  The possibility that the vacuum energy density $\rho_\Lambda$ is, indeed,
varying in time, has been investigated lately from the running vacuum models
perspective. Motivated by such models, in the present work, we relate the
decaying vacuum energy $\rho_\Lambda(t)$ with a scalar field $\phi$. We derive
the equations of motion from such a premise and implement the first-order
formalism in order to obtain analytical solutions to the cosmological
parameters. We show that those are in agreement with recent Planck
observational data. We discuss the physical consequences of having
$\rho_\Lambda(t)$ related to $\phi$.
