Microscopic derivation of the Bohr-Mottelson collective Hamiltonian and its application to quadrupole shape dynamics
arXiv:1606.08547 · doi:10.1088/0031-8949/91/6/063014
Abstract
We discuss the nature of the low-frequency quadrupole vibrations from small-amplitude to large-amplitude regimes. We consider full five-dimensional quadrupole dynamics including three-dimensional rotations restoring the broken symmetries as well as axially symmetric and asymmetric shape fluctuations. Assuming that the time-evolution of the self-consistent mean field is determined by five pairs of collective coordinates and collective momenta, we microscopically derive the collective Hamiltonian of Bohr and Mottelson, which describes low-frequency quadrupole dynamics. We show that the five-dimensional collective Schrödinger equation is capable of describing large-amplitude quadrupole shape dynamics seen as shape coexistence/mixing phenomena. We summarize the modern concepts of microscopic theory of large-amplitude collective motion, which is underlying the microscopic derivation of the Bohr-Mottelson collective Hamiltonian.
arXiv comment62 pages, 6 figures, Review article, Invited Comment in Focus Issue of Physica Scripta to celebrate the 40-year anniversary of the 1975 Nobel Prize to A. Bohr, B. R. Mottelson and L. J. Rainwater (Phys. Scr. 91 (2016) 063014). arXiv admin note: text overlap with arXiv:1606.04717
References in corpus (78)
- Relativistic Nuclear Energy Density Functionals: Mean-Field and Beyond
- Structure of even-even nuclei using a mapped collective Hamiltonian and the D1S Gogny interaction
- The Skyrme Interaction in finite nuclei and nuclear matter
- Subbarrier fusion reactions and many-particle quantum tunneling
- Beyond the relativistic mean-field approximation (III): collective Hamiltonian in five dimensions
- Triaxial Angular Momentum Projection and Configuration Mixing calculations with the Gogny force
- Configuration mixing of angular-momentum projected triaxial relativistic mean-field wave functions
- Configuration mixing of angular-momentum and particle-number projected triaxial HFB states using the Skyrme energy density functional
- Finite amplitude method for the RPA solution
- Time-odd components in the mean field of rotating superdeformed nuclei
- Microscopic Analysis of Nuclear Quantum Phase Transitions in the N=90 region
- Continuum Linear Response in Coordinate Space Hartree-Fock-Bogoliubov Formalism for Collective Excitations in Drip-line Nuclei
- Role of deformation on giant resonances within the QRPA approach and the Gogny force
- Quadrupole collective states within the Bohr collective Hamiltonian
- Transverse wobbling-a collective mode in odd-A triaxial nuclei
- Finite amplitude method for the quasi-particle-random-phase approximation
- Configuration mixing of angular-momentum projected triaxial relativistic mean-field wave functions. II. Microscopic analysis of low-lying states in magnesium isotopes
- A microscopic benchmark-study of triaxiality in low-lying states of 76Kr
- Microscopic Description of Spherical to Gamma-Soft Shape Transitions in Ba and Xe Nuclei
- Title: Quadrupole collective inertia in nuclear fission: cranking approximation
- Beyond relativistic mean-field studies of low-lying states in neutron-deficient krypton isotopes
- Energy Density Functional analysis of shape evolution in N=28 isotones
- Structure of Krypton isotopes calculated with symmetry conserving configuration mixing methods
- Multipole strength function of deformed superfluid nuclei made easy
- Microscopic description of large-amplitude shape-mixing dynamics with inertial functions derived in local quasiparticle random-phase approximation
- Low energy collective modes of deformed superfluid nuclei within the finite amplitude method
- Finite Amplitude Method for Charge-Changing Transitions in Axially-Deformed Nuclei
- Dipole responses in Nd and Sm isotopes with shape transitions
- Self-consistent Skyrme QRPA for use in axially-symmetric nuclei of arbitrary mass
- Linear response of light deformed nuclei investigated by self-consistent quasiparticle random-phase-approximation
- Neutron shell structure and deformation in neutron-drip-line nuclei
- Microscopic Structure of High-Spin Vibrational Excitations in Superdeformed 190,192,194Hg
- Adiabatic Selfconsistent Collective Coordinate Method for Large Amplitude Collective Motion in Superconducting Nuclei
- Shape evolution of giant resonances in Nd and Sm isotopes
- Implementation of the finite amplitude method for the relativistic quasiparticle random-phase approximation
- Feasibility of the finite amplitude method in covariant density functional theory
- Microscopic description of oblate-prolate shape mixing in proton-rich Se isotopes
- Chiral vibrations in the A=135 region
- Shape fluctuations in the ground and excited 0+ states of 30Mg and 32Mg
- Multipole modes in deformed nuclei within the finite amplitude method
- Shape mixing dynamics in the low-lying states of proton-rich Kr isotopes
- Microscopic calculation of the wobbling excitations by using the Woods-Saxon potential as a nuclear mean-field
- Density functional approaches to collective phenomena in nuclei: Time-dependent density-functional theory for perturbative and non-perturbative nuclear dynamics
- Nuclear moments of inertia and wobbling motions in triaxial superdeformed nuclei
- Shape transition and fluctuation in neutron-rich Cr isotopes around N = 40
- Open problems in microscopic theory of large-amplitude collective motion
- Gauge-Invariant Formulation of Adiabatic Self-Consistent Collective Coordinate Method
- Continuum particle-vibration coupling method in coordinate-space representation for finite nuclei
- Angular Momentum Projection and Quadrupole Correlations Effects in Atomic Nuclei
- Efficient calculation for the quasiparticle random-phase approximation matrix
- Testing Skyrme energy-density functionals with the QRPA in low-lying vibrational states of rare-earth nuclei
- Shape changes and large-amplitude collective dynamics in neutron-rich Cr isotopes
- Continuum quasiparticle linear response theory using the Skyrme functional for multipole responses of exotic nuclei
- Collective inertia of Nambu-Goldstone mode from linear response theory
- Microscopic Derivation of Collective Hamiltonian by Means of the Adiabatic Self-Consistent Collective Coordinate Method
- Low-energy E1 strength in select nuclei: Possible constraints on the neutron skins and the symmetry energy
- An efficient method for computing the Thouless-Valatin inertia parameters
- The Low-Energy Quadrupole Mode of Nuclei
- Triaxial quadrupole deformation dynamics in sd-shell nuclei around 26Mg
- Barrier penetration and rotational damping of thermally excited superdeformed nuclei
- Complex-energy approach to sum rules within nuclear density functional theory
- Microscopic derivation of the quadrupole collective Hamiltonian for shape coexistence/mixing dynamics
- Low-frequency modes in deformed neutron-rich nuclei: Pairing- and -vibrational modes of neutron
- Bohr Hamiltonian with a deformation-dependent mass term: physical meaning of the free parameter
- Di-neutron correlation in soft octupole excitations of neutron-rich Ni isotopes beyond N=50
- Periodic-orbit approach to the nuclear shell structures with power-law potential models: Bridge orbits and prolate-oblate asymmetry
- Effects of Time-Odd Components in Mean Field on Large Amplitude Collective Dynamics
- Nuclear shell structures in terms of classical periodic orbits
- Towards a practical approach for self-consistent large amplitude collective motion
- Gaussian Overlap Approxomation for the quadrupole collective states
- Diabatic Mean-Field Description of Rotational Bands in Terms of the Selfconsistent Collective Coordinate Method
- A Model Analysis of Triaxial Deformation Dynamics in Oblate-Prolate Shape Coexistence Phenomena
- Open problems in nuclear structure near drip lines
- Local harmonic approaches with approximate cranking operators
- Gauge Symmetry in the Large-amplitude Collective Motion of Superfluid Nuclei
- BCS-pairing and nuclear vibrations
- Spatial structure of Cooper pairs in nuclei
- Quadrupole shape dynamics in view from a theory of large amplitude collective motion
Cited by in corpus (11)
- Theory of Nuclear Fission
- Beyond the Unified Model
- The time-dependent generator coordinate method in nuclear physics
- Effective density functionals beyond mean field
- Thouless-Valatin Rotational Moment of Inertia from the Linear Response Theory
- Triaxial-shape dynamics in the low-lying excited state: Role of the collective mass
- Enhanced collectivity of gamma vibration in neutron-rich Dy isotopes with N=108 - 110
- Five-dimensional collective Hamiltonian with improved inertial functions
- Evolution of giant monopole resonance with triaxial deformation
- Structure of Krypton Isotopes using the Generalised Bohr Hamiltonian Method
- Gauge symmetry breaking in the adiabatic self-consistent collective coordinate method