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4.4 Nuclear Astrophysics
experience with particle detection and background
suppression at very low energies is beneficial for direct
measurements at astrophysical relevant energies using
recoil separators.
Developments in nuclear theory
and astrophysical modelling
Advances in nuclear theory for astrophysics will be
strongly coupled to the development of improved nuclear
structure theory as described elsewhere in this report.
However, there are a number of specific details which
have to be considered additionally for nuclear astrophysics
or which emphasize slightly different aspects than
those in pure nuclear theory. Nuclear structure models
have to predict nuclear properties required for the calculation
of astrophysical reaction rates (weak rates, β
decays, rates involving the strong and electromagnetic
interaction) and the behaviour of nuclear matter at various
temperatures and densities. Nuclear burning produces
a large range of nuclei from proton- to neutron-dripline
and the goal is to consistently describe their properties.
In general, reaction rates are very sensitive to the nuclear
input and current models lead to quite different predictions
far from stability. For equilibrium conditions (such
as the proposed (n,γ)-(γ,n) equilibrium in the r-process
or the Nuclear Statistical Equilibrium (NSE) reached in
deep layers of ccSN), the required input reduces to separation
energies, ground state properties, and partition
functions. For non-equilibrium reactions (and weak reactions
are rarely in equilibrium) additional information is
required, as outlined below. An additional complication
arises from the fact that nuclei are in thermal contact with
the astrophysical plasma and thus nuclear properties
and reactions are altered through the influence of thermal
population or de-population of excited states.
The description of reactions relevant for nuclear astrophysical
applications greatly depends on the density
of levels available. Several electro-weak processes
involving light nuclei have been computed in the context
of Effective Field Theory. These include an accurate
determination of the pp and hep reactions for hydrogen
burning in the Sun and the calculation of the response of
deuterium to neutrinos necessary for the measurement
of solar neutrinos at the Sudbury Neutrino Observatory
(SNO). Effective Field Theory approaches have also been
used for the determination of realistic nucleon-nucleon
interactions of a quality similar to that obtained by more
phenomenological approaches. From the nuclear astrophysics
point of view a recent relevant development
has been the extension of ab-initio approaches to the
description of astrophysically relevant reactions. Several
reactions including the 2 H(α,γ) 6 Li, 3 H(α,γ) 7 Li, 3 He(α,γ) 7 Be
and 7 Be(p,γ) 8 B have been computed within the Variational
Monte Carlo and No-Core Shell Model approaches.
Figure 7. This figure from a review by Smith and Rehm (Ann. Rev.
Nucl. Part. Sci. 51(2001)130) illustrates how nuclear astrophysics
modelling requires theoretical information is across the chart of
nuclei.
Currently, both approaches assume a potential model
for the description of scattering states and derive the
spectroscopic information of the states involved from a
full ab-initio calculation. The first attempts to extend the
No-Core Shell Model and the Coupled Cluster Model to
open quantum systems are under way and it is expected
that in a few years the first fully ab-initio calculations
of nuclear reactions involving light nuclei will become
available.
Light nuclei are characterized by the existence of
states with a clear cluster structure. The Hoyle state
in 12 C at an excitation energy of 7.764 MeV is probably
the most famous one as it determines the triple α rate.
These states can be described by the nuclear cluster
model that allows for a description of nuclear bound
and scattering states under the assumption that the
many body wave function can be approximated by an
antisymmetric cluster product state. An exciting recent
development has been the extension of cluster models
to include more flexible wave functions and realistic
nucleon-nucleon interactions. These improved models
include the Antisymmetric Molecular Dynamics and the
Fermionic Molecular Dynamics (FMD) and have been
quite successfully applied for the description of nuclear
structure problems. These models are very promising
tools for the description of astrophysically important
nuclear reactions as they combine the flexibility in the
choice of basic wave functions for bound and scattering
states with the virtue of accounting for the relevant
degrees of freedom and correlations among nucleons.
A first exploratory calculation of the 3 He(α,γ) 7 Be reaction
in the FMD approach is already available and additional
applications are expected in the future.
For medium and heavy nuclei where the density of
states is high enough and many resonances contribute,
the most frequently used model is the Hauser-Feshbach
approach. The majority of reactions around stability in
early, advanced, and – to a certain extent – explosive
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