Nuclear compressibility and the isoscalar monopole resonance in a relativistic continuum random phase approximation

The distribution of isoscalar monopole strength is calculated in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ using the Dirac-Hartree random phase approximation. The resulting strength has a wide distribution and the average energy is lower than one would expect from the high compressibility coefficient in nuclear matter inherent in the relativistic theories. The distribution of the monopole strength has several peaks but only the highest peak in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ can reliably be related to the ‘‘breathing’’ mode and thus to the nuclear compressibility.