壳层模型代数Sp(8)真空表示的解析玻色子实现问题

决定壳层模型酉辛代数Sp(2d)的任意表示的玻色子实现问题,已经完全解决了.一些作者找到了Sp(2)一般表示和Sp(2d)(d>1)的特殊情况的表示封闭解析解.我们用不同的方法解决了Sp(6)真空表示和Sp(4)一般表示的解析玻色子实现问题.现在,我们把这个方法推广到Sp(8)的真空不可约表示的情形.决定Sp(8)真空不可约表示的解析玻色子实现问题比Sp(6)复杂得多.很难找到精确解.但是,本文得到了近似的结果.

FOUNDATION OF NUCLEAR ALGEBRAIC MODELS

Based upon Tomonoga-Rowe's many body theory, we find that the algebraic models, including IBM and FDSM are simplest extension of Rowe-Rosensteel's sp(3R).Dynkin-Gruber's subalgebra embedding method is applied to find an appropriate algebra and it's reduction chains conforming to physical requirement. The separated cases sp(6) and so(8) now appear as two branches stemming from the same root D6-O(12). Transitional ease between sp(6) and so(8) is inherently include.

Proton-neutron symplectic model description of ^(106)Cd

In this study,a microscopic shell-model description of the low-lying collective states in the weakly deformed nucleus ^(106)Cd within the recently proposed microscopic version of the Bohr-Mottelson model is provided.A good description of the excitation energies of the lowest ground,γ,andβquasibands is obtained without the adjustable kinetic energy term.Furthermore,γdegrees of freedom are shown to play a crucial role in the description of spectroscopy of this nucleus.A modified SU(3)SU(3)preserving high-order interaction is used to produce aγ-unstable type of odd-even staggering,observed experimentally between the states of the quasi-γband.The current approach enables the characterization of observed intraband and interband quadrupole collectivity.The findings of this study propose an alternative interpretation of the fundamental question regarding the nature of low-energy vibrations,as well as the emergence of deformation and collectivity in weakly deformed atomic nuclei.

Matrix elements in the SU(1,1)⊗SO(6)limit of the proton-neutron symplectic model

The matrix elements along the reduction chain Sp(12,R)⊃SU(1,1)⊗SO(6)⊃U(1)⊗SUpn(3)⊗SO(2)⊃SO(3)of the proton-neutron symplectic model(PNSM)are considered.Closed analytical expressions are obtained for the matrix elements of the basic building blocks of the PNSM and the Sp(12,R)symplectic generators,allowing the computation of matrix elements of other physical operators as well.The computational technique developed in the present study generally provides us with the required algebraic tool for performing realistic symplectic-based shell-model calculations of nuclear collective excitations.Utilizing two simple examples,we illustrate the application of the theory.

Shell-model representations of the microscopic version of the Bohr-Mottelson collective model

The structure of the irreducible collective spaces of the group Sp(12,R),which many-particle nuclear states are classified according to the chain Sp(12,R)⊃U(6)⊃SO(6)⊃SU_(pn)(3)⊗SO(2)⊃SO(3)of the proton-neutron symplectic model(PNSM),is considered in detail.This chain of the PNSM was recently shown to correspond to a microscopic shell-model version of the Bohr-Mottelson collective model.The construction of the relevant shell-model representations of the Sp(12,R)group along this chain is considered for three nuclei with varying collective properties and from different mass regions.It is shown that the SU_(pn)(3)basis states of the Sp(12,R)representations belonging to the SO(6)irreps with seniorityυ≥υ0,withυ0 denoting the maximal seniority SO(6)irrep contained in the Sp(12,R)bandhead,are always Pauli allowed,but organized in a different way into different SO(6)shells.This is in contrast to the case of filling the levels of the standard three-dimensional harmonic oscillator and using the plethysm operation.Although the SU_(pn)(3)multiplets withinυ<υ0 are not all Pauli forbidden,it is safe to discard them.The results obtained in the present work are important for the practical application of the microscopic version of the Bohr-Mottelson collective model.

Microscopic shell-model description of irrotational-flow dynamics in^(102)Pd

The structure of the low-lying collective excitations in 102Pd is examined within the recently proposed microscopic shell-model version of the Bohr-Mottelson(BM)collective model.A good description of the excitation energies of the lowest ground,γ,andβbands,as well as the staggering function between the collective states of theγband and some other energy-dependent quantities,is obtained.The low-energy intraband and interband quadrupole dynamics is reasonably well described within the present proton-neutron sympletic based shell-model approach without the use of an effective charge and compared with the predictions of nuclear structure models.The obtained results of the present study shed light on the question of the existence of irrotational-flow type quadrupole dynamics,which lies on the ground of the original BM model of quantized vibrations and surface-wave rotations in atomic nuclei.

On the microscopic shell-model version of the Bohr-Mottelson collective model

The recently proposed microscopic shell-model version of the Bohr-Mottelson(BM) collective model is considered in more detail in the coordinate representation.The latter possesses a clear and transparent physical meaning,which reveals several features of the new version of the collective model missed in the previous formulation.The relationship to the original BM model is considered,along with the relationships between the different limiting submodels of the microscopic version of the BM model,which closely resemble the relationships of the original Wilets-Jean and rotor models.The kinematically correct many-particle wave functions of the microscopic version of the BM model,conserving the experimentally observed integrals of motion,are shown to consist of collective irrotational-flow and intrinsic components-in accordance with the original BM unified model.The general BM Hamiltonian is obtained as a contraction limit of the microscopic many-particle nuclear Hamiltonian,or,alternatively,by restricting the latter to the scalar O(m) irreducible collective space.