= Solution
The first equation is a prescribed first-order removal law. For a constant absorption coefficient,
$$
\frac{dN_{\rm Th}}{N_{\rm Th}}=-\sigma_{a\rm Th}\phi(t)\,dt.
$$
Integrating from the initial condition gives
$$
\ln\frac{N_{\rm Th}(t)}{N_{\rm Th0}}=-\sigma_{a\rm Th}\int_0^t\phi(t')\,dt',
$$
and hence
$$
\boxed{N_{\rm Th}(t)=N_{\rm Th0}e^{-\sigma_{a\rm Th}\Phi(t)}.}
$$
The <neutron fluence> $\Phi$ is the time integral of scalar <neutron flux>; it has inverse-area units, making $\sigma\Phi$ dimensionless. Constant flux is not needed for this integration, but a constant effective coefficient is.
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