Strength function for the giant isovector monopole resonance

The theory of the strength function for giant resonances is extended to exhibit the explicit energy dependence of the width and shift functions for the giant isovector monopole. An integral sum rule on the width GAMMA/sub M/(E) relates its normalization to the second moment M2 of the strength function and leads to a relation GAMMA/sub M/(E/sub M/)GAMMA/sub s//4 = M2 between M2 and the width at the maximum, which involves the width GAMMA/sub s/ of the distribution in energy of the spreading matrix elements. An estimate of GAMMA/sub M/(E/sub M/)approx. =8 MeV based on the absorptive part of the optical potential together with random-phase approximation calculations of M2 leads to the result GAMMA/sub s//2approx. =2hω, supporting the intermediate coupling model of Lane, Thomas, and Wigner. Using the sum rule expressions of Lane and Mekjian to evaluate the Coulomb matrix element M/sub A/M between an isobaric analog state and its corresponding isovector monopole, we test this strength function for the isovector monopole by calculating the spreading widths for the ground state analogs of nuclei from 38Cl to 208Pb. The good agreement with the systematic dependence upon mass number and isospin resolves the long-standing discrepancy between the estimate GAMMA/sub M/(E/sub M/)approx.8--10 MeV and the value GAMMA/sub M/(E/sub A/)< or =2 MeV needed to account for the spreading widths of the isobaric analog state