An important question in nuclear structure theory is: how reliably can we calculate
the properties of nuclei, using the tools of quantum many-body theory that are at our disposal?

For example, the binding energies of nuclei far from stability are needed to understand the peaks in the
distribution of elements in the universe. Many of these nuclei cannot be measured, and so one relies on
theory. This leads naturally to the question of what theoretical ingredients must be included to get reliable
energies for the nucleosynthesis calculations. In a recent paper, Almudena Arcones and I showed that the
predicted abundances are sensitive to the theorical treatment. In particular the usual self-consistent mean
field theory gives different predictions depending on whether correlation effects are included or not. This
may be seen on the accompanying figure.

The above study was made possible by an earlier work, "Structure of even-even nuclei" . Here we
calculated a variety of nuclear properties across the chart of nuclides, entirely in the framework of a
well-defined computational theory. With a global scope, the theory not only gives predictions for all nuclei,
but its reliability can be assessed by comparing with known experimental data. An example of the work is the
transitions between low excited states and the ground state.
The figure on the left shows the comparison between theory and experiment on the excitation energies in
nuclei having even numbers of protons and neutrons. The figure on the right shows the comparison of the
transition strengths between the lowest excited state and the ground state. Another fundamental property
of nuclei is their size. The next two figures show the comparison between mean field theory and experiment for all measured nuclei. The present theory has an average error of 0.5%, which is much better
than any phenomenological theory. Notice the points in red on the top figure. As a result of our study,
it was determined that the experimental data reported in a compilation was in error. The comparison with the
corrected values is in the lower figure.

The role of pairing in nuclei is still imperfectly understood, despite more than 50 years of study. My first
research paper was an estimate of the many-body effects contributing to the nuclear pairing interaction,
just as phonon exchanges contribute to pairing interaction in superconductors. The paper
"Odd-even mass differences from self-consistent mean field theory"
shows how far we have progressed. The figure
below shows the calculated odd-even binding energy differences as a function of neutron number. The
theory is based on a phenomenological short-range interaction having one adjustable parameter.