Exact canonically conjugate momentum to the quadrupole tensor and a microscopic derivation of the nuclear collective hamiltonian

Two momenta conjugate to the mass quadrupole tensor are given. The first is a canonical momentum only in a subspace of the shell model space. A microscopic collective kinetic energy in terms of this momentum and the quadrupole tensor is then obtained and compared with that of Bohr's hamiltonian. The second momentum is, on the other hand, canonically conjugate to the quadrupole tensor in the entire state space.     

Rotational states and interacting bosons

Rotational states are investigated in terms of the interacting boson model. A ground-state rotational band is built from a shell-model many-nucleon system. It is shown that the S and D collective nucleon pairs play dominant roles in low-spin states of the band and that this S-D dominance is broken in high-spin states. The intrinsic hamiltonian is constructed from the effective nucleon-nucleon interaction used in the shell model calculation and the intrinsic state of the rotational band is shown to be comprised primarily of S and D pairs. We introduce a λ boson which is a linear combination of s, d and higher angular momentum bosons, and the boson intrinsic state is given by the λ boson condensate state. The s and d bosons constitute approximately 90 % of the λ boson, and the boson intrinsic state reproduces very well the energy and the intrinsic quadrupole moment of the nucleon intrinsic state. The s-d boson hamiltonian is constructed from the S and D pairs, while effects of non S-D pairs are also included by renormalization of the boson hamiltonian. The renormalization is made by using the λ boson. The s-d boson quadrupole operator is derived similarly. The boson hamiltonian and quadrupole operator thus derived reproduce well the exactly calculated values for low-spin states of the rotational band, although the accuracy decreases in high-spin states. It is shown that the IBM possesses the same physical picture of the rotational states as the Nilsson scheme with pairing correlations. It is therefore concluded that the IBM is capable of describing low-lying rotational states.     

Three-magnon bound states in the two-dimensional isotropic and anisotropic Heisenberg ferromagnet

The existence is shown of bound complexes of three magnons in a two-dimensional simple cubic Heisenberg ferromagnet. The Heisenberg spin hamiltonian is replaced by Dyson's boson hamiltonian. The spurious features of this hamiltonian are treated explicitly. Using Faddeev's formalism, detailed calculations of the three-magnon bound state energy curves have been performed both for the isotropic and the longitudinally anisotropic ferromagnet. Attention is paid to the possibility of observing these three-magnon bound states experimentally.     

Generic dissipation of entanglement

We find states for a multi-level system which are stable under a very general model of dissipation, one which is governed simply by generic rate parameters; in general such stable states are not entangled. We exhibit such a state explicitly for a two-qubit system. We then specialize to a more physical model of dissipation, one which is governed by pure dephasing. In such a case it is possible, by choice of the dephasing rates, to have a stable, and limiting, entangled state under the evolution governed by the free hamiltonian and pure decoherence. We exhibit such a choice explicitly which has a stable and limiting two-qubit state of maximum entanglement (Bell state).     

Low-collective scissors mode

Realistic microscopic RPA calculations for¹⁵⁶Gd with a deformed Woods-Saxon mean field, quadrupole-quadrupole, spin-spin and symmetry-restoring residual interactions show that the purely collective scissors mode of the two-rotor model is fragmented over orbital isovector 1⁺ states, lying at 2–7 MeV. The strongest experimentally observed magnetic dipole state is interpreted as performing a low-collective scissors-type of geometrical motion. This conclusion evolves from the identification of the above state with the strongest RPA excitation, which reproduces well the experimental energy,B(M1) value and (e, e′) form factor, has the largest overlap with the scissors state and can be represented as a low-collective scissors type vibration.     

On the description of dissipative collective motion

We use a recently developed time-dependent projection method to describe the dissipation of collective motion coupled to an intrinsic system. The underlying physical picture is similar to that of the linear response approach. Our approach is, however, different from the conceptual point of view. We do not resort to a quasistatic picture but use instead a time-dependent projector. Furthermore, we project on a model space which includes the intrinsic hamiltonian in addition to the collective subspace. In this way we obtain a Fokker-Planck equation for the collective variables which is coupled to a transport equation describing the evolution of the temperature of the intrinsic system.     

核多体系统输运现象的微观理论

首先回顾了描写核多体系统输运现象的一些主要模型和方法,然后介绍了输运现象微观动力学基础研究上一些新的结果,强调了单粒子运动动力学特征在建立集体输运方程和理解超重核合成机制上的重要作用。能量耗散和熵产生的数值计算结果表明,集体运动耗散过程可分为退相干、弛豫和定态等3 个阶段,弛豫过程通常表现为非常复杂的反常扩散过程。在这些理论工作的基础上,提出了一种自洽地分离核多体系统集体和单粒子变量的可能途径。In this article, I provide a simple review on conventional methods and models on the transport phenomenon of nuclear many-body systems. By exploiting the basic idea of time-dependent projection operator, I recommend a novel method to derive the transport equation for collective motion which is embedded on the microscopic dynamics of timedependent single-particle motion. It is emphasized that the microscopic dynamics of single-particle motion should play an important role for understanding the dynamics of nuclear reaction and the synthesis mechanisms of new superheavy elements. The numerical results of energy dissipation and entropy production indicate that the collective motion passes through three stages, such as dephasing/decoherence, statistical relaxation and stationary state. The statistical relaxation is a complex anomalous diffusion process in general. With the aid of above analysis and results, a possible way to define the collective and single-particle variables for the realistic nuclear many-body systems is proposed.     

Wave functions for low-lying states of light deformed nuclei using a “realistic” hamiltonian and their test by inelastic scattering: The case of 20Ne

Nuclear structure wave functions for the ground and low-lying excited states of ²⁰Ne, obtained from the angular momentum projected deformed particle-hole model using a “realistic” many-nucleon hamiltonian (kinetic energy plus a Brueckner G-matrix based on the Hamada-Johnston potential), are used as input to microscopic antisymmetrised DWBA analyses of inelastic proton scattering from ²⁰Ne. This nuclear structure model, which has been previously shown able to describe the essential features of the giant multipole resonances of both ²⁰Ne and ²⁸Si, predicts angular distributions for inelastic proton scattering, exciting a number of states below 9 MeV in ²⁰Ne, in qualitative agreement with the available data; a somewhat surprising result given the nuclear structure model's completely microscopic formulation. Anomalies observed in the assignment of some predicted levels to experimental states suggest some shortcomings in the form adopted for the hamiltonian.     

Microscopic analysis of nuclear collective motions in terms of the boson expansion theory: (I). Formulation

A normal-ordered linked-cluster boson expansion theory, previously worked out by one of the authors (T.K.) and Tamura, has been developed further by reformulating it in a “physical” quasiparticle subspace which contains no spurious particle-number excitation modes. The expansion coefficients of the collective hamiltonian for low-lying quadrupole motions are determined starting from a microscopic fermion hamiltonian including self-consistent higher-order (many-body) interactions derived in our previous work. The contributions from the non-collective states with all possible non-collective one-boson excitations having I^π = 0⁺− 4⁺, which can directly couple to the collective states with one or two phonons, are taken into account in a systematic and compact way.     

Giant resonances on excited states

We derive modified RPA equations for small vibrations about excited states. The temperature dependence of collective excitations is examined. The formalism is applied to the ground state and the first excited state of ⁹⁰Zr in order to confirm a hypothesis which states that not only the ground state but every excited state of a nucleus has a giant resonance built upon it.     

Microscopic description of collective states near the yrast line of nuclei with stable octupole deformation

Collective states near the yrast line in nuclei with stable octupole deformation are discussed in the framework of the random phase approximation (RPA) based on the cranking model. These vibrational states are characterized by the quantum number of generalized signature (eigenvalue of the operator S_x = PR_x^?1(π)). In the zero-octupole deformation limit the RPA equations of motion are reduced to the well-known ones characterized by both values of parity and signature, respectively. The connection of the translational and rotational symmetry of the model hamiltonian with the spurious solutions of the RPA equation of motion is discussed. Expressions for the reduced probabilities B(E1), B(E2) and B(E3) are obtained. These expressions confirm the conclusions of phenomenological models for the strong E1 and E3 intraband transitions in nuclei with stable octupole deformation.     

Do we understand IBM parameters?

A microscopic calculation of interacting-boson model (IBM) parameters is performed for Xe isotopes within the framework of the broken-pair model. We employ a shell-model hamiltonian which reproduces the spectra of near-magic and semi-magic nuclei. As a first approximation we adopt the idea of Otsuka, Arima and Iachello, that IBM states represent fermion states built from collective S- and D-pairs — the SD space. We show that at least two effects are needed to explain the empirical values of IBM parameters. Firstly there is a reduction in collectivity of S- and D-pairs in states with several broken pairs, due to the Pauli-blocking effect of the latter. Secondly the shell-model hamiltonian mixes the SD space with other fermion states which are not explicitly represented in the IBM. Among the latter, states with a collective G-pair (J = 4) are the most important, but they contribute less than half of the total renormalization of the parameters. The calculated IBM parameters χ of the E2 transition operators exhibit similar trends to those which occur in the IBM hamiltonian.We explain the IBM Majorana force as a renormalization effect on states with even J; not as a repulsion in states with odd J. The latter emerge as rather pure states which mix little with the non-collective fermion space. This indicates that they may be experimentally observable.With our calculated parameters the IBM spectra and E2 transitions are of comparable quality to those obtained in IBM fits of the data.     

Damping of nuclear collective motion in the extended mean-field theory

The dissipation mechanism in slow nuclear collective motion is studied in the frame of the extended mean-field theory. The collective motion is treated explicitly by employing a travelling single-particle representation in the semi-classical approximation. The rate of change of the collective kinetic energy is determined by: (i) one-body dissipation, which reflects uncorrelated particle-hole excitations as a result of the collisions of particles with the mean field, (ii) two-body dissipation, which consists of simultaneous 2 particle-2 hole excitations via direct coupling of the residual two-body interactions, and (iii) potential dissipation due to the redistribution of the single-particle energies as a result of the random two-body collisions. In contrast to the first two processes the potential dissipation exhibits memory effects due to the large values of the local equilibration times.     

The nuclear scissors mode from various aspects

Three methods to describe collective motion, random phase approximation (RPA), Wigner function moments (WFM) and the Green’s Function (GF) method are compared in detail and their physical content analyzed on an example of a simple model, the harmonic oscillator with quadrupole-quadrupole residual interaction. It is shown that they give identical formulae for eigenfrequencies and transition probabilities of all collective excitations of the model, including the scissors mode, which is the subject of our special attention. The exact relation between the RPA and WFM variables and the respective dynamical equations is established. The transformation of the RPA spectrum into the one of WFM is explained. The very close connection of the WFM method with the GF one is demonstrated. The normalization factor of the “synthetic” scissors state and its overlap with physical states are calculated analytically. The orthogonality of the spurious state to all physical states is proved rigorously. A differential equation describing the current lines of RPA modes is established and the current lines of the scissors mode analyzed as a superposition of rotational and irrotational components.     

Collective excitations in the unitary correlation operator method and relativistic QRPA studies of exotic nuclei

The collective excitation phenomena in atomic nuclei are studied in two different formulations of the random-phase approximation (RPA): (i) RPA based on correlated realistic nucleon-nucleon interactions constructed within the unitary correlation operator method (UCOM) and (ii) relativistic RPA derived from effective Lagrangians with density-dependent meson-exchange interactions. The former includes the dominant interaction-induced short-range central and tensor correlations by means of unitary transformation. It is shown that UCOM-RPA correlations induced by collective nuclear vibrations recover a part of the residual long-range correlations that are not explicitly included in the UCOM Hartree-Fock ground state. Both RPA models are employed in studies of the isoscalar giant monopole resonance in closed-shell nuclei across the nuclide chart, with an emphasis on the sensitivity of its properties on the constraints for the range of the UCOM correlation functions. Within the relativistic quasiparticle RPA (RQRPA) based on the relativistic Hartree-Bogolyubov model, the occurrence of pronounced low-lying dipole excitations is predicted in nuclei towards the proton drip line. From the analysis of the transition densities and the structure of the RQRPA amplitudes, it is shown that these states correspond to the proton pygmy dipole resonance. The text was submitted by the authors in English.     

Analysis of Boltzmann-Langevin dynamics in nuclear matter

The Boltzmann-Langevin dynamics of harmonic modes in nuclear matter is analyzed within linear-response theory, both with an elementary treatment and by utilizing the frequency-dependent response function. It is shown how the source terms agitating the modes can be obtained from the basicBL correlation kernel by a simple projection onto the associated dual basis states, which are proportional to the RPA amplitudes and can be expressed explicitly. The source terms for the correlated agitation of any two such modes can then be extracted directly, without consideration of the other modes. This facilitates the analysis of collective modes in unstable matter and makes it possible to asses the accuracy of an approximate projection technique employed previously.