Defining “k_f-factors” for threshold reactions

Abstract

The k₀-method (De Corte in The k₀-standardization method: move to the optimization of neutron activation analysis. Habil. Thesis, Ghent University, Belgium, 1987) was developed solely for the use of (n, γ) nuclear reactions in neutron activation analysis. For this, a definition of only the thermal and epi-thermal flux was needed. The fast flux of the fission neutrons was not taken into account although it was considered for primary interferences by De Corte₀. The energy distribution of the fission neutrons can be rather well described by a Watt distribution but is reactor dependent. To complicate things, the activation cross-section behaviour is nuclide dependent. In order to incorporate threshold reactions in the k₀-method we propose to use predefined k_f-factors, measuring the fast flux using a Ni-58 monitor, and to introduce an h-factor that accounts for all deviations for a specific reaction and irradiation facility. It is shown, based on data from Verheijke, that there are useful correlations for Ni-58, Ti-47 and Ti-48. Activation cross section functions indicate that there are possible more relations that might allow h-factors to be predicted.

Appendix 1: Interference corrections factors based on k f’s

Interference reactions can be split in two types:

• 1. (n, p), (n, α) reactions on target elements (b) that result in a product that also is formed by an (n, γ)-reaction on element (a).

• 2. (n, n’), (n, 2n) reactions where the target nuclide is one of the natural occurring nuclides of the element under activation and the product is the same as formed by the (n,γ)-reaction.

Correction for threshold reaction interferences of type 1, when the concentration of the interfering element, c_b, is known becomes:

$${c}_{a}= {c^{\prime}}_{a}-{I}_{b on a}. {c}_{b}$$

(9)

With correction factor for interference:

$${\mathrm{on\,a}\,(\mathrm{n},\upgamma)\,\mathrm{reaction}: I}_{b on a}(g/g)=\frac{{k}_{f,b}}{{k}_{0,a}}\cdot \frac{ {f}_{f,b} {h}_{b,i}}{{{G}_{th,a} f+{G}_{epi,a} {Q}_{0,a}(\alpha )}}$$

(10)

$$\mathrm{on\,a\,threshold\,reaction}:{I}_{b on a}(g/g)=\frac{{k}_{f,b}}{{k}_{f,a}}\cdot \frac{ {h}_{b,i}}{{ {h}_{a,i}}}$$

(11)

Correction for threshold reaction interferences of type 2, when the interfering element is the analyte itself and thus unknown, becomes:

$${c}_{a}= {c^{\prime}}_{a}* {I}_{a}$$

(12)

$$\mathrm{With\,correction\,factor\,for\,all\,interfering\,reactions}, j: {I}_{a}(-)=\frac{ {{G}_{th,a} f+{G}_{epi,a} {Q}_{0,a}(\alpha )}}{{{G}_{th,a} f+{G}_{epi,a} {Q}_{0,a}\left(\alpha \right)+\frac{{f}_{f}}{{k}_{0,a}}\sum {k}_{f,j}{h}_{j,i}}}$$

(13)

The type 2 reaction that can interfere the standard k₀ (n, γ)-reaction most is (n, n’), however (n, 2n) can also be of importance. The most important produced isotopes are Se-77 m, Sr-87 m, Cd-111 m, Sn-117 m, Ba-135 m and Ba-137 m, of which Sn-117 m is causing a serious interference up 50% and more. The proposed k_f’s for most interfering reactions are given in Table 1.