Theories and predictions of nucleon-nucleus scattering
The definition of matter profiles and spectra of proton- and neutron rich nuclei is very topical. So also are tests of those specifications by their use in
analyses of scattering data as such (radio-active) nuclei can now be formed as
beams of ions at heavy ion facilities. Of particular importance with scattering is to find credible estimates of their cross sections with hydrogen at all
energies. While scattering of radio-active ion beams (RIBS) from hydrogen is
an empirical (and interesting) study in its own right, it is also a precursor
to an analysis of more complex reaction processes. Another topical interest
is the role played by radioactive neutron (or proton) rich nuclei
in nuclear astrophysics problems. Whatever the objective, from intrinsic
knowledge of unusual nuclei to any of the quite diverse applications, a
detailed understanding of reactions of such nuclei with nucleons at all energies are required. The methodologies that I will describe
span the energy range 0 to 250 MeV (at least) in validity.
The results of numerous applications will be shown, at least for the second
of the two methods I consider.
The first basic scattering theory to be developed is one pertinent for use
in analyzing low energy data (0 to 10 or more MeV, typically). The second is one applicable for higher energies where the density of states in the nucleus
involved is large and with which, an optical potential built upon folding two
nucleon interactions with a ground state density matrix of the nucleus is valid.
Low energy cross sections from the collision of nucleons with nuclei
show sharp as well as broad resonances upon a smooth, energy dependent
background. Those resonances correlate to states in the discrete spectrum
of the target. To interpret such scattering data then requires use of a
complex coupled channel reaction theory. Such a theory has been developed
and forms the MCAS, a multi-channel algebraic scattering theory. The
relevant information, the scattering matrices, are determined therefrom
by matrix methods with the important ingredient being the Green functions for
the scattering. The matrix structure of the inherent Green functions
not only facilitates extraction of the sub-threshold (compound nucleus)
bound state spin-parity values and energies but also readily gives the
energies and widths of resonances in the scattering regime.
The second theory I will develop is that of the g-folding optical potential.
The theory is a first order one involving the two-nucleon g matrices between
a projectile nucleon and each and every nucleon in the nucleus in the collision.
Three ingredients are required to form the attendant complex, energy dependent,
and non-local optical potentials. Those ingredients are the NN g matrices
themselves (or an equivalent effective NN interaction when the optical
potential is to be formed in coordinate space), the bound state wave functions
for single nucleons that fold the effective NN interaction, and the one body
density matrix elements (OBDME) which scale individual nucleon contributions
in the folding. Details of the effective interaction and diverse applications
to scattering from stable nuclei to probe their specifics in structure as well
as in RIB scattering to define matter profiles of halo and non-halo type in
radioactive nuclei will be given. If time allows I will also discuss the
distorted wave approximation for inelastic scattering and show examples of
analyses of such reactions from light mass and exotic nuclei.