Download A new parameter set of fission product mass yields systematics

A NEW PARAMETER SET OF FISSION PRODUCT MASS YIELDS SYSTEMATICS
J. Katakura
Nuclear Data Center, Department of Nuclear Energy Systems,
Japan Atomic Energy Agency (JAEA)
Tokai-mura, Naka-gun, Ibaraki-ken, 319-1195 Japan
The mass yields curve (A,E) is expressed in a similar manner to the Moriyama-Ohnishi
systematics as follows:
 ( A, E )  N s s ( A, E )  N a a ( A, E )
 N s s ( A, E )  N a  h1 ( A, E )   l1 ( A, E )  F  h 2 ( A, E )   l 2 ( A, E ) ,
where s(A, E) and a (A,E) are symmetric and asymmetric components, respectively.
Asymmetric components are then divided into heavy h (A,E) and light l (A, E) components to
give two Gaussian curves (1 and 2). Five Gaussians are produced in this systematics. The three
components: s(A, E) , h1(A, E) and h2 (A,E) in the above equation are expressed as:
1
 s ( A, E ) 
2  s
1
 h1 ( A, E ) 
2  h1
1
 h 2 ( A, E ) 


exp  ( A  As ) 2 / 2 s2 ,
2  h 2




exp  ( A  Ah1 ) 2 / 2 h21 ,
exp  ( A  Ah 2 ) 2 / 2 h22 ,
and the other two functions l1(A,E) and l 2(A, E) for the light fragment are given by reflecting
h1(A, E) and h2 (A,E) about the symmetric axis As  (A f  )/2 . As , Ah1 and Ah2 are the
mass numbers corresponding to the peak positions of the Gaussian distribution curves, and  s ,  h1
2
and  h2 are the dispersions of these distributions. A f denotes the mass number of the fissioning
nuclide, and  is the average number of prompt neutrons emitted per fission. N s, N a and F are
normalization factors to be determined by systematics:
2
2
N s  200 /(1  2 R) ,
N a  200 R /(1  F )(1  2 R),
where R is the ratio of the asymmetric component to the symmetric component, and F is the ratio of
asymmetric component 1 to asymmetric component 2. The total yield is normalized to be 200%. There
2
2
2
are eight parameters to be determined in this systematics: , Ah1 , Ah2 ,  s ,  h1 ,  h2 , R and F .
Expressions for the eight parameters

  1.404  0.1067( A f  236)  14.986  0.1067( A f  236) 1.0  exp( 0.00858E * ),
*
*
where E is the excitation energy ( E  E  BN in which E is the incident energy, and BN is
the binding energy). This expression for  is the same as that proposed by Wahl at the IAEA
Research Coordination Meeting in 1999.
1
R  112.0  41.24 sin (3.675S ) 
BN
1.0
1.0
 0.993
 0.2067 E
 0.0951
0.331
 s  12.6,
 h1  (25.27  0.0345 A f  0.216Z f )(0.438  E  0.333BN 0.333 ) 0.0864
 h 2  (30.73  0.0394 A f  0.285Z f )(0.438  E  0.333BN 0.333 ) 0.0864
Ah1  0.5393( A f   )  0.01542 A f (40.2  Z 2f / A f )1 / 2
Ah 2  0.5612( A f   )  0.01910 A f (40.2  Z 2f / A f )1 / 2
F  10.4  1.44S
where S is the shell energy formula given by Meyer and Swiatecki, which is given by the equation:
S ( N , Z )  5.8s( N , Z ),
1
F ( N )  F (Z )
s( N , Z ) 
 0.26 A 3 ,
2
( 12 A) 3
5
3 5
F ( N )  qi ( N  M i 1 )  ( N 3  M i31 ) , for M i 1  N  M i ,
5
qi  q(n) ,
5
5
3 M i3  M i31

, for M i 1  n  M i ,
5 M i  M i 1
Mi are the magic numbers ( Z = 50, 82, 114 and N = 82, 126, 184); Z 100 and N 164
employed in Moriyama-Ohnishi systematics have been removed in the present systematics.
2

