$\beta$-decay rates of ${}^{121–131}\mathrm{Cs}$ in the microscopic interacting boson-fermion model

$\beta$-decay rates of ${}^{121–131}\mathrm{Cs}$ have been calculated in the framework of the neutron-proton interacting boson-fermion model (IBFM-2). For odd-$A$ nuclei, the decay operator can be written in a relatively simple form in terms of the one-nucleon transfer operator. Previous studies of $\beta$ decay in IBFM-2 were based on a transfer operator obtained by using the number operator approximation (NOA). In this work a new form of the one-nucleon transfer operator, derived microscopically without the NOA approximation, is used. The results from both approaches are compared and show that the deviation from experimental data is reduced without using the NOA approximation. Indications about the renormalization of the Fermi and Gamow-Teller matrix elements are discussed. This is a further step toward a more complete description of low-lying states in medium and heavy nuclei which is necessary to compute reliable matrix elements in studies of current active interest such as double-$\beta$ decay or neutrino absorption experiments.

Figure 1

Excitation spectra of Cs and Xe isotopes for positive parity. The energy of the first ${\frac{7}{2}}^{+}$ state was taken as the zero of the energy. Lines correspond to calculated energies, and experimental data (symbols) were extracted from [18].

Figure 2

Log $ft$ values from $1/2_1^{+}$ states in Cs isotopes to (a) $1/2_1^{+}$ and (b) $3/2_1^{+}$ states in Xe isotopes.