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urning can be treated in such a statistical reaction
model, averaging over resonances and individual transitions.
It can describe reaction cross sections as long
as the required input (masses, low-lying states, level
densities, optical potentials, γ-strengths, fission barriers)
are provided or predicted by other models. Even
at stability, the astrophysically relevant low interaction
energies pose a challenge, as there are few data to constrain
the input and also other reaction mechanisms may
compete. This is especially true for explosive burning
producing nuclei far from stability, with low level densities
at the compound formation energy. Where the Hauser-
Feshbach model is applicable, the emphasis is on a
reliable prediction of the input, both at low interaction
energies and far away from stability. Currently, this is
done by macroscopic-microscopic models or by fully
microscopic models.
Both ground and excited states and transitions
among them can be accurately described by the interacting
shell-model which takes all correlations among
valence nucleons into account. This model can even
be used under finite temperature conditions provided
the temperature of the environment is low enough to
allow for a state by state calculation. Currently, due to
computational limitations, the shell-model is restricted
to light or intermediate mass nuclei and to nuclei with a
single closed shell, like r-process waiting point nuclei.
Extensions of this model for heavy nuclei are certainly
needed for future astrophysical applications and to
derive the nuclear physics input necessary for Hauser-
Feshbach calculations. For the description of nuclei near
the drip-line it is necessary to supplement the standard
shell-model by a correct treatment of the continuum.
This can be achieved within the Shell-Model Embedded
in the Continuum and Gamow Shell Model approaches.
These approaches will allow for the calculation of reaction
rates for nuclei where the density of levels is so low
that the Hauser-Feshbach approach is not applicable
any more.
Several astrophysical applications and in particular the
description of weak processes relevant for supernova
evolution require the consistent treatment of finite temperature
and correlation effects, making the Shell-Model
Monte Carlo (SMMC) the natural choice for the description
of thermal properties of nuclei. A hybrid model that
combines SMMC calculations with the Random Phase
Approximation (RPA) approach has been used for the
calculation of electron capture rates for nuclei with A>65
showing that electron capture on these nuclei determine
the evolution of the core of massive stars during the
collapse phase prior to the supernova explosion. Future
applications will require the development of theoretical
models that allow for the calculation of the relevant rates
in a thermodynamic consistent way. First attempts along
this direction have already been done by extending the
proton-neutron Quasiparticle RPA at finite temperatures
by the thermofield dynamics formalism. Extensions of the
model to more realistic interactions and the inclusion of
correlations beyond RPA are expected in the future.
Global calculations of nuclear level densities are either
based on phenomenological approaches like the backshifted
formula or combinatorial models. These models
describe the known data rather well. However, with the
development of new experimental techniques based on
wavelet analysis of giant resonances that allow for the
extraction of level densities of states with good parity
and angular momentum, it is desirable to derive the level
densities in a fully microscopic approach. Shell-Model
Monte Carlo calculations have been very successful
in the description of level densities for medium-mass
nuclei. A future tackling of the sign problem inherent to
fermionic Monte Carlo calculations will permit the use
of realistic interactions and consequently an improved
description of level densities.
The description of ground state properties and particularly
masses for medium and heavy nuclei is currently
based on variations of the Density Functional Theory.
Hartree-Fock-Bogoliubov calculations using the Skyrme
parametrization of the density functional have recently
been able to predict the known masses with a root-meansquare
deviation below 600 keV. The first calculations
based on the non-local Gogny parametrization have been
performed recently. The microscopic nature of these
calculations make them the natural choice for extrapolations
far from the region of known nuclei as demanded
by r-process calculations. Nevertheless, alternative
approaches based on the macroscopic‐microscopic
model and microscopically inspired mass formulas like
the Duflo-Zuker should also be considered given their
current success in predicting known masses. Future
applications of mean-field approaches will focus not only
on the calculations of masses but also on the evolution
of single particle energies. Currently, different functional
parametrizations predict very different single-particle
properties. However, a correct description of these properties
is very important for the determination of direct
contributions to capture reactions that are expected to
be important in the rp-process and r-process far from
stability.
The understanding of r-process nucleosynthesis
represents one of the largest challenges in nuclear
astrophysics. r-process calculations require the determination
of different nuclear properties of several thousand
nuclei. Most of these nuclei have never been produced
in the laboratory and consequently their properties and
relevant reactions must be determined theoretically.
This includes neutron captures, photodissociations
and β-decays. Additionally, in environments with large
neutron-to-seed ratios, fission reactions including neu-
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