S
-D channel, the deuteron, and a virtual state in the
S
channel, the `di-proton', give rise to an additional channel
in the optical potential, the deuteron pickup channel.
Charlotte Elster
Associate Professor, Department of Physics and Astronomy
Ohio University, Athens, OH 45701
I. Research Description
A long standing aim of `classical' nuclear physics has been the application of the nuclear force as obtained from two nucleon data and the prediction of many body phenomena therefrom. During the last years the PI and collaborators have made considerable progress towards this goal in the area of proton and neutron scattering from nuclei at intermediate energies. This progress has partially been due to the rapid developments in high performing computing technologies.
An important goal in the application of multiple scattering theory to nuclear systems is to determine the nonrelativistic optical potential for elastic nucleon-nucleus scattering within the framework of the Spectator Expansion of multiple scattering theory. A consistent ab-initio calculation of the first order term of this expansion implies the construction of `full-folding' optical potentials from realistic single particle wave functions (describing the ground state of the target nucleus) convoluted with nucleon-nucleon (NN) t-matrices (derived from nuclear forces based on meson exchange) as well as the modification of the optical potential through the nuclear medium.
The exact calculation of the optical potential requires a three
dimensional integration, in which the integration variable is coupled to
the energy of propagation of the projectile and target nucleon. This very
fact leads to a full-folding optical potential which treats the
off-shell behavior and the energy dependence of the NN t-matrix
when carrying out the integration. When integrating to negative
energies, the pole structure of the NN t-matrix has to be taken carefully
into account. This pole structure, a true bound state in the
S-D channel, the deuteron, and a virtual state in the
S channel, the `di-proton', give rise to an additional channel
in the optical potential, the deuteron pickup channel.
We calculated elastic scattering observables for 
O, 
Ca,
and 
Pb at projectile energies ranging from 65 to 200 MeV
projectile energy and compared the full calculation to calculations in
which the energy of the NN t-matrix is fixed at half the projectile
energy. We found that this fixed energy prescription describes the full
calculation remarkably well for proton scattering at 200 MeV projectile
energy. For energies below 200 MeV we found that the influence
of the deuteron and di-proton state slowly gains importance as lower
energies are approached.
We also tested the validity of the factorized off-shell `
'
approximation in the energy regime between 65 and 400 MeV and found
that this approximation, which only retains the non-locality
given through the NN t-matrix is even at lower energies a very
good representation of the full-folding calculation based on a
fixed energy in the NN t-matrix as far as the
elastic nucleon-nucleus observables are concerned.
In summary, we performed calculations of the first order optical
potential for nucleon-nucleus scattering consistent within the first
order spectator expansion of multiple scattering theory. Within this
first order term, the effect of the nuclear medium is taken into account
by including the coupling of the struck target nucleon to the residual
nucleus via the same mean field force from which the nuclear density
matrix is derived. One of the most noteworthy results is the correct
prediction of the spin
observables for elastic proton scattering from light (O) as well
as heavy (
Zr, Pb) nuclei as low as 65 MeV. Another
important result is the correct prediction of total cross section
measurements for neutron scattering from light
(
C, O) as
well as heavy (Zr, Pb) nuclei in the energy regime
between 75 and 600 MeV.
In the calculation of the full-folding optical potential the off-shell
structure of the NN t-matrix enters as crucial ingredient. However,
realistic, on-shell equivalent NN potentials have a very similar
off-shell structure close to the on-shell condition, so that off-shell
differences cannot be seen in the elastic observables for
nucleon-nucleus scattering.
Acknowledgment
This work was performed in part under the auspices of the U. S.
Department of Energy under contract No. DE-FG02-93ER40756 with
Ohio University. We thank the Ohio Supercomputer Center (OSC) for
the use of their facilities under Grant
No. PHS206,
the National Energy Research Supercomputer Center
(NERSC) for the use of their facilities
under the FY1996 and FY1997 Massively Parallel Processing Access
Program,
the Pittsburgh Supercomputer Center
(PSC) for the use of their facilities under Grant No. PHY950010P.
We also thank the Arctic Region Supercomputing Center (ARSC) for the
use of their resources, which were made available through the metacenter
regional alliance project funded by the Advanced Scientific Computing
Program of the
National Science Foundation, Award number ASC-9418357.
The calculations were mostly performed on Cray T3E (and earlier on Cray T3D)
Massively Parallel Systems. A smaller fraction was carried out on
the Cray YMP8/64 at OSC.
II. Selected Relevant Publications
O
at 200 MeV projectile energy as function of the momentum transfer q and
the nonlocal, orthogonal variable K.