Isospin symmetry-breaking in compound and precompound nuclear reactions

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The preequilbrium formalism of the Unified Theory of Nuclear Reactions serves as the formal framework for studying the consequence of isospin symmetry-breaking. A T-violating generalization of the energy-average fluctuation cross section is obtained by (a) choosing a “chained-partition” representation of the closed-channel Hilbert space, from the “simple” doorway through subspaces of increasing “complexity,” (b) introducing explicitly the symmetry-breaking component of the A-body Hamiltonian, (c) following its effects through the entire formal framework, and (d) applying standard statistical approximations. An isospin-conversion mechanism emerges in an explicit microscopic representation. Its functional relationship to the mean isospin-mixing interaction strength is realized by performing an approximate diagonalization of a realistic subspace and by employing random matrix theory. Our analysis suggests that near “complete” mixing is common in compound as well as some precompound processes and that its energy dependence can be very rapid. Simplifications of the general formula are noted. One by-product is the T-violating version of the Hauser-Feshbach expression involving a single mixing parameter. The relationship of this parameter to the mixing interaction strength is precisely clarified, and an approximate analytic relation is provided. Employing an extended exciton model with isospin properly incorporated, the statistical theory is applied to a comparative study of the photoalpha-particle reactions 28Si( γ, α 0) 24Mg and 30Si( γ, α 0) 30Mg in their giant dipole resonance regions. Although the former is isospin-forbidden, its energy-integrated experimental cross section is about twice that of the latter which is isospin-allowed. This discrepancy is explained.