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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 environments.