46
1 Energy Release in Nuclear Reactions, Neutrons, Fission, and Characteristics …
the total (surface + Coulomb) configuration energy of the nucleus becomes
U T otal = a S A
2/3
Σ S +
15
16
a C
a S
Z
2
A
η
N
2 Σ C
.
(1.116)
With a S = 18 MeV and a o = 1.2 fm, 15a C /16a S ~ 0.0375. These values are
assumed in what follows.
1.12 Results
The publication from which this material is adopted, Reed (2011), describes programs
for carrying out the above calculations. These programs need only be run once, after
which the run of total energy for any (A, Z) as a function of γ can be obtained by
scaling S and C according as (1.116). The programs use a lattice comprising two
million cells: (N Z , N R , N φ ) = (200, 100, 100); this choice was found to provide
both reasonably expedient run times and sensible accuracy. To minimize computation time, the programs assume that the nucleus is axially symmetric, although not
equatorially symmetric. The results of the programs are listings of S and C as
functions of γ ; these have been collected into a spreadsheet, ActivationCurve.xls,
which can be employed to evaluate (1.116) for any choice of (A, Z).
Figure 1.17 shows the deformation energy, that is, the change in total configuration
energy in the sense (deformed nucleus minus original nucleus) versus d/R O for nuclei
of uranium [(A, Z) = (235, 92)] and zirconium [(A, Z) = (90, 40)]. The value of d/R O
at the moment of fission is 1.369; see the discussion following (1.108) above.
-10
0
10
20
30
40
50
60
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Deformation energy (MeV)
d/R o
235 U
90 Zr
Fig. 1.17 Deformation energy curves for 90 Zr (top curve) and 235 U (bottom curve)
1 Energy Release in Nuclear Reactions, Neutrons, Fission, and Characteristics …
the total (surface + Coulomb) configuration energy of the nucleus becomes
U T otal = a S A
2/3
Σ S +
15
16
a C
a S
Z
2
A
η
N
2 Σ C
.
(1.116)
With a S = 18 MeV and a o = 1.2 fm, 15a C /16a S ~ 0.0375. These values are
assumed in what follows.
1.12 Results
The publication from which this material is adopted, Reed (2011), describes programs
for carrying out the above calculations. These programs need only be run once, after
which the run of total energy for any (A, Z) as a function of γ can be obtained by
scaling S and C according as (1.116). The programs use a lattice comprising two
million cells: (N Z , N R , N φ ) = (200, 100, 100); this choice was found to provide
both reasonably expedient run times and sensible accuracy. To minimize computation time, the programs assume that the nucleus is axially symmetric, although not
equatorially symmetric. The results of the programs are listings of S and C as
functions of γ ; these have been collected into a spreadsheet, ActivationCurve.xls,
which can be employed to evaluate (1.116) for any choice of (A, Z).
Figure 1.17 shows the deformation energy, that is, the change in total configuration
energy in the sense (deformed nucleus minus original nucleus) versus d/R O for nuclei
of uranium [(A, Z) = (235, 92)] and zirconium [(A, Z) = (90, 40)]. The value of d/R O
at the moment of fission is 1.369; see the discussion following (1.108) above.
-10
0
10
20
30
40
50
60
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Deformation energy (MeV)
d/R o
235 U
90 Zr
Fig. 1.17 Deformation energy curves for 90 Zr (top curve) and 235 U (bottom curve)