1.8 Energy Spectrum of Fission Neutrons
27
0.0
0.1
0.2
0.3
0.4
0
2
4
6
8
1 0
Probability
Neutron energy (MeV)
Fig. 1.6 Energy spectrum of neutrons released in fission of 235 U
∞
0
P(E) d E = 1 ⇒ K
∞
0
√
E e
−E/α d E = 1.
(1.65)
Setting x =
√
E/α renders this as
2K α
3/2
∞
0
x
2 e
−x
2 dx = 1.
(1.66)
This integral evaluates to
√ π/4, hence
K =
2
√ π α 3/2 .
(1.67)
To determine the mean neutron energy E, we take a probability-weighted
average of E over all possible energies:
E =
∞
0
E P(E) d E = K
∞
0
E
3/2 e
−E/α d E.
(1.68)
Again setting x =
√
E/α renders this in dimensionless form as
27
0.0
0.1
0.2
0.3
0.4
0
2
4
6
8
1 0
Probability
Neutron energy (MeV)
Fig. 1.6 Energy spectrum of neutrons released in fission of 235 U
∞
0
P(E) d E = 1 ⇒ K
∞
0
√
E e
−E/α d E = 1.
(1.65)
Setting x =
√
E/α renders this as
2K α
3/2
∞
0
x
2 e
−x
2 dx = 1.
(1.66)
This integral evaluates to
√ π/4, hence
K =
2
√ π α 3/2 .
(1.67)
To determine the mean neutron energy E, we take a probability-weighted
average of E over all possible energies:
E =
∞
0
E P(E) d E = K
∞
0
E
3/2 e
−E/α d E.
(1.68)
Again setting x =
√
E/α renders this in dimensionless form as