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

J
Â
K=-J 2 2 2
^
sym Krot ( U, J) = exp(
-K
/ Ko)ª
s
(3.1.8)
while for axially asymmetric deformations (U nuclei
at inner saddle deformations for N > 144 and super
long mode outer saddle):
asym 2
( ) @ 2 2ps^s|
K U
rot
(3.1.9)
where K is the projection of the spin J on the
–1 nuclear symmetry axis, ;
is the spin distribution parameter, and t
is the thermodynamic temperature F | = (6/p 2
·m 2 Ò(1 – 2/3e) in which ·m 2 2 -2
-2
K 0 = ( s| -s
^ )
- 2 s | = Ft |
Ò is the average value of
the squared projection of the angular momentum of
the single particle states and e is the quadrupole
deformation parameter. The other spin cut-off
parameter s 2 ^ is given by the equation:
2
^ ^
2 -2
0
( )
s = F t = 04 . mr 1+ 1/ 3e
(3.1.10)
where F ^ is the nuclear momentum of inertia
perpendicular to the symmetry axis (equals the rigid
body value at high excitation energies (pairing
correlations are completely destroyed), and there
are experimental values at zero temperature so that
interpolations can be made using the generalized
super fluid model equations [3.1.31]. The mass
asymmetry for S1(S2) modes at outer saddles
doubles the rotational enhancement factors, as
defined by Eqs (3.1.8, 3.1.9).
Adiabatic approximation might be valid up to
a critical energy (U r ), with damping of rotational
modes being anticipated by Hansen and Jensen
[3.1.33] at higher excitation energies. The damping
of rotational modes as a function of excitation
energy might differ for axially symmetric and
triaxial nuclei:
ax ( ) -
K U = s 1 F( U)
1
rot
tax
rot
( 2
^ ) +
ax
rot ( ps ) +
( )
K ( U) = K ( U) 2 2 - 1 F( U)
1
-1
FU ( ) = ( 1 + exp( U-Ur)/d r)
.
(3.1.11)
(3.1.12)
(3.1.13)
Shell effects in level density are modelled with
the shell correction dependence of the ‘a’
parameter, as recommended by Ignatyuk et al.
[3.1.31]. The value of the main a parameter is
defined by fitting neutron resonance spacing ·D obs Ò
or systematics [3.1.34], while the shell correction
dependence of the a parameter is defined using the
following equation [3.1.30]:
( ( ) )
Ïa1+
d Wf( U -Econd )/ U -Econd
,
Ô
2
aU ( ) = ÌU
> Ucr = 047 . acrD -mD
Ô
2
aU ( cr ) = £ = -
ÓÔ
acr , U Ucr 047 . acrD mD
(3.1.14)
where m = 0, 1, 2 for even–even, odd-A and odd–
odd nuclei, respectively; f(x) = 1 – exp(–0.064x) is
the dimensionless function defining the damping of
shell effects; condensation energy is E cond =
0.152a cr Δ², where Δ is the correlation function, ã is
the value of the asymptotic a parameter at high
excitation energies, and a cr is the a parameter value
at the excitation energy U = U cr . When ã parameter
values for equilibrium ã n and saddle ã f deformations
are identical, the a f /a n ratio of fissioning and
residual nuclei depends solely upon the respective
shell correction values of dW f(n) taken from
Ref. [3.1.35] (dW n) and Ref. [3.1.28] (dW f). See
Ref. [3.1.9] for more details.
3.1.3. Analysis of fission cross-sections
The observed fission cross-section (s nF (Em))
can be calculated as follows:
sym
asym
nF
s nF (E n ) = s nF + s
= s (E ) + s (E )
nFSL n nF( S1+ S2)
n
nfSL n
X
Âs
n, xnfSL(E
n )
x= 1
s nf ( S1+ S2) n
X
Âs
n, xnf ( S1+ S2)
x= 1
n
= s (E ) +
+ (E ) +
(E )
(3.1.15)
These equations depend on symmetric s nFSL (E n )
and asymmetric s nF(S1+S2) (E n ) fission cross-sections,
and contributions of emissive fission to both terms.
We will show that the contributions of emissive
fission chances are strongly dependent on the
asymptotic value of the a f parameter, while the
branching ratio of symmetric/asymmetric fission
depends on both the contributions of fission
chances and the damping of collective modes at
saddle deformations.
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