Relativistic Approach to Isoscalar Giant Resonances in $^{208}Pb$

We calculate the longitudinal response of 208Pb using a relativistic random-phase approximation to three different parameterizations of the Walecka model with scalar self-interactions. From a nonspectral calculation of the response---that automatically includes the mixing between positive- and negative-energy states---we extract the distribution of strength for the isoscalar monopole, dipole, and high-energy octupole resonances. We employ a consistent formalism that uses the same interaction in the calculation of the ground state as in the calculation of the response. As a result, the conservation of the vector current is strictly maintained throughout the calculation. Further, at small momentum transfers the spurious dipole strength---associated with the uniform translation of the center-of-mass---gets shifted to zero excitation energy and is cleanly separated from the sole remaining physical fragment located at an excitation energy of about 24 MeV; no additional dipole strength is observed. The best description of the collective modes is obtained using a ``soft'' parameterization having a compression modulus of K=224 MeV