Among many other finite quantal systems, the atomic nucleus takes on a unique and stun-ning collective aspect characterized by the remarkable regularity of its energy spectra. The most simple, yet essential collective motion is of quadrupole type, where the equilibrium shape of a nucleus can be a spherical vibrator, an ellipsoidal deformed rotor and an object in between, de-pending on the number of protons and/or neutrons. Deformation occurs as a consequence of the spontaneous symmetry breaking of the nuclear mean field, and the rotational motion manifests itself as a realization of symmetry-restoration mechanism, which is a general concept in physics. Therefore, understanding the quadrupole collective dynamics from a microscopic perspective has always been an intriguing subject in nuclear many-body physics. Thanks to the developments in experimental techniques, it has nowadays become possible to study various collective modes of excitation in medium-heavy and heavy nuclei.

Self-consistent mean-field theory with a given microscopic energy density functional (EDF), such as Skyrme, Gogny and other interactions in relativistic regimes, has provided both universal and accurate description of bulk properties of finite nuclei over almost entire chart of nuclides, including mass, intrinsic deformation, and giant resonances, etc. To obtain the spectroscopic observables, however, one should go beyond the mean-field approximation to take quadrupole correlations into account and to restore the broken symmetries. A number of studies have been done rigorously in terms of the configuration mixing and/or the restoration of broken symmetries, but are computationally demanding and much involved particularly when the triaxial degrees of freedom enter. Alternatively, phenomenological study within the interacting boson model (IBM) of Arima and Iachello has witnessed enormous success in reproducing the low-lying structure of medium-heavy and heavy nuclei. While the IBM reflects a certain microscopic picture associated with the underlying many-fermionic dynamics, the problem concerning how this model is justified for general cases of quadrupole collective states has remained an open question.

We have proposed a novel way of deriving a Hamiltonian of the IBM from microscopic self-consistent mean-field theory. The IBM in this context refers to the proton-neutron IBM (IBM-2), which distinguishes the proton and the neutron degrees of freedom. Since a nucleus is comprised of protons and neutrons, we discuss the IBM-2 throughout, which reflects a microscopic picture much better than the simpler version of the IBM. The constrained mean-field calculation with a fixed EDF provides energy landscape, i.e., the potential energy surface for the quadrupole collec-tive dynamics, which is subsequently mapped onto the corresponding classical limit of the boson Hamiltonian with respect to the boson coherent state. This mapping process yields strength pa-rameters of the IBM Hamiltonian, thereby alIowing to analyze the energies and the wave functions of excited states with good quantum numbers in the laboratory frame, and the quantum fluctua-tion that is missing in the mean-field approximation. The methodology is so general that it can be applied to all situations of the quadrupole collective states in principle, including those of heavy exotic nuclei. The initial work was published in Ref. [1], addressing the proof of principle. Subsequently, the validity of the methodology was further addressed in Ref. [2], introducing an unambiguous way of deriving the IBM Hamiltonian with the help of wavelet transform, and was applied to the systematic spectroscopic analyses of medium-heavy nuclei.

At the microscopic level, the IBM has its own long-lasting problem of not being able to de-scribe the moment of inertia of rotational band when applied to well-deformed nuclei. We have shown how the IBM can be justified for the description of axially symmetric, strongly-deformed nuclei from the successful density functional approach [3]. In the deformed nuclei, the way that the nucleon system responds to the rotational cranking is shown to be substantially different from the one for the corresponding boson system. To remedy this deviation between deformed nucleon and boson systems, we proposed to introduce a rotational kinetic term in the boson Hamiltonian, and derived its coupling constant so that the rotational response of the boson system becomes iden-tical to that of the nucleon system. As a consequence, the rotational bands of strongly-deformed rare-earth and actinoid nuclei are reproduced to almost perfect precision, without any adjustment of the excitation energies. Furthermore, this study sheds lights upon, and provides one with a crucial piece of information about the critical comment, which was made in the past by Bohr and Mottelson from a microscopic theory, as to the validity of the IBM for deformed nuclei.

Intriguing coIlective phenomena are also seen in medium-heavy nuclei in which the triaxial de-grees of freedom needs to be included. The concept of the quantum phase transition (QPT), as well as the critical-point symmetry, serves as a paradigm for elucidating the complex nuclear structural evolution as function of nucleon number, and has been a subject tested by various microscopic perspectives. By employing the procedure of Ref. [1], a number of spectroscopic studies have been carried out [2,4,5,6,7] for those nuclei in many of which triaxiality plays an important role. Typical shape transitions between nearly spherical and weakly deformed γ-unstable nuclei in the mass regions A〓100~ 130 were reproduced using the Skyrme EDF in Ref. [2], while evidence for E(5) critical-point symmetry for some Ba and Ru isotopes was addressed there. Moreover, it was suggested in Ref. [2] that a large number of γ-soft 0(6) nuclei may be observed in the right-lower quadrant of the doubly-magic nucleus (208)Pb, which should be examined experimentally in the future. The heavy nuclei around the mass A 〓 190 exhibit competition between prolate and oblate intrinsic states, resulting in a spectacular shape coexistence as observed experimentally. We have studied the spectroscopic systematics of these nuclei based on the IBM Hamiltonian derived from finite-range Gogny EDF [4,5,6]. Particularly we discussed the possibility of the coexistence of prolate and oblate shapes in Pt isotopes, and suggested that a single configuration, without in-troducing the intruder configuration of cross-shell excitation, is sufficiently well for Pt nuclei. We further predicted, prior to a measurement, the transition from prolate to oblate shapes in heavy Os and W nuclei as a function of neutron number N and the transition points N = 116. Along this line, we gave the first theoretical explanation on the y-ray spectroscopy of neutron-rich Kr isotopes, carried out at the REX-ISOLDE facility at CERN [7]. Contrary to some earlier measure-ments, we concluded from both theoretical and experimental viewpoints that the shape evolution in the considered Kr nuclei occurs quite slowly, and that no sudden onset of deformation is ob-served. This result certainly has a significant impact, because the neutron-rich nuclei with mass A〓100, including the Kr isotopes, represent an intersection of collective and single-particle de-grees of freedom, and also should be of common interest for the studies of shell structure, QPT, mass measurement and astrophysical processes.

All these findings are robust such that they are almost independent of the particular choice and the details of the EDFs used. This was further tested and confirmed by comparing the spectra, as well as the transition rates between the excited states, generated by the IBM Hamiltonian based on the EDF in relativistic mean-field (RMF) model with those by the geometrical five-dimensional collective Hamiltonian derived from the same RMF interaction [8]. In addition, peculiar features inherent to these two collective models are compared in detail, by which their current limitations and possible ways of improvements are suggested.

One of the important consequences of these analyses concerns the issue of the regularity in the level structure of non-axial (γ-soft) nuclei. The non-axial nuclei have been studied based on the two conflicting physical pictures: the rigid-triaxial and the γ-unstable rotor models. Since vast majority of the observed non-axial nuclei fall exactly in between the two geometrical models, the relation between the two has been of intriguing subject. In the IBM framework, the non-axiaI nuclei are described only by the 0(6) dynamical symmetry, which is nothing but a realization of the γ-unstable rotor picture. Any IBM Hamiltonian composed of only up to two-body terms can never reproduce the level structure of non-axially symmetric nuclei, partly because the two-body Hamiltonian does not reproduce a stable triaxial minimum which is however seen in microscopic energy surface. We then proposed to introduce, for the first time, an essential three-body boson term in the proton-neutron IBM so as to reflect the microscopic calculation [9]. With such suitably chosen boson Hamiltonian, we have demonstrated that the above-mentioned empirical feature of non-axial nuclei can be explained naturally and that the finding resulting from this study is independent of the type of the EDFs used [9].

Finally, the nuclear structural evolution is analyzed through the ground-state properties, in which the quantum fluctuation (correlation) is included by the diagonalization of the boson Hamil-tonian formulated by an EDF. The correlation effect turns out to be significant in the transitional nuclei, and can reproduce the correct systematics of the two-neutron separation energies [2]. Also the empiricaI proton-neutron interaction can be evaluated by the so-called δV(pn)plot, which reflects how the collectivity correlates with the underlying shell structure.

本論文は8 章からなり、その研究内容は、原子核の四重極変形の自由度に着目し、フェルミ粒子多体系に対する微視的理論であるエネルギー密度汎関数(Energy Density Functional (EDF)) を動的対称性で特徴づけられる相互作用するボゾン模型(Interactive Boson Model (IBM)) と対応させ、安定線から原子核の励起スペクトルを予言することを目指したものである。

第1章は、イントロダクションであり、フェルミ粒子多体系としての原子核の集団運動を概観し、エネルギー密度汎関数(EDF) に基づく微視的計算が原子核の基底状態の記述に成功をおさめている一方、その励起構造の記述のためには、固有座標系で得られた自己無撞着解が破った対称性を回復させる必要からくる困難が紹介されている。相互作用するボゾン模型(IBM) との対応づけが、この困難を解消するための有力な手段であるという本論文の主題が提示され、論文全体の構成が記述されている。原子核構造の理論的研究の現状と問題点を捉え、新たな研究への着想は論文提出者の見識を示している。

第2章では、本研究で行われた計算の具体的手法が記述されている。まず、EDF計算により四重極変形を特徴づけるパラメータ(βF,γ F) の関数としてエネルギーを求める。同様に、IBM のハミルトニアンをボゾンに対する変形度βB とγB と関係づけ、それらの関数としてエネルギーを求め、それぞれの変形度の大きさを換算した上で、wavelet 法を用いて、変形度に対する依存性が全体としてEDF 計算を再現するようIBM ハミルトニアンのパラメータが決定される。変形度の対応づけおよび用いられたwavelet 法はともによく考慮されておりこの手法の信頼性の高さを示している。

第3章では、大きく変形した原子核のスペクトルがsd ボゾンのみのIBM では再現できないという問題に対して、IBM ハミルトニアンにLL 項を加えることによりそれが解消されることが示されている。IBM 自体の模型空間の狭さに起因すると考えられる問題を、模型空間を変えずに現象論的な項を導入することにより繰り込めることを示した結果で、その適用性が期待される。

第4章では、変形度の小さな原子核への適用が行われ、レモン型の原子核からパンケーキ型の原子核への相転移が議論されている。IBM のもつ対称性と変形パラメータ空間におけるエネルギー面の特徴との対応から、重い不安定原子核においてE(5)臨界点の存在が示唆されている。計算結果に対する吟味による原子核の構造変化の理解を深めた内容である。

第5章では、集団運動に対する他の幾何学模型による計算との比較がなされ、本研究の手法の一般性が示されるとともに、それぞれの手法の特失が分析され、研究の位置づけが示されている

第6章では、三軸非対称な変形をもつ原子核の議論がなされている。IBM ハミルトニアンにボゾンの3 体力を導入することにより、2 体力のみのIBM では記述できない安定な三軸非対称変形が予言されるとともに、エネルギースペクトルの規則性を再現させることが可能であることが論じられている。

第7 章では、平均場近似では記述されない、基底状態における相関をIBM で求められた基底状態エネルギーにより議論されている。現象論的に知られている陽子-中性子相関とそれに起因する集団運動が自然に再現されることが示されている。

第8 章では上記の結果がまとめられ、本研究の一般性と適用範囲およびこの手法に基づく原子核構造研究の今後の展開が示されている。

以上のように本論文は、原子核の微視的理論であるEnergy Density Functional をInteractive Boson Model に関連づけた一連の研究をまとめたもので、原子核の分光学的性質への予言力をもたせ、安定領域から離れた原子核構造を系統的に研究する方向性を示したもので、今後の研究展開に大きく貢献するものである。

なお、本論文は共同研究であるが、論文提出者が主体となって計算及び解析を行ったもので、論文提出者の寄与が十分であると判断する。

従って、博士(理学) の学位を授与できると認める。