Workshop on the physics of nucleons and nuclei
Session 6: Density functionals: effective forces; dense matter; hyperons; EOS
[T. Duguet, R. Furnstahl, P. Guichon, L. Guo, R. Janssens, H. Matevosyan, T.
Papenbrock, J. Stone, A. Thomas]
16-17 October 2006, Washington, DC
1. Overall scientific goals
A major experimental focus for the future is to determine the properties of exotic nuclei:
the evolution of nuclear shell structure as one goes towards more neutron rich nuclei; the
properties of neutron-rich nuclei involved in the r-process; the limits of existence as one
varies the neutron-to-proton ratio; the stability and properties of superheavy nuclei. This
is the fundamental justification for a new rare isotope accelerator, RIA. Apart from the
intrinsic scientific interest, such data will play an important role in nuclear astrophysics,
including the understanding of the structure and properties of neutron stars. In such dense
systems one also expects hyperons to play a significant role and facilities aimed at
measuring the properties of nuclei containing hyperons and here both Jlab and J-PARC
can be expected to play an important role.
On the theoretical side the challenge is to develop energy density functionals, and ideally
a single, unified energy density functional (UNEDF), which is able to reproduce the
results of these new experimental investigations. Of course, as well as describing the new
data such an approach must also reproduce the properties of the nuclei that we already
know, including their bulk properties, low energy excitations, shape coexistence and
fission.
2. General theoretical issues
Nuclei display specific properties that make them particularly challenging quantum
many-body systems. They are self-bound, of finite size and have traditionally been
regarded as being composed of two types of fermions, protons and neutrons. Ultimately,
however, they are eigenstates of the QCD Hamiltonian, with its fundamental degrees of
freedom being quarks and gluons. There is enormous potential for cross fertilization
between nuclear structure and QCD-based hadronic physics. The famous EMC effect
(named after the European Muon Collaboration at CERN) which showed a fundamental
change in the quark structure of bound nucleons may contain vital insight for the nuclear
many-body problem. At high enough densities dense nuclear matter may become quark
matter or even superconducting quark matter and one of our fundamental challenges is to
produce a unified theory across such phase boundaries.
Spontaneous symmetry breaking plays a crucial role in nuclei (translational, rotational,
particle number and time reversal invariance). The inclusion of the kinematic and
dynamic correlations associated with the corresponding Goldstone modes is of particular
importance and still poses some serious conceptual difficulties within energy density
functional (EDF) approaches. There are significant challenges in the many-body physics
needed to describe low-energy nuclear spectroscopy with EDF approaches. Methods such
as QRPA, projected GCM and so on, need to be developed further. In addition, one
would like to develop the microscopic foundations of the EDF approach in terms of chiral
effective field theory, renormalization group methods, realistic two- and three-body
forces and perhaps QCD itself. One would like to see a significant improvement (perhaps
a factor of five) in the accuracy of the predictions of known masses and separation
energies in the near future. As far as unknown nuclei are concerned, the goal is to
enhance the predictive power of the EDF approach through well-quantified uncertainties
and the inclusion of theoretical error bars (from systematic expansions and improved
fitting techniques).
In terms of the formulation of the many-body problem, it will be important to explore abinitio methods for calculating nuclear matter (e.g. Brueckner-Hartree-Fock and
variational chain summation methods), light nuclei (Green Function Monte Carlo and
No-Core Shell Model techniques) or light and medium mass nuclei (Coupled Cluster
methods) and to tie them to the EDF approach. It will be essential to develop a deeper
understanding of the origins of three-body forces or equivalently the density dependence
of the phenomenological EDF; this is an obvious meeting point for nuclear structure and
hadronic physics.
The latter developments will benefit other fields as interdisciplinary connections will be
exploited. Obvious examples are the behaviour of the EDF in the unitary and dilute limits
which are relevant to cold atoms or the connection to EDF approaches to electronic
systems.
The EDF used for finite nuclei will need to describe the properties of nuclei far from
stability sufficiently well that it can be relied on to describe the equation of state needed
in a neutron star surface. Another crucial constraint for the theory will come from an
unexpected source, parity violating electron scattering (PVES), which can provide
crucial, model independent information on the differences between charge and matter
distributions in nuclei. The first experiment of this kind on 208Pb at Jefferson Lab is
eagerly awaited.
In order to reliably treat dense matter it will be essential to treat relativity in a satisfactory
way. In addition, one will need to be able to account for the presence of hyperons and
eventually quark matter. Achieving this in a framework that matches smoothly onto the
usual many-body formulation in terms of a non-relativistic EDF is a great challenge.
3. Essential investments
A next generation advanced facility for rare isotope beams is essential to reach the goals
laid out above. New data in medium mass neutron-rich nuclei are required to constrain
and disentangle current or theoretically improved EDFs. The predictions made with
currently available functionals differ very strongly in the experimentally unknown
territory (regions of nuclei with large neutron-to-proton ratio throughout the periodic
table and superheavy nuclei). Specifically, a divergence occurs as one fills the "next
major shell" when moving along isotopic chains and no experimental constraints are
currently available for this next major shell. Having experimental information on masses,
on the evolution of shells, on the types of collective behaviour and so on, over ten mass
units into the next major shell will certainly be necessary to constrain the predictions of
the models further out towards the drip-line. In that respect, a facility of the next
generation built in the US will have a major impact.
Model independent information on the differences in the distribution of charge and matter
(or protons and neutrons), which can be obtained using PVES will provide extremely
important constraints on what constitutes a realistic EDF. Future work at Jefferson Lab
on hypernuclei, on the nature of short range correlations across the periodic table and on
the microscopic origins of the EMC effect will provide essential information for
understanding the structure of finite nuclei as well as the properties of dense matter. The
study of parton distributions in region x>1, which is forbidden on a free nucleon, will
provide important, quantitative insights into the role of correlations and even multi-quark
configurations in nuclei. In order to effectively exploit these outstanding physics issues it
is essential to proceed with the 12 GeV Upgrade at Jefferson Lab.
From the theoretical perspective it will be important to have state of the art
supercomputers in order to exploit the modern EDFs and the developments in many-body
theory. In order to fully exploit the new experimental facilities one will require
investment in phenomenological support commensurate with the investment in hardware.
This needs to begin with increased support for graduate students and postdoctoral fellows
as well as new faculty positions linked to the physics programs at RIA and Jefferson Lab.