A statistical method for the study of beta decay giant resonances

Instead of the semi-empirical theory for estimating β-decay strength function, due to Takahashi and Yamada, we consider a formal theory, that of spectral distributions. This theory gives the strength as a bilinear expansion in polynomials, defined by the spectra in the initial and final model spaces, as recently outlined by Draayer, French and Wong. This formally exact theory is approximated in parctice by restricting the expansion to polynomials of low order, and relying on the central limit theorem for convergence. We start our calculation with a simple picture of the β-decay strength, which amounts to considering only the first term in the polynomial expansion, and we calculate β-decay lifetimes for some nuclei. Then we go on to apply techniques developed by Li, Ginocchio and Chang and Wong for evaluating terms up to the central-limit-theorem limit in order to include the correlation of the β-decay operator with the hamiltonian. With the extended theory, we find a more-or-less adequate agreement between theory and experiment. Finally, in order to study the structure of the theory, and to test the validity of certain assumptions made in its application, we consider as a specific example, the Gamow-Teller transition in (ds)5, between (J,T) = (5/2, 3/2) and (3/2, 1/2). The smoothed strength and strength sums evaluated by this distribution method are compared to the shell-model results and satisfactory agreement is found. We expect that the main application of the theory will be to β-decay in heavier nuclei. (orig.)