# 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  
The s-factors for \({}^{241}\)Am are plotted in Figure 6a as a function of neutron temperature \(T_{n}\), for two sample temperatures, \(T_{s}\) = 300 K(black) and 1000 K (red), which are calculated by inserting \(\sigma(E,\ T_{s})\) into Equation (7). The s-factors corresponding to \(\Delta_{2}^{W}(E)\), \(\Delta_{4}^{W}(E)\), and \(\Delta_{4}^{H}(E)\), that is, \(\mathrm{s}_{2}^{W}\), \(\mathrm{s}_{4}^{W}\), \(\mathrm{s}_{4}^{H}\), are shown by solid-, dotted-, and dashed lines, respectively. The difference for two sample temperatures is so small that black and red lines are not separated in Figure 6a. To show the difference between two sample temperatures, the ratios of s-factors are plotted in Figure 6c,d for three kinds of joining functions, indicated by solid-, dotted-, and dashed lines, respectively. The deviation of the ratio from the unity is less than 0.5% for a wide neutron temperature range from 0 K to 1000 K.  
Figure 5: (**a**) Westcott g-factor for \({}^{151}\)Eu as a function of neutron temperature \(T_{n}\), for two sample temperatures, \(T_{s}\) = 300 K(black) and 1000 K (red); (**b**) Expanded figure of (**a**); (**c**) Ratio of Westcott g-factor for \(T_{s}\) = 1000 K to that for 300 K; (**d**) Expanded figure of (**c**). Figure 6: \(Cont\). Contrary to the sample temperature effect, there are noticeable differences between s-factors corresponding to \(\Delta_{2}^{W}(E)\), \(\Delta_{4}^{W}(E)\), and \(\Delta_{4}^{H}(E)\), as shown in Figure 6a,b. Figure 6e,f shows the ratio of s-factors calculated with \(\Delta_{4}^{W}(E)\) or \(\Delta_{4}^{H}(E)\) to that calculated with \(\Delta_{2}^{W}(E)\). The deviation of the ratio from the unity is as large as about 20% for a wide neutron temperature range. In Figure 6b, the expanded version of Figure 6a, the difference between s\({}_{4}^{W}\) and s\({}_{2}^{W}\), and also between s\({}_{4}^{H}\) and s\({}_{2}^{W}\), is clearly shown. A difference of a few % points is also noticed for the ratios between s\({}_{4}^{W}\)/s\({}_{2}^{W}\) and s\({}_{4}^{H}\)/s\({}_{2}^{W}\) in Figure 6e,f. The s-factors for \({}^{151}\)Eu are plotted in Figure 7a-f, as in Figure 6 for \({}^{241}\)Am. As shown in Figure 7a, the s-factor for \({}^{151}\)Eu crosses the zero at about 160 K and 1160 K. To show the difference quantitatively between two sample temperatures, the ratios of s-factors are plotted in Figure 7c,d for three kinds of joining functions, indicated by solid-, dotted-, and dashed lines, respectively. The deviation of the ratio from the unity is about 0.5 to 1.5% in the neutron temperature range from 300 K to 400 K. However, for example, in the case of an epithermal index r = 0.1, this sample temperature effect on a reaction rate is limited to the level in the order of 0.1%, since the absolute value of the s-factor for \({}^{151}\)Eu is small. There is a noticeable difference between s-factors, s\({}_{4}^{W}\)/s\({}_{2}^{W}\), and s\({}_{4}^{H}\)/s\({}_{2}^{W}\), as shown in Figure 7e,f. The deviation of the ratio from the unity seems to diverge at about 160 K and 1160 K. The reason is that the value of the s-factor crosses the zero point at these neutron temperatures. Since the s-factor is close to zero at these points, the effect induced by the deviations on the reaction rate is limited. However, for the important neutron temperature region at about 300-400 K, the deviation from the unity is about 30% in the case of \(\Delta_{4}^{H}(E)\) and strongly varies from 12% to 34% in the case of \(\Delta_{4}^{W}(E)\). This observation demonstrates the importance of a careful determination of the joining function shape.