New low-mass members of Chamaeleon I and $\epsilon$ Cha
  The goal of this paper is to increase the membership list of the Chamaeleon
star forming region and the $\epsilon$ Cha moving group, in particular for
low-mass stars and substellar objects. We extended the search region
significantly beyond the dark clouds. Our sample has been selected based on
proper motions and colours obtained from Gaia and 2MASS. We present and discuss
the optical spectroscopic follow-up of 18 low-mass stellar objects in Cha I and
$\epsilon$ Cha. We characterize the properties of objects by deriving their
physical parameters, both from spectroscopy and photometry. We add three more
low-mass members to the list of Cha I, and increase the census of known
$\epsilon$ Cha members by more than 40%, confirming spectroscopically 13 new
members and relying on X-ray emission as youth indicator for 2 more. In most
cases the best-fitting spectral template is from objects in the TW Hya
association, indicating that $\epsilon$ Cha has a similar age. The first
estimate of the slope of the initial mass function in $\epsilon$ Cha down to
the sub-stellar regime is consistent with that of other young clusters. We
estimate our IMF to be complete down to $\approx 0.03$M$_{\odot}$. The IMF can
be represented by two power laws: for M $<$ 0.5 M$_{\odot}$ $\alpha = 0.42 \pm
0.11$ and for M $>$ 0.5 M$_{\odot}$ $\alpha = 1.44 \pm 0.12$. We find
similarities between $\epsilon$ Cha and the southernmost part of Lower
Centaurus Crux (LCC A0), both lying at similar distances and sharing the same
proper motions. This suggests that $\epsilon$ Cha and LCC A0 may have been born
during the same star formation event
