Comment on Macroscopic Analysis of (P,N) Reactions Page: 4 of 10
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_~ 2
--2- -
U =(N--Z) U1/2A (4)
2
In a recent paper one of us (GWH) attempted to extract the isospin
dependent term, U , by simply taking the difference between -the neutron and
proton optical potentials at the neutron and proton energies involved in the
reaction. It was asserted that this procedure describes the energy dependence
208 209
of the (p,n) reaction on . Pb and Bi.- However, the scheme contains
implicit assumptions which need to be spelled out before it can truly be
considered to provide a useful charge-independent form factor. Moreover,
we will show that the success in fitting the (p,n) excitation functions is
due primarily to the use of neutron parameters derived from low energy
neutron elastic scattering rather than from the use of a particular form
factor..-
When a parametrization of the nucleon-nucleus optical potentials over
a range of nuclei and energies has been obtained, U1 may in principle be
extracted in a straightforward way. However, when a parametrization for
only~-a single nucleus is obtained, one is forced to make assumptions con-
cerning the division of the energy dependence between the isoscalar and
isovector parts of the optical potentials. In particular, a typical paramet-
rization of the nuclear optical potentials for the target nucleus, A, is
UA U - U '(Ep) - EU (Ep) + Uc (5) -
U U - U'(E )+EU(E) -(6)
where U contains the explicit energy dependence of the isoscalar part of
U, U is the Coulomb correction term fotthe 3protonpotential due to this -
208
energy dependence and =(N-Z)/4A. The magnitude of U for Pb is nearly
10% of the real part of U and is nearly the.same size as the symmetry term,
U1. To extract an average U from (5) and (6) we have
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Kunz, P. D.; Rickertsen, L. D. & Hoffmann, G. W. Comment on Macroscopic Analysis of (P,N) Reactions, report, January 1, 1973; Boulder, Colorado. (https://digital.library.unt.edu/ark:/67531/metadc1018707/m1/4/?rotate=270: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.