We show that the second-order phase transition between spherical and deformed shapes of atomic nuclei is an isolated point following from the Landau theory of phase transitions. This point can occur only at the junction of two or more first-order phase transitions which explains why it is associated with one special type of structure and requires the recently proposed first-order phase transition between prolate and oblate nuclear shapes. Finally, we suggest the first empirical example of a nucleus located at the isolated triple-point.

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Calculations of nuclear masses, using nuclear density functional theory, are presented for even-even nuclei spanning the nuclear chart. The resulting binding energy differences can be interpreted in terms of valence proton-neutron interactions. These are compared globally, regionally, and locally with empirical values. Overall, excellent agreement is obtained. Discrepancies highlight neglected degrees of freedom and can point to improved density functionals. PACS numbers: 21.30.Fe, 21.10.Dr, 21.60.Jz, 71.15.Mb As with other many-body systems, the structure of the atomic nucleus depends on the interactions of its constituents , protons and neutrons. These interactions, reflecting the strong and Coulomb forces, and the Pauli Principle, are complex. Nevertheless, their understanding is critical to interpreting nuclear structure and its evolution with N and Z. Similar issues arise in other finite complex systems, such as nanostructures, and there is increasing overlap in the theoretical tools applied. In nuclei, where two kinds of fermions come into play, the proton-neutron (p-n) interaction plays the key role in the development of long-range collective correlations, including non-spherical shapes. Due to the shell structure of nuclei, p-n interactions of the valence (open shell) nucle-ons are the most important. Since nuclear masses embody the sum of all nucleonic interactions, they provide a laboratory in which it is possible to isolate and extract specific interactions using appropriate mass differences [1]. In particular, the average interaction of the last two protons with the last two neutrons in an even-even nucleus is given by the following double difference of binding energies [2, 3]: δV pn (Z, N) = 1 4 [{B(Z, N) − B(Z, N − 2)} − {B(Z − 2, N) − B(Z − 2, N − 2)}] (1) With the 2003 mass evaluation [4], it became possible to evaluate a much larger set of δV pn values. These have revealed [5, 6, 7, 8] striking bifurcations near closed shells and systematic patterns spanning major shells [5]; a correlation between δV pn values and growth rates of collec-tivity [6]; and intriguing patterns in specific regions [7]. While simple calculations with schematic zero-range interactions give reasonable results in the deformed rare earth nuclei, they fail completely in the actinides [7]. Clearly, a more sophisticated approach is needed. The indicator (1) involves masses of four neighboring even-even nuclei. Theoretical understanding of the behavior of δV pn throughout the whole nuclear chart thus calls for an approach that is capable of predicting nuclear masses with arbitrary Z, N values. Such an approach must fulfill several strict requirements. First, it should be rooted in microscopic theory. Second, it must be general enough to be confidently applied to regions of the nuclear landscape whose properties are largely unknown. Third, it should be capable of handling symmetry-breaking effects resulting in a variety of intrinsic nuclear deformations. These requirements are met by density functional theory (DFT) in the formu...

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The evolution of collective nuclear structure is discussed from a horizontal perspective, that is, as a function of the number of valence protons and neutrons. Starting from an explicit recognition of the importance of the valence residual p-n interaction in the equilibrium shape and structure of nuclei, the phenomenological N p N n scheme is presented, and validated via an analysis of empirical p-n interaction strengths. Applications of the N p N n scheme are presented which exploit this paradigm of structural evolution. The physics underlying occasional deviations from the N p N n scheme is extracted and new signatures of structure and of nuclear shape components are developed which will be useful for the study of exotic nuclei with radioactive beams. Finally, the smooth correlations of many observables with N p N n leads to a study of the correlations between different collective observables themselves. The remarkable results stemming from this approach are summarized.