In a previous paper, the convergence of the effective field theory approach of Furnstahl, Serot and Tang to the nuclear many-body problem was studied by applying it to selected doubly-magic, and neighboring single-particle and single-hole, nuclei far from stability. The success of that approach, interpreted through density functional theory, would imply reliable densities. In this paper, the single-particle (Kohn--Sham) wave functions are probed using weak transitions near the Fermi surface. The weak currents are the Noether currents derived from the effective Lagrangian. The general single-particle transition matrix elements, from which any semi-leptonic weak rate can be calculated, are obtained in terms of upper and lower components of the Dirac wave functions. Here beta-decays in nuclei neighboring ¹³²Sn are studied and compared with available experimental data. Calibration of the theoretical results for such decays may also have useful application in element formation.

PACS numbers: 23.40.--s, 23.40.Hc