Workshop on the physics of nucleons and nuclei
Session 5: Threshold physics; narrow states in the continuum; halos; exotic mesons;
excited baryons; coupled channel calculations & continuum shell model
[T. Barnes, V. Burkert, A. Dzierba, T.-S. H. Lee, C. Myers, W. Nazarewicz,
K. Nollett, A. P. Szczepaniak, I. Thompson]
16-17 October 2006, Washington, DC
Today, much interest in various fields of physics is devoted to the study of small quantum
systems (hadrons, nuclei, atoms, molecules, quantum dots, etc.) that are coupled to an
environment of scattering wave functions. Research in nuclear and hadronic physics
beautifully contributes to this program.
Nuclei and hadrons are correlated open quantum systems: their structure and reactions
are profoundly affected by environment, i.e., continuum of decay channels. The
continuum connects structure theory and reaction theory in many ways. First, it impacts
the structure of bound states, especially if many-body correlations give rise to virtual
excitations. Secondly, the continuum is explicitly present above particle production or
cluster breakup thresholds. The positive-energy continuum is often divided into
resonances and non-resonant background. While this division is useful it is also somehow
artificial. Indeed, in many situations the non-resonant amplitude may have peaks or
bumps of dynamical origin that cannot be attributed to fully-fledged resonances.
The major challenge for nuclear theory is to develop theories and algorithms that would
allow a unification of structure and reaction aspects of weakly bound or unbound nuclei
and hadrons. The coupled-channel techniques and modern applications of the continuum
shell model are universal tools that can be used in this context. Possible areas of crossfertilization include spectroscopy, nature of resonances, threshold anomalies, clustering
and exotics, and decay studies.
I. Continuum in nuclear systems
Recent investigations of the role of the positive-energy, many-body continuum in nuclear
structure and reactions are reviewed in the following subsections. Particular attention is
given to neutron-rich systems. This is because the neutron excess strongly affects the
nuclear environment (effective interaction and fundamental excitation modes), and
because in those systems continuum appears particularly low in energy.
A. The halo
As the continuum is approached from below, towards the breakup threshold, one- and
two-nucleon halo nuclei appear near the particle drip lines. These nuclei have large
spatially extended wave functions that reside for much of the time in classically
forbidden regions. The phenomenon of halo remains a symbol of dripline physics; it
involves many-body quantum correlations governed by virtual scattering to the space of
unbound states. Halo nuclei continue to challenge our knowledge of nuclear structure
and few-body dynamics.
B. Three-body continuum dynamics
Above thresholds, three-body systems have been found in which complicated dynamical
correlations and enhancements appear which may or may not be true resonances. The
‘soft dipole’ or ‘pygmy’ resonances in which only the halo neutrons slowly oscillate
against the core have been predicted, however they do not appear as resonances in
calculations explicitly including three-body continuum. In three-body studies of the twoproton radioactivity, it has been found that the pairing interaction in the exterior
correlates protons to enhance the $L$=0 cluster-nucleus relative motion. In spectroscopy
of mirror nuclei, particularly strong Thomas-Ehrman shifts have been seen in two-proton
states that are near or above the continuum threshold.
C. Many-body continuum dynamics
In studies of nuclear systems, we have to learn how to combine the detailed many-body
description in the interior (e.g., provided by the nuclear shell model) with external
scattering boundary conditions for states above the breakup thresholds and how to
calculate nucleon-nucleon effective interactions appropriate for both scattering and bound
states. In very light many-body systems, ab initio methods such as the GFMC and NCSM
can predict resonant and non-resonant wave functions given suitable R-matrix boundary
conditions. For medium mass nuclei, the real-energy continuum shell model in the
Hilbert space formulation can be used to couple interior shell-model configurations to
exterior scattering states. Alternatively, the complex-energy Gamow shell model in the
rigged Hilbert space formulation naturally includes both Gamow resonances and a
nonresonant continuum of scattering states. These modern techniques allow for
calculations of bound and unbound many-body states, including decay widths, and
provide microscopic framework for description of direct nuclear reactions. In heavy
nuclei, HFB framework provides natural starting point. Here, the challenge is to
understand the transition or mapping from the pairing field in mean-field calculations to
real nucleon pairs such as those appearing at large distances in two-neutron halo systems.
D. Barrier penetration
Proton emitters, the narrow resonances beyond the proton drip line, are unique
laboratories of quantum-mechanical tunneling in three dimensions. The theoretical
description in terms of coupled-channels technique provides a wealth of information on
shell structure and wave functions of nuclei in the proton-rich region of the nuclear
landscape. In studies of heavy-ion scattering near the Coulomb barrier, it has been found
that couplings to the rotational or vibrational excited states almost always enhance the
tunneling probabilities by several orders of magnitude over that expected from frozennucleus scattering. Furthermore, the second derivative (d2EF(E)/dE2) of the fusion
excitation functions shows a wealth of ‘signature patterns’ for different characteristic
modes of inelastic excitations. Currently the controversy is on the fusion probability
distribution when one of participants is a halo nucleus and the inelastic modes are
necessarily the breakup channels. The interesting theoretical question to ask is to what
extent the breakup modes are reversible or irreversible. Most (but not all!) experiments
do not show a large fusion enhancement for halo projectiles, but large coupled-channels
breakup calculations are not easy to perform near threshold, and further theoretical work
is needed.
II. Excited baryons
The excited baryon program has two main components. The first one is to establish the
systematics of the baryon spectrum that is crucial for our understanding of these
fundamental building blocks of matter. The second component is to use electron beams to
determine the transition form factors from the nucleon ground state to the known baryon
states. These measurements probe the internal structure of excited states and provide
information about the confining forces of the 3-quark system. The contribution of
nucleon’s meson cloud to the structure of the (1232) resonance have been discovered in
such experiments and similar information on the structure of the Roper resonance has
recently been obtained. Despite these successes, the study of excited baryons continues
to be a challenge in hadron physics.
A. Baryon Spectroscopy
Most known baryon states have been discovered using elastic N  N scattering
analyses before 1980. The widely accepted symmetric constituent quark models based
on (broken) spin-flavor SU(6) and orbital excitation O(3) symmetry predict a large
number of excited states that have currently no clear correspondence in experiments. As
alternatives, it has been shown that the known baryon states fit also in other symmetry
schemes, such as the diquark-quark models, which predict a reduced number of excited
states. The current challenge is to identify some of the higher lying baryon states with
masses of 1.8 to 2.2 GeV. A large experimental effort is currently underway and planned
for the next several years at Jefferson Lab using the CLAS detector to search for some of
these states with linearly or circularly polarized photon beams. In conjunction with
longitudinally (along the beam) and transversely polarized proton and polarized neutron
targets, the search will cover almost all final states N, N, N, K, K, and N, and
provide complete or nearly complete information that is needed to determine the meson
production helicity amplitudes. To process these very extensive data, efficient and sound
methods for performing empirical amplitude analyses are also being developed. These
efforts are absolutely crucial for the completion of the strangeness=0 baryon
spectroscopy portion of the Jefferson Lab N* program.
B. Transition form factors
The measurements of transition form factors for the identified baryon states require
electron beams of sufficiently large energy span to probe the long and short distance
structure of the nucleon. Sufficient momentum transfer is required to separate the 3-quark
confining forces from the more peripheral meson contributions. The program has started
with energies below 6 GeV, and requires the energy doubling of the JLab accelerator to
12 GeV to allow probing the nucleon core at distance scales where constituent quarks
may loose their identity as effective degrees of freedom and contributions from the bare
quarks may begin to emerge. Jefferson Laboratory is the only place where these
experiments can be carried out at modest Q2, and after the 12 GeV upgrade at high Q2.
C. Excited baryon analysis center
The Excited Baryon Analysis Center (EBAC) is providing theoretical support for
experimental baryon spectroscopy and transition form factors programs. A full
understanding of the influence of continuum on hadron structure is crucial for identifying
the true resonance states and interpreting the extracted transition form factors in terms of
quark and meson contributions. At the present time, the focus of the dynamical coupledchannel analyses at EBAC is on a rigorous theretical treatment of the effects of N
channels and interpretations of the extracted N* parameters in terms of constituent quark
models. The major near-term goal is to make connections with Lattice QCD calculations.
EBAC is also working with experimental groups to improve the empirical amplitude
analyses that are needed to obtain first-run results by processing very large amounts of
data.
III. Exotic mesons
Understanding the mechanism underlying confinement of color charges remains as one of
key challenges in modern physics. Hadron resonances dominated by gluonic excitations,
e.g. glueballs and hybrids are expected to have properties, e.g. pole positions and widths,
similar to those of ‘normal’ hadronic resonances. Based on existing data and theoretical
models it is expected that the rate of production of exotics may be comparable to
production of ‘ordinary’ meson resonances of similar mass, like the 2, and photon beams
may be favorable towards the excitation of exotic JPC quantum numbers.
A. Study with CLAS detector
A first experiment to study mesons with exotic quantum numbers in the mass range
below 2 GeV using photon beams up to 6 GeV is scheduled to take data in 2007. There
are also plans to study JPC = 1–+ exotic hybrid mesons in the p and p’ decay modes
using quasi-real photproduction on 4He. The spin-0 and isospin-0 target nucleus
simplifies the partial wave analysis significantly.
B. GlueX program
The GlueX program for Hall D at Jlab targets the light meson spectrum in the mass range
around 2 GeV where both, the lattice gauge theory and models of low energy QCD
predict existence of states with exotic quantum numbers that cannot be attributed to
valence quarks alone. Evidence of exotic mesons have been reported but is not
overwhelming. Photon beam with energy of E ~ 9 GeV, which will be available with 12
GeV upgrade, may be ideal for producing exotic mesons, since at this energy t-channel
Regge recurrences is expected to dominate and may excite virtual quark-anti-quark states
with quantum number that are close but not necessarily identical to that of the photon.
Linear polarization enables to isolate production mechanisms and help in the partial wave
analysis. The GlueX detector is optimized for good geometrical coverage and energymomentum resolution required for partial wave analysis.