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the continuum, as done, e.g., in the Gamow shell model.
The introduction of Monte Carlo (MC) techniques has
also permitted the domain of SM studies to be extended
to heavier nuclei.
Perspectives
One can expect that the size of the model spaces that
can be handled by the SM will continue to increase in
the coming years, thanks to computational and to conceptual
developments. This will make this method one
of the main tools to understand the physics of medium
mass nuclei far from stability. Much progress should
also be made in the coming years on the derivation of
effective interactions well suited for the SM in a given
model space. Such derivations will benefit from the
developments that are made for ab initio methods and
should ultimately provide a link between shell model and
QCD-based Hamiltonians. They will greatly benefit from
overlap between the applications that can be handled
by both approaches.
The SM also provides the correlated nuclear wave
functions that are needed for the description of the
nuclear weak processes, either the well established
ones, as the β decays, or the hypothetical ones, linked
to new fundamental physics, like the neutrinoless double
β decay. The modeling of the interaction of dark
matter particles with nuclei will also demand precise
nuclear wave functions for medium-heavy nuclei. Not
least, the SM calculations can provide the microscopic
input needed to model many astrophysical processes
as for instance, supernova explosions and the paths of
nucleosynthesis.
Energy density functional methods
The spectra of medium-heavy and heavy nuclei display a
rich variety of single-particle and collective phenomena.
Their simultaneous description requires large configuration
spaces that exceed what can be numerically handled
in ab-initio methods and in the interacting shell model.
The family of microscopic approaches based on nuclear
Energy Density Functionals (EDF) provides a complete
and accurate description of ground-state properties
and characteristic excitations over the whole nuclide
chart. Currently no other method achieves comparable
accuracy at the same computational cost.
Although EDF methods based on effective interactions
have extensively been used on the self-consistent meanfield
level for more than three decades, this framework
has more recently been reinterpreted as the nuclear analogue
of density functional theory. Nuclear EDF models
coexist on two distinct levels. On the first one a single
product state provides the density matrix that enters
the EDF. The short-ranged in-medium correlations are
integrated out into an energy functional that is formulated
either through a systematic expansion in local densities
and currents representing distributions of matter, spins,
momentum and kinetic energy and their derivatives, or
through a folding with finite-range form factors, and that
in combination with an expansion in powers of nucleon
densities. Both relativistic and non-relativistic realizations
are employed in studies of nuclear matter and finite
nuclei. Correlations are incorporated through breaking
of symmetries of the exact Hamiltonian. On the second
level, often called “beyond mean-field approach”, the
many-body energy takes the form of a functional of all
transition density matrices that can be constructed from
a specific set of product states. This set is chosen to
restore symmetries broken by a single product state or
(and) to perform a mixing of configurations that correspond
to specific collective modes using, for instance,
the (Q)RPA or the generator coordinate method. The
latter includes correlations related to finite-size fluctuations
in a collective degree of freedom, and can be
also used to restore selection rules that are crucial for
spectroscopic observables. Energy functionals have
so far been constructed mostly phenomenologically,
with typically about 10 parameters adjusted to reproduce
empirical properties of symmetric and asymmetric
nuclear matter, and bulk properties of simple, spherical
and stable nuclei.
The most remarkable achievements in the last years
include the development of microscopic mass models,
first systematic large-scale structure calculations that
include long-range correlations associated with largeamplitude
vibrational motion and with the restoration
Q s
(eb)
1
0
-1
-2
74
Kr
yrast exp.
excited exp.
Skyrme prolate
Skyrme oblate
Gogny prolate
Gogny oblate
2 4 6 8
spin (h _ )
Figure 1. Spectroscopic quadrupole moments of shape-coexisting
states in radioactive 74 Kr have been extracted by employing 74 Kr
RIB from the SPIRAL facility at GANIL. Such direct measures of
nuclear shapes represent stringent tests for theoretical models
beyond the mean-field approach and energy density functionals.
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Perspectives of Nuclear Physics in Europe – NuPECC Long Range Plan 2010 | 107