Our current work has two distinct foci:
A. Multi-Channel Algebraic Scattering Theory (MCAS). This research focuses on the interaction of nucleons (protons and neutrons) or mass-3 and mass-4 nuclei with light and medium-mass nuclei. A method of coupled channels is used to obtain detailed information about the scattering of these systems, as well as the structure of the compound nuclei formed as bound states of the projectile with the target nucleus. With the advent of Radioactive Ion Beam (RIB) experimental facilities, such as ISAC and ISAC-II at TRIUMF, where beams of unstable, radioactive nuclei can be produced and accelerated, the range of nuclei that is subject to detailed experimental study has increased enormously. We are no longer confined to the narrow valley of stable nuclei in the chart of the nuclides, but can travel up the slopes and even plateaus of radioactive nuclei to either side, out to the proton and neutron drip lines. The drip lines are where the nuclei become unstable to emission of either protons or neutrons. Using a recently (2003) developed methodology for Multi-Channel Algebraic Scattering (MCAS), such unstable nuclear systems can also be studied by theory which has some predictive power. For example, in a 2006 Physical Review Letter, we published results for the proton-unstable nucleus 15F that showed, not only a particle-unstable ground state, but several narrow resonances at higher energy. Such states have now been confirmed experimentally in a paper published by Mukha, et al. in June, 2009. The MCAS procedure treats scattering of nucleons (in the future possibly also light nuclear clusters) from light- to medium-mass nuclei. The method can also deal with the target nucleus having particle-unstable excited states. The method having been tested for well-known stable systems, is now being applied to unstable systems, also nuclei at and beyond the drip lines. These studies are useful, not only to the experimentalists at RIB facilities, but also to astrophysicists, since we can provide reliable information on radiative capture (fusion) processes at very low energies for nuclear systems important to stellar evolution and nucleogenesis MCAS is a development based on older work by Pisent and myself in 1987, 1989 and 1995 on resonances in nuclei (see publications) and the application of some techniques of few-body physics (see B., below) to many-particle problems, notably the use of separable interactions and sturmian expansions. Within this theory, we consider scattering of nucleons off nuclei, allowing for coupling to excited states of the target nucleus. The target nucleus, at present, is described by a collective model, but the MCAS method allows for satisfying the Pauli principle, by the use of Orthogonalizing Pseudopotentials (OPP), which can readily be included in the MCAS process. MCAS has a number of desirable features, in addtion to the ability to maintain the Pauli principle within a collective model. A process is available for locating all resonances, no matter how narrow, or wide, and determining the widths, and finding all subthreshold bound states of the compound system. The method yields the full S-matrix, so all sorts of elastic- and inelastic-scattering observables can be calculated, including spin observables.
The MCAS theory was first tested and applied to neutron scattering from 12C, finding all the resonances to 6 MeV, and bound states, and calculating the total elastic scattering cross sections. The parameters of the collective model were adjusted to fit the well-established experimental cross section. Since then, without further adjustment of the model parameters, we have calculated the scattering of protons from 12C and polarizations in both neutron and proton scattering. We have also obtained excellent agreement with recently measured analysing powers in n + 12C scattering. We have now moved to other nuclear systems, in particular systems away from the line of stability. One, on mass-15 nuclei, demonstrated how narrow states can form in a nucleus, such as 15F, which is particle unstable. This is in agreement with recent experimental data, and we predict further narrow states above the maximum energy of those experiments. To achieve this result, we introduced a new concept of Pauli hindered configurations, to take into account that single-particle levels may be partially filled. Another work on the mass-7 nuclei from the neutron drip line to the proton one has been published. See the publications from 2003 to the present.
B. Few-Body Physics. I have worked on few-body problems for over 25 years. My most recent work in this field has been on pion absorption and production on very light nuclei, in collaboration with the Padova group. The work is on pion absorption on the deuteron and the three-nucleon system with two-cluster final states. This uses the same basic mechanisms and input on (πN), (NN) and (πNΔ) interactions as in the deuteron problem The three-nucleon system is treated exactly in a Faddeev-based theory. Final-state interactions are correctly taken into account. Several papers reporting on this work have been published; see the publications list.
My former Ph.D. student, Thomas Melde, completed a thesis (2001) on the
complete coupled three-body to four-body theory of the
πNNN-NNN system, which has been developed by members
of the collaboration in Padova.
These papers elaborate the complicated set of coupled
integral equations for this problem, but these are too complicated
to allow for exact solutions in the foreseeable future.
With Dr. Melde, we have developed approximations and calculational
techniques for the solution of these equations for a simplified,
schematic, one-dimensional toy model. This gave us experience
in the structure of the equations and have proved useful in developing methods
for treating more realistic problems.
In particular, we discovered that the approximation scheme including the
presence of a dynamical pion in the three-nucleon system
yields structures that resemble what is traditionally considered three-nucleon
forces, but the equations include additional
trerms of a topologically different structure that, till now, had not been
included in considerations of the three-nucleon force.
These new terms show the potential to solve long-standing problems in the
theoretical calculations of the three-nucleon system.
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