Application of simple ramsauer model to neutron total cross sections Page: 3 of 6
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APPLICATION OF A SIMPLE RAMSAUER MODEL
TO NEUTRON TOTAL CROSS SECTIONS
R.W.BAUER', J.D.ANDERSON', S.M.GRIMES2, V.A.MADSEN3
' Lawrence Livermore National Laboratory, Livermore, CA, USA,
2 Ohio University, Athens, OH, USA,
3 Oregon State University, Corvallis, OR, USA
The simple nuclear Ramsauer model has been used successfully to fit neutron total cross
sections for over three decades, but has not been widely used because the foundations of the
model seem so unrealistic. We have shown that the Glauber calculations with the inclusion
of refraction and optical model calculations essentially validate this simple model for neutron
total cross sections in the neutron energy range of 5-50 MeV. This model yields a simple
formula for parameterizing the energy dependence of the neutron total cross section. We
have applied the model to nuclei ranging from vanadium to bismuth. Using the simplest
parameterization, we obtain fits of the data to within 2.5%. With the addition of a single
parameter, we can improve these fits to less than 1.5%.
The original Ramsauer analysis of scattering cross sections was applied to electron scattering
from atoms at energies so low that only a single phase shift, i.e., that for I = 0, was non-
zero. More recently, Lawson' and Peterson have applied the model to total neutron cross
sections at MeV energies. In this situation, clearly a number of phase shifts are non-zero. If
the condition for maximum cross section (S=/2) is met at different energies for different i
values, the energy oscillations in the total cross section will be damped out. Furthermore, the
energy modulations are very sensitive to the magnitude of the imaginary potential. A large
value for the absorptive potential will damp out the oscillations. This damping out, for
example, appears to occur for the absorption cross section for alpha particles.
The early analysis by Peterson2 showed that maxima and minima in the total cross section
having the features of the Ramsauer effect could be observed. Peterson, however, did not
examine the features of the nuclear potential required to produce this behavior. Franco3 used
the Glauber approximation to model the process and determined that the equal phase shift
assumption was not required. It was only necessary that the average phase shift vary slowly
with energy for Ramsauer maxima and minima to occur. Since he did not include refraction
at the nuclear surface, his results did not provide a detailed description of the data.
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Bauer, R.W.; Anderson, J.D.; Grimes, S.M. & Madsen, V.A. Application of simple ramsauer model to neutron total cross sections, article, April 29, 1997; California. (https://digital.library.unt.edu/ark:/67531/metadc691950/m1/3/: accessed April 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.