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4.3 Nuclear Structure and Dynamics
of broken symmetries, the description of phenomena
related to the evolution of shell structure in nuclei far from
stability, including new regions of deformation, shape
coexistence and shape phase transitions, applications
to nuclear reactions and fission, predictions of exotic
modes of multipole response in neutron-rich nuclei,
advances in the correct treatment of the continuum,
and accurate global microscopic calculations of the
nuclear input for astrophysical applications.
Perspectives
The main goal of the EDF approach to nuclear structure
in the next decade will be the construction of a consistent
microscopic framework that describes ground-state
properties, nuclear excitations and reactions at a level
of accuracy comparable with experimental results, and
provide reliable predictions for systems very far from
stability, including data for astrophysical applications
that are not accessible in experiments.
Many recent studies have demonstrated that none
of the existing effective interactions or energy density
functionals provides the flexibility needed for a complete
and accurate description of the large body of
nuclear structure data. It seems mandatory to include
higher-order terms, e.g. more complex density functionals
or higher-order momentum dependences, and
three-body terms, and to identify a hierarchy that can
be used as guiding principle. A second open question
is the reliability of extrapolations far from the regions of
the nuclide chart where the parameters of the EDF have
been adjusted. Both issues call for the development of
controlled approximations that will establish a qualitative
and quantitative connection of the nuclear EDF framework
with first principles of the N-body problem and
low-energy QCD in the spirit of EFT, with the ultimate
goal of limiting phenomenology to the final fine-tuning of
the EDF. This would also create a link to similar efforts
currently being made in other branches of nuclear structure,
and open the road towards the construction of a
coherent set of methods for low-energy nuclear physics,
each adapted to the relevant degrees of freedom and
the complexity of a given nuclear system.
The second challenge is the systematic simultaneous
treatment of correlations related to restoration of broken
symmetries and fluctuations in collective coordinates.
The rapid expansion of available computing resources
allows for their explicit treatment in an unprecedented
manner. In order to enable EDF-based models to make
detailed predictions of excitation spectra and electromagnetic
transition rates in medium-heavy and heavy
nuclei with arbitrary shapes and/or characterized by
soft potential energy surfaces, it is important to develop
accurate and efficient algorithms that perform the full
restoration of symmetries broken by the static nuclear
mean field (translational, rotational, particle number) and
take into account fluctuations around the mean-field
minimum for very general shapes.
Third, it would be desirable to establish a connection
to reaction theory that overcomes the limitations of
existing time-dependent mean-field theory and microscopic
optical models, aiming at a unified framework for
the description of structure and reactions of complex
heavy nuclei.
Symmetries in nuclei
and phase transitions
One fundamental goal of nuclear structure physics is
to evidence regularities and simple features of nuclear
spectra, providing a comprehensive understanding of
the origin of such regularities in the complex nuclear
many-body systems. These features are known to be
associated with the so-called dynamical symmetries,
which include both symmetries of the mean field and
symmetries of the residual interactions among the particles,
and which are characterized by definite underlying
algebraic structures. The interest in recent years has
been focused on the search for new dynamical symmetries
(so-called critical point symmetries), associated
with the critical points characterizing the quantum
phase transitions connecting mass regions with different
behavior along chains of isotopes (or isotones)
and named after the corresponding group structure
(E(5), X(5), etc). Possible candidates have been found
in different mass regions, with results not always conclusive,
but most of the other suggested candidates
lie outside the stability region and will be accessible
only by the new radioactive beam facilities. From the
theoretical side, different approaches have been utilized
to describe the phase transitional behavior. The original
seminal papers have used the collective framework
based on the Bohr Hamiltonian. Alternative approaches
have extensively used the Interacting Boson Model while
other approaches have more recently investigated phase
transitions from a more microscopic point of view, as
those based on mean field theories.
Perspectives
The issue of quantum phase transitions in nuclei is far
from being fully explored and great steps are expected
in the coming years on the theory side. The major extensions
will concern the explicit treatment of the nucleus as
a fluid with two components (protons and neutrons) the
treatment of excited states, a generalization to odd-even
systems (treated as a mixture of bosons and fermions).
108 | Perspectives of Nuclear Physics in Europe – NuPECC Long Range Plan 2010