  We analyze the dynamics of a Luttinger model following a quench in the
electron-electron interaction strength, where the change in the interaction
strength occurs over a finite time scale $\tau$. We study the Loschmidt echo
(the overlap between the initial and final state) as a function of time, both
numerically and within a perturbation scheme, treating the change in the
interaction as a small parameter, for all $\tau$. We derive the corrections
appearing in, a.) the Loschmidt echo for a finite quench duration $\tau$, b.)
the scaling of the echo following a sudden ($\tau \to 0$) quench, and c.) the
scaling of the echo after an adiabatic ($\tau \to \infty$) quench. We study in
detail, the limiting cases of the echo in the early time and infinite time
limit, and provide scaling arguments to understand these in a general context.
We also show that our perturbative results are in good agreement with the exact
numerical ones.
