Interpretation of Weak and Electromagnetic Processes inC12in the Particle-Hole Model

Reasons for the success of the particle-hole approach adopted by O'Connell, Donnelly, and Walecka in the unified interpretation of the semileptonic weak and eletromagnetic processes in the ($A=12\mathrm{}$ nuclear system will be examined. The example of the analyses of $0^{+}$0 ↔ $1^{+}$1 transitions in the context of the particle-hole model (PHM) and the intermediate-coupling model (ICM) brings to light two facts: (1) the nuclear matrix elements relevant to the $0^{+}$0 ↔ $1^{+}$1 transitions do not scale in a unique fashion from the PHM to the ICM; (2) the $0^{+}$0 ↔ $1^{+}$1 processes at low momentum transfer are overwhelmingly dominated by the Gamow-Teller matrix element. The dominance of a set of processes by one nuclear transition operator is the key to the success of the one-parameter scaling of the particle-hole amplitudes used by O'Connell, Donnelly, and Walecka.