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.