The Study On Giant Resonance Properties Of Nucleus In A Relativistic Approach

Recently,the relativistic mean field theory based on an effective Lagrangian with non-linear meson self-interactions has achieved a great success in describing bulk properties of nuclei,not only spherical but also deformed nuclei and nuclei far from the ft -stable line. It is therefore of interest to investigate the implications of this model for dynamical processes,especially the collective giant resonances. The relativistic random phase approximation (RRPA) is a relativistic extension of the random phase approximation for studying microscopically nuclear dynamical excitations and giant resonances. The consistency of RRPA calculations requires two aspects:first,it demands that the relativistic mean-field wave 'function of nucleus and the particle-hole residual interactions in the RRPA are calculated in a same effective Lagrangian. Second,the consistent treatment of RRPA within RMF approximation requires the configurations including not only the pairs formed from the occupied Fermi states and unoccupied states but also the pairs formed from the Dirac states and occupied Fermi states.Using the fully consistent RRPA method,we have studied the properties of collective multipole excitations for several closed-shell and closed sub-shell nucleus in the isoscalar modes and isovector modes. The results indicate that the effects of the Dirac sea states are pronounced in the collective multipole excitations for nuclei,especially on the isoscalar giant modes,but become weaker for light nuclei,while the contributions on the isovector modes are negligible. The contribution to the giant resonances from the currents of vector mesons are also examined,it shows that currents of vector mesons play an important role in collective giant resonances.By studying the properties of collective multipole excitations of nuclei,a general conclusion is that those effective Lagrangians recently developed can well describe not only the nuclear ground state properties of finite nuclei,stable and unstable ones up to the nuclei drip lines,but also the collective excited states and giant resoancnes in doubly closed shell nuclei. This should be an incentive to apply the RRPA method with non-linear effective Lagrangians to study other systems such asunstable nuclei near drip lines. For nuclei with the extreme value of N/Z,low-lying collective excitations are found in isovector dipole modes,which are mainly due to the particle-hole excitation of weakly bound states near Fermi surface and the isospin mixture effect.Up to now,the method,we used in studying the properties of collective multipole excitations of nuclei,treat the continuum by a discretization procedure with expanding wave functions in a harmonic oscillator basis. This approximation can be justified for very narrow resonances and gives a global description of the contributions from the continuum. A complete treatment of the continuum can be carried out by the continuum RRPA with a Green' s function method. At the other hand,we can perform the RRPA calculation with the continuum replaced by a set of outgoing single particle resonances,it indicates that the resonances in the continuum play an important role in the description of nuclear dynamical processes,such as collective giant resonances.Energies,widths and wave functions of the single particle resonant continuum are determined by solving scattering states of the Dirac equation with proper asymptotic conditions for the continuous spectrum in the r'elativistic mean field theory. The relativistic regular and irregular Coulomb wave functions are calculated numerically. The resonance states in the continuum for some stable nucleus in Sn-isotopes and nucleus in Ca-isotopes are calculated. The results show that the S-matrix method is a reliable and straightforward and feasible way in the determination of single particle resonances.