  The mass spectra of gas-phase clusters in cluster beams have a rich structure
where the relative heights of the peaks compared to peaks corresponding to
clusters of neighbor sizes reveal the stability of the clusters as a function
of the size $N$. In an analysis of the published mass spectrum of carbon
clusters cations $C_N^{+}$ with $N\leq$16 we have employed the most common
descriptor of cluster stability, which is based on comparing the total energy
of the cluster of size $N$ with the averaged energies of clusters with sizes
$N$+1 and $N$-1. Those energies have been obtained from density functional
calculations. The comparison between the stability function and the mass
spectrum leaves some experimental features unexplained; in particular, the
correlation with the detailed variation of the height of the mass peaks as a
function of size $N$ is not satisfactory. We then propose a novel stability
descriptor which improves matters substantially, in particular the correlation
with the detailed variation of the height of the mass peaks. The new stability
index is based on comparing the atom-evaporation energy of the cluster of size
$N$ with the averaged atom-evaporation energies of clusters with sizes $N$+1
and $N$-1. The substantial improvement achieved is attributed to the fact that
evaporation energies are quantities directly connected with the processes
controllig the cluster abundances in the beam.
