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.     

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.     

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.     

Transition from spherical to deformed shapes of nuclei in the Monte Carlo shell model

The transition from spherical to deformed shapes is studied in terms of large-scale shell-model calculations for Ba isotopes as a function of valence nucleon number with fixed single-particle space and Hamiltonian. A new version of the Monte Carlo shell model is introduced so as to incorporate pairing correlations efficiently, by utilizing condensed pair bases. The energy levels and electromagnetic matrix elements are described in agreement with experiments throughout the transitional region. The orbital M1 sum rule is calculated as a measure of the deformation evolution, and the Q-phonon picture is shown to be reasonable from spherical to deformed nuclei.     

On a RPA method with angular momentum projection

In view of projecting the angular momentum eigenstates out of the intrinsic RPA states, we first study linear relations between deformed and spherical phonons. By use of these relations, the deformed RPA Hamiltonian can be expressed in terms of the spherical phonons in the form of a displaced harmonic oscillator. The angular momentum projection can be applied to an intrinsic RPA state determined by the reduced Hamiltonian, and the correspondence with the macroscopic deformed phonon model of Lipaset al. can be done at this stage. Two important parameters, the constant term in the linear relations and the strength of the spherical phonon Hamiltonian, are evaluated and compared with the best-fit values obtained by Lipaset al.     

On the shell model and its application to the deformation energy of heavy nuclei

The technical realisation of the shell model with arbitrary fields is presented in detail, with special emphasis of the unusual and large deformations of the nuclear shape as they may occur in the fission process. We discuss how realistic parametrisations of the nuclear shape and the potential well can be developed and how the parameters of the average fields can be determined. We restrict ourselves to wells with a Woods-Saxon distribution in the radial coordinate. By means of Strutinsky's shell correction approach, the single particle energies deserve to calculate the potential part of a collective Hamiltonian. Its behaviour with varying deformation is discussed both qualitatively and quantitatively. Considered are the deformation types of elongation (1), necking (2), reflection (3) and axial (4) asymmetry of the nuclear shape. Evidence is given for geometrical symmetries which can be correlated to normal modes in finite nuclei. The transition from spherical to deformed nuclei is presented in detail for the radium isotopes, revealing the importance of hexadecapole deformations. Finally, we give an extensive and systematic presentation of the energies and of the deformations at the various stationary points of the deformation energy for the nuclei in the actinide region and for the hypothetical superheavy nuclei.     

Rotational structure of the odd-proton nuclide 171Tm:A projected shell model study

Deformed odd-mass nuclei are ideal examples where the interplay between single-particle and collective degrees of freedom can be studied. Inspired by the recent experimental high-spin data in the odd-proton nuclide 171 Tm, we perform projected shell model(PSM) calculations to investigate structure of the ground band and other bands based on isomeric states. In addi- tion to the usual quadrupole-quadrupole force in the Hamiltonian, we employ the hexadecapole-hexadecapole(HH) interac- tion, in a self-consistent way with the hexadecapole deformation of the deformed basis. It is found that the known experi- mental data can be well described by the PSM calculation. The effect of the HH force on the quasiparticle isomeric states is discussed.     

Phase transition from deformed to γ-instable Os isotopes and the structure of the giant resonances

The collective potential energy surfaces and kinetic energies are constructed empirically by using the experimental low energy spectra for the Os isotopes. Giant dipole resonances and photon scattering are calculated within the DCM based in the so-obtained collective Hamiltonian. The potential energy surfaces show a phase transition from prolately deformed (Os) to γ-instable (Os) nuclei. This is also reflected in the structure of the giant resonances.     

First-order quantum phase transitions: Test ground for emergent chaoticity,regularity and persisting symmetries

We present a comprehensive analysis of the emerging order and chaos and enduring symmetries, accompanying a generic (high-barrier) first-order quantum phase transition (QPT). The interacting boson model Hamiltonian employed, describes a QPT between spherical and deformed shapes, associated with its U(5) and SU(3) dynamical symmetry limits. A classical analysis of the intrinsic dynamics reveals a rich but simply-divided phase space structure with a Hénon–Heiles type of chaotic dynamics ascribed to the spherical minimum and a robustly regular dynamics ascribed to the deformed minimum. The simple pattern of mixed but well-separated dynamics persists in the coexistence region and traces the crossing of the two minima in the Landau potential. A quantum analysis discloses a number of regular low-energy U(5)-like multiplets in the spherical region, and regular SU(3)-like rotational bands extending to high energies and angular momenta, in the deformed region. These two kinds of regular subsets of states retain their identity amidst a complicated environment of other states and both occur in the coexistence region. A symmetry analysis of their wave functions shows that they are associated with partial U(5) dynamical symmetry (PDS) and SU(3) quasi-dynamical symmetry (QDS), respectively. The pattern of mixed but well-separated dynamics and the PDS or QDS characterization of the remaining regularity, appear to be robust throughout the QPT. Effects of kinetic collective rotational terms, which may disrupt this simple pattern, are considered.     

U(5)-SU(3) nuclear shape transition within the interacting boson model applied to dysprosium isotopes

In the framework of the interacting boson model (IBM) with intrinsic coherent state, the shape Hamiltonian from spherical vibrator U(5) to axially symmetric prolate deformed rotator SU(3) are examined. The Hamiltonian used is composed of a single boson energy term and quadrupole term. The potential energy surfaces (PES’ s) corresponding to the U(5)-SU(3) transition are calculated with variation of a scaling and control parameters. The model is applied to ^150–162Dy chain of isotopes. In this chain a change from spherical to well deformed nuclei is observed when moving from the lighter to heavier isotopes. ¹⁵⁶Dy is a good candidate for the critical point symmetry X(5). The parameters of the model are determined by using a computer simulated search program in order to minimize the deviation between our calculated and some selected experimental energy levels, B(E2) transition rates and the two neutron separation energies S_2n. We have also studied the energy ratios and the B(E2) values for the yrast state of the critical nucleus. The nucleon pair transfer intensities between ground-ground and ground-beta states are examined within IBM and boson intrinsic coherent framework.     

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.     

A generalized Hartree-Fock-Bogoliubov approach for the description of band structures in nuclei: (II). The generalized Hartree-Fock-Bogoliubov theory in the intrinsic frame of reference

The problem of the occupation number calculation for the generalized Hartree-Fock-Bogoliubov (GHFB) approach is solved by introducing an intrinsic frame of reference, where the generalized density matrix and the average field Hamiltonian becomes diagonal with respect to the nulcear spin I. Using variational methods a dynamical equation is obtained, which determines the intrinsic density matrix. Its eigenvalues are defined by means of additional kinematical conditions following from the Pauli principle. A special symmetry of the intrinsic average field Hamiltonian allows us to divide the quasiparticle states in to two conjugated groups having positive quasiparticle energies and the corresponding negative quasiparticle energies, respectively. A generalized Coriolis interaction and new self-consistency conditions are derived. The relation of the present model to the self-consistent cranking model is discussed. As a numerical example the equilibrium deformation for a system of nucléons moving in a spherical oscillator potential and interacting via simple quadrupole forces is calculated.     

Coupling of one and two quasiparticles to a Bohr-Mottelson core in195,196,197,198Hg

A new model for coupling the motion of particles to that of a quadrupole collective core with rotations andβ andγ vibrations is proposed. The Hamiltonian describing the core is obtained by quantising the classical Hamiltonian associated with the quadrupole degrees of freedom. The inertial parameters and the deformation energy surface are determined microscopically. The spherical shell model particles interacting among themselves by pairing are coupled to the core by aλ ²-pole (λ=0, 2, 4) potential. The theory is applied to^195–198Hg. The predicted results agree very well the experimental data. A comparison of the present model to the other formalism is also given.     

Destruction of26Al via the26Al(n,p)26Mg-reaction

An angular analogue to the Giant Dipole (the Giant Angle Dipole) is described. Such collective vibrational motion is specifically investigated for the case of a spin saturated large particle number system contained in a deformed harmonic oscillator well. The model predicts the ratio of the Angle Dipole to Giant Dipole excitation as equal to the deformation.     

On the moment of inertia of a quantum harmonic oscillator

An original method for calculating the moment of inertia of the collective rotation of a nucleus on the basis of the cranking model with the harmonic-oscillator Hamiltonian at arbitrary frequencies of rotation and finite temperature is proposed. In the adiabatic limit, an oscillating chemical-potential dependence of the moment of inertia is obtained by means of analytic calculations. The oscillations of the moment of inertia become more pronounced as deformations approach the spherical limit and decrease exponentially with increasing temperature.