# Statistical Weighting Factor on thermal neutron importance

The problem is concerning the use of a thermal fluxed squared weighting factor in a thermal reactor.

I have seen in sources the thermal flux in a reactor is squared as a statistical weighting factor, for example looking at temperature feedback. Say a number of thermocouples are measured in a reactor, the weighting of the importance of the thermocouples are to flux squared. Why is this when the reaction rate is equal to the flux? Is it simple statistics I'm not understanding.

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$$\Delta \rho \cong -\frac{\int_V \! \mathrm{d}^3r \phi(\mathbf{r}) \Sigma_a(\mathbf{r}) \phi(\mathbf{r})} {\int_V \! \mathrm{d}^3r \phi(\mathbf{r}) \Sigma_f(\mathbf{r}) \phi(\mathbf{r})}$$

It seems like because of a result of one group perturbation theory. Page 223 of J. Duderstadt Nuclear Reactor Analysis. Since the temperature feedback is changing the thermal utilisation, which is the ratio between the absorbed and utilised thermal neutrons.

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