New energy functional for heavy nuclei – NEWFUN

The theoretical modelling of atomic nuclei has to be based on the interactions between protons and neutrons and the intricacies of many-body quantum mechanics. While recent progress allows for describing light nuclei from first principles, the complexity of heavy nuclei can still only be addressed with approximate methods that limit the modelling to the most relevant degrees of freedom.

The method of choice for the systematic description of all nuclei is the so-called energy-density functional approach that uses proton and neutron density distributions obtained from a quantum-mechanical wave function. Presently used forms of these models do not satisfactorily describe the properties of heavy nuclei in all detail, with the main deficiencies concerning deformation properties and details of the single-particle structure. This problem cannot be solved with improved adjustment protocols for the model's parameters but requires extended forms of the nuclear energy density functional. This project focuses on the impact of higher-order terms in derivatives.

A new extended form of the so-called Skyrme energy-density functional that contains forth-order terms in derivatives has been formulated and implemented into our numerical tools for the description of complex nuclei. This required new developments concerning the efficient representation of the energy functional in terms of generalised nucleonic densities and the analysis of the functional's physics content. The particular mathematical properties of such terms also required the development of dedicated algorithms for the numerical solution of the model equations.

In parallel, we improved the overall efficiency of our numerical tools. These allow now for the systematic calculation of all bound nuclei, thereby enabling unprecedented systematic analyses of the model's predictive power.

Adjusting the parameters of a restricted form of such extended Skyrme EDF to suitable data has been used to improve the description of the bulk properties of nuclei that control the average behaviour of the nuclear binding energy when going from the lightest to the heaviest nuclei and beyond to neutron stars, and also the average deformability of a nucleus. The latter is crucial for the predictive modelling of the potential barriers that stabilise very heavy nuclei against fission.

What has not yet been achieved is bringing a similar improvement to the nuclear shell structure. From what we learned during the project, this will require the inclusion of additional terms of the generalised energy density functional that we neglected so far. Work in that direction is now underway.

The project also catalysed several fruitful collaborations with experimental groups on the interpretation of their new measurements of nuclear masses, charge radii, and electromagnetic moments, that will continue well into the future.

The project aims at the improved theoretical modelling and consistent interpretation of experimental data on very heavy and superheavy atomic nuclei with charge numbers Z greater than 82 and neutron numbers N beyond 126. These finite self-bound systems, many of which owe their very existence to quantal shell effects, exhibit a rich phenomenology of excitation and decay modes that are governed by the competition between the strong nuclear interaction, Coulomb repulsion, surface effects, and quantal shell structure of single-particle states. The available experimental data begin to reveal a consistent picture of their structure in terms of deformed shapes and shells, which at present, however, is not yet satisfactorily described by purely microscopic models. The main deficiency that has been clearly identified, and which is common to all presently available types of effective interactions, concerns the distance between single-particle levels near the Fermi energy. While global trends of observables are unaffected, the description of individual features of specific nuclei is in many cases lacking.

The goal of our project is to arrive at an unprecedented level of accuracy for the theoretical description of very heavy and superheavy nuclei through the adjustment of an effective interaction containing qualitatively new and hitherto unused higher-order terms. The fit of its parameters will take into account information about relevant properties of states of heavy nuclei and be accompanied by an analysis of statistical errors. The resulting interactions will subsequently be employed in systematic symmetry-unrestricted self-consistent mean-field calculations of a wide spectrum of observables of interest addressed in in-beam gamma-ray and conversion-electron spectroscopy, implanted-ion decay spectroscopy, and laser spectroscopy. The results then can be used for the planning and evaluation of experiments at existing and future heavy-ion-beam facilities.

We expect this project to make a decisive contribution to the progress in the theoretical description of the heaviest elements that will expand our understanding of these systems.