Rigorous Spectral Representation Of Relativistic Random Phase Approximation For Finite Nuclei

The relativistic random phase approximation (RRPA) is one of the mostsuccessful tools for treating nuclear many-body effects in quantum hadrodynamics. It is a rel-ativistic extension of the nonrelativistic random phase approximation and represents the small amplitude limit of the time-dependent relativistic mean-field theory. In the framework of RRPA one can solve the relativistic integral equation, for example the Bethe-Salpeter equation, and obtains the properties of the nuclear many-body system. In the last decade, the RRPA not only yielded good results of the excited state of spheri-cal nuclei around the stable region, but also was widely applied to the description of the isotopes far from theβ-stability line. But a scheme which included the contributions of the exchange term and retardation effects Simultaneously and was able to describe the true finite nuclear system was neglected.One of authors established a three-dimensional relativistic two-body wave equa-tion to replace the four dimensional Bethe-Salpeter equation. The three-dimensional equation is relativistic self-closed and it takes the full retardation effects into account. With the method, a rigorous spectral representation of the RRPA was given. In this RRPA the explicit expressions for the annihilation term, the exchange term and the kernel for the fermion line renormalization(self-energy term) were obtained rigorously in a form that depends only on one energy variable and the retardation effects was taken into account properly. This scheme provides a simpler and more systematic treatment of the RRPA. In order to compare the relative contributions of the above subkernels and the retardation effects, it is desirable to investigate the properties of the finite nu-clei using this scheme. In this paper the rigorous spectral representation of the RRPA is applied to calculate the low-lying excitation states of finite nuclei and its longitudinal and transverse response function for quasielastic electron scattering in the QHDI and QHDⅡmodel.The low-lying excited states of 12C,16O,40Ca and the longitudinal and trans-verse response functions for quasielastic electron scattering off 12C and 40Ca are calcu-lated in the frameworks of the QHDI and QHDII models of quantum hadrodynamics.By using the rigorous spectral representation of the relativistic random phase ap-proximation, the exchange vertex and retardation effects are taken into account simul-taneously and properly. We pointed out that the reproduction of the correct order of the 1- and 3- excited states of 16O is due to the contribution of the exchange vertex. For the excitation of 12C and 40Ca, the affect of exchange term is not more significant than one for 16O, but it lead to an increase of the energies of excitation states in better agreement with the experimental data.There is no significant influence of the retardation effects on the low-lying excited states. On the contrary, the retardation effects plays an important role in the electron scattering process of nuclei. The theoretical longitudinal responses of 12C and 40Ca in-cluding the contributions of the exchange vertex and retardation effects are suppressed and reproduce the experimental data better than the results excluding them. For the transverse responses, the corrections of RRPA are propagated only by theωandρmesons. Theρmeson correlations are weak and theωcouples only to the isoscalar part of the transverse current, so they result in weak correlation for the transverse re-sponses. The exchange term and retardation effects are decline a lettle the amplitude of transverse responses.In QHDⅡmodel, the contribution ofρandπdisappear in relativistic mean field for a isospin symmetric system. But they are not negligible in calculation of excitation states. The theoretical low-lying exacted states and response functions including the contributions ofρandπfits better to the experimental than the results excluding them.