Advances in Theoretical Nuclear  Physics
The traditional problem in nuclear physics is that nuclear interactions are strong and model dependent. Different models for the strong repulsive force between nucleons (proton and neutrons) at short distances lead to different predictions at high momenta or high virtual energies. The optimal way to deal with these high-momentum parts is to convert the problem first to a low-energy theory. Since short-distance details are not resolved in such a theory, they can be replaced by simpler interactions, while maintaining all low-energy predictions. Then so called “renormalization group” techniques can be used to derive the low-momentum theory[1] in a systematic manner. This is illustrated in figures 1 and 2, where all commonly used microscopic nuclear forces evolve to a universal low-momentum interaction (shown in Fig. 2) after application of the aforementioned procedure.
Figure 1
  
Figure 2
Figure 1.
Different nucleon-nucleon interaction potentials as a function of the relative momentum k of the two nucleons.
Figure 2.
The resulting low-momentum interactions, derived by eliminating the high-momentum (k > 2.1 fm-1) components using renormalization group techniques. The very different interactions in figure 1 become very similar when the high momentum components are eliminated.

An added benefit of this technique is that the low-momentum theory also can be constructed systematically in “chiral effective field theory”[2]. Effective field theory separates nuclear physics from the more complicated problem of hadronic physics, while maintaining a direct connection to the underlying theory of Quantum Chromodynamics. In addition, low-momentum effective interactions are a common feature in modern nuclear many-body developments, where the strong high-momentum modes are systematically removed.

The nuclear many-body problem is extremely rich. It describes systems spanning 18 orders of magnitude in size from nucleons to neutron stars. A significant advantage of low-momentum interactions is that they can be directly applied to nuclear many-body systems with model-independent results and without uncontrolled resummations. For systems with A<100 particles, prime approaches are exact shell model diagonalizations[3] and the coupled cluster method[4] widely used in quantum chemistry. First applications of low-momentum interactions to the nuclear shell model are very promising and provide a microscopic basis for studies of the emergent phenomena of nuclei investigated at ISAC. In nuclear physics, many-body interactions are inevitable. Chiral effective field theory makes it possible to systematically derive three and many-nucleon interactions, with weaker three-nucleon forces for low-momentum theories. As a result, it will be possible to include microscopic three-nucleon interactions beyond the light nuclei. For A>100 particle systems, the method of choice is density functional theory,[5] and its microscopic foundations are now well-understood. Advances for nuclear matter also motivate a program to derive the universal nuclear density functional from microscopic interactions.

These considerations lead to a long-term vision of nuclear theory that is both microscopic and predictive, giving an understanding of nucleonic matter under extreme compositions, temperatures and densities, both on the earth and in stars. This new understanding has many common themes with atomic and condensed matter systems: How does the structure of matter change with its composition? What is the many-body physics of complex and collective phenomena in nuclear systems? How are shape transitions in nuclei and the crust of neutron stars related to frustrated systems and the phase diagram of asymmetric matter? How does nucleonic matter respond to external probes, for instance interactions with neutrinos in supernovae or neutron star cooling? What are the large-scattering length features in nuclear structure, resonant nuclear reactions and neutron matter? Nuclear physics is entereing new and exciting times.•

B.K. Jennings (TRIUMF)
A. Schwenk (NTC, Indiana University)
[1] S.K. Bogner, T.T.S. Kuo and A. Schwenk, Phys. Rept. 386 (2003) 1, S.K. Bogner, A. Schwenk, R.J. Furnstahl and A. Nogga, nucl-th/0504043, A. Nogga, S.K. Bogner and A. Schwenk, Phys. Rev. C70 (2004) 061002(R).
[2] U. van Kolck, Prog. Part. Nucl. Phys. 43 (1999) 337; E. Epelbaum, nucl-th/0509032.
[3] E. Caurier et al., Rev. Mod. Phys. 77 (2005) 427, and references therein.
[4] M. Wloch et al., Phys. Rev. Lett. 94 (2005) 212501, and references therein.
[5] M. Bender, P.-H. Heenen and P.-G. Reinhard, Rev. Mod. Phys. 75 (2003) 121, and references therein.
 

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