Relativistic approach to isoscalar giant resonances in ²⁰⁸Pb

We calculate the longitudinal response of ²⁰⁸Pb using a relativistic random-phase approximation to three different parametrizations of the Walecka model with scalar self-interactions. From a nonspectral calculation of the response—which 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, 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 physical excitations. The best description of the collective modes is obtained using a “soft” parametrization having a compression modulus of K=224 MeV.