The isovector monopole state and the escape width of double analog resonances

An irreducible vector operator is used to generate isovector monopole states with welldefined values of T and T_z in N > Z nuclei. Reduced transition strengths are calculated in two different ways and the results seem compatible. The Wigner-Eckart theorem is used to derive expressions for the mixing of the monopole states with the ground state and its analog states. Expressions for the escape widths of the monopole states are also derived. An application is made to double analog resonances, and it is found, contrary to expectations, that the mixing with the T?1 monopole state is unable to account for the observed elastic partial width of these resonances in medium and heavy nuclei. The reason for this is the small escape width of the monopole state.