Nuclear reaction theory is an integral need for the study of nuclei near
the limits of stability.
First of all, the structure of those nuclei can be strongly affected
by their weakened binding energies, and their theoretical description requires
a unified treatment of bound orbitals and open channels. This directly touches
on reaction theory, which treats the dynamics of the open channels. A unified
description of excited states in weakly bound nuclei and reactions on weakly
bound nuclei is an important goal of contemporary nuclear structure physics.
Indeed, as stated in the NSAC Nuclear Theory Report:
"Tying nuclear structure directly to nuclear reactions within
a coherent framework applicable throughout the nuclear landscape is an important
goal. For light nuclei, ab-initio methods hold the promise of direct
calculation of low-energy scattering processes, including those important
in nuclear astrophysics, and tests of fundamental symmetries. In
nuclear structure for heavier nuclei, the continuum shell model and modern
mean-field theories allow for the consistent treatment of open channels,
thus linking the description of bound and unbound nuclear states and
direct reactions. On the reaction side, better treatment of nuclear structure
aspects is equally crucial. The battleground in this task is the
newly opening territory of weakly bound nuclei where the structure and
reaction aspects are interwoven and where interpretation of future data
will require advances in understanding of the reaction mechanism."
The importance of the particle continuum was discussed in the early days
of the multiconfigurational Shell Model and the mathematical formulation within
the Hilbert space of nuclear states embedded in the continuum of decay channels
goes back to Feshbach. A unified description of nuclear structure and nuclear
reaction aspects is much more complicated and became possible in realistic
situations only recently in the framework of the large-scale Continuum Shell
Model. A promising approach is to expand the space of states to include
Gamow (or resonant) states and the complex non-resonant continuum. The resulting
complex-energy Gamow Shell Model (GSM) is a natural generalization of the
SM concept for open quantum systems. Much work needs to be done in optimizing
the GSM basis to develop the method into a practical tool for heavy nuclei.
There is a second need for reaction theory as a tool to interpret experimental
measurements and extract nuclear structure information. The direct reaction
theory that was developed in the 1960's is still the framework for analyzing
reaction data, but the more extreme conditions that exist close to the drip
lines may invalidate the approximations that are commonly used. Key issues
are the treatment of continuum states and the evolution of optical potentials
for nuclei at the limits of stability. The conventional DWBA method may not
be realistic here. It may be necessary to treat higher-order processes explicitly,
in particular in the analysis of low-energy experiments. The validity of the
eikonal approximation also needs to be examined.The field needs a new generation
of robust computer codes that experimenters can use with confidence to extract
nuclear structure information from cross section measurements.
A new interface is needed between nuclear structure theory and the input
spectroscopic data it can provide for reaction theory. It may be necessary
to replace the notion of a spectroscopic factor with something more useful
over a wide range of conditions. Another approach is treat structure and reactions
on equal footing in a consistent complete calculation.
Three-body breakup reactions of halo nuclei offers a rich set of experimental
observables containing in principle information about the correlations in
the initial nuclei. The development of theoretical techniques is sorely needed
to make use of this information. While the Fadeev method can provide a standard
of accuracy for treating the three-body continuum, it is unclear whether
it is computationally feasible in the halo nucleus context. At the least,
one can develop simplified methods and test them with that theory.
Fusion reactions with nuclei far from stability is another area where the
conventional method (coupled-channels calculations) needs to be revised. The
close vicinity of the continuum in drip line nuclei makes it necessary to
include explicitly the breakup prior to the fusion process in the calculations.
It would be very useful to be able to perform such calculation in order to
test the simplified methods.
Two-nucleon transfer reactions are also potentially of great importance
to nuclear spectroscopy near the limits of stability. Pairing is essential
to nuclear structure, giving importance to a reaction theory that explicitly
treats the pairing correlations. We already have a theory for two-particle
transfer reactions, but developing it to a quantitative tool is still to be
done. Convergence issues and issues of the weak binding of halo nuclei
need to be revisited, and again comparison of more approximate methods with
the Fadeev standard will be helpful.
We would like to develop techniques to determine or constrain low-energy
capture reaction cross sections by indirect methods, using data obtained from
reactions whose cross sections can be more easily measured. An outstanding
example is the use of Coulomb dissociation to infer electromagnetic capture
cross sections. Another indirect method to infer the cross sections for low-energy
neutron capture is the Trojan horse method where the neutron capture is replaced
by a neutron transfer reaction. The reliability of these procedures needs
to be assessed and the conditions where they can be applied needs to be determined.
Can laboratory reactions be used to constrain the nuclear matter equation
of state? This important question has been often posed but the answer is
still not clear. In particular, the isospin dependence of the nuclear matter
binding energy would be invaluable to the construction of the equation of
state for application to dense star cores. We would like to assess the progress
in this area, and compare the constraints obtained by transport measurements
with those obtained from the systematics of structure observables.
Finally, an important goal for the next decade will be to extend the ab
initio efforts on light mass systems to reaction observables, developing
the theoretical tools that will permit accurate calculations of reaction
phenomena such as astrophysical S-factors, break-up cross sections, and
the alpha-capture reactions leading to the production of 12C and 16O in stellar