Restoration of Isospin Symmetry in Highly Excited Nuclei

Explicit relations between the isospin mixing probability, the spreading width $\Gamma_{IAS}^{\downarrow}$ of the Isobaric Analog State (IAS) and the statistical decay width $\Gamma_c$ of the compound nucleus at finite excitation energy, are derived by using the Feshbach projection formalism. The temperature dependence of the isospin mixing probability is discussed quantitatively for the first time by using the values of $\Gamma_{IAS}^{\downarrow}$ and of $\Gamma_c$ calculated by means of microscopic models. It is shown that the mixing probability remains essentially constant up to a temperature of the order of 1 MeV and then decreases to about 1/4 of its zero temperature value, at higher temperature than $\approx$ 3 MeV, due to the short decay time of the compound system.