  We discuss a simple and analytically solvable measurement model which
describes the famous Quantum Zeno Effect (QZE) and Inverse Zeno Effect (IZE),
that correspond to the slow down and to the increase of the decay rate caused
by measurements (or, more in general, by the interaction of an unstable state
with the detector and the environment). Within this model one can understand
quite general features of the QZE and IZE: by considering an unstable quantum
state, such as an unstable particle, whose decay width as function of energy is
$\Gamma(\omega)=g^{2}\omega^{\alpha},$ then -- under quite general assumptions
-- the QZE occurs for $\alpha\in(0,1)$, while the IZE for $\alpha
\in(-\infty,0)\cup(1,\infty).$ This result is valid also for more realistic
measurement models than the one described in this work. We then apply these
considerations to the decay of the neutron, for which $\alpha=5.$ Hence, the
realization of the IZE for the neutron decay (and for the majority of weak
decays) is in principle possible. Indeed, trap experiments find a lifetime that
is $8.7\pm2.1$ s shorter than beam experiments, suggesting that the IZE could
have taken place.
