We examine the general nature of nuclear odd-even mass differences by employing neutron and proton mass relations that emphasize these effects. The most recent mass tables are used. The possibility of a neutron excess dependence of the staggering is examined in detail in separate regions defined by the main nuclear shells, and a clear change in this dependency is found at Z = 50 for both neutrons and protons. A further separation into odd and even neutron (proton) number produces very accurate local descriptions of the mass differences for each type of nucleons. These odd-even effects are combined into a global phenomenological expression, ready to use in a binding energy formula. The results deviate from previous parametrizations, and in particular found to be significantly superior to a recent two term, A −1 dependence.

We investigate the emergence of halos and Efimov states in nuclei by use of a newly designed model that combines self-consistent mean-field and three-body descriptions. Recent interest in neutron heavy calcium isotopes makes ^{72}Ca (^{70}Ca+n+n) an ideal realistic candidate on the neutron dripline, and we use it as a representative example that illustrates our broadly applicable conclusions. By smooth variation of the interactions we simulate the crossover from well-bound systems to structures beyond the threshold of binding, and find that halo configurations emerge from the mean-field structure for three-body binding energy less than ∼100  keV. Strong evidence is provided that Efimov states cannot exist in nuclei. The structure that bears the most resemblance to an Efimov state is a giant halo extending beyond the neutron-core scattering length. We show that the observable large-distance decay properties of the wave function can differ substantially from the bulk part at short distances, and that this evolution can be traced with our combination of few- and many-body formalisms. This connection is vital for interpretation of measurements such as those where an initial state is populated in a reaction or by a beta decay.

We investigate even-even two-proton Borromean systems at prominent intermediate heavy waiting points for the rapid proton capture process. The most likely single-particle levels are used to calculate three-body energy and structure as a function of proton-core resonance energy. We establish a linear dependence between two-and three-body energies with the same slope, but the absolute value slightly dependent on partial wave structure. Using these relations we estimate low-lying excited states in the isotones following the critical waiting points. The capture rate for producing a Borromean bound state is described based on a full three-body calculation for temperatures about 0.1-10 GK. In addition, a simple rate expression, depending only on a single resonance state, is found to comply with the three-body calculation for temperatures between 0.1 and 4 GK. The rate calculations are valid for both direct and sequential capture paths. As a result the relevant path of the radiative capture reactions can be determined. We present results for E1 and E2 photon emission, and discuss occurrence preferences in general as well as relative sizes of these most likely processes. Finally, we present a method for estimating proton capture rates in the region around the critical waiting points.

We combine few-and many-body degrees of freedom in a new computationally efficient model applicable to both bound and continuum states and adaptable to different subfields of physics. We formulate a self-consistent three-body model for a core nucleus surrounded by two valence nucleons, where the core is treated in the meanfield approximation and the same effective Skyrme interaction is used between both core and valence nucleons. We apply the model to 26 O, where we reproduce the known experimental data as well as phenomenological models with more parameters. The decay of the ground state is found to proceed directly into the continuum without effect of the virtual sequential decay through the well-reproduced d 3/2 resonance of 25 O.

The challenging nuclear many-body problem is discussed along with classifications and qualitative descriptions of existing methods and models. We present detailed derivations of a new method where cluster correlations coexist with an underlying mean-field described core structure. The variation of an antisymmetrized product of cluster and core wave functions and a given nuclear interaction, provide sets of self-consistent equations of motion. First we test the technique on the neutron dripline nucleus 26 O, considered as 24 O surrounded by two neutrons. We choose Skyrme effective interactions