We have deduced compound nuclear isospin mixing in 28 Si* and 26 A1* at excitation energies between 33 and 65 MeV. The 7-ray yield from the decay of giant dipole resonances built on excited states is found to be suppressed, implying that isospin mixing is small. By comparison with data from the literature at lower excitation energy, we conclude that isospin is a better symmetry in these compound nuclei at high excitation energy.PACS numbers: 24.80. Dc, 24.30.Cz, 24.60.Dr, 25.70.Gh Over 30 years ago, Wilkinson predicted that at high excitation energies, the compound nucleus, whose lifetime is determined primarily by the strong interaction, should not live long enough for isospin symmetry to be broken by the relatively weak Coulomb interaction [1], More recently, Kuhlmann [2] and Harney, Richter, and Weidenmuller [3] have proposed that compound nuclear isospin mixing should be characterized by an isospinviolating spreading width F^ which is approximately constant with mass number and excitation energy. This proposal was made on the basis of a large body of data, mostly measurements in different compound nuclei. However, spreading widths deduced from these data scatter over more than 1 order of magnitude [2, 3].The concept of a constant isospin-violating spreading width leads to a definite expectation concerning the excitation energy E* dependence of isospin mixing within a given nucleus. At energies where the compound nuclear decay width F is much greater than D, the level spacing, compound nuclear reaction theory implies that the mixing should depend on T^/F. Hence at high E*, where r ^> r^, the mixing should become small as Wilkinson suggested. At very low E* where F is small, the mixing is weak, on the average, because levels are widely spaced. Thus an additional expectation is that the mixing should be a maximum at energies where F ~ D.Although some previous experiments have suggested a decrease in isospin mixing over a narrow interval in E* (see Ref.[3]), the general form of the energy dependence of isospin mixing has not been demonstrated clearly. An additional motivation for a better understanding of compound nuclear isospin symmetry breaking stems from the recent interest in applying similar concepts to the interpretation of measured and proposed compound-nuclear parity [4] and time-reversal violation experiments [5], These are all examples of a partially broken symmetry in a quantum statistical mechanical system. The underlying symmetry breaking mechanism should be best understood in the case of isospin, making isospin violation a potentially ideal case to study the nature of broken symmetries in complex systems [3].In this Letter we present evidence that isospin mixing is small in 28 Si and 26 A1 compound nuclei at high E*, where F is very large. Our results, when combined with those from other experiments at lower E*, support the predicted energy dependence over a wide range of excitation energies.Our technique involves comparing measured and calculated inclusive 7-ray cross sections for the statistic...
