Spreading widths of isobaric analog states and the isovector giant monopole resonance

Abstract

A global analysis of the experimental spreading widths Γ ↓ of 65 isobaric analog states (IAS) in the range A = 110 to 238 has been performed assuming isospin mixing via the Coulomb force with T < = T 0−1 doorway states mediated by coupling to the ( T 0−1)-component of the giant isovector monopole resonance (IVM). Excellent agreement has been achieved over the entire range, thus establishing general smooth trends for the parameters describing the resonance. The excitation energy of the resonance, E( IVM)≈V 0/A 1 3 −(T 0+1)V 1/A was found to reproduce the IAS data with V 0 in the range 155 to 170 MeV and V 1≈55 MeV. These values are taken from recent theoretical estimates of Auerbach and the extreme hydrodynamical estimate of Bohr, Damgaard and Mottelson. The charge-dependent matrix elements were found factors of two to three stronger than hydrodynamic or microscopic estimates, but in almost perfect agreement with an expression based on sum rules derived by Lane and Mekjian. A strength-function approach developed by MacDonald and Birse for the damping widths of isovector monopole resonances was successfully employed. However, it became necessary to introduce an explicit dependence on nuclear deformation to describe a splitting of the IVM strength due to coupling to the β-vibration component of the isovector quadrupole resonance (IVQ). The postulated β-dependence describes the strong increase with neutron excess of the spreading widths for several rare-earth nuclei, and an essentially one-parameter fit to all experimental spreading widths gives χ 2/⨍ ≈ 1.2 . It is further concluded that the density of doorway states which are responsible for the isospin mixing is much lower than the density of all underlying states of lower isospin with the same spin and parity as the IAS, and the ratio decreases exponentially with increasing excitation energy.