# Bias Effects on g- and s-Factors in Westcott Convention
## 1 Introduction  
Neutron activation analysis (NAA) using well-thermalized neutrons is a powerful tool utilized in various application fields. For NAA, information of neutron capture cross sections for isotopes to be analyzed and a neutron energy spectrum at an irradiation position are required. The energy spectrum of well-thermalized neutrons is approximated to be the sum of two components, a Maxwellian distribution corresponding to neutron temperature \(T_{n}\) and an epithermal \(dE/E\) flux distribution cut off at a suitable lower limit of energy. This flux notation is known as the Westcott convention [1] and is widely utilized in NAA. The neutron activation reaction rate \(\mathrm{R}_{x}\) for the isotope x is expressed as  
\[\mathrm{R}_{x}=\ \mathrm{N}_{x}\cdot\mathrm{\Phi}_{0}\cdot\mathrm{\sigma}_{x0} \cdot\mathrm{(g}_{x}+\mathrm{r}\cdot\mathrm{s}_{x}) \tag{1}\]  
where \(\mathrm{N}_{x}\) is the number of the isotope x, \(\mathrm{\Phi}_{0}\) is the neutron flux, r is the epithermal index that represents the relative strength of the epithermal component, \(\mathrm{\sigma}_{x0}\) is the cross section at 0.0253 eV neutrons, and the g- and s-factors are functions of \(T_{n}\). The g- and s-factors depend on the departure of the cross-section law from the 1/v form (for a 1/v law, g = 1 and s = 0). NAA is also one of the powerful tools determining neutron capture cross sections [2; 3; 4; 5]. In order to improve the accuracy of NAA and/or neutron capture cross sections, a number of improvements have been made. The epithermal \(dE/E\) flux distribution was refined as \(dE/E^{1+\alpha}\)[6], introducing an adjusting parameter \(\alpha\), and the s-factor was revised toreflect the refined form. Recently, finer forms have been proposed by introducing two [7] or three [8] adjusting parameters and were used for accuracy improvement of resonance integrals and s-factor [7]. The cut-off region of the epithermal \(dE/E\) flux component is often approximated by a unit step function, which was introduced in [PERSON]'s report in 1959 [1]. In the revised version of [PERSON]'s report in 1970 [9], several revised forms of \(\Delta_{i}^{W}\) (\(i\) = 1 to 4), called now joining functions, were introduced. The joining function expresses not only a sharp cut-off energy of the \(dE/E\) flux component but also a rather more gradual cut and an additional bump. The systematic effect on the s-factor induced by a change in a joining function from a unit step function was studied for re-evaluation of neutron capture cross section of \({}^{241}\)Am measured by a neutron activation method [10]. Neutron activation analysis for isotopes with a prominent neutron resonance below 0.5 eV as in \({}^{241}\)Am needs a careful analysis taking into account the resonance below 0.5 eV; an experimental technique has been developed to eliminate or reduce the low-energy resonance effect [5]. In the study of resonance integrals or s-factor in [7], adjusting parameters in the joining function \(\Delta_{4}^{W}\) was investigated from the neutron energy spectrum obtained by a detailed Monte Carlo simulation. It is expressed as \(\Delta_{4}^{H}\) in this paper, and its formula is given in Section 2. Although a height of a bump in both forms is almost the same, there is a noticeable difference on a high-energy side tail of the bump up to a few eV. Therefore, in the case of the \(\Delta_{4}^{H}\) form, a bias effect on s-factor and reaction rate might be non-negligible for isotopes if there are huge resonances below a few eV. This paper studies in detail the bias on the s-factor and the reaction rate induced by the joining function form \(\Delta_{4}^{H}\). As the other bias origins on g- and s-factors, neutron temperature dependence has already been studied in the report by [PERSON] [9]. Recently, the neutron temperature effect has been investigated by taking into account [PERSON]'s \(\Delta_{i}^{W}\) functions [11]. An experimental technique to measure neutron temperature was developed because of its importance [12].