Epilogue
In this book, extensive microscopic
analyses of elastic scattering of protons at select energies in the range 10 MeV
to 800 MeV and from diverse nuclei (3He to 238U) have
been made as have fully microscopic model calculations of such coordinate space optical potentials describing proton-12C elastic scattering at 18 energies in the range
from 40 to 800 MeV. Both differential cross section and analyzing power data have been predicted at all energies
considered.
The complex optical potentials were
formed by folding effective NN interactions with the density matrices of the ground state
of the target nuclei. For 12C a complete
shell model
calculation provided those density matrices. The effective interactions were
obtained by mapping half-off-shell NN g matrices (solutions of BBG equations) associated with Bonn potentials supplemented above pion threshold
by short ranged Gaussian NN optical potentials so that all NN
scattering phase shifts to over 1 GeV were reproduced. The results of the g-folding process are complex, nonlocal proton-nucleus potentials. Solution of the
integro-differential Schrodinger equations formed with those optical potentials
resulted in good to excellent fits to elastic scattering data at all energies, both
the cross sections and the analyzing powers.
The results confirm the large effect of
the (knock-out) exchange amplitudes in the elastic scattering process and which
make the coordinate space optical potentials nonlocal. In almost all past coordinate
space studies of pA elastic scattering, be they with a Schrodinger,
Dirac or relativistic impulse approximation formulation, inherent exchange amplitudes either have been ignored
or localized.
Although the predictions of the
scattering are good at all energies they are better for energies below pion
threshold than above. Notably at energies above pion threshold, my best results for the forward scattering
angle analyzing powers overpredict the data. This may be due to the treatment
of pion production and resonance effects being too simplistic and not providing
pertinent off-shell properties of the NN t- and g matrices at those energies to specify the appropriate
details of the effective interactions. Nevertheless to analyze the Helium
isotopes, I have used the BCC3 boson exchange model NN interaction
modulated by NN optical potentials with which the SM97 NN
scattering phase shifts to 2.5 GeV were reproduced to specify NN t-
and g-matrices at 800 MeV. Coordinate space effective interaction forms
that map those t- and g-matrices have been determined and then
used in a g-folding process to specify a complex and nonlocal optical potential for 800 MeV protons incident on 3,4He.
The structure of the target used in that folding was determined from a large
space shell model calculation; the ground state wave function of which leads to
an electron scattering longitudinal form factor in good agreement with measured
values. Thereby all quantities required in the folding process were preset to
make solution of the associated nonlocal p-3,4He Schrodinger
equations predictive of the scattering phase shifts, and so of the differential
cross sections and spin transfer observables. The predicted results agree
very well with the observation for momentum transfer values to that at which
the cross section is of the order of 0.1 mb/sr.
The cross section and analyzing power results obtained from the coordinate space nonlocal optical potentials formed by g folding
at 25, 30, and 40 MeV are in quite reasonable agreement with the data obtained
with targets of mass 6 to 238; the 40 MeV results the more so. In general the
cross section predictions give the magnitudes and trends of the peaks in the
data but the minima are too sharply defined.
The comparisons between the calculated results and the data for 25 and
30 MeV proton elastic scattering remain reasonable but the disparities are more
pronounced than at higher energies. Nevertheless, the g folding optical
potentials remain a reasonable first approximation, sufficiently so that the
results may still select between different structure inputs. Also the
associated distorted wave functions and effective interactions still should be appropriate
for use in DWA analyses of inelastic scattering from stable
nuclei, or of radioactive beam ions, as well as of other reaction calculations.
The scattering of 65 to 300 MeV protons
from nuclei remain as the best set with which the g-folding optical potentials give matches to data. Those
data then can be used in analyses to select between diverse options for the
nucleonic based structure of the target nucleus. I have shown how that is
possible with analyses of nucleon scattering from 208Pb for which I had spectroscopy from a
Skyrme-Hartree-Fock description of the nucleus to compare with
what is usually used, a simple packed
shell model representation. A clear preference was noted for
use of the SHF prescription with both magnitudes and shapes of angular
distributions. Of note was the sensitivity of proton scattering to the neutron
matter distribution in 208Pb.
Finally I have used the microscopic
model of nucleon-nucleus optical potential to predict successfully the total reaction
cross sections. As with the predictions of the
angular dependent observables, for optimum results for the
light masses in particular it is essential to use the best (nucleon based) model
specification of nuclear structure available. Marked improvement in results
were obtained when, for 9Be and 12C in this study, complete
shell model calculations were used to define the OBDME required in the folding processes. Of most
significance however is the use of medium modified effective interactions for
predictions to compare well with measured values of the integral observables. Of
note are the variations of the partial reaction cross sections with mass and
energy. They follow very well a simple, three parameter, and functional form.
Those parameters have values that vary smoothly with mass and/or energy
suggesting that the total and total reaction cross sections at energies, and
perhaps for target mass, that have not been measured as yet, may be estimated
with some confidence.
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