Hong-Zhou Sun

A new recursion relation of CFP for the system of identical bosons

A new recursion relation of coefficients of fractional parentage (CFP) with seniority provides an efficient algorithm for computation. As a result of the generalised Wigner-Eckart theorem of semisimple Lie groups, the CFP are factorised into isoscalar factors (ISF) of the symmetry group of n bosons. The evaluations are done in the scheme of second quantisation. An analytic formula of the multiplicity of an irreducible representation (IR) of O(3) in an IR of O(N) is presented. A complete label (including seniority) of the states for the system of bosons, each with angular momentum l, is also presented.

Coefficients of fractional parentage for a double-l boson system

The generalised coefficients of fractional parentage (CFP) for a double-l boson system are defined. The formulae of CFP with seniority are presented when the states of this system are classified according to two group chains. The calculations are done in the scheme of second quantisation. The results show that the computation of CFP in this way is very efficient.

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.

Fermion dynamical symmetry model of 2s-1d shell

In the framework of shell model, we discussed the fermion dynamical symmetries in 2s-1d shell. Assuming the L-S coupling and the Wigner supermultiplet, we get a U(24) fermion dynamical symmetry. All possible subgroup chains are discussed. We have found that 32S seems to exhibit U(5) dynamical symmetry.

N=4 supersymmetric morse oscillator and its spectrum-generating algebra

In this paper N = 4 supersymmetry of generalized Morse oscillators in one dimension is studied. Both bound states and scattering states of its four superpartner Hamiltonians are analyzed by using unitary irreducible representations of the noncompact Lie algebra su(1,1). The spectrum-generating algebra governing the Hamiltonian of the N = 4 supersymmetric Morse oscillator is shown to be connected with the realization of Lie superalgebra osp(1,2) or B(0,1) in terms of the variables of a supersymmetric two-dimensional harmonic oscillator.

Coefficients of fractional parentage of a boson system with F-spin

Wavefunctions of bosons each with angular momentum I and F-spin 1/2 are classified according to the group chain U(2N) contains/implies (U(N) contains/implies O(N) contains/implies O(3))*SU(2). The boson number, seniority, reduced F-spin, total angular momentum, and total F-spin quantum numbers are used to label the wavefunctions. The corresponding coefficients of fractional percentage (CFP) are factorized into F-spin and angular momentum parts. The F-spin parts are calculated by an analytical formula and the angular momentum parts are calculated by recursion technique. The isoscalar factors of U(2N) contains/implies U(N) contains/implies O(N) and the F-spin part of the CFP for the cases F= Fmax and F=Fmax-1 are given explicitly.

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.

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.