A Variational Consideration in Analogue Resonances

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It was pointed out by Fujita and Ikeda!) that narrowness of the widths of isobaric peaks represents the validity of the AhrensFeenberg approximation (A.F.), and nonvanishing of the normal allowed fl transition matrix element is due to the deviation from the A.F. approximation (a sort of Random Phase Approximation). The presence of the symmetry-breaking part of the Hamiltonian gives, therefore, a finite value to the width of resonance peak. Recently the normal mode analysis of excited states by using the equation of motion was put into the frame of the modified variational treatment by Sawada.2) In the present paper this method can be applied to the description of isobaric analogue resonance (T _) and Gamow-Teller resonance (Y_), and we shall show that the Coulomb energy shift J and the resonance width r can be derived from a variational . consideration. Commutation relation between the Hamiltonian Hand the relevant transition operator m (for example, T_ and Y_) satisfies, in the A.F. approximation, the following eq ua tion,1l' 8)

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