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

FIG. 4.5.14. Experimental Y(M) (full circles), Y a (M) (open
circles) and Y S (M) (open squares) from the modal decomposition,
and their description Y des(M) (solid lines),
Y a,des(M) (dashed lines) and Y S,des(M) (dash–dotted lines).
Therefore, the proposed two-modal parameterization
can be applied in the development of
fragment mass yield systematics based on six
descriptive parameters: Y a /Y S , M a , s a , s S , g 1 and g 2 ,
the values of which depend on the nucleon
composition of the compound nuclei and incident
particle energy.
4.5.5.1. Description parameters
The calculation of M a values for a given compound
nucleus and particle energy is based on the
following consideration. As noted above, this value
is practically independent of proton energy, so M a =
M a (Z CN ,A). M H,a /Z CN at E p = 10.3 (full circles) and
22.0 MeV (open circles) are shown in Fig. 4.5.15 as
functions of (Z CN ) 2 /A of the compound nuclei: the
experimental points lie on a straight line, which can
be approximated by the linear function:
M H,a = a M A/Z CN + b M Z CN
204
(4.5.12)
where a M and b M are parameters of the systematics.
Uncertainty limits correspond to 0.2 u in M H
FIG. 4.5.15. Ratios of average masses of heavy fragments
from asymmetric fission to atomic numbers of compound
nuclei M H/Z CN as a function of Z CN/A of the compound
nuclei at E p = 10.3 MeV (full circles) and 22 MeV (open
circles).
The mass yield variance for asymmetric fission
(s a) is shown in Fig. 4.5.16 as a function of A (left
hand side) and Z CN (right hand side) of different
compound nuclei for E p = 10.3 and 22 MeV. At both
proton energies, s a is linearly dependent on Z CN;
but within one element, s a is practically
independent of the isotope, reflecting the previous
observation that the Y a(Z F) curves for isotopes of
one element coincide. The difference in the average
s a for isotopes of neighbouring elements (lines on
left hand side of Fig. 4.5.16) increases with
increasing proton energy. We conclude that s a is
mainly dependent on Z CN and on E* = Q R + E part A t /
A (where A t is the target nucleus mass), and can be
described by the following equation:
s a = A/Z CN(Z CN – a a)(b a + c a(E*) 0.25 ) (4.5.13)
where a a , b a and c a are parameters of the
systematics.
Unfortunately we were unable to define a
simple parameterization function for g 1 and g 2 .
However, since these values depend mainly on Z CN
and the range of interest of Z CN for practical applications
is rather narrow (90–98), we have
determined these parameters separately for every
Z CN (see Table 4.5.9).
s S was parameterized on the basis of the well
known equation: s 2 S = θ/C, where θ is the fissioning
nuclei temperature, and C is the stiffness with
respect to mass asymmetric deformations.
Figure 4.5.17 presents the dependence of the
experimental values C on Z CN 2 /A — from Th to Bk,
C can be approximated by the linear function: