In 1956 A. Kerman explained the observed energy levels of the lowest K = 1/2 and K = 3/2 bands in 183W as resulting from rotational perturbations due to the effects of the Coriolis force. Following from that seminal paper, in this work we consider Kerman's problem when one of the Nilsson single-particle levels involved is a resonant state. This is the simplest model of Coriolis mixing that allows for analytical expressions derived in first-order perturbation theory, without losing the main physical ingredients of the continuum effects. We present results for the perturbed solution of the ground state band energies as a function of the state width, which suggest a general behavior of both increased moment of inertia and staggering.

While the phenomenon of one- and two-neutron ground-state halo nuclei is well established, the effects of weak binding on nuclear excitation properties remain largely unexplored. Motivated by this question and by recent data in 40Mg we investigate the coupling of weakly bound (halo) valence neutrons to a core using the known properties of 40Mg to explore and illustrate possible particle-core coupling schemes and their impact on the low-lying excitation spectrum.

Spectroscopic strengths for the 18Fg,m(d,p)F19 reactions to members of the ground-state band in F19 are interpreted in the rotational model. The analysis considers two different coupling schemes, namely, the strong and decoupled limits of the particle rotor model to describe the ground and isomeric states of F18, as well as the transitions to the ground-state band in F19. Our results, obtained using Nilsson amplitudes for the neutron levels 12[220], 32[211], and 52[202] calculated at a deformation ϵ2=0.32 are in agreement with the measurements and USDB shell-model calculations.

Recent results from RIKEN/RIBF on the low-lying level structure of 29F are interpreted within the Particle-Rotor Model. We show that the experimental data can be understood in the Rotation-aligned Coupling Scheme, with the 5/2+ ground state as the bandhead of a decoupled band. In this picture, the energy of the observed 1/21+ state correlates strongly with the rotational energy of the core and provides an estimate of the 2+ energy in 28O. Our analysis suggests a moderate deformation, ϵ2∼0.16, and places the 2+ in 28O at ∼ 2.5 MeV.

In a recent experiment, carried out at the Radioactive Isotope Beam Factory/RIKEN, the F25(p,2p)O24 reaction was studied at 270 MeV/A in inverse kinematics. Derived spectroscopic factors suggest that the effective core of F25 significantly differs from a free O24 nucleus. We interpret these results within the particle-rotor model and show that the experimental level scheme of F25 can be understood in the rotation-aligned coupling scheme with its 5/21+ ground state as the bandhead of a decoupled band. The excitation energies of the observed 1/21+ and 9/21+ states correlate strongly with the rotational energy of the effective core, seen by the odd proton, and allow us to estimate its 2+ energy at ≈3.2MeV and a moderate quadrupole deformation ϵ2≈0.15. The measured fragmentation of the πd5/2 single-particle strength is discussed, and some further experiments suggested.

The superfluid tunneling model is applied to the calculation of ground-state-to-ground-state α decay in the even-even neutron-deficient Te-Ba nuclei. We show that there is a larger α-particle formation probability in nuclei of this region above Sn100 when compared to analogous nuclei above Pb208. This is consistent with the expected systematic variation of the pair gap Δ as a function of mass number. The recent experimental data on the α decay of the N=Z nuclei Te104 and Xe108 are shown to leave open the possibility of enhanced α-particle formation involving nucleon correlations beyond the standard treatment of like-nucleon pairing, which is the mechanism suggested as underlying "superallowed" α decay.

Spectroscopic factors, extracted from one-neutron knockout and Coulomb dissociation reactions, for transitions from the ground state of Mg33 to the ground-state rotational band in Mg32, and from Mg32 to low-lying negative-parity states in Mg31, are interpreted within the rotational model. Associating the ground state of Mg33 and the negative-parity states in Mg31 with the 32[321] Nilsson level, the strong coupling limit gives simple expressions that relate the amplitudes (Cjℓ) of this wave function with the measured cross sections and derived spectroscopic factors (Sjℓ). To obtain a consistent agreement with the data within this framework, we find that one requires a modified 32[321] wave function with an increased contribution from the spherical 2p3/2 orbit as compared to a standard Nilsson calculation. This is consistent with the findings of large-scale shell model calculations and can be traced to weak binding effects that lower the energy of low-ℓ orbitals.

We discuss a phenomenological shell model analysis of the structure of 48 , 49 , 50Ca. Based on simple arguments, we propose wavefunctions fit to the available data on spectroscopic factors derived from direct one neutron addition and removal reactions. These empirical wavefunctions are then used to calculate properties of low-lying states in 49 , 50 , 51Ca, which are consistent with available experimental data. Our analysis appears to capture the main ingredients at play in the low-lying properties of these nuclei and emphasize the prominent role of pairing correlations. We also present predictions that could motivate further work.

The superfluid tunneling model is applied to the calculation of half-lives of the observed α decays in N=84 isotones. Results of our calculations are compared to experimental data on the ground-state α decays along the isotonic chain from Nd144 to Re159. Good agreement is found. The α decays of the known high-spin isomers in Lu155, Hf156, Ta157, and W158 are also well reproduced, once a reduction in the pairing strength is taken into account. This includes reproduction of the main features of the recently observed fine structure from Lu155(25/2-) and Hf156(8+). Predictions for the α-decay fine structure of Ta157(25/2-) and W158(8+) high-spin isomers are presented.