关键词: 非中心电耦极矩/
赝自旋对称性/
Dirac方程/
三对角化表示
English Abstract
Tridiagonal representation with pseudospin symmetry for a noncentral electric dipole and a ring-shaped anharmonic oscillator potential
Gao Jie,Zhang Min-Cang
1.College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710119, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 14101020155) and the Fundamental Research Funds for the Central Universities, China (Grant No. GK201402012).Received Date:31 July 2015
Accepted Date:28 September 2015
Published Online:20 January 2016
Abstract:The concepts of pseudospin symmetry in atomic nuclei and spin symmetry in anti-nucleon are reviewed. The exploration for understanding the origin of pseudospin symmetry and its breaking mechanism, and the empirical data supporting the pseudospin symmetry are introduced. A noncentral anharmonic oscillatory potential model is proposed, in which a noncentral electric dipole and a double ring-shaped component are included. The pseudospin symmetry for this potential model is investigated by working on a complete square integrable basis that supports a tridiagonal matrix representation of the Dirac wave operator. Then, solving the Dirac equation is translated into finding solutions of the recursion relation for the expansion coefficients of the wavefunction. The angular/radial wavefunction is written in terms of the Jacobi/Laguerre polynomials. The discrete spectrum of the bound states is obtained by diagonalization of the radial recursion relation, and the property of energy equation is discussed for showing the exact pseudospin symmetry. Several particular cases obtained by setting the parameters of the potential model to appropriate values are analyzed, and the energy equations are reduced to that of the anharmonic oscillator and that of the ring-shaped non-spherical harmonic oscillator, respectively. Finally, it is pointed out that the exact spin symmetry exists also in this potential model.
Keywords: noncentral electric dipole/
pseudospin symmetry/
Dirac equation/
tridiagonal representation
