Some comments on resolution and the analysis and interpretation of experimental results from differential neutron measurements Page: 12 of 32
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It is reasonable to define om as an average over the primary group. Then
Eq. (3) can be generalized to the expression
jW(l,p)dp J<
W(i,p) o(i,p)dp
(11)
The complexity introduced hy the secondary-neutron terms must be dealt with
by approximation. Two approaches are mentioned helow. Selection of a
method depends on the information available and personal preferences.
One possihle approach involves replacing Eq. (11) by
°m ^W(l,P)dP f ^ JW(i,p) oA(i,p)dp
(12)
where oA is an approximation to the true cross section. Since the sec-
ondary neutron energies are lower than those of the primary group, oA can
be deduced from experiment in the following way: The experimenter commences
the experiment at low energy under conditions where the secondary neutrons
arc cither not present or are ineffective. He then proceeds toward higher
energies. Kcsults from the lower energy measurements are used, wlten required,
to calculate higher-onerg> cross sections by means of Eq. (12). This boot-
strap approach is recommended when no information is available on the cross
section at the start of the experiment, however, it assumes that the experi-
menter can span a broad range of energies. This is not always possible.
The bootstrap approach is quite effective for threshold reactions, but is
less satisfactory for reactions such as neutron capture which can exhibit
iarge cross sections at low energy.
A second approach is possible if some prior information on the shape of
the cross section over a wide range of energies is available. This may be
possible if other experiments have been performed or if theoretical calcula-
tions have been made. Starting with Eq. (11),
Y
m
^|w(l,p)dp +Y] Jv
W(i,p) dp
is obtained by algebraic manipulation.
(13)
o (t, P )
o
m
n:
S[E(i,p)]
A__
S.(K )
A m
(14)
Then assume
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Smith, D. L. Some comments on resolution and the analysis and interpretation of experimental results from differential neutron measurements, report, November 1, 1979; Illinois. (https://digital.library.unt.edu/ark:/67531/metadc1092970/m1/12/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.