  Population studies of the orbital characteristics of exoplanets in
multi-planet systems have highlighted the existence of an anticorrelation
between the average orbital eccentricity of planets and the number of planets
of their host system, that is, its multiplicity. This effect was proposed to
reflect the varying levels of violence in the dynamical evolution of planetary
systems. Previous work suggested that the relative violence of the dynamical
evolution of planetary systems with similar orbital architectures can be
compared through the computation of their angular momentum deficit (AMD). We
investigated the possibility of using a more general metric to perform
analogous comparisons between planetary systems with different orbital
architectures. We considered a modified version of the AMD, the normalized
angular momentum deficit (NAMD), and used it to study a sample of 99
multi-planet systems containing both the currently best-characterized
extrasolar systems and the solar system, that is, planetary systems with both
compact and wide orbital architectures. We verified that the NAMD allows us to
compare the violence of the dynamical histories of multi-planet systems with
different orbital architectures. We identified an anticorrelation between the
NAMD and the multiplicity of the planetary systems, of which the previously
observed eccentricity-multiplicity anticorrelation is a reflection. Our results
seem to indicate that phases of dynamical instabilities and chaotic evolution
are not uncommon among planetary systems. They also suggest that the efficiency
of the planetary formation process in producing high-multiplicity systems is
likely to be higher than that suggested by their currently known population.
