Angular momentum in sub-barrier fusion: Experimental study using the isomer ratioCem137/137Ceg

The ratio of the yields for the isomer (${\mathit{J}}^{\mathrm{\pi }}$=11/$2^{\mathrm{-}}$,${\mathit{t}}_{1/2}$=34.4 h) and ground state (3/$2^{+}$, 9.0 h) of ${}_{}{}^{137}{}_{}{}^{}\mathrm{Ce}$ populated in the reactions ${}_{}{}^{128}{}_{}{}^{}\mathrm{Te}$ ${(}^{12}$C,3n), ${}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}$ ${(}^7$Li,3n), ${}_{}{}^{136}{}_{}{}^{}\mathrm{Ba}$ ${(}^3$He,2n), ${}_{}{}^{136}{}_{}{}^{}\mathrm{Ba}$ ${(}^4$He,3n), and ${}_{}{}^{137}{}_{}{}^{}\mathrm{Ba}$ ${(}^3$He,3n) were measured from energies above the Coulomb barrier to energies typically 20–30% below the barrier by observing the delayed x- and γ-ray emission. In the first three reactions we observed an approximately constant value for the isomer ratio at energies far below the barrier. This indicates an approximately constant average angular momentum at low bombarding energies. We analyze isomer ratios and cross sections using a coupled-channels model for the fusion and a statistical model for the decay of the compound nucleus. Absolute values of the angular momentum J¯ in the entrance channel are deduced from the isomer ratio. The values of J¯ exhibit the behavior predicted for low energies and the expected variation with the reduced mass of the entrance channel.