucleon interaction based onBrueckner- Hartree-Fock calculations of hypernuclear matter. The results suggest that the core nuclei and thecorresponding hypernuclei have similar deformations withthe same sign. Some light single-Λ hypernuclei are substantiallydeformed and the Λ binding energy is modified bythe deformation.
[sagawa-10:2007]	K. Hagino and H. Sagawa. Three-body model calculations for 16Cnucleus. Phys. Rev. C, 75:021301(R)/1-5, 2007.
	We apply a three-body model consisting of two valence neutrons and thecore nucleus 14C in order to investigate the ground state propertiesand theelectronic quadrupole transition of the 16C nucleus. The discretized continuumspectrum within a large box is taken into accountby using a single-particle basis obtained from a Woods-Saxon potential. The calculated B(E2) value from the first 2+ state to the ground stateshows good agreement with the observed data with the corepolarization charge which reproduces theexperimental B(E2) value for 15C. We also show that the present calculation well accounts forthe longitudinal momentum distribution of 15C fragmentfrom the breakup of 16C nucleus. We point out thatthe dominant (d5/2)2 configuration in the ground state of 16C plays a crucial role forthese agreement.
[sagawa-11:2007]	Wei Zou, Gianluca Colo, Zhongyu Ma, Hiroyuki Sagawa, and Pier Francesco Bortignon. Tensor correlations and evolution of single-particle energies in medium-mass nuclei. Phys. Rev. C, 77:014314/1-6, 2008.
	We analyze the evolution of the spin-orbit splittingsin the Ca isotopes and in the N=28 isotones. We also focus on thereduction of the spin-orbit splittings associated with f and porbits from 48Ca to 46Ar. We conclude that adding the tensorcontribution can qualitatively explain in most cases the empirical trends, whereas this is not the case if one simply employs existing Skyrme parameterizations without the tensor forces.
[sagawa-12:2007]	H. Sagawa. Isospin asymmetry of A=14 nuclei. Journal of Phys. G, 34:949-960, 2007.
	We study the isospin asymmetry in the isoscalar (IS) excitationsin the mirror nuclei 14O and 14C by using the Hartree-Fock(HF)+random phase approximation (RPA)linear response function theory with a Skyrme interaction to takeinto account the continuum effect properly. The asymmetry in the IS monopole, dipole responses ispointed out in the continuum near the particle threshold with respect tothe excitation energy and the sum rule strength. On the other hand, no clear sign of the asymmetry is found inthe giant resonance (GR) region. In the quadrupole case, the calculated strengths of the mirror nuclei show almost thesame energy dependence from the threshold to the GR region. It is found that the transition densities of the monopole responseshow an extended halo structure near the threshold, while those of GR regionshow a typical radial dependence of the compressionalcollective mode without any halo effect. Contrary to the transition densities of the monopole response, those of quadrupole response do notshow any sign of the extended feature of wave functions neither near thethreshold nor the GR energy region. Calculated strength distributions of the IS multipole statesare compared with recent experimentaldata obtained by the multipole decomposition analysis of α inelastic scattering on 14O.
[sagawa-13:2007]	K. Hagino, H. Sagawa, J. Carbonell, and P. Schuck. Manifestation of BCS-BEC crossover behavior in Borromean nuclei. Phys. Rev. Lett., 99:1-4, 2007.
	We investigate the spatial structure of two-neutron wave functionin a Borromean nucleus 11Li using a three-body modelof 9Li +n + n, which includes many-body correlations stemmingfrom the Pauli principle. The behavior of the neutron pair at differentdensities is simulated by calculating the two-neutron wave function at severaldistances between the core nucleus 9Li and the center of mass of the twoneutrons. With this representation, a strong concentration of the neutron pairon the nuclear surface is for the first time quantitativelyestablishedfor neutron-rich nuclei. That is, the neutron pair wave function in 11Li has an oscillatory behaviorat normal density, while it becomes a well localized single peakin the dilute density region around the nuclear surface. We point out that these featurescorrespond tothe BCS and BEC-like structuresof the pair wave function found in the innite nuclear matter.
[sigeru-w-01:2007]	S. Watanabe. ChristoffelDarboux formula for zonal spherical functions for the Gelfand pair (U(n),U(n - 1)). Journal of Mathematical Analysis and Applications, 338(2):1378-1386, February 2008.
	In this paper, first we show that an analogy of the ChristoffelDarboux formula holds for the zonal spherical functions for the Gelfand pair (U(n),U(n - 1)). Next, making use of it, we deal with the problem on point-wise convergence of Fourier expansion by means of the zonal spherical functions for (U(n),U(n - 1)).
[t-watanb-01:2007]	Toshiro Watanabe. Convolution equivalence and distributions of random sums. Probability Theory and Related Fields to appear, 2008.
	A serious gap in the proof of Pakes's paper on the convolution equivalence of infinitely divisible distributions on the line is completely closed. It completes the real analytic approach to Sgibnev's theorem. Then the convolution equivalence of random sums of IID random variables is discussed. Some of the results are applied to random walks and Levy processes. In particular, results of Bertoin and Doney and of Korshunov on the distribution tail of the supremum of a random walk are improved. Finally, an extension of Rogozin's theorem is proved.

Refereed Proceeding Papers

[sagawa-14:2007]	Wei Zou, Gianluca Colo, Pier Francesco Bortignon, Zhongyu Ma, and Hiroyuki Sagawa. The effect of the tensor force on single-particlestates and on the isotope shift. In Proc. of International Symposium on "Physics on Unstable Nuclei"(ISPUN07), 2007.
	We analyze the evolution of the spin-orbit splittingsin the Ca isotopes and in the N=28 isotones. We also focus on thereduction of the spinorbit splittings associated with f and porbits from 48Ca to 46Ar. We conclude that adding the tensorcontribution can qualitatively explain in most cases the empirical trends,whereas this is not the case if one simply employs existing Skyrme parameterizations without the tensor forces.
[sagawa-15:2007]	H. Sagawa and K. Hagino. PAIRING CORRELATIONS IN HALO NUCLEI. In Proc. of International Symposium on "Physics on Unstable Nu- clei"(ISPUN07), 2007.
	Pairing correlations in weakly bound nuclei (so called Borromean nuclei)on the edge of neutron drip line, 6He and 11Li, is studied by using a three-body model in which two valence neutronsinteract with each other by a density-dependent contact force. We point out that the di-neutron type correlation plays a dominant rolein these nuclei 6He and 11Li having the coupled spin ofthe two neutrons S=0. The behavior of the neutron pair at differentdensities is simulated by calculating the two-neutron wave function atseveral distances between the core nucleus and the center of mass of the twoneutrons.
[sagawa-16:2007]	H. Sagawa and S. Yoshida. ISOSCALAR AND ISOVECTOR NUCLEAR MATTER PROPERTIESAND GIANT RESONANCES. In Proc. of International Symposium on "Exotic States of Nuclear Matter"(EXOCT07), 2007.
	Correlations among several nuclear matter properties areinvestigated in the Skyrme Hartree Fock (SHF) and the relativistic mean field (RMF) models. Linear correlations between the neutron skin thickness, the pressure of the neutron matter and also the symmetry energyare shown using various Hamiltonian and Lagrangian of mean field models. I also discussed the correlations between the isovector propertiesand the incompressibility K. Charge exchange spin-dipole (SD) excitationof 90Zr and 208Pb are studied in order to extract the neutronskin thickness and to determine the neutron matter EOS at the same time.
[sagawa-17:2007]	Hiroyuki Sagawa and Satoshi Yoshida. ISOSCALAR AND ISOVECTOR NUCLEAR MATTER PROPERTIESAND GIANT RESONANCES. In Proc. of the XVII-th InternationalSchool in "Nuclear Physics, Neutron Physics and Applications", 2007.
	Isoscalar and isovector nuclear matter propertiesare investigated in the Skyrme Hartree Fock (SHF) and the relativistic mean field (RMF) models. The Skyrme parameters are related analytically to the isoscalar and theisovector nuclear matter properties of the Hamiltonian density. Linear correlations are found among the isovector nuclear matter properties ofthe Hamiltonian density in both the SHF and the RMF models.
[sagawa-18:2007]	Gianluca Colo, Pier Francesco Bortignon, and Hiroyuki Sagawa. NONRELATIVISTIC NUCLEAR ENERGY FUNCTIONALS INCLUDING THE TENSOR FORCE. In Proc. of International Symposium on "Physics on Unstable Nuclei"(ISPUN07), 2007.
	We adopt non-relativistic approach to studynuclear energy density functionals, especially ocusing the tensorforce. We adopt a Skyrme force SLy5 and study the effect of tensor force onthe isotope shift of single-particle energies.

Books

[sagawa-19:2007]

H. Sagawa and N. Yoshida. Quantum Information Theory (in Chinese). Dalian Institute of Technology Press, 2007.

Academic Activities

[sagawa-20:2007]	A. Odahara, Y. Gono, Y. Wakabayashi, T. Fuykuchiand H. Sagawa, T. Shimoda, A. Sato, T. Hori, T. MAsue, K. Tajiri, and K. Kuri. Study of High-spin Shape Isomers, 2007.
	The excitation energies of high-spin isomers (HSI)are observed systematically at excitation energiesbetween 8.5 and 9.0MeVfor N=83 isotones with 60 ≤ Z ≤ 67. The spins and the paritiesare identified to be 49/2+ and 27+ for odd and odd-odd nuclei, respectively, from the decay scheme of the isomers. The proton pairing correlations of HSI areextracted empirically for the first timeby using the systematic evidence of excitationenergies of the N=83isotones. It is found that the pairing correlations of HSI aresubstantially large compared with those of the ground states. Theoretical studies of the excitation energies and the pairingcorrelations are also performed and show reasonable agreement withthe experimental data
[sigeru-w-02:2007]	S. Watanabe, 2007. Reviewer of Mathematical Reviews published by AmericanMathematical Society
	We adopt non-relativistic approach to studynuclear energy density functionals, especially ocusing the tensorforce. We adopt a Skyrme force SLy5 and study the effect of tensor force onthe isotope shift of single-particle energies.

Ph.D, Master and Graduation Theses

[sagawa-21:2007]	Takashi Koyama. Graduation Thesis: Non-local theories by using entangled photon, University of Aizu, 2007. Thesis Advisor: H. Sagawa
[sagawa-22:2007]	Kazutomo Satou. Graduation Thesis: Comparisons of Quantum Cryptography Protocols, University of Aizu, 2007. Thesis Advisor:H. Sagawa
[sagawa-23:2007]	Kazutomo Satou. Graduation Thesis: Comparisons of Quantum Cryptography Protocols, University of Aizu, 2007. Thesis Advisor:H. Sagawa
[sigeru-w-03:2007]	Akio Tsujino. A New System of Functions Associated with Taylor Expansion, University of Aizu, 2007. Thesis Advisor: Watanabe, S
[sigeru-w-04:2007]	Naoki Kamiya. A New System of Functions Obtained by Laguerre Polynomials, University of Aizu, 2007. Thesis Advisor: Watanabe, S
[sigeru-w-05:2007]	Yuusuke Watanabe. New Functions Dened by Generating Functions Associated with Trigonometric Functions, University of Aizu, 2007. Thesis Advisor: Watanabe, S
[sigeru-w-06:2007]	Hifumi Watanabe. New Functions Obtained by Generating Functions Associated with Hyperbolic Functions, University of Aizu, 2007. Thesis Advisor: Watanabe, S
[sigeru-w-07:2007]	Akio Mizusaki. Generalization of Functions Generated by Logarithm, University of Aizu, 2007. Thesis Advisor: Watanabe, S

Others

[kihara-01:2007]	Hiroshi Kihara. 54th Topology Symposium, August 2007. We organized the symposium with N.Kamiya, N.Kawazumi and N.Iwase
[kihara-02:2007]	Hiroshi Kihara. C(infinity)-spaces and holomorphic spaces, September 2007. Algebraic and Geometric Models of Spaces and Their Perspectives(at Shinshu University)

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