Qi-Zhi Han

The Fock wave function as classified by the supergroup chain U(N/M)⊃OSp(N/M)⊃O(N)×Sp(M)

The wave functions for bosons and fermions, classified according to the supergroup chain U(N/M)⊃OSp(N/M)⊃O(N)×Sp(M)⊃⋅ ⋅ ⋅, are given in this paper. The method presented here adheres closely to the standard raising and lowering method commonly used in quantum mechanics. When the so‐called star representation [n} is decomposed into the irreducible representation of the OSp(N/M), one obtains a reducible, but not completely reducible, representation of the OSp(N/M). This decomposition is quite different from a regular Lie group chain and has very interesting physical implications.

IRREDUCIBLE REPRESENTATIONS OF QUASI-SPIN GROUP SO(5)(T)

A recurrent method for irreducible representation calculation of five-dimensional quasispin group SO(5)t is proposed. The explicit IRs in physical orthonormal basis with multiplicity up to three, such as (2tt), (2t + t) and when are given.

Coupling Coefficients of Quasispin Group SO(5)t

A recurrent method for coupling coefficient calculations of five-dimensional quasispin group SO(5)t is proposed. The explicit coupling coefficients such as , and with are given.

THE FRACTIONAL PARENTAGE COEFFICIENTS FOR A DOUBLE-J FERMION SYSTEM

The coefficients of fractional parentage (CFPs) for a double-j fermion system are defined. The CFPs are given when the wave functions are classified according to the group chains U(N) ⊃ U(N1) × U(N2) ⊃ SP(N1) × SP(N2) ⊃ O(31) × O(32) ⊃ O(3) and U(N) ⊃ SP(N) ⊃ SP(N1) × SP(N2) ⊃ O(31) × O(32) ⊃ O(3). Using these CFPs many repeating calculations can be avoided.

DESCRIPTION OF THE HEXADECAPOLE DEFORMATION PARAMETER IN THE SDG INTERACTING BOSON MODEL

The hexadecapole deformation parameter beta(4) Of the rare-earth and actinide nuclei is investigated in the framework of the sdg interacing boson model. An explicit relation between the geometric hexadecapole deformation parameter beta(4) and the intrinsic deformation parameters epsilon(4), epsilon(2) are obtained. The deformation parameters beta(4) of the rare-earths and actinides are determined without any free parameter. The calculated results agree with experimental data well. It also shows that the SU(5) limit of the sdg interacting bosom model can describe the beta(4) systematics as well as the SU(3) limit.

A FORTRAN program for the CFPs of a boson system with F spin

Abstract A simple FORTRAN program called CFPBF calculates the fractional parentage coefficients (CFPs) of identical boson system with F spin. The program CFPBF is based on an algorithm which uses the generalized Wigner-Eckart theorem of semisimple compact Lie groups. It is not only convenient for the discussion of the role of F spin but also more efficient for the CFPs calculation in the proton-neutron interacting boson model.

Coefficients of Fractional Parentage of the Boson System with Single l and F-Spin 1/2

A system of identical bosons with single angular momentum l and F-spin 1/2 is under consideration. The classification of it’s wave functions and the factorization of it’s coefficients of fractional parentage are discussed by using Lie group theory. The branching rules of the group reductions and an approach to evaluate the CFP of the system are given.

A CHECKING METHOD ON CALCULATING CODE FOR THE EIGENVALUE PROBLEM OF MANY-PARTICLE SYSTEMS

Abstract The interaction Hamiltonian and the classification of the state of a many particle system are discussed in the framework of dynamical symmetry theory. An explicit criterion and an effective checking procedure on the computer calculating code for evaluating the eigenvalues of many particle systems are proposed.

An IBM2 Description on the Staggering Phenomenon in the Barium Isotopes

A description on the even-even Barium isotopes for to and in the framework of neutron-proton interacting boson model is carried out. By introducing the quadrupole interactions among like bosons into the Hamiltonian, the staggering phenomenon in the quasi- bands is reproduced pretty well. The physical mechanism behind the improvement is discussed.

SYMMETRIES OF FRACTIONAL PARENTAGE COEFFICIENTS WITH ISOSPIN

A system of identical fermions with single angular momentum j and isospin is under consideration. The classification of its wave functions, the factorization and the symmetry of fractional parentage coefficients are discussed by using the generalized Wigner-Eckart theorem of semisimple compact Lie groups.