Theory Research On Pseudospin Symmetry

We firstly summarized some nuclear structure models, and then introduce relativistic mean field theory (RMF) and its application to spherical nuclei. At Last the characteristics of pseudospin symmetry are researched in details. It briefly includes several following aspects:(1) Some nuclear models such as liquid drop model, Fermi gas model, shell model, project shell model and Bohr model are summarized.(2) RMF theory was introduced intensively. By using Euler-Lagrange equation, Dirac equation for nucleon, Klein-Gordon equation for mesons and electric-magnetic equation for photons are obtained from the general RMF lagrangian which describes nucleon, mesons and photons.(3) Based on RMF theory, the origin of pseudospin symmetry was intensivelyexplained and the conditions which can meet the ideal pseudospin symmetry werepresented. The conditions are Σ = 0 or dΣ/dr = 0 . By numerically solving Diracequation with Woods-Saxon potential, the characteristics of pseudospin splitting with the variation of Woods-Saxon potential s three parameters: the depth of nuclear potential, nuclear radius and nuclear diffusivity were analyzed. Some conclusions about pseudospin symmetry were obtained. Because the variations of parameters for R and V₀ are related with the number of nucleon and the parameter for diffusivity describes the characteristics of nuclear surface, all the conclusions obtained by us are meaningful to analyze nuclear properties.(4) Because the exact pseudospin symmetry which requires the condition ofΣ = 0 or dΣ/dr= 0 means that Dirac Hamiltonian is invariant in su(2)transformation, We present the uniform representation of pseudospin doublets in pseudospin space.