  Context: R Coronae Borealis (RCB) variables and their non-variable
counterparts, the dustless Hydrogen-Deficient Carbon (dLHdC) stars have been
known to exhibit enhanced s-processed material on their surfaces, especially
Sr, Y, and Ba. No comprehensive work has been done to explore the s-process in
these types of stars, however one particular RCB star, U Aqr, has been under
scrutiny for its extraordinary Sr enhancement. Aims: We aim to identify RCB and
dLHdC stars that have significantly enhanced Sr abundances, such as U Aqr, and
use stellar evolution models to begin to estimate the type of neutron exposure
that occurs in a typical HdC star. Methods: We compare the strength of the Sr
II 4077 $\AA$ spectral line to Ca II H to identify the new subclass of Sr-rich
HdCs. We additionally use the structural and abundance information from
existing RCB MESA models to calculate the neutron exposure parameter, $\tau$
Results: We identify six stars in the Sr-rich class. Two are RCBs, and four are
dLHdCs. We additionally find that the preferred RCB MESA model has a neutron
exposure $\tau$ ~ 0.1 mb$^{-1}$, which is lower than the estimated $\tau$
between 0.15 and 0.6 mb$^{-1}$ for the Sr-rich star U Aqr found in the
literature. We find trends in the neutron exposure corresponding to He-burning
shell temperature, metallicity, and assumed s-processing site. Conclusions: We
have found a sub-class of 6 HdCs known as the Sr-rich class, which tend to lie
in the halo, outside the typical distribution of RCBs and dLHdCs. We find that
dLHdC stars are more likely to be Sr-rich than RCBs, with an occurrence rate of
~13\% for dLHdCs and ~2\% for RCBs. This is one of the first potential
spectroscopic differences between RCBs and dLHdCs, along with dLHdCs having
stronger surface abundances of $^{18}$O.
