Question 5.5: According to Table 5.8, U-235 is a non-1/v absorber. If its ......

Introduction to Nuclear Reactor Physics [1368692]

According to Table 5.8, U-235 is a non-1/v absorber. If its absorption cross section at 0.025 eV is 681.77 barns, what value should we use for its absorption cross section for the entire thermal energy range? Assume the operating temperature of the fuel is 1000°C.

TABLE 5.8
Non-1/v Factors G(T) for Some Common Nuclear Materials
T (°C)	Cd	Sm-149	X-135	$\frac{U-233}{G_f}$	$\frac{U-233}{G_a}$	$\frac{U-235}{G_f}$	$\frac{U-235}{G_a}$	$\frac{U-238}{G_a}$	$\frac{Pu-239}{G_f}$	$\frac{Pu-239}{G_a}$
30	1.32	1.62	1.16	0.99	1.00	0.98	0.89	1.00	1.05	1.07
100	1.60	1.89	1.21	0.99	1.00	0.96	0.96	1.00	1.11	1.16
200	1.96	2.09	1.23	0.99	1.00	0.94	0.95	1.00	1.25	1.34
400	2.56	2.18	1.19	1.00	1.00	0.92	0.93	1.00	1.69	1.89
600	2.90	2.08	1.09	1.00	1.01	0.91	0.92	1.01	2.20	2.53
800	3.05	1.92	0.99	1.01	1.02	0.90	0.92	1.02	2.66	3.10
1000	3.06	1.76	0.89	1.02	1.03	0.89	0.91	1.02	3.00	3.54
Source: Lamarsh, J.R. and Baratta, A.J., Introduction to Nuclear Engineering, Prentice Hall, Upper Saddle River, NJ, 2001.

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Its absorption cross section for the entire thermal energy range is $σ_a = G \times σ_a$ (0.025 eV). Since the value of G is 0.91 when the flux is Maxwellian, the absorption cross section we should use is $σ_a$ = G × 681.77 = 630.40 barns.

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