Evaluating Quantities of Interest Other Than Nuclide Densities in the Bateman Equations

Figures & data

TABLE I Known Values Provided by Greenwood

${\sigma }_{D,\mathrm{N}\mathrm{i}}$	2180 (eV‧b)	${\sigma }_{D,\gamma ,\mathrm{N}\mathrm{i}}$	2180 (eV‧b)	${\sigma }_{\alpha {,}^{59}\mathrm{N}\mathrm{i}}$	11.6 (b)
${\sigma }_{\gamma ,\mathrm{N}\mathrm{i}}$	4.43 (b)	${\sigma }_{\gamma {,}^{58}\mathrm{N}\mathrm{i}}$	4.6 (b)	${\sigma }_{\gamma {,}^{59}\mathrm{N}\mathrm{i}}$	80.4 (b)
${\sigma }_{\gamma {,}^{60}\mathrm{N}\mathrm{i}}$	2.8 (b)	${\sigma }_{\gamma {,}^{61}\mathrm{N}\mathrm{i}}$	2.4 (b)	$\frac{{\hat{E}}_{\alpha {,}^{59}\mathrm{N}\mathrm{i}}}{{\hat{E}}_{\gamma ,\mathrm{N}\mathrm{i}}}$	349

*Reference 10.

TABLE II Data Used by Griffin for the Damage Calculation to Replicate Greenwood’s 1983 Work

Nuclide	Initial Abundance	${\sigma }_{\gamma }$ (b)	${\sigma }_{\alpha }$ (b)	${\sigma }_D$ (eV‧b)
^58Ni	0.683	4.6	—	2180
^59Ni	—	80.4	11.6	2031 782
^60Ni	0.317	—	—	2180
^56Fe	—	—	—	—

*All data except for the damage-energy cross section for ⁵⁹Ni were collected from Greenwood’s work.¹⁰

TABLE III Total Radiation Damage Values Calculated by Griffin and Greenwood

Fluence $\left(\frac{\mathrm{n}}{\mathrm{c}{\mathrm{m}}^2\cdot \mathrm{s}}\right)$	Griffin (dpa)	Greenwood (dpa)	$\frac{\mathrm{G}\mathrm{r}\mathrm{i}\mathrm{f}\mathrm{f}\mathrm{i}\mathrm{n}-\mathrm{G}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{n}\mathrm{w}\mathrm{o}\mathrm{o}\mathrm{d}}{\mathrm{G}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{n}\mathrm{w}\mathrm{o}\mathrm{o}\mathrm{d}}$
1 × 10^19	2.21187275413709 × 10^–4	2.232 × 10^–4	−0.9018%
5 × 10^19	1.16957935067565 × 10^–3	1.180 × 10^–3	−0.8831%
1 × 10^20	2.49780579147511 × 10^–3	2.520 × 10^–3	−0.8807%
5 × 10^20	1.87438751410419 × 10^–2	1.890 × 10^–2	−0.8261%
1 × 10^21	5.26794967436920 × 10^–2	5.300 × 10^–2	−0.6047%
5 × 10^21	7.91261352108844 × 10^–1	8.090 × 10^–1	−2.1927%
1 × 10^22	2.57858761683475	2.641	−2.3632%
5 × 10^22	2.58209870982475 × 10^1	2.642 × 10^1	−2.2673%
1 × 10^23	5.27007842237555 × 10^2	5.401 × 10^1	−2.4240%
5 × 10^23	1.45120997114276 × 10^2	1.476 × 10^2	−1.6795%
1 × 10^24	1.69428461825151 × 10^2	1.698 × 10^2	−0.2188%

*References 10 and 20.

Fig. 1. Number densities for Greenwood’s test problem computed with Griffin and comparison between Griffin’s and Greenwood’s radiation damage estimates¹⁰ (in units of dpa).

TABLE IV Initial NNDs of the Pressurized Water Reactor Quarter Pin Geometry*

Nuclide	Fuel	Cladding	Helium Gap	Coolant
^1H	—	—	—	4.564169 × 10^–2
^2H	—	—	—	6.847042 × 10^–6
^4He	—	—	2.4044 × 10^–4	—
^16O	4.6388987016955 × 10^–2	—	—	2.285945 × 10^–2
^17O	1.1299982803332 × 10^–4	—	—	8.689893 × 10^–6
^90Zr	—	4.3 × 10^–2	—	—
^234U	9.4547057010024 × 10^–6	—	—	—
^235U	9.6732555765221 × 10^–4	—	—	—
^238U	2.2274213159141 × 10^–2	—	—	—

*In units of $\frac{\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}}{\mathrm{b}\cdot \mathrm{c}\mathrm{m}}$.

Fig. 2. Comparisons of KERMA differences to the Bateman equations: (a) interval difference and (b) cumulative difference.

Fig. 3. Comparisons of fission density differences to the Bateman equations: (a) interval difference and (b) cumulative difference.

Fig. 4. Comparisons of decay energy density differences to the Bateman equations: (a) interval difference and (b) cumulative difference.

L. GREENWOOD, “A New Calculation of Thermal Neutron Damage and Helium Production in Nickel,” J. Nucl. Mater., 115, 2, 137 (1983); https://doi.org/10.1016/0022-3115(83)90302-1.

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