Nuclear rotational-vibrational collective motion with nonvanishing vortex-spin

The theory of linear collective motion is developed by the method of canonical transformations, recovering, as special cases, the earlier results of Casimir, Bohr-Mottelson, and Villars. In the approximation of constant Eckart-frame vectors, the kinetic energy Hamiltonian is shown to commute with the invariant operators of the collective motion symmetry group CM(3). The collective motion approach of Tomonaga, and the symmetry approach of Gell-Mann, are discussed and shown to be essentially equivalent, and to be properly contained in the CM(3) structure. The invariant operators of CM(3) are determined and shown to imply two invariants for nuclear collective motion: the volume Λ and the vortex-spin v. Representations of CM(3) are obtained and related to wavefunctions of the generator-coordinate form.     

Collective Hamiltonian for Multi-O(4) Model

The collective Hamiltonian up to the fourth order for multi-O(4) model is derived based on the self-consistent collective-coordinate (SCC) method,which is formulated in the framework of the time-dependent Hartree-Bogoliubov (TDHB) theory.The validity of the collective Hamiltonian is checked in the two special cases of the multi-O(4) modelthe case where the number of the shells is equal to one (a single j-shell case),and the case where the Hartree-Bogoliubov equilibrium point is spherical (the spherical case).The collective Hamiltonian constitutes a good starting point to study nuclear shape coexistence.     

原子核振动与转动模型（Ⅰ）推转玻尔─莫特逊哈密顿量和偶偶核正常转动谱分析

从推转壳模型出发，导出了转动频率未量子化的集体振动－转动哈密顿量，称为推转玻尔－莫特逊哈密顿量（ＣＢＭＨ）．引入合理的集体运动位势，由ＣＢＭＨ可以得到解析形式的转动谱公式．应用这一振动－转动模型，对偶偶变形核的正常转动能谱进行了分析，取得了满意的结果．     

Vibrational and Rotational Motions Model of Nucleus(Ⅰ) Cranking Bohr-Mottelson Hamiltonian and Analyses of the Rotational Bands of Even-Even Nuclei

Starting from cranking shell model,a collective vibrational and rotational Hamiltonian(cranking Bohr-Mottelson Hamiltonian CBMH)is derived,in which the rotational frequency is not quantized.Introducing a reasonable collective potential,the formula for the rotational spectrum can be obtained.The formula is applied to analyze the rotational bands of even-even nuclei with satisfactory results.     

Collective potentials and dipole and quadrupole giant resonances

The dynamic collective model is extended into the energy region immediately above the giant dipole resonances, i.e. into an energy region between 20 and 28 MeV. The total Hamiltonian is constructed and the dynamical problem is solved by diagonalizing the Hamiltonian in the basis of a five-dimensional harmonic oscillator. In schematical studies the splitting of giant quadrupole resonances is shown. For some elements the potential energy surfaces (PES) are constructed within the collective model developed by Gneuss et al. and the quadrupole resonances have been calculated in the framework of the dynamic collective model. In the last part the agreement with experimental data is shown.     

Application of the SCC method to the multi-O(4) model: The collective Hamiltonian

The collective Hamiltonian up to the fourth order for a multi-O(4) model is derived for the first time based on the self-consistent collective-coordinate(SCC) method,which is formulated in the framework of the time-dependent Hartree-Bogoliubov(TDHB) theory.This collective Hamiltonian is valid for the spherical case where the HB equilibrium point of the multi-O(4) model is spherical as well as for the deformed case where the HB equilibrium points are deformed.Its validity is tested numerically in both the sp...     

Phase factors in bases for solutions of time-dependent schrödinger equations

The time-dependent Schrödinger equation is formulated within a model space by means of a finite set of coupled, linear differential equations. The basis is spanned by a set of orthogonal and well-defined many body wave-functions, which are solutions of a model Hamiltonian in a “moving frame”. As a by-product one is able to separate approximatively collective potential, collective kinetic, and intrinsic excitation energy for arbitrary collective motion. For the two types of motion discussed in greater details (i.e. center of mass and quadrupole motion), the expressions for the collective kinetic energy approach their correct asymptotic values.     

Energy surfaces,collective potentials and collective inertia parameters

The Hill-Wheeler equation is used to derive a collective Hamiltonian from an energy surface. Two simple ansatz are proposed for the collective Hamiltonian, which is then calculated explicitly in a hierarchy of approximations. The consistency of the method is verified in an illustrative example.     

Random matrices, fermions, collective fields, and universality

We first relate the random matrix model to a Fokker-Planck Hamiltonian system, such that the correlation functions of the model are expressed as the vacuum expectation values of equal-time products of density operators. We then analyze the universality of the random matrix model by solving the Focker-Planck Hamiltonian system for large N. We use two equivalent methods to do this, namely the method of relating it to a system of interacting fermions in one space dimension and the method of collective fields for large N matrix quantum mechanics. The final result using both these methods is the same Hamiltonian system of chiral bosons on a circle, which manifestly exhibits the universality of the random matrix model.     

Microscopic structure of <Superscript>126</Superscript>Ba in IBM terms

The yrast band of the nonaxially deformed ¹²⁶Ba nucleus is described by the Hamiltonian of the interaction boson model. Its parameters are calculated on the basis of a microscopic theory within a spherical mean field, and residual interactions that include pairing and multipole factorized forces. Each state of the yrast band is considered independently of others, allowing us to study variations in the superfluid properties of the nucleus and the quasiparticle structure of collective D phonons with spin. The calculations are performed in an expanded configuration space that includes the collective D phonon states, and noncollective states in which an additional phonon of positive parity whose spin assumes values of 0 to 6 is present along with the D phonons. It is shown that the collective Hamiltonian parameters cannot be reproduced without considering the effect of the noncollective states.     

Nucleon-pair shell model: Formalism and special cases

A formalism is described for a nucleon-pair shell model (NPSM) for even-even and even-odd nuclei. The building blocks of the model space are collective nucleon pairs of angular momenta J = 0,2,… for an even system, and nucleon pairs plus one unpaired nucleon for an odd system. Analytical formulas are given for the matrix elements of a general Hamiltonian. Without any space truncation, the NPSM is equivalent to the shell model in full space, while with a special choice for the building blocks and Hamiltonian it reduces to the broken pair model, the favored-pair model of Hecht and the fermion dynamical symmetry model.     

Validity of an algebraic-variational approach to the theory of collective motion for an exactly soluble shell model with R(5) symmetry

An algebraic-variational approach to the theory of collective motion previously applied in variant forms to pairing and monopole interaction models is here developed for an exactly soluble shell model Hamiltonian with R(5) symmetry. The spectrum of this class of Hamiltonian operators has previously been shown to represent a two-dimensional vibrator-rotator. The approximation scheme developed yields almost exact results up to the two-phonon level in the spherical region and goes over smoothly into a theory of the lowest states of the ground state rotational band in the deformed regime.     

A basis-free approach to time-reversal for symmetry groups

We develop a basis-free approach to time-reversal for the quantal angular momentum group,SU2, and apply these methods to the physical symmetrySU2_isospin,SU3_flavor,SU3_nuclear and the nuclear collective symmetry groupSL(3,R) of Gell-Mann and Tomonaga.     

Rotations of nuclei with reflection asymmetry correlations

We propose a collective Hamiltonian that incorporates interactions capable of generating rotations in nuclei with simultaneous presence of octupole and quadrupole deformations. It is demonstrated that the model formalism could be applied to reproduce the staggering effects observed in nuclear octupole bands. On this basis, we propose that the interactions involved would provide a relevant handle in the study of collective phenomena in nuclei and other quantum mechanical systems with reflection asymmetry correlations.     

Microscopic calculation of the collective motion in76Kr

A microscopic calculation of Bohr's collective Hamiltonian is used to describe the collective motion in the⁷⁶Kr isotope. A single-particle basis calculated in a deformed Woods-Saxon potential leads to the potential energy surface obtained by the Strutinsky renormalization procedure, and to the inertial functions determined in the cranking model approximation. The collective Schrödinger equation is solved numerically. The low-energy, even parity states in⁷⁶Kr are analyzed in the frame of this model. The theoretical results involve the potential energy and the inertial parameters as functions of intrinsic quadrupole deformations, the collective levels and wave functions including their transitions and electromagnetic moments. A good agreement between experiment and theory is obtained without adjusting specifically for this nucleus any parameter in the model. Some results regarding statical and dynamical characteristics of even-even^{74, 78, 80}Kr isotopes are also presented.     

Backscattering in the one-dimensional many-fermion system

The Sawada Hamiltonian model is generalized to include the backscattering interaction in a one-dimensional many-fermion system. The collective excitations of the particle-density fluctuations and the backscattering dielectric function are obtained. It is shown that the giant Kohn anomaly of the longitudinal phonon spectrum, observed in the quasi-one-dimensional conductors, is qualitatively reproduced within the present approach.