# Bias Effects on g- and s-Factors in Westcott Convention
## 3 Results and Discussions
### s-Factors for \({}^{241}\)Am and \({}^{151}\)Eu for Sample Temperatures of 300 and 1000 K
Figure 6: (**a**) s-factors, s\({}_{2}^{W}\) (solid line), s\({}_{4}^{W}\) (dotted line), s\({}_{4}^{H}\) (dashed line) for \({}^{241}\)Am as a function of neutron temperature \(T_{n}\), for sample temperatures \(T_{s}\) = 300 K (black) and 1000 K (red); (**b**) Expanded figure of (**a**); (**c**) Ratios of s\({}_{2}^{W}\) (solid line), s\({}_{4}^{W}\) (dotted line), s\({}_{4}^{H}\) (dashed line) between \(T_{s}\) = 300 K and 1000 K; (**d**) Expanded figure of (**c**); (**e**) Ratios of s-factors, s\({}_{4}^{W}\)/s\({}_{2}^{W}\) (dotted line) and s\({}_{4}^{H}\)/s\({}_{2}^{W}\) (dashed line) for \(T_{s}\) = 300 K; (**f**) Expanded figure of (**e**). Figure 7: _Cont._  
Hereafter, results are shown corresponding to the sample temperature of 300 K only, since its effect is small, as discussed for \({}^{241}\)Am and \({}^{151}\)Eu. g- and s-Factors for \({}^{197}\)Au, \({}^{59}\)Co, \({}^{103}\)Rh, \({}^{115}\)In, \({}^{177}\)Hf, and \({}^{226}\)Ra  
A joining function shape effect on g- and s-factor is discussed for other six isotopes, i.e., \({}^{197}\)Au, \({}^{59}\)Co, \({}^{103}\)Rh, \({}^{115}\)In, \({}^{177}\)Hf, and \({}^{226}\)Ra. The calculated g- and s-factors for these isotopes are plotted in Figures 8-13. Figures 8-13 (a) show g-factors, and (b) is the enlarged view of (a) in the neutron temperature region from 250 K to 450 K. Figures 8-13 (c) show s-factors, and (d) is the enlarged view of (c). Figures 8-13 (e) show the ratio of s-factors, that is, \({}^{W}_{4}\)/s\({}^{W}_{2}\) and \({}^{H}_{4}\)/s\({}^{W}_{2}\), and (f) is the enlarged view of (e). The capture cross section of \({}^{197}\)Au is used as the neutron cross section standard at 0.0253 eV, and the 1/v law can be applied well, as shown in Figure 3a. The deviation from the unity of the g-factor is only 0.6% at 0.0253 eV. The absolute value of the s-factor of \({}^{197}\)Au shown in Figure 8c is relatively large compared to that of the other 1/v law isotope \({}^{59}\)Co, since a prominent neutron resonance exists at 4.91 eV. The deviation of s\({}^{H}_{4}\) from \({}^{59}_{2}\) increases from 0% to 10% as the neutron temperature increases from 0 K to 1600 K. This deviation observed in the case of s\({}^{H}_{4}\) is prominent compared to the case of s\({}^{W}_{4}\). The deviation in the case of s\({}^{W}_{4}\) is only about 0.6% at a neutron temperature of 300 K. Considering the large size of the s-factor of \({}^{197}\)Au, a bias induced by a joining function ambiguity exceeds 1%. Since the s-factor of \({}^{197}\)Au is sometimes used as the standard nuclear value to determine other isotopes s-factor or resonance integrals, the bias of about 1% cannot be neglected. It should be noted that the bias increases furthermore as neutron temperature increases. Figure 9a-f show results for \({}^{59}\)Co. The capture cross section of \({}^{59}\)Co is also used as the standard for thermal neutron capture cross sections and resonance integrals. The capture cross section of \({}^{59}\)Co obeys the 1/v raw well, as shown in Figure 3b. Since there is no resonance below 10 eV, the deviation of the g-factor from the unity is extremely small, as shown in Figure 9a,b. The s-factors shown in Figure 9c,d for three joining functions are almost degenerating. As shown in Figure 9e,f, the deviation originating in a joining function ambiguity is less than 0.1% for a wide neutron temperature range. From the results for \({}^{59}\)Co, it is expected that the bias effect originating in a joining function shape is negligible for isotopes obeying the 1/v law well. The order of the bias for isotopes obeying the 1/v law would be roughly estimated from the results of \({}^{197}\)Au and \({}^{59}\)Co. Figure 10a-f show the results for \({}^{103}\)Rh. There is a huge resonance at 1.26 eV in \({}^{103}\)Rh. Therefore, the g-factor increases as neutron temperature increases, as shown in Figure 10a,b. The s-factor also monotonically increases as a function of neutron temperature, as for \({}^{197}\)Au.