Fission Product Yield Data for the Transmutation of Minor Actinide ...

4.3. FIVE GAUSSIAN SYSTEMATICS FOR FISSION PRODUCT MASS YIELDS
Systematics of fission product mass distribution
with five Gaussian functions is proposed for
application to minor actinide fission by neutrons
and protons of energies above 100 MeV. This
systematics is also applicable to fission by neutrons
and protons of lower energy and to spontaneous
fission. The mass distributions calculated using the
systematics have been compared with various kinds
of measured data, and good agreement was found.
4.3.1. Introduction
As part of the agreed programme of work for
the IAEA Coordinated Research Project (CRP) on
Fission Product Yield Data for the Transmutation of
Minor Actinide Nuclear Waste we have developed
systematics for fission product mass yields and
collected the measured yield data from experiments
performed in Japan. The data collected were for
243 Am, 241 Am, 237 Np and 248 Cm fission by 25 and
30 MeV protons, and were presented at the
Research Coordination Meeting in 2001. The fission
yield systematics described in this report were
developed in accord with the objectives of the CRP.
Moriyama–Ohnishi [4.3.1] developed systematics
in 1974 using five Gaussian functions for the
description of fission product mass yields, based on
the data available at that time. However, these
systematics fail to reproduce recently measured
fission product mass distributions from high energy
neutron and proton induced fission. The basic
structure of the systematics is unique and is still
usable when suitable parameters in the systematics
are determined from recently measured data.
Therefore, the parameters were examined using
more recently measured data published after the
Moriyama–Ohnishi systematics had been originally
developed. The parameters of five Gaussian
functions were derived [4.3.2] as described in this
section.
4.3.2. Basic structure of present systematics
Mass distribution y(A) in the systematics is
expressed as follows:
Jun-ichi Katakura
Japan Atomic Energy Agency, Japan
y( A) = Nsy s( A) + Nay a(
A)
= Nsy s( A) + Na[ y h1( A) + y l1(
A)
+ F{ y ( A)
+ y ( )}]
h2
l A 2
(4.3.1)
where y s (A) and y a (A) are symmetric and
asymmetric components, respectively. The
asymmetric component y a (A) is split up into a
heavy y h(A) and a light y l(A) component, each of
which consists of two components 1 and 2. Each
component is assumed to be of Gaussian shape:
y
x
1
2 2
( A) = exp{ -( A-Ax) /
2s
x}
2ps
x
(4.3.2)
where subscript x denotes s, h1, h2, l1 and l2, representing
the five Gaussian functions in this systematics.
However, the heavy components y h1 (A) and
y h2 (A) are related to the light components y l1 (A)
and y l2(A) by reflection about the symmetry axis
A s = (A f – v – )/2, where A f is the mass of fissioning
nuclide and v – is the average number of emitted
neutrons. This relationship reduces the number of
independent Gaussian functions to three. As the
total mass yield distribution is normalized to a total
of 200%, the parameters N s and N a are assumed to
have the following form:
N s = 200/(1 + 2R) (4.3.3)
N a = 200R/{(1 + F)(1 + 2R)} (4.3.4)
where R is the ratio of the asymmetric to the
symmetric component, and F is the ratio of the
asymmetric component 1 to the asymmetric
component 2. The above expression of the normalization
assures the total sum of yields to be 200.
As seen in the above expressions for the mass
distribution, there are eight independent
parameters to be determined (v – , R, F, s s , s h1 , s h2 ,
A h1 and A h2 ). We have to investigate whether these
parameters are applicable to the high energy fission
of minor actinides.
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